2024-03-28T13:18:06Zhttp://i-rep.emu.edu.tr:8080/oai/request
oai:i-rep.emu.edu.tr:11129/672013-02-22T07:28:51Zhdl_11129_66
EMU I-REP
author
Keleshteri, Marzieh Eini
2012-11-30T06:43:35Z
2012-11-30T06:43:35Z
2011
Keleshteri, Marzieh Eini. (2011). A Survey on Mathematical Modeling of Cancer Incidence Rates. Thesis (M.S.), Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, Gazimagusa: Cyprus.
http://hdl.handle.net/11129/67
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Assist. Prof. Dr. Mehmet Ali Tut
ABSTRACT: Bioinformatics is a novel interdisciplinary field which attempts to response the biological questions by the assist of other basic sciences as well as computer sciences. Cancer modeling is a real example of such these endeavors in order to help oncologists to find new ways to cure and prevent cancer diseases or predict, estimate, and analyze this hazard in order to step forward to a better future. In this arena mathematics and statistics have played great roles and enabled biology, oncology, and epidemiology to achieve new results by applying some mathematical and statistical methods such as various graphs and tools to compare the different criteria, curve fitting as well as analyzing and predicting the future data, time series and Markov processes to model the natural phenomena and study their behaviors. However this field is still like a young sapling which requires enough patience and care of scientists to bring forth.
This thesis is mainly to make a survey generally on bioinformatics and specifically investigations on cancer cases as an application. First chapter provides a general overview about bioinformatics and its application. Then some preliminary concepts are explained including required biological information about cancer and its causes to comprehend the next concepts and implications better. Many scientists have tried to offer an applicable model for cancer incidence rate which can be acceptable and interpretable biologically. Second chapter provides some past findings about cancer incidence models as a background for readers with little biological information. In fact, the focus of this research is mainly on mathematical modeling of cancer incidence rates. In addition, chapter three is discussing about the cancer incidence. For instance some factors affecting on the process of cancer incidence such as the place and time period of living, sex, race, and the amount of development are checked. In chapter four some curve fittings are performed by MATLAB software, and also special mathematical model which is called Furrier model has been fitted to the real cancer incidence rates data with the best goodness of fit. Keywords: bioinformaics, biomathematics, cancer, incidence rate, mathematical modeling, curve fitting, Furrier model. ……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Biyoenfoformatik, son zamanlarda gelişen çoklu disiplinlerin içinde barındırıldığı bir başlıktır. Biyolojik veri tabanları üzerindeki bilgilerin incelenmesi ve onlar üzerinde kararların verilmesi oldukça önemli bir aşamayı içermektedir. Günümüzün en önemli sağlık vakalarından birisi durumundaki kanser olaylarının incelenmesi ve modellenmesi bu araştırma sahasının en önemli uygulamalarından biridir. Bu tez, biyoenformatik konusunda temel tanımlamaların daha önce yapılmış çalışmaların özetlendiği ve örnek olarak kanser vakalarıyla ilgili verilerin MATLAB paketi yardımıyla modellenmesini içeren bir çalışmadır.
Anahtar kelimeler: biyoenformatik, biyomatematik, kanser, kanser vaka hızı, matematiksel modelleme, Fourier modeli.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Cancer - Research - Mathematical Modeling
Bioinformatics - Biomathematics - Cancer - Incidence Rate -Curve Fitting - Furrier Model
A Survey on Mathematical Modeling of Cancer Incidence Rates
Thesis
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oai:i-rep.emu.edu.tr:11129/932012-12-25T13:54:00Zhdl_11129_66
EMU I-REP
author
Hasanbulli, Mustafa
2012-11-30T13:14:43Z
2012-11-30T13:14:43Z
2010
Hasanbulli, Mustafa. (2010). Asymptotic Behavior of Solutions to Nonlinear Neutral Differential Equations. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/93
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2010. Supervisor: Assoc. Prof. Dr. Svitlana Rogovchenko.
In Chapter 2 of this thesis, in the first part, we deal with asymptotic behavior of nonoscillatory solutions to higher order nonlinear neutral differential equations of the form (x (t) + p (t) x (t − τ ))(n) + f (t, x (t) , x (ρ (t)) , x (t) , x (σ (t))) = 0,for n ≥ 2. We formulate sufficient conditions for all non-oscillatory solutions to behave like polynomial functions at infinity. For the higher order differential equation (x (t) + p (t) x (t − τ ))(n) + f (t, x (t) , x (ρ (t))) = 0, we provide necessary and sufficient conditions that guarantee existence of non-oscillatory
solutions with polynomial-like behavior at infinity. In Chapter 3, we look into oscillation problem of second order nonlinear neutral differential equations
r (t) ψ (x (t)) (x (t) + p (t) x (τ (t)))
+ q (t) f (x (t) , x (σ (t))) = 0
and r (t) (x (t) + p (t) x (τ (t)))
+ q (t) f (x (t) , x (σ (t))) = 0.
en
Eastern Mediterranean University (EMU)
Mathematics
Asymptotic Behavior - Oscillation - Positive Solutions - Neutral Equations
Asymptotic Behavior of Solutions to Nonlinear Neutral Differential Equations
Thesis
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oai:i-rep.emu.edu.tr:11129/1432012-12-25T14:43:08Zhdl_11129_66
EMU I-REP
author
Gazioğlu, Ersan
2012-12-03T13:20:56Z
2012-12-03T13:20:56Z
2011
Gazioglu, Ersan. (2011). Grover Algorithm. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/143
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
Although, the past years brought many exciting and pathfinder achievements in computer science, computer engineers still agreed on a point that the computers of the next generation should be the quantum computers. These will be computation devices to make direct use of quantum mechanical phenomena, such as superposition and entanglement, to carry out operations on data. However, the quantum computer means we need a quantum programming language to understand and to be able to use it. Sadly, the quantum computing is improved so slowly that we can say it is still in its infancy. Even so, after the big surprise of Peter Shor in 1994[12], Lov Grover came across in 1996 [9] with another surprising algorithm that searches an unsorted database in less than linear time unlike the models of classical computation.
en
Eastern Mediterranean University (EMU)
Mathematics
Quantum Search - Search - Quantum Computing - Grover's Algorithm
Grover Algorithm
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/1562012-12-26T06:25:23Zhdl_11129_66
EMU I-REP
author
Dolma, Fatma
2012-12-05T07:02:18Z
2012-12-05T07:02:18Z
2012
Dolma, Fatma. (2012). Implementing Petri Nets for Modelling and Simulation in Biosciences. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/156
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2012. Supervisor: Prof. Dr. Rza Bashirov.
ABSTRACT: It was in 1993 that Petri nets were introduced for modelling of biochemical reactions. Since that time Petri nets are increasingly used to dive deep into the details of functioning of cumbersome biological processes. In this context, Petri nets have become anindispensable tool for modeling and simulation of biochemical reactions, biomedical systems, processes arising in molecular biology and genetics. This thesis intends to present a comprehensive overview of bibliography on application of Petri nets in biosciences. Based on analysis of bibliographical information covering the period of from January 1993 to July 2010, we provide statistical data on subject areas investigated with Petri nets, use of Petri net types, analysis methods as well as dedicated software tools. We detail HFPN – a Petri net with extension that combines both discrete and continuous components in it – and Cell Illustrator 5.0 – a licensed powerful software tool for modeling and simulation of biological systems. In order to show effectiveness of both HFPN and Cell Illustrator in modelling and simulation of biopathways, we introduce three case studies: (i) validation of the p53 transcriptional activity through modelling with HFPN and performing simulation in Cell Illustrator software; (ii) modelling of gene regulatory mechanism of the lac operon and glycolytic pathway; (iii) circadian rhythms in Drosophila. Keywords:Petri Nets,metabolic pathways, signal transduction networks, gene regulatory pathways.
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ÖZ: Petri ağları biyokimyasal reaksiyonları modellemek için ilk defa 1993 yılında önerilmiştir. O zamandan bu yana Petri ağları giderek daha karmaşık biyolojik süreçlerin işleyişini ayrıntılı olarak irdelemek için kullanılır.Bu bağlamda, Petri ağları biyokimyasal reaksiyonlarda, biyomedikal sistemlerde, moleküler biyoloji ve genetikte ortaya çıkan süreçlerin modellerinin oluşturulması ve simülasyon yapılması için vazgeçilmez bir araç haline gelmiştir. Bu tezin amacı Petri ağlarının biyolojik bilimlerde uygulamalarına kapsamlı bir genel bakış sunmaktır.Bu amaçla Ocak 1993 - Temmuz 2010 dönemini kapsayan bibliyografik bilgilereistinaden, Petri ağları aracılığı ile araştırmalar yapılan biyolojik bilim alanlarına, Petri ağı türlerinin kullanımına, çözümleme yöntemlerineve özel yazılım araçlarına ilişkin istatistiki veriler sağlamiştır. Hibrid fonksiyonel Petri ağı ayrık ve sürekli bileşenleri içinde birleştiren bir uzantıya sahip Petri ağı türüdür.Cell Illustrator 5.0 biyolojik süreçlerin modellenmesi ve simülasyonu için kullanılan etkili bir araçtır.Hem hibrid fonksiyonel Petri ağının hem de Cell Illustrator yazılımının etkinliği aşağıdaki üç örnekle irdelenmektedir:
(i)p53 transkripsiyonel aktifliğinin simülasyon yaparak doğrulanması;
(ii) lacoperon gen düzenleyici mekanizmasının ve glikolitik yolun modelinin
oluşturulması;
(iii) Drosophilaiçin sirkadiyen ritim modelinin oluşturulması.
Anahtar Kelimeler: Petri ağları, metabolik yollar, sinyal iletimi kaskadlar, gen düzenleyici yollar
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Petri Nets
Logic, Symbolic and mathematical
Petri Nets - Metabolic Pathways - Signal Transduction Networks - Gene Regulatory Pathways
Implementing Petri Nets for Modelling and Simulation in Biosciences
Thesis
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oai:i-rep.emu.edu.tr:11129/1842012-12-26T07:25:16Zhdl_11129_66
EMU I-REP
author
Aktöre, Hatice
2012-12-10T11:24:01Z
2012-12-10T11:24:01Z
2011
Aktore, Hatice. (2011). Multiplicative Runge-Kutta Methods. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/184
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Assist. Prof. Dr Mustafa Rıza.
ABSTRACT: In this thesis the multiplicative Runge-Kutta Method is developed employing the idea of the ordinary Runge-Kutta Method to multiplicative calculus. The multiplicative Runge-Kutta Methods for the orders 2,3, and 4 are developed and discussed. The developed algorithms are applied to examples where the solutions of the Ordinary Differential Equations are known. This gives the opportunity to check the relative error of the calculation reliably. The results in the multiplicative case are also compared with the results from the ordinary Runge-Kutta Methods of the corresponding order. We can see that the Multiplicative Runge-Kutta Method is advantageous to the ordinary Runge-Kutta method of the same order if the solution is of exponential nature. Finally for completeness the multiplicative Finite Difference method is also presented.
Keywords: Multiplicative Calculus, Runge-Kutta-Method, Ordinary Differential Equations,Numerical Solution.
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ÖZ: Bu tezde, Runge-Kutta metodu temel alınarak çarpımsal analiz kurallarına göre 2, 3 ve 4. dereceden çarpımsal Runge-Kutta yöntemleri bulunmuş ve incelenmiştir. Bulunan yöntemler çözümleri bilinen adi diferansiyel denklemlere örnek olarak uygulanmıştır. Böylece hesaplamalardaki hata oranlarının güvenilir bir şekilde kontrol edilmesi sağlanmıştır. Çarpımsal Runge-Kutta metodundan elde edilen sonuçlar ayni dereceden bilinen Runge-Kutta metodu sonuçlarıyla karşılaştırıldı. Bu sonuçlara göre, çözümü eksponensiyel olan denklemlerde çarpımsal Runge-Kutta metodunu kullanmanın ayni dereceden bilinen Runge-Kutta metoduna göre daha avantajlı olduğu görülmüştür. Son olarak da çarpımsal Finite Difference metodu anlatılmıştır.
Anahtar Kelimeler: Çarpımsal Analiz, Runge-Kutta-Yöntemi, Adi Diferensiyel Denklemler, Sayısal Çözümler
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Multiplicative Calculus - Runge-Kutta-Method - Ordinary Differential Equations - Numerical Solution
Differential Equations - Numerical Solutions
Runge - Kutta Formulas
Multiplicative Runge-Kutta Methods
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/2032012-12-26T07:35:51Zhdl_11129_66
EMU I-REP
author
Bekar, Şerife
2012-12-12T12:36:53Z
2012-12-12T12:36:53Z
2011
Bekar, Serife. (2011). q-Matrix Summability Methods. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/203
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2010. Supervisor: Assist. Prof. Dr. Hüseyin Aktuğlu.
ABSTRACT: In this thesis, we mainly focus on q-analogs of matrix methods such as Cesaro, Holder, Euler and Hausdorff methods. A summability method which is generated by an infinite matrix is called a matrix method. As it is well known the first order Cesaro summability method (C, 1), which is generated by the Cesaro matrix of order one, plays an important role in the theory of matrix summability methods. For this reason we first introduce a method to find q-analog of the Cesaro matrix of order one. By using the same method we also obtain q-analogs of Cesaro matrices of order. Summability properties of C1(qk), a natural q-analog of the first order Cesaro method are studied. Using C1(qk), we define a q-density function and evaluate q-density of some subsets of N. As an application of qdensity function, q-statistical convergence which is stronger than statistical convergence is defined. In the last part, we use the relation between Cesaro and Hausdorff matrices to obtain the general form of q- Hausdorff methods. Also, we show that q- Cesaro and q-Holder matrices can be obtained from the general form of q-Hausdorff matrices. Moreover, by using a q-analog of the generating sequence of Euler method, we can obtain a q-Euler method. Finally, we prove the general summability properties of q-Hausdorff methods.
Keywords: Matrix Summability Methods, Statistical Convergence, q-Integers, Cesaro Matrix, Hausdorff Methods, Density Functions.
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ÖZ: Bu tezde esas olarak Cesaro, Holder, Euler ve Hausdorff gibi matris metodlarının genelleş
tirmeleri üzerine yoğunlaşılmıştır. Bir sonsuz matris tarafından tanımlanan toplanabilirlik metoduna matris toplanabilirlik metodu denir. Birinci dereceden Cesaro matrisi tarafından üretilen, matris toplanabilirlik metodu (C, 1), matris metodlar teorisinde önemli bir rol oynamaktadır. Bu sebepten dolayı öncelikle birinci dereceden q- Cesaro matrislerini bulmak ic¸in bir metod verilmiştir. Bu methodu kullanarak _ 2 N olmak üzere . dereceden q- Cesaro matrislerinin genel formu elde edilmiştir. Birinci dereceden Cesaro matrisinin en doğal q-analoğu olarak görülen C1(qk)’nın bazı toplanabilirlik özellikleri verilmiştir. C1(qk)’yı kullanarak q-yoğunluk fonksiyonu tanımlandı ve bu yoğunluk fonksiyonu yardımı ile N’nin bazı alt kümelerinin q-yoğunlukları hesaplandı. Ayrıca bu q-yoğunluk fonksiyonunun bir uygulaması olarak q-istatistiksel yakınsaklık kavramı verilmiştir. Burada tanımlanan q-istatistiksel yakınsaklığın istatistiksel yakınsaklıktan daha güc¸lüu olduğu ispatlanmıştır. Son kısımda Cesaro ve Hausdorff matris metodları arasındaki ilişki kullanılarak q-Hausdorff matris metodlarının genel formu verilmiştir. Ayrıca bu genel formu kullanarak q- Cesaro ve q-Hölder metodlarının elde edilebildiği gösterilmiştir. Buna ek olarak Euler methodu üreten dizinin bir q-analoğu kullanılarak, bir q-Euler matrisi elde edilmiştir. Son olarak q- Hausdorff metodlarının bazı toplanabilirlik özellikleri ispatlanmıştır.
AnatharKelimeler: Matris Toplanabilirlik Metodu, İstatistiksel Yakınsaklık, q-tamsayıları, Cesaro Matrisi, Hausdorff Metodu, Yoğunluk Fonksiyonu.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Matrix Summability Methods - Statistical Convergence - q-Integers - Ces'aro Matrix
Hausdorff Methods - Density Functions
q-Matrix Summability Methods
Thesis
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oai:i-rep.emu.edu.tr:11129/2172012-12-26T07:43:00Zhdl_11129_66
EMU I-REP
author
Özergin, Emine
2012-12-13T12:50:48Z
2012-12-13T12:50:48Z
2011
Ozergin, Emine. (2011). Some Properties of Hypergeometric Functions. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/217
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Assoc. Prof. Dr. Mehmet Ali Özarslan.
ABSTRACT: This thesis consists of five chapters. The first chapter gives brief information about the thesis. In the second chapter, we give some preliminaries and auxilary results which we will use in thesis. In chapter three, the extension of beta function containing an extra parameter, which proved to be useful earlier, was used to extend Appell’s hypergeometric functions of two variables and extend Lauricella’s hypergeometric function of three variables. Furthermore, linear and bilinear generating relations for these extended hypergeometric functions are obtained by defining the extension of fractional derivative operator. Some properties of the extended fractional derivative operator are also presented. In chapter four, we consider generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new generalizations. In chapter five, we present various families of generating functions for a class of polynomials in two variables. Furthermore, several general classes of bilinear, bilateral or mixed multilateral generating functions are obtained for these polynomials.
Keywords: Generating functions, Hypergeometric function, Fractional derivative operator, Gamma function, Beta function.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tez beş bölümden oluşmuştur. Birinci bölümde tezin içeriği ile ilgili genel bilgiler verilmiştir. İkinci bölümde, tez boyunca kullanılacak olan temel bilgiler ve sonuçlar verilmiştir. Üçüncü bölümde, daha önceden kullanışlı olduğu ıspatlanmış olan ve ekstra bir parameter içeren genişletilmiş beta fonksiyonu kullanılarak, iki değişkenli genişletilmiş Appell hipergeometrik fonksiyonları ve üç değişkenli genişletilmiş Lauricella hipergeometrik fonksiyonları verilmiştir. Yine bu bölümde, yeni bir kesirli türev operatörü tanımlanarak, genişletilmiş hipergeometrik fonksiyonlar için lineer ve bilineer doğurucu fonksiyon bağıntıları elde edilmiştir. Genişletilmis¸ kesirli türev operatörünün bazı özellikleri de sunulmuştur. Dördüncü bölümde, genişletilmiş gamma, beta ve hipergeometrik fonksiyonlar ele alınmıştır. Bu yeni genelleşmeler için, bazı rekürans bağıntıları, dönüşüm formülleri ve integral gösterimler elde edilmiştir. Beşinci bölümde, iki değişkenli polinom sınıfı için bir çok doğurucu fonksiyon aileleri sunulmuştur. Yine bu bölümde, bu polinomlar için daha geniş bilineer, bilateral ve karışık multilateral doğurucu fonksiyon sınıfları elde edilmiştir.
Anahtar Kelimeler: Doğurucu fonksiyon, Hipergeometrik fonksiyon, Kesirli türev operatörü, Gamma fonksiyonu, Beta fonksiyonu.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Generating Functions - Hypergeometric Function - Fractional Derivative Operator - Gamma Function - Beta Function
Some Properties of Hypergeometric Functions
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/2182012-12-26T07:43:26Zhdl_11129_66
EMU I-REP
author
Vedi, Tuba
2012-12-13T13:11:49Z
2012-12-13T13:11:49Z
2011
Vedi, Tuba. (2011). Some Schurer Type q-Bernstein Operators. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/218
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Assoc. Prof. Dr. Mehmet Ali Özarslan.
ABSTRACT: In this thesis consist of six chapters. The introduction is given in the first chapter. In the second chapter, some necessary definitions, preliminaries and theorems are given. In this
chapter, we also give the important theorems; by Korovkin and Volkov, Bernstein polynomials in one two variables, q-Bernstein, Bernstein-Chlodowsky and q-Bernstein Chlodowsky polynomials. In the third chapter, q-Bernstein Schurer operators are defined. Many properties and results of these polynomials, such as Korovkin type approximation and the rate of convergence of these operators in terms of Lipschitz class functional are given. In the fourth chapter q-Bernstein-Schurer-Chlodowsky operators are introduced. Korovkin type approximation theorem is given and the rate of convergence of this approximation is obtained by means of modulus of continuity of the function is obtained. In the fifth chapter, Schurer-type q-Bernstein Kantorovich operators are defined. Moreover the order of convergence of the operators in terms of modulus of continuity of the derivative of the function, and elements of Lipschitz classes are discussed. In the last chapter, Kantorovich type q-Bernstein operators are defined. Furthermore, Korovkin type approximation theorem is proved and the rate of convergence of this
approximation are given.
Keywords: q-Bernstein Schurer operators, Korovkin theorem, Schurer Type q-Bernstein Polynomials, Kantorovich type q-Bernstein-Schurer-Chlodovsky operators.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tez altı bölümden olusmaktadır. Birinci bölüm giris kısmı olarak verilmistir. İkinci
bölümde, tez boyunca ihtiyaç duyulacak bazı tanımlar, tanımlarla ilgili bazı temel özellikler
ve teoremler verilmistir. Ayrıca Korovkin and Volkov Teoremleri, bir ve iki değiskenli
Bernstein Polinomları, q-Bernstein Polinomları ve Bernstein Chlodowsky and q-Bernstein
Chlodowsky Polinomları incelenmistir. Üçüncü bölümde q-Bernstein Schurer Operatörleri tanımlanmıstır. q-Bernstein Schurer Operatörlerinin yakınsaklığı Korovkin Teoremi yardımıyla ve Liptsitz sınıfındaki yakınsaklığı incelenmistir. Dördüncü bölümde q-Bernstein Schurer-Chlodowsky Operatörü tanımlanmıstır. Korovkin tipli yakınsaklık teoremi, fonksiyonun ve fonksiyonunun türevinin süreklilik modülü yardımıyla yakınsama hızları hesaplanmıstır. Besinci bölümde Schurer tipli q-Bernstein Kantorovich Operatörleri tanımlanmıstır. Bu operatörlerin modüllerinin ve türevlerinin yakınsaklıkları hesaplanmıstır. Altıncı bölümde Kantorovich tipli q-Bernstein-Schurer-Chlodowsky Operatörleri tanımlanmıstır. Bununla birlikte Korovkin tipli teorem yaklasımı ispatlanmıs ve bu yakınsamanın yakınsaklık derecesi hesaplanmıstır.
Anahtar Kelimeler: q-Bernstein Schurer Operatörleri, Korovkin Teoremi, Schurer Type q-Bernstein Operatörleri, Kantorovich Type q-Bernstein-Schurer-Chlodovsky operatörleri.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Mathematical Operators
Q-Bernstein Schurer Operators - Schurer Type Q-Bernstein Operators - Kantorovich Type Q-Bernstein Schurer
Chlodowsky Operators - Korovkin Theorem
Some Schurer Type q-Bernstein Operators
Thesis
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oai:i-rep.emu.edu.tr:11129/2202012-12-26T07:45:04Zhdl_11129_66
EMU I-REP
author
Savun, İpek
2012-12-13T14:20:38Z
2012-12-13T14:20:38Z
2010
Savun, Ipek. (2010). Stability of Systems of Differential Equations and Biological Applications. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/220
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2010. Supervisor: Assoc. Prof. Dr. Svitlana Rogovchenko.
ABSTRACT: In this thesis, we deal with systems of ordinary differential equations and discuss the stability properties of their solutions. We classify equilibrium points of linear systems with respect to their type and stability and discuss the methods for investigating the stability properties of nonlinear systems. Existence of periodic solutions which plays an important role in stability theory is also discussed. In addition, some important ecological applications, such as Lotka-Volterra predator-prey model, competition model and nutrient-prey-predator model with intratrophic predation, modeled by the systems of differential equations are also considered. Recent results obtained for these applications are also included.
Keywords: Stability, Periodic solution, Predator-prey model, Intratrophic predation.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezde, birinci dereceden denklem sistemleri ve sistemlerin çöozümlerinin kararlılığı üzerinde çalıştık. Lineer sistemlerin kritik noktalarını türlerine ve kararlılıklarına göre sınıflandırdık, lineer olmayan sistemlerin kararlılık özelliklerini inceleyen metodları ele aldık. Çözümlerin kararlılık analizinde önemli rol oynayan periyodik çözümlerin varlığı üzerinde çalıştık. Bunlara ek olarak, diferansiyel denklemlerle ifade edilebilen bazı önemli ekolojik uygulamaları inceledik. Örneğin; Lotka-Volterra av-avcı ilişki modeli, türler arası rekabet modeli ve intratropik avlanma etkisindeki besin-av-avcı modeli. Bu uygulamalarla ilgili elde edilen yeni sonuçlara da yer verdik.
Anathar Kelimeler: Kararlılık, Periodik çözüm, Av-avcı ilişkisi, Intratropik avlanma.
en
Eastern Mediterranean University (EMU)
Mathematics
Stability - Periodic Solution - Predator-Prey Model - Intratrophic Predation
Stability of Systems of Differential Equations and Biological Applications
Thesis
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oai:i-rep.emu.edu.tr:11129/2302012-12-26T07:49:57Zhdl_11129_66
EMU I-REP
author
Kaffaoğlu, Havva
2012-12-14T11:08:21Z
2012-12-14T11:08:21Z
2011
Kaffaoglu, Havva. (2011). Szasz and Phillips Operators Based on q-Integers. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/230
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2011. Supervisor: Prof. Dr. Nazım Mahmudov.
ABSTRACT: In this thesis, q-Szász-Durrmeyer (0 < q < 1) and q-Phillips (q > 0) operators are defined and some properties of these operators are studied. More precisely, local approximation results for continuous functions in terms of modulus of continuity are proved and Voronovskaja type asymptotic results are investigated.
Keywords: q-Szász-Durrmeyer operators, k-functional, modulus of continuity, qcalculus, q-Phillips operators, q-integers, q-gamma functions, rate of convergence, qintegral.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezde, q-Szász-Durrmeyer ( 0 < q < 1) ve q-Phillips ( q > 0 ) operatörleri tanımlanmış ve bu operatörlerin bazı özellikleri incelenmiştir. Daha açık olarak, süreklilik modülü cinsinden, sürekli fonksiyonlar için yerel yaklaşım sonuçları ispatlanmış ve Voronovskaja tipli asimtotik sonuçlar incelenmiştir.
Anahtar kelimeler: q-Szazs-Durrmeyer operatörleri, k-fonksiyonel, süreklilik modülü, q-hesap, q-Phillips operatörleri, q-tamsayılar, q-gamma fonksiyonları,
yakınsama hızı, q-integral.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Q-Szasz - Durrmeyer Operators - K-Functional - Modulus of Continuity - Q-Calculus - Q-Phillips Operators
Q-Integers - Q-Gamma Functions - Rate of Convergence - Q-Integral
Szasz and Phillips Operators Based on q-Integers
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/3062013-01-10T00:00:27Zhdl_11129_66
EMU I-REP
author
Alola, Andrew Adewale
2013-01-09T09:49:15Z
2013-01-09T09:49:15Z
2012
Alola, Andrew Adewale. (2012). Analysis of Possibility Theory for Reasoning under Uncertainty. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/306
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2012. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: The purpose of this thesis is to analyze the possibility theory for reasoning under uncertainty. The relationship and difference between probability and possibility theories are presented. The areas of application of possibility theory are studied. The advantages of possibility theory over the probability theory in modeling uncertainty are described. The quantitative and qualitative possibilities are considered. The possibility measure, the possibility distribution and the imprecise probability are discussed.
Keywords: Possibility, imprecision, possibility measure, possibility distribution.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı belirsizlik durumunda uslamlama yapmak için olabilirlik teorisini incelemektir. İhtimal ve olabilirlik teorileri arasındakı farklılıklar ve benzerlikler sunulur. Olabilirlik teorisinin uygulama alanları öğrenilir. Belirsizliğin modellenmesi için olabilirlik teorisinin ihtimal teorisine göre avantajları anlatılır. Kontitatif ve kalitatif olabilirlikler dikkate alınır. Olabilirlik ölçüsü, olabilirlik dağılımı ve kesin olmayan ihtimal tartışılır.
Anahtar Kelimeler: Olabilirlik, belgisizlik, olabilirlik ölçüsü, olabilirlik dağılımı, kesin olmayan ihtimal.
en
Eastern Mediterranean University (EMU)
Mathematics
Applied Mathematics and Computer Science
Possibility - Probabilities
Possibility - Imprecision - Possibility Measure - Possibility Distribution
Analysis of Possibility Theory for Reasoning under Uncertainty
Thesis
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oai:i-rep.emu.edu.tr:11129/3202013-01-11T00:00:42Zhdl_11129_66
EMU I-REP
author
Kürt, Cemaliye
2013-01-10T08:35:33Z
2013-01-10T08:35:33Z
2012
Kurt, Cemaliye. (2012). Euler Characteristic of Groups – C.T.C. Wall’s Approach. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/320
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2012. Supervisor: Assist. Prof. Dr. Müge Saadetoğlu.
ABSTRACT: This work concentrates on the Euler characteristic of groups and points out that, this number can also be a rational one. We give some background material on the Euler theorem and the relevant topics. We also review the Fundamental Group and the Covering Space theories. We give C.T.C. Wall’s definition for the Euler characteristic of a group. We fill in the gaps in the proofs of certain formula given under the notions of L-class and M-class. Finally, we describe the exact structure of subgroups of free products of groups via some examples.
Keywords: Euler characteristic, Euler theorem, Fundamental Group Theory, Covering Space Theory, C.T.C. Wall’s definition, L-class, M-class, free products of groups.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu çalışmada grupların Euler karakteristiği baz alınarak, C.T.C. Wall’un bu sayının
rasyonel olabileceğini gösterdiği çalışması irdelenmiştir. Euler Teorem’in temel özellikleri ve ilgili konuları verildi. Bunun yanında, Temel Gurup ve Örtü Uzayları Teorileri özetlendi. Gurupların Euler karakteristikleri için C.T.C. Wall’un tanımı verildi ve hemen ardından L ve M sınıfları için formüller ispatlandı. En son olarakta, serbest grupların alt gruplarının yapısı örneklerle incelendi.
Anahtar Kelimeler: Euler karakteristik, Euler teorem, Temel Gurup Teorisi, Örtü Uzayları Teorileri, L ve M sınıfları.
en
Eastern Mediterranean University (EMU)
Mathematics
Group Theory
Euler Characteristic - Euler Theorem - Fundamental Group Theory - Covering Space Theory
C.T.C. Wall's Definition - L-class - M-class - Free Product of Groups
Euler Characteristic of Groups – C.T.C. Wall’s Approach
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/3252013-01-11T00:00:52Zhdl_11129_66
EMU I-REP
author
Bodur, Ersin Kuset
2013-01-10T11:46:58Z
2013-01-10T11:46:58Z
2012
Bodur, Ersin Kuset. (2012). Fuzzy Utility Based Decision Analysis in the Credit Scoring Problem. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/325
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2012. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
A method that uses fuzzy c-means (FCM) is proposed for credit scoring based on unsupervised learning of a set training data. Data vectors are composed of significant applicant attributes and corresponding expert decisions. Two new statistical cost functions Jm and Jσ are introduced to evaluate the candidate models by k -fold cross validation based on the mean and the standard deviation of the decision attributes. A linguistic approach based on the fuzzy-valued Choquet integral is suggested to rank the consumer loan applicants. The lower and upper imprecise probabilities are used as a capacity measure in Choquet integral to determine the utility ranking of the consumer loan applicants. This thesis proposes an algorithm to calculate the applicant’s non-expected utility by using imprecise probabilities of accepted cases over the Fuzzy C-Means clusters for fuzzy Choquet integral. The method is applied on consumer loan evaluations for a financial institution to verify expert decisions in parallel to extracting linguistic rules of decision making. In the suggested approach linguistic fuzzy valued Choquet integral is used as measure of fuzzy utility. The results indicate that the proposed method is successful in ranking the consumer loan applications with only six fails in total of 135 applications.
Keywords: Fuzzy c-means, Fuzzy clustering, Sugeno integral, Fuzzy valued Choquet integral, imprecise probability
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bulanık- c -ortalaması (FCM) kullanan ve anlamlı basvuru nitelikleri ve karsılıgı uzman kararından olusan bir modelleme veri kümesiyle yönlendirilmemis ögrenmeye dayanan kredi puanlama metodu önerilmektedir. Degerlendirmeye aday modelleri k -kat çapraz saglamayla karar niteliginin ortalama ve standard sapmasına dayanan Jm ve Jσ adında iki yeni istatistiksel maliyet fonksiyonu tanımlanmaktadır. Tüketici kredisi için basvuran müsterileri sıralamak üzere bulanık degerli Choquet integrale dayanan sözel bir yaklasım önerilmektedir. Choquet integralde kapasite ölçüsü olarak tüketici kredisi basvurularının fayda sıralamasını belirlemek üzere alt ve üst belirsizlik olasılıkları kullanılmaktadır. Bu tez basvuranların umulmadık faydasını hesaplamak üzere Choquet integralin kapasite ölçüsü olarak bulanık- c -ortalaması kümelerindeki uzmanlarca onaylananların belirsiz olabilirliligi kullanan bir algoritma önermektedir. Önerilen metod bir finans kurulusunun tüketim kredisi degerlendirmelerinde bir yandan karar vermenin sözel kurallarını bulurken, diger taraftan uzman kararlarını sınamak üzere uygulanmıstır. Önerilen yaklasımda bulanık-sayı degerli ölçüt kullanan Choquet integrali kullanılmıstır. Sonuçlar ileri sürülen metodun tüketici kredisi basvurularını sıralamada toplam 135 basvurudan yalnızca altı yanılmayla basarılı oldugunu göstermektedir.
Anahtar Kelimeler: Bulanık- c -ortalaması, bulanık sınıflandırma, Sugeno integral, bulanık degerli Choquet integral, kesin olmayan ihtimal.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Computational Intelligence - Decision Making
Fuzzy Systems - Fuzzy Logic - Expert Systems (Computer Science)
Fuzzy - C-Means - Fuzzy Clustering - Sigeno Integral
Fuzzy Valued Choquet Integral - Imprecise Probability
Fuzzy Utility Based Decision Analysis in the Credit Scoring Problem
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/3502013-01-18T00:00:35Zhdl_11129_66
EMU I-REP
author
Rizaner, Fatma Bayramoğlu
2013-01-17T11:14:56Z
2013-01-17T11:14:56Z
2012
Rizaner, Fatma Bayramoglu. (2012). Dynamics of a Single Species under Periodic Habitat Fluctuations and Allee Effect. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/350
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2012. Supervisor: Assoc. Prof. Dr. Svitlana P. Rogovchenko.
The dynamics of a single species and harvested single species that goes extinct when rare, is described by nonlinear differential equations a)Ń = rN ﴾1 – N/K﴿ ﴾N/K – A/K﴿ b)Ń = rN ﴾1 – N/K﴿ ﴾N/K – A/K﴿-hN, (1) where a parameter A(0<A<K) is associated with the Allee effect, r is the
intrinsic growth rate, h is the harvesting and K is the carrying capacity of the
environment. The intention of this thesis is to study the existence of periodic
solutions and their stability properties assuming that r, A, h and K are continuous
T - periodic functions. Using rather elementary techniques, we completely describe
populations dynamics analyzing influences of both strong (A>0)and weak (A<0)Allee effects. We discuss the effect of harvesting on a single species population in a
fluctuating environment whose dynamics is described by a nonlinear differential
equation. We consider separately cases of harvesting (h>0)(stocking (h<0)), weak Allee effect (A≤0)and strong Allee effect (A>0). Thus, we answer
questions regarding the location of positive periodic solutions and their stability
complementing the research in a recent paper by Padhi [14]. Bounds for periodic
solutions and estimates for backward blow-up times are also established.
Furthermore, we demonstrate advantages of our approach on simple examples to
which the results in the cited paper fail to apply. Keywords: Nonlinear differential equation, Allee effect, periodic solutions, stability, blow up, existence, positive solutions, harvesting. …………………………………………………………………………………………………………………………………………………………………………………………………………………… ÖZ: Yetersiz nüfus yogunlugundan dolayı soyu tükenmekte olan tek bir türün ve hasat edilen tek bir türün dinamikleri dogrusal olmayan asagıdaki diferansiyel denklemlerle tanımlanabilir, a)Ń = rN ﴾1 – N/K﴿ ﴾N/K – A/K﴿ b)Ń = rN ﴾1 – N/K﴿ ﴾N/K – A/K﴿-hN, (1) Burada, A parametresi A(0<A<K) Allee etkisi ile iliskilidir, r içsel büyüme oranı, h hasat kaldırma ve K çevrenin tasıma kapasitesidir. Bu tezin amacı r, A, h ve K’nin sürekli T - periyodik fonksiyonlar oldukları kosullarda, periyodik çözümlerin varlıgını ve onların denge özelliklerini arastırmaktır. Temel teknikler kullanarak güçlü (A>0) ve zayıf (A<0) Allee etkileri incelenerek nüfus dinamikleri tamamıyla elde edilmislerdir. Dinamikleri dogrusal olmayan diferansiyel denklemlerle tanımlanan dalgalanma ortamındaki tek bir nüfusun hasatı incelenmemistir. Bu durumda ayrı ayrı hasat (h>0) (stok (h<0)), zayıf Allee etkisi (A≤0) ve güçlü Allee etkisi (A>0) dikkate alınmıştır. Bu arastırmayla Padhi’nin makalesinde [14] ortaya çıkan pozitif periyodik çözümlerin konumları ve bunların istikrarlarıyla ilgili soruları aydınlattık. Periyodik çözümlerin sınırları ve geri darbe süreleri de tanımlanmıstır. Ayrıca, bu çalısmada önerilen yaklasımın avantajı Padhi’nin makalesinde [14] önerdigi sonuçların uygulanmayacagı basit örnekler yardımıyla gösterilmistir.
en
Eastern Mediterranean University (EMU)
Mathematics
Differential Equations, Nonlinear
Nonlinear Differential Equation - Allee Effect - Periodic Solutions - Stability - Blow Up - Existence - Positive Solutions - Harvesting
Dynamics of a Single Species under Periodic Habitat Fluctuations and Allee Effect
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/6402013-08-14T23:00:33Zhdl_11129_66
EMU I-REP
author
Hürol, Simruy
2013-08-14T05:00:26Z
2013-08-14T05:00:26Z
2013
Hurol, Simruy. (2013). Numerical Methods for Solving Systems of Ordinary Differential Equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/640
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assist. Prof. Dr. Mehmet Bozer.
ABSTRACT: This thesis concantrates on numerical methods for solving ordinary differential equations. Firstly, we discuss the concept of convergence, local-truncation error, globaltruncation error, consistency, types of stability, zero-stability, and weak-stability. Afterwards, we inform some materials for Euler and Runge-Kutta method. The given ordinary differential equation is analyzed on Euler and Runge-Kutta method to find the approximated solution with the given initial conditions. Then, the stability of each method is examined briefly. We also focus on numerical methods for systems. Then, the reason of the stiff system is discussed. After investigating the numerical methods, we gave advantages and disadvantages of Euler method and Fourth Order Runge-Kutta method. Finally, numerical experiments is applied on Explicit Euler method and Explicit Fourth Order Runge-Kutta method. The approximated solutions with different step-size and analytical solutions of methods are computed in Matlab
software. The computation of approximated solutions of methods are compared with analytical solutions. Then we discussed the accuracy of these methods when they are applied to the specified system in Chapter 7. Finally, we conclude that Explicit Fourth Order Runge-Kutta method is more accurate than the Explicit Euler method. Keywords: Ordinary Differential Equations, Numerical solutions, Euler’s method, Runge-Kutta method, Stiff System
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ÖZ: Bu çalışmada adi diferansiyel denklemlerin çözümü için sayısal yöntemler irdelenmiştir. İlk olarak, yakınsama kavramı, yerel kesme hatası, küresel kesme hatası, tutarlılık, kararlılık türleri, sıfır kararlılık ve zayıf kararlılık kavramları incelenmiştir. Ayrıca, Euler ve Runge-Kutta metodları verilmiştir. Verilen bir diferansiyel denklemin, yaklaşık çözümünü bulmak için Euler ve Runge-Kutta yöntemi verilen başlangıç koşulları ile analiz edilmiş ve her bir yöntem için kararlılık kısaca ele alınmıştır. Daha sonra, verilen sistemler için sayısal yöntemlere odaklanılmış ve sert sistemin çıkış sebebi incelenmiştir. Euler yöntemin ve dördüncü dereceden Runge- Kutta yöntemin avantajları ve dezavantajları verilmiştir. Son olarak, sayısal deneyler üzerinde Açık Euler ve Açık dördüncü dereceden Runge-Kutta yöntemleri uygulanmıştır. Farklı adım büyüklüğü ele alınarak yaklaşılan çözümler ve yöntemleri nanalitik çözümleri Matlab yazılımıkullanılarak hesaplanmıştır. Elde edilen yaklaşılır çözümler ile analitik çözümler karşılaştırılmıştır. Daha sonra yöntemler Bölüm 7’de belirtilen sistem üzerine uygulanıp yöntemlerin doğruluğu tartışılmıştır. Son olarak, Açık Runge-Kutta yöntemin yaklaştırılmış çözümünün Açık Euler methoduna göre daha az hatalı olduğu sonucuna varılmıştır. Anahtar Kelimeler: Adi Diferensiyel Denklemler, Sayısal Çözümler, Euler Yöntemi, Runge-Kutta Yöntemi, Sert Sistemi.
en
Eastern Mediterranean University (EMU)
Mathematics
Applied Mathematics and Computer Science
Differential Equations
Ordinary Differential Equations - Numerical Solutions - Euler's Method - Runge-Kutta Method - Stiff System
Numerical Methods for Solving Systems of Ordinary Differential Equations
Thesis
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oai:i-rep.emu.edu.tr:11129/6542013-08-14T23:01:00Zhdl_11129_66
EMU I-REP
author
Demez, Hülya
2013-08-14T08:07:25Z
2013-08-14T08:07:25Z
2013
Demez, Hulya. (2013). Combinatorial Optimization: Solution Methods of Traveling Salesman Problem. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/654
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assist. Prof. Dr. Arif Akkeleş.
ABSTRACT: Traveling Salesman Problem has been one of the most interesting and challenging problem in the literature. It is include a large area in combinatorial optimization problem. A variety of Exact and Heuristic Algorithms are usable algorithms for solving TSP. Branch and Bound Algorithm is an exact algorithm that is developed for solving TSP type problems. Furthermore, Genetic Algorithm is one of the extensively algorithm within the Heuristic Algorithm. In this work, we looked into symmetric and asymmetric matrices to solve TSP. We used Genetic and Branch-and-Bound Algorithms as the solution methods to get the shortest path. Keywords: Traveling Salesman Problem, Heuristic Algorithm, Exact Algorithm, Branch and Bound Algorithm, Genetic Algorithm.
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ÖZ: Gezgin Satıcı Problemi, literatürdeki en ilginç ve en iddealı problem olarak çalışılan, kombinasyonel eniyileme problemlerinin başında gelmektedir. Çözümü için birçok Sezgisel ve Kesin Çözüm Yöntemleri geliştirilmektedir. Dal ve Sınır Algoritmaları, gezgin satıcı ve benzer yapıdaki problemlerin çözümü için geliştirilen Kesin Çözüm Yöntemi olmakla birlikte, Genetik Algoritmalar da Sezgisel Yöntemlerin başında gelmektedir. Bu çalışmada Gezgin Satıcı Problemlerinin çözümü için simetrik ve asimetrik matrisler ele alınmıştır. En kısa turları elde etmek için de Dal ve Sınır ve Genetik Algoritmaları kullanılmaktadır.
Anahtar Kelimeler: Gezgin Satıcı Problemi, Sezgisel Yöntem, Kesin Çözüm Yöntemi, Dal ve Sınır Algoritması, Genetik Algoritma.
en
Eastern Mediterranean University (EMU)
Mathematics
Applied Mathematics and Computer Science
Traveling - Salesman Problem
Traveling Salesman Problem - Heuristic Algorithm - Exact Algorithm - Branch and Bound Algorithm - Genetic Algorithm
Combinatorial Optimization: Solution Methods of Traveling Salesman Problem
Thesis
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oai:i-rep.emu.edu.tr:11129/6672013-08-14T23:00:50Zhdl_11129_66
EMU I-REP
author
Selimi, Meral
2013-08-14T11:58:33Z
2013-08-14T11:58:33Z
2013
Selimi, Meral. (2013). Fourier Series and Integrals. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/667
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Prof. Dr. Agamirza Bashirov.
ABSTRACT: This thesis consists of six chapters. Introduction is in the first chapter. In the second chapter we present a method for solving partial differential equation by use of Fourier series. The method is called separation of variables. In the third chapter we show that the Fourier series converges under certain reasonable general hypothesis. We give important results like Riemann-Lebesgue Lemma, Dirichlet kernels and three important conditions for the convergence of Fourier series at a point Dini’s, Lipchitz and Dirichlet-Jordan conditions. In the fourth chapter Fourier series are studied in more general point of view, considering functions as elements of abstract inner product space. Bessel’s inequality, Parseval’s identity, Cesaro summability and Fejer kernels are important results that are given. In the fifth chapter is set the problem of uniform convergence of Fourier series based on piecewise-smooth functions. In addition it is given Weierstrass approximation theorem and Gibbs phenomenon, the case when the function is not uniformly convergent. In the last chapter we deal with convergence of Fourier integrals. First we introduce the Fourier integral formula and then give the analogs of Dini’s, Lipchitz and Dirichlet- Jordan conditions for Fourier integrals. Keywords: Dirichlet kernels, Bessel’s inequality, Parseval’s identity, Cesaro summability, Fejer kernels.
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ÖZ: Bu tez altı bölümden oluşmaktadır. Birinci bölüm giriş bölümüdür. İkinci bölümde Fourier serileri kullanarak kısmi türevli denklemin çözüm metodunu sunmaktayız. Bu metoda değişkenlerine ayırma metodu denir. Üçüncü bölümde genel hipotezler altında Fourier serilerinin yakınsaklığı gösterildi. Riemann Lebesgue Lemma , Dirichlet çekirdekleri gibi önemli sonuçlar verildi ve Fourier serilerinin bir noktada yakınsaması için üç önemli koşul: Dini, Lipshctiz ve Dirichlet-Jordan'dır. Dördüncü bölümde Fourier serilerinin soyut iç çarpım uzaylarının elemanları olan fonksiyonlar olduğu dikkate alınarak , geniş çapta çalışıldı.Bunlar arasında en önemlileri Bessel eşitsizliği, Parseval özdeşiliği, Cesaro toplanabilirlik ve Fejer çekirdekleridir.
Beşinci bölümde parçalı düzgün fonksiyonlar üzerine Fourier serilerinin düzgün yakınsaması problemi ortaya konulmuştur.Bunun yanı sıra fonksiyon düzgün yakınsak olmadığında Weistrass yaklaşım teoremi ve Gibbs fenomeni verilmiştir. Son bölümde Fourier integrallerinin yakınsaması ele alınmıştır. Öncelikle Fourier integral formülü ve sonra Fourier integralleri için Dini, Lipschitz ve Dirichlet-Jordan şartlarının benzerleri verilmiştir. Anahtar Kelimeler: Dirichlet çekirdekleri, Bessel eşitsizliği, Parseval özdeşliği, Cesaro toplanabilirlik, Fejer çekirdekleri.
en
Eastern Mediterranean University (EMU)
Mathematics
Differential Equations - Fourier Series
Dirichlet Kernels - Bessel's Inequality - Parseval's Identity - Cesaro Summability - Fejer Kernels
Fourier Series and Integrals
Thesis
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oai:i-rep.emu.edu.tr:11129/6792013-08-15T23:00:42Zhdl_11129_66
EMU I-REP
author
Sadeghi, Hamid Mir-Mohammad
2013-08-15T10:44:27Z
2013-08-15T10:44:27Z
2010
Sadeghi, Hamid Mir-Mohammad. (2010). Fuzzy Intelligent Traffic Control System. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/679
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Science, Dept. of Applied Mathematics and Computer Science, 2010. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: The aim of this thesis is to develop the fuzzy intelligent traffic control system for the optimal controlling of the traffic flow at the traffic intersections. The proposed fuzzy control system is used to effectively manage the urban traffic junction of the intersections of the city Famagusta (Gazimagusa), North Cyprus. The importance of the proposed fuzzy intelligent traffic control system consists in consideration of uncertainty and vagueness of information about the values of the input and output parameters of the system. Using the input parameters and based on the inferences from the fuzzy rules, the fuzzy traffic controller decides how to adjust the extension time of the green phase of traffic lights. The computer simulation is carried out using Matlab software. The optimal extension time of the green phase is determined using the Mamdani inference engine.
The effectiveness of the fuzzy traffic controller with four input parameters is explained.
Keywords: Fuzzy System, Traffic Control, Fuzzy Logic Controller.
……………………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı yol kavşağında trafik akışını optimal kontrol etmek için bulanık trafık sistemini geliştirmektir. Önerilen bulanık kontrol sisteminin kullanılmasında amac Kuzey Kıbrıs’ın Gazimağusa şehrinde kentsel trafik kavşağını etkili yönetmekdir. Önerilen bulanık trafik sisteminin önemli özelliği sistemin giriş ve çıkış parametre değerlerinin belirsizlik halinde başarıyla kullanılabilmesinden ibaretdir. Bulanık trafik kontrol sistemi giriş parametrelerini kullanarak ve bulanık kurallardan elde edilen neticeye dayanarak trafik ışıklarının yeşil fazının ayarlanması konusunda karar veriyor. Matlab yazılımını kullanarak bilgisayar simulyasyonu oluşturulmaktadır. Trafik ışıklarının yeşil fazının optimal ayarlanması için Mamdani sonuc çıkarma yöntemi kullanılmaktadır. Dört parametreli bulanık trafik kontrollerin etkinliği açıklanıyor.
Anahtar kelimeler: Bulanık Sistem, Trafik Kontrol, Bulanık Mantık Kontroller.
en
Eastern Mediterranean University (EMU)
Applied Mathematics and Computer Science
Traffic Engineering - Computer Systems
Traffic Control - System Design - Fuzzy Systems
Intelligent Control Systems
Fuzzy System - Traffic Control - Fuzzy Logic Controller
Fuzzy Intelligent Traffic Control System
Thesis
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oai:i-rep.emu.edu.tr:11129/13422014-09-19T23:00:51Zhdl_11129_66
EMU I-REP
author
Obi, Olivia Ada
2014-09-19T10:40:58Z
2014-09-19T10:40:58Z
2013-09
Obi, Olivia Ada. (2013). Stability of autonomous and non autonomous differential equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1342
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu.
ABSTRACT: In this thesis, we dealt with Autonomous and non Autonomous systems of ordinary differential equations and the stability properties of their solutions were discussed with some basic results. We also discussed and analyzed methods of investigating the stability of nonlinear systems and classified equilibrium points (critical points) of linear systems with respect to their stability. Liapounov's direct method for stability of Autonomous and non Autonomous Equations was analyzed in detail. Some important Ecological applications such as Lotka-Volterra Competition Model and Predator-Prey Model modeled by differential Equations were discussed in details with relevant examples. Keywords : Autonomous and Non Autonomous differential equations, Stability, Predator-prey Model, Equilibrium points, Liapounov's Direct Method. …………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ : Bu tezde, otonom ve otonom olmayan adi difransiyel denklem sistemleri ve bu sistemlerin çözümlerinin stabilite özellikleri tartışılmıştır. Ayrıca, doğrusal olmayan sistemlerin stabilitesi üzerine bazı metodlar çalışılmış ve analiz edilmiş ve doğrusal sistemlerin stabilite özelliklerine göre denge noktaları sınıflandırılmıstır. Otonom ve otonom olmayan denklemlerin stabilitesi için Lyapounov Direkt metodu detaylı bir şekilde analiz edilmiştir. Son olarak, diferansiyel denklemlerce modellenmiş olan Lotka-Volterra Yarışma modeli ve Predator Prey modeli gibi bazı önemli ekolojik uygulamalar ayrıntılı bir şekilde incelenmiştir.
Anahtar Kelimeler : Otonom ve otonom olmayan diferansiyel denklemler, Stabilite, Predator-Prey Model, Denge Noktaları, Liapounov Direkt Metod.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Differential Equations
Autonomous and Non Autonomous Differential Equations, Stability, Predator-prey Model, Equilibrium Points, Liapounov's Direct Method
Stability of autonomous and non autonomous differential equations
Thesis
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oai:i-rep.emu.edu.tr:11129/13522014-09-25T23:00:36Zhdl_11129_66
EMU I-REP
author
Çatma, Güneş
2014-09-25T13:13:03Z
2014-09-25T13:13:03Z
2013-07
Çatma, Güneş. (2013). Bernoulli and euler polynomials. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1352
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu.
ABSTRACT: This thesis provides an overview of Bernoulli and Euler numbers. It describes
the Bernoulli and Euler polynomials and investigates the relationship between the classes of the two polynomials. It also discusses some important identities using the _nite di_erence calculus and di_erentiation. The last part of this study is concerned with the Generalized Bernoulli and Euler polynomials. Furthermore, the properties obtained in the second chapter are also examined for the generalized Bernoulli and Euler polynomials in this part of the thesis. The Complementary Argument Theorem, the generating functions, the Multiplication and the Euler-Maclauren Theorems are widely used in obtaining the mentioned results.
Keywords: Bernoulli -Euler Polynomials, Generalized Bernoulli -Euler Polynomials, Finite Difference.
…………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu çalışmada Bernoulli ve Euler sayıları ile Bernoulli ve Euler polinomları arasındaki ilişkiler incelenmiştir. Bernoulli sayıları için ardışıklık, kapalılık ve üreticilik gibi temel özellikler çalışılmıştır. Bunun yanında Bernoulli ve Euler Polinomları arasındaki ilişkiler incelenip her ikisi için de geçerli olan türev, integral, fark ve simetri özellikleri incelenmiştir. Ayrıca Genelleştirilmiş Bernoulli ve Euler polinomları için de türev, intregral özellikleri çalışılmıştır. Anahtar Kelimeler: Bernulli-Euler Polinomları, Genelleştirilmiş Bernoulli-Euler
Polinomları, Sonlu Fark.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Bernoulli - Euler Polynomials, Generalized Bernoulli - Euler Polynomials, Finite Difference
Bernoulli and euler polynomials
Thesis
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oai:i-rep.emu.edu.tr:11129/13732014-10-01T23:00:44Zhdl_11129_66
EMU I-REP
author
İyikal, Övgü Çıdar
2014-10-01T07:35:53Z
2014-10-01T07:35:53Z
2013-08
İyikal, Övgü Çıdar. (2013). Smoothing based on stretched interpolated moving average approach. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1373
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
ABSTRACT: In this thesis, some smoothing techniques in multivariate and functional data analysis such as, kernel smoothing, local linear regression (LLR), spline smoothing and smoothing together with principal components analysis through conditional expectation (PACE) methods are considered. Their details are studied and a new smoothing method benefiting from moving average concept and applicable under certain conditions is proposed. Due to the steps involved in its logic, the proposed method is named Strecthed Interpolated Moving Average (SIMA). Its application to different data sets produced better results in terms of involved error, compared with LLR and similar results when compared with PACE.
Keywords: Karhunen–Loève Expansion, Stretched Interpolated Moving Average, Principal Component Scores, Lag Interval, Weight Function.
…………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezde, çok değişkenli ve fonksiyonel veri analizinin; çekirdek pürüzsüzleştirme, yerel lineer regresyon (LLR), spline pürüzsüzleştirme, ve koşullu beklenti ile temel bileşenler analizi (PACE) gibi bazı pürüzsüzleştirme tekniklerine yer verilmiştir. Bunların ayrıntıları incelenmiş ve belirli koşullar altında hareketli-ortalamadan yararlanılarak yeni bir pürüzsüzleştirme tekniği önerilmiştir. Kendi mantığı içinde yer alan adımları nedeniyle önerilen yöntem Gerilmiş İnterpolasyonlu Hareketli-Ortalama (SIMA) diye adlandırılır. SIMA’nın farklı verilerde yapılan uygulamasında LLR uygulamasına kıyasla daha iyi sonuçlar elde edilmiş, PACE ile kıyaslandığında ise benzer sonuçlar elde edilmiştir. Anahtar Kelimeler: Karhunen–Loève Açılımı, Gerilmiş Interpolasyonlu Hareketli-Ortalama, Temel Bileşenler Skorları, Gecikme Aralığı, Ağırlık Fonksiyonu.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Smoothing (Statistics)
Kernel functions
Karhunen-Loeve Expansion, Stretched Interpolated Moving Average, Principal Component Scores, Lag Interval, Weight Function
Smoothing based on stretched interpolated moving average approach
Thesis
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oai:i-rep.emu.edu.tr:11129/13772014-10-01T23:00:47Zhdl_11129_66
EMU I-REP
author
Abbasi, Akbar
2014-10-01T11:18:33Z
2014-10-01T11:18:33Z
2013-07
Abbasi, Akbar. (2013). Environmental radiation in high exposure building materials. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Physics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1377
Doctor of Philosophy in Physics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics, 2013. Supervisor: Prof. Dr. Mustafa Halilsoy.
ABSTRACT: In this thesis, we investigated the specific radioactivity concentrations of Ra, Th and K in different types of commonly used granite stone samples collected from the Tehran city of Iran by means of a high-resolution HPGe gamma-spectroscopy system. The result of Th, Ra and K are ranged from 18 to 178, 6 to 160 and 556 to1539 Bq kg- , respectively. The radium equivalent activities ( ) are lower than the limit of 370 Bq kg- set by NEA (Nuclear Energy Agency, OECD 1979) except in two samples. The internal hazard indexes have been found well below the acceptable limit in most of the samples. Five samples of investigated commercial granite stones do not satisfy the safety criterion illustrated by UNSCEAR (United Nations Scientific Committee on the Effects of Atomic Radiation, 1993). Applying dose criteria recently recommended by the EC [European Commission (1999)] for superficial materials, all investigated samples meet the exemption dose limit of 0.3 mSv y- . Also in this thesis, health hazards from gamma radiation doses due to granite and radon concentration have been calculated. The dose rate of exposure from granite building materials on humans is obtained as a result of an external exposure from gamma-emitting radionuclides in the granites. Another mode of exposure is from the inhalation of the decay products of Rn and Rn. The radon exhalation rates have also been studied and values were in the range of 0.32±0.01 to 7.86±1.65 Bq m- h- . For two models of standard living rooms (5.0 m×4.0 m area; 2.8 m), the radon concentration ( and the absorbed dose ( ) rates were calculated and the results were found to be 10.64–29.32 Bq m- , 3.84–68.02 nGy h- and 0.02–0.33 mSv y- for Model 1, 10.07–15.38 Bq m- and 2.29–39.99 nGy h- for Model 2, respectively. According to our estimations, mechanical ventilation systems ( ) in a room all granite samples would produce radon concentration of <100 Bq m- .
Finally, radon exhalation rates and radon concentrations in selected granite stones were measured by means of a gamma-spectroscopy system (passive method) and an AlphaGUARD (active method). The radon exhalation rates measured by the passive and active methods were compared and the results of this study were similar, with the active method being 22 % higher than the passive method.
Keywords: Radioactivity, Internal Hazard, Radiation Dose, Radon Exhalation, Passive Method, Active Method.
…………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezde yüksek çözünürlüklü HPGe gama spektroskopi sistemi kullanarak Tahran/IRAN daki farkli tür granit taşlarının Ra, Th ve K kaynaklı radyoaktivite yoğunlukları incelenmiştir. Sırası ile; Th, Ra ve K için 18 - , 6 – 160 ve 556 – Bq/kg sonuçlari elde edilmiştir. İki örnek dışında (1979) OECD Nükleer Enerji Ajansının Koyduğu sınır değer olan 370 Bq/kg altinda değerler bulunmuştur. Pekçok örnekde tehlike (risk) indisleri kabul edilir limitlerde elde edilmiştir. İncelenen ticari granit taşlarından 5 örnek, UNSCLEAR (1993, Atomik Radyasyonun etkileri üzerine Birleşmiş Milletler Bilimsel Komitesi) in koyduğu güvenlik şartlarını sağlamaktadır. yılında Avrupa Komisyonunun önerdiği ölҫek kuralları ışığında yüzeysel maddeler incelenmiş ve . mSv/yıl sınır değeri aşılmamıştır.
Granitteki gama ışınlarından ve radon yoğunluklarından oluşan sağlık riskleri de hesaplanmıştır. Granit yapı materyallerinin insana ışınlanma doz hızı, granitteki gama ışını yayan radyonukleitlerin diş işinlamasi sorunu oluşmaktadir.
Diger bir maruz kalma ise Rn ve Ra nin bozunma ürünlerinin solunumla alınmasıdır. Radon yayma oranları . ± . – 7.86±1.15 Bq/m .sa bulunmuştur. 5×4 (alan m )× 2.8 m’li standart odasında iki model için radon yoğunluğu (Ci) ve sogurulan doz (D) hesap edilmiştir. Hesaplanmış sonuҫlar Model `in: 10.64 -29.32 Bq/m , 3.84 – 68.02 nGy/sa ve 0.02 – 0.33 mSv/yıl. Model 2`in: 10.07 – 15.38 Bq/m , ve 2.29 – 39.99 nGy/sa bulunmuştur. Öngörümüze göre, mekanik havalandırma sistemli ( ) odada granit örneklerinin ürettiği radon yoğunluğu Bq/m altındadır.
Sonuҫ olarak, seҫilmiş granit taşların radon ҫıkış oranı ve yoğunlukları gama Spektroskopi sistemi ile (pasif yöntem) ve AlphaGUARD (aktif yöntem) ile ölҫülmüştür. Bu iki yöntemde sonuçlar kıyaslanmış olup benzer sonuҫlar yanında aktif yöntemde % daha yüksek veriler tesbit edilmiştir.
Anahtar kelimeler: Radyoaktivite, Konutlardaki Tehlike, Işınım Dozları, Radon Ҫıkışı, Pasif ve Aktif Yöntemler.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Physics
Radiation - Radioactivity
Building materials - Health aspects
Radioactivity, Internal Hazard, Radiation Dose, Radon Exhalation, Passive Method, Active Method
Environmental radiation in high exposure building materials
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/13792014-10-01T23:00:31Zhdl_11129_66
EMU I-REP
author
Al Shnaikat, Lina Abed Al-Hakim Hamdan
2014-10-01T12:11:13Z
2014-10-01T12:11:13Z
2013-06
Al Shnaikat, LinaAbed Al-Hakim Hamdan. (2013). Type-2 fuzzy logic in modeling uncertainity. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1379
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: Thisthesis aims to analyze the type-2 fuzzy logic and sets to model uncertainty. Basic concepts of type-2 fuzzy sets are described. Operations on type-2 fuzzy sets are performed. Generalized and interval type-2 fuzzy sets are represented. Mamdani and Sugeno type-2 fuzzy systems are considered. Keywords:Fuzzy logic and Sets,Uncertainty, Generalized and Interval Type-2 Fuzzy Sets, Mamdani and Sugeno Type-2 Fuzzy Systems.
…………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı tip-2 bulanık mantık ve kümeler teorisini kullanarak belirsizligi modellemedir. Tip-2 bulanık kümeler ile ilgili temel kavramlar açıklanır. Tip-2 bulanık kümeler üzerinde işlemler gerçekleştirilir. Genelleştirilmişve aralık tip-2 bulanık kümeler belirtilir. Mamdani ve Sugeno tip-2 bulanık sistemler incelenir.
Anahtar Kelimeler:Bulanık Mantık ve Kümeler,Belirsizlik, Genelleştirilmişve Aralık Tip-2 Bulanık Kümeler, Mamdani ve Sugeno Tip-2 Bulanık Sistemler.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Fuzzy Logic
Fuzzy Logic and Sets, Uncertainty, Generalized and Interval Type-2 Fuzzy Sets, Mamdani and Sugeno Type-2 Fuzzy Systems
Type-2 fuzzy logic in modeling uncertainity
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/14052014-10-09T23:00:54Zhdl_11129_66
EMU I-REP
author
Yılmaz, Banu
2014-10-09T11:40:53Z
2014-10-09T11:40:53Z
2014-02
Yılmaz, Banu. (2014). Some properties of appell polynomials. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Computer Engineering, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1405
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Mehmet Ali Özarslan.
ABSTRACT: This thesis consists of five chapters. The first Chapter gives general information
about the thesis. In the second Chapter, some preliminaries and auxilary results that are
used throughout the thesis are given. The original parts of the thesis are Chapters 3, 4 and 5 which are established from [35], [46] and [48]. In Chapter three, extended 2D Bernoulli and 2D Euler polynomials are introduced. Moreover, some recurrence relations are given. Differential, integrodifferential and partial differential equations of the extended 2D Bernoulli and the extended 2D Euler polynomials are obtained by using the factorization method. The special cases reduces to differential equation of the usual Bernoulli and Euler polynomials. Note that the results for the usual 2D Euler polynomials are new. In Chapter four, we consider Hermite-based Appell polynomials and give partial differential equations of them. In the special cases, we present the recurrence relation, differential, integro-differential and partial differential equations of the Hermite-based Bernoulli and Hermite-based Euler polynomials. In Chapter five, introducing k-times shift operators, factorization method is generalized. The differential equations of the Appell polynomials are obtained. For the special case k = 2, differential equation of Bernoulli and Hermite polynomials are exhibited. Keywords: 2D Bernoulli polynomial, 2D Euler polynomial, extended 2D Bernoulli
polynomial, extended 2D Euler polynomial, Hermite-based Appell polynomials, factorization
method.
…………………………………………………………………………………………………………………………………………………………………………………………………………
ÖZ: Bu tez beş bölümden oluşmuştur. Birinci bölümde, tez ile ilgili genel bilgiler verilmiştir. İkinci bölümde, tezde kullanılan tanım ve kavramlar hakkında temel bilgiler ve sonuçlar verilmiştir. Bu tezin orijinal kısımları [35], [46] ve [48] nolu referanslardan ortaya çıkan üçüncü, dördüncü ve beşinci bölümlerdir. Üçüncü bölümde, iki değişkenli genişletilmiş Bernoulli ve Euler polinomları tanımlanmıştır. Buna ek olarak, iki değişkenli genişletilmiş Bernoulli ve Euler polinomlarının sağladığı rekürans bağıntıları verilmiştir. Faktorizasyon metodu kullanılarak, bu polinom ailelerinin sağladığı diferensiyel, integro-diferensiyel ve kısmi diferensiyel denklemler bulunmuştur. Özel durumlar, Bernoulli ve Euler polinomlarının diferensiyel denklemlerine düşer. Belirtelim ki, sonuçlar iki değişkenli Euler polinomları için yenidir. Dördüncü bölümde, Hermite tabanlı Appell polinomları göz önüne alınmış ve bu polinomların sağladığı kısmi diferensiyel denklemler bulunmuştur. Özel durumlar olarak, Hermite-tabanlı Bernoulli ve Hermite-tabanlı Euler polinomlarının diferensiyel, integrodiferensiyel ve kısmi diferensiyel denklemleri verilmiştir.
Beşinci bölümde, k-defa artıran ve k-defa azaltan operatörler kullanılarak, faktorizasyon metodu genişletilmiş ve böylece Appell polinomlarının diferensiyel denklemleri bulunmuştur. Özel olarak, k = 2 için Bernoulli ve Hermite polinomlarının diferensiyel denklemleri verilmiştir. Anahtar Kelimeler: İki değişkenli Bernoulli polinomu, iki değişkenli Euler poliiv nomu, genişletilmiş iki değişkenli Bernoulli polinomu, genişletilmiş iki değişkenli Euler polinomu, Hermite-tabanlı Appell polinomları, faktorizasyon metodu.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
2D Bernoulli Polynomial, 2D Euler Polynomial, Extended 2D Bernoulli Polynomial, Extended 2D Euler Polynomial, Hermite-Based Appell Polynomials, Factorization Method
Some properties of appell polynomials
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/14202014-10-17T23:00:34Zhdl_11129_66
EMU I-REP
author
Elfadel, Ajaeb
2014-10-17T05:15:37Z
2014-10-17T05:15:37Z
2014-02
Elfadel, Ajaeb. (2014). Cryptography by means of linear algebra and number theory. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1420
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Müge Saadetoğlu.
ABSTRACT: This thesis focuses on the techniques of cryptography in linear algebra and number theory. We first give the necessary review on modular arithmetic. Under Linear Algebra, Hill cipher cryptographic technique and its variations are studied. Under number theory, on the other hand, the definition of Euler function, and some important theorems in this regard are given. The cryptographic techniques such as the Caesar cipher, Exponential transformations and the Public key cryptographic techniques are explained. Finally, some more advanced cryptographic techniques such as the Digraph trans-formations are given.
Keywords: Hill cipher, Euler theorem, Caesar cipher, Exponential method, Public Key method, Monoalphabetic cipher, Digraph transformations.
…………………………………………………………………………………………………………………………
ÖZ: Bu yüksek lisans tezinde Lineer Cebir ve Sayılar kuramı kavramları kullanan şifreleme yöntemleri anlatılmıştır.
Tezin giriş kısmı tezde sıkça kullanılan modüler aritmetik ile ilgili ön bilgi vermektedir.Lineer cebir de Hill Şifreleme yöntemi baz alınmıştır.Sayılar kuramı bölümünde ise, Euler fonksiyonu tanıtılıp, bu fonksiyonla ilgili temel teoremler verildikten sonra, bu teoremleri kullanan şifreleme yöntemleri aktarılmıştır.Sezar Şifreleme, Üstel transformasyon ve Asimetrik şifreleme yöntemleri işlenen şifreleme yöntemlerinden bazılarıdır. Son olarak da daha ileri derecede şifreleme imkanı sunan ‘tek sesi temsil eden iki harf’ yöntemi anlatılmıştır.
Anahtar Kelimeler: Hill Şifreleme, Euler Teoremi, SezarŞifreleme, Üstel ransform-asyon, Asimetrik şifreleme, Tek sesi temsil eden iki harf metodu.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Number theory
Linear Algebra
Hill Cipher, Euler Theorem, Caesar Cipher, Exponential Method, Public Key Method, Monoalphabetic Cipher, Digraph Transformations
Cryptography by means of linear algebra and number theory
Thesis
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oai:i-rep.emu.edu.tr:11129/14262014-10-17T23:00:44Zhdl_11129_66
EMU I-REP
author
Abdulnabi, Nisreen Lukman
2014-10-17T12:41:20Z
2014-10-17T12:41:20Z
2014-02
Abdulnabi, Nisreen Lukman. (2014). Prospect theory in decision making process. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1426
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: This thesis purposes the investigation of the prospect theory in decision making process. The theoretical aspects and basic concepts of the prospect theory for the decision making under uncertainty and risk are analyzed. The editing and evaluation phases of prospect theory are discussed. The expected utility, value and weighting functions are calculated. The utility functions for rational decision making by evaluating gains and losses are considered. Keywords: Prospect theory, Decision making, Expected utility, Value and weighting functions, Utility functions.
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ÖZ: Bu tezin amacı karar verme sürecinde beklenti teorisini araştırmaktır. Kararsızlık ve risk durumlarında karar verme için beklenti teorisinin teorik yönleri ve temel kavramları incelenir. Bekleme teorisinin düzenleme ve değerlendirme aşamaları ele alınır. Beklenen fayda, değer ve ağırlık verme fonksiyonları hesaplanır. Rasyonel karar verme için kazanç ve zarar değerlendirilerek fayda fonksiyonları dikkate alınır. Anahtar Kelimeler: Beklenti teorisi, Karar verme, Beklenen fayda, Değer ve ağırlık verme fonksiyonları, Fayda fonksiyonları.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Decision Making - Mathematics
Prospect Theory, Decision Making, Expected Utility, Value and Weighting Functions, Utility Functions
Prospect theory in decision making process
Thesis
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oai:i-rep.emu.edu.tr:11129/14312014-10-28T00:00:45Zhdl_11129_66
EMU I-REP
author
Zebari, Amar Yahya
2014-10-27T09:55:57Z
2014-10-27T09:55:57Z
2014-02
Zebari, Amar Yahya. (2014). Regression modeling for incidence of diabetics. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1431
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Mehmet Ali Tut.
ABSTRACT: Biostatistics is one of the important approaches for decision makers in the health sciences for mathematical modeling and predictions. The choosing of a topic of diabetes to be applied in this study due to the importance of finding a cure of this disease, which is the incidence rates increased in the last years. The reason of this increased and the types are investigated by the researchers, to illustrate how some variables as weight and age its effects on diabetes.
The study was conducted on a sample of 1385 patients with diabetes, randomly selected from the community data diabetics in the Diabetics Center province of Duhok/ Kurdistan Region of Iraq, of 10,083 patients with diabetes, and applies the theories of linear regression on this data to create a mathematical equation helps us to anticipate future injury rates. The results are then compared with the results of statistical study on the Greek Cypriot patients less than 15 years of age, to clarify the differences and to clarify the effects. The use of the Statistical Software Packages for Social Sciences (SPSS) in this study is to obtain more accurate results and reduce the time and voltage. This study basically is the application of linear regression modeling to cases of diabetic patients. Chapter one included a brief about diabetes and its type and reference to some other statistical researches conducted on diabetic's data. Chapter two is about the theories and concepts that can use it in application this study and obtained requires results. The third chapter is the application of these statistical theories on diabetic's data that there is a belief that have an effect on incidence this disease like weight and family genetic history, and analyze the results graphically and illustrations using the Statistical Package for Social Sciences which is referred as SPSS, then modeling a mathematical regression equation for these data. The results showed several statistics about the Duhok data. Several differences in terms of means between males and females were listed. Duhok data and its statistics were compared with a data related with Cyprus region.
A regression function was also constructed for predicting diabetes for some next time periods. An exponential model fitted the current Duhok data.
Keywords: Biostatistics, Statistical Analysis, Diabetes, Regression Analysis, Mathematical Modeling, Statistical Software Packages for Social Sciences (SPSS).
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ÖZ: Biyoistatistik, sağlık bilimleriyle ilgili biyolojik veri analizi ve modellemesinde kullanılabilen önemli bir daldır. Bu çalışmada Irak’ın Duhok bölgesi için diyabetik hastalarla ilgili bilgilerin analizi yapılarak özellikle erkek ve kadın hastalar arasındaki değişik statistiki ilişkilerin tesbit edilmesine çalışılmıştır. Ayrıca Kıbrıs’daki bir durum analizindeki verilerle de Dukok verileri arasında bir karşılaştırma yapılmıştır. Ayrıca Duhok bölgesindeki diyabetli hasta sayısının ilerleyen zaman dilimlerindeki değişimin kestirilebilmesi için regresyon analizi de yapılarak sözkonusu verilerin en iyi exponansiyel modelle modellenebildiği ortaya konmuştur.
Anahtar Kelimeler: Biyoistatistik, İstatistiksel Veri Analizi, Diyabet, Matematiksel Modelleme, Regresyon Analizi.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Biostatistics, Statistical Analysis, Diabetes, Regression Analysis, Mathematical Modeling, Statistical Software Packages for Social Sciences (SPSS)
Regression modeling for incidence of diabetics
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/14352014-10-29T00:00:48Zhdl_11129_66
EMU I-REP
author
Alani, Ahmed Sami Abdulghafour
2014-10-28T13:50:33Z
2014-10-28T13:50:33Z
2014-01
Alani, Ahmed Sami Abdulghafour. (2014). Principal component analysis in statistics. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1435
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
ABSTRACT: Researchers and students sometimes need to deal with large volumes of data, causing them to have difficulty in the analysis and interpretation of these data. In the statistical analysis of high dimensional data, it is required to reduce the dimension of data set without losing any important information. One way of achieving this goal is the use the principal component analysis (PCA). The PCA objectives are to extract an important part of information from the data set, reducing the size of data with no damage to data and information. This is achieved by finding a new set of independent (uncorrelated) variables called principal components which are obtained as a linear combination of the original variables. The calculation of PCs means the computation of eigenvalues and eigenvectors for a positive-semidefinite symmetric matrix. The first PC has the largest proportion of variance of the data, and the second component has the second largest proportion of variance and is orthogonal to the first principal component. Remaining PCs represents the remainin variance in descending order, and each PC is orthogonal to its prdecesor. After computing the PCs, the first several PCs that represents the large part of variation are selected for use in further analysis. Finally, discussion of correlation between the PCs and original variables and determine which variable has more influence on each PC.
Keywords: Principal Component Analysis (PCA), orthogonal matrix, eigenvalue, eigenvector, singular value decomposition (SVD), covariance, correlation.
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ÖZ: Araştırmacılar ve öğrenciler çalışmalarında büyük veri kitleleri ile çalışmak durumunda kalabilirler. Bu durum verilerin analizinde ve yorumunda güçlükler yaratabilir. Büyük boyutlu verilerin istatistiksel analizinde verideki önemli bilgileri kaybetmeden veri boyutu indirgemesi yapılması gereksinimi vardır. Bu amaca ulaşmanın yollarından bir taneside temel bileşenler analizi (TBA) dir. TBA’nın amacı verideki önemli bilgi içeriğini çıkarmak, veri boyutunu indirgerken veriye ve içerdiği bilgiye hasar vermemektir. Bu hedefe ulaşırken temel bileşenler (TB) denen, mevcut değişkenlerin lineer bir kominasyonu olan, birbirinden bağımsız yeni değişkenler tanımlanır. TB’lerin hesabında prensip olarak pozitif-yarıkesin simetrik bir matrisin özdeğer ve özvektörlerinin hesabı gerekir. Birinci TB verideki salınımın (varyasyonun) en büyük kısmını, ikinci TB birinciye orthogonal olub verideki salınımın ikinci en büyük kısmını temsil eder. Benzer şekilde geriye kalan TB’lerde azalan oranda salınımı temsil eder ve her biri kendinden önce gelene ortogonaldir. TB’lerin saptanmasından sonra, verideki salınımın büyük kısmını temsil eden ilk birkaç TB, daha ileri analiz ve yorumda kullanılmak üzere seçilir. TB’ler ile verideki değişkenler arasındaki ilişki ve hangi değişkenlerin TB üzerinde daha büyük etkisi olduğu incelenir.
Anahtar kelimeler: Temel bileşenler analizi (TBA), ortogonal matris, özdeğer, özvektör, tekil değer ayrışımı (TDA), kovaryans, korelasyon.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Principal Component Analysis (PCS), Orthogonal Matrix, Eigenvalue, Eigenvector, Singular Value Decomposition (SVD), Covariance, Correlation
Principal component analysis in statistics
Thesis
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oai:i-rep.emu.edu.tr:11129/14392014-10-31T00:00:42Zhdl_11129_66
EMU I-REP
author
Al-Rubaiy, Hayder Mosa Merza
2014-10-30T08:10:48Z
2014-10-30T08:10:48Z
2014-02
Al-Rubaiy, Hayder Mosa Merza. (2014). Query processing for data retrieval from distributed database management system. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1439
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: The goal of this thesis is to analyze an importance of a distributed database management system for data retrieval process. The characteristics of distributed database management systems are defined. The homogeneous and heterogeneous distributed database management systems are presented. The main objectives of data replication and data allocation are highlighted, and data fragmentation by query processing is implemented. The relational algebra operations and Structured Query Language (SQL) statements are applied to determine different types of data fragmentation.
Keywords: Distributed Database Management System, Homogeneous and heteregeneous distributed database management systems, Data replication, Data allocation, Data fragmentation, Query processing, Strucured Query Language (SQL).
…………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı veri erişimi işlemi için dağıtımlı veritabanı yönetim sisteminin önemini araştırmaktır. Dağıtımlı veritabanı yönetim sisteminin özellikleri tanımlanır. Homojen ve heterojen dağıtımlı veritabanı yönetim sistemleri gösterilir. Veri çoğaltma ve veri tahsisi vurgulanır, ve sorgu işlemleri kullanmakla veri parçalanması hayata geçirilir. İlişkisel cebir operatörleri ve Yapısal Sorgulama Dili (SQL) komutları uygulamakla veri parçalanmasının farklı türleri belirlenir.
Anahtar Kelimeler: Dağıtımlı Veritabanı Yönetim Sistemi, Homojen ve Heterojen Dağıtımlı Veritabanı Yönetim Sistemleri, Veri çoğaltma, Veri tahsisi, Veri parçalanması, Veri sorgulama, SQL Yapısal Sorgulama Dili.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Distributed databases
Database management
Distributed Database Management System, Homogeneous and Heteregeneous Distributed Database Management Systems, Data Replication, Data Allocation, Data Fragmentation, Query Processing, Structured Query Language (SQL)
Query processing for data retrieval from distributed database management system
Thesis
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oai:i-rep.emu.edu.tr:11129/14772014-11-16T00:00:49Zhdl_11129_66
EMU I-REP
author
Demirci, Yılmaz
2014-11-15T13:37:36Z
2014-11-15T13:37:36Z
2013-09
Demirci, Yilmaz. (2013). Security of learning management systems. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1477
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
ABSTRACT: In this thesis I discuss the security issues of the Moodle Learning Management System. Therefore first the security vulnerabilities of web applications in general are discussed and then the security risks of Moodle and its solutions are presented. Furthermore a complete step-by-step installation guideline is proposed in order to create a Moodle installation with maximum security.
Keywords: Moodle, security of Moodle, security risks of 2013.
…………………………………………………………………………………………………………………………
ÖZ: Bu tezde Moodle Öğrenme Yönetim Sistemi’ nin güvenlik sorunlarını ele aldım. Bu sebeple web uygulamarının genel güvenlik açıkları öncelikle ele alındı ve sonra Moodle’ ın güvenlik riskleri ve bunların çözümleri sunuldu. Ayrıca, maksimum güvenlikte bir Moodle kurulumu yapmak için adım adım tam bir kurulum rehberi önerildi.
Anahtar Kelimeler: Moodle, Moodle güvenliği, 2013 yılının güvenlik riskleri.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Information Technology
Systems and Data Security
Moodle, Security of Moodle, Security Risks of 2013
Security of learning management systems
Thesis
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oai:i-rep.emu.edu.tr:11129/14992014-11-20T00:00:45Zhdl_11129_66
EMU I-REP
author
Al-Obaidi, Maysaa Jasim Mahmood
2014-11-19T08:22:01Z
2014-11-19T08:22:01Z
2013-07
Al-Obaidi, Maysaa Jasim Mahmood. (2013). Fuzzy game theory for decision analysis. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1499
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Rashad Aliyev.
ABSTRACT: The purpose of this thesis is to consider the synergy of fuzzy logic theory and game theory for the analysis of the decision making process. The different techniques of fuzzy game theory versus their crisp prototypes are described. The properties of the crisp and fuzzy cooperative and non-cooperative games are compared. The fuzzy mixed strategy, fuzzy dominant strategy, and fuzzy Nash equilibrium are investigated.
Keywords: Fuzzy Logic, Game Theory, Fuzzy Cooperative and Non-cooperative Games, Fuzzy Mixed Strategy, Fuzzy Dominant Strategy, Fuzzy Nash Equilibrium.
…………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı bulanık mantık ve oyun teorilerinin sinerjisini karar verme sürecinde araştırmaktır. Bulanık oyun teorisinin farklı teknikleri ile onların karşılıklı klasik prototipleri incelenir. Klasik ve bulanık işbirlikli ve işbirliksiz oyunların özellikleri kıyaslanır. Bulanık karma gengüdüm, bulanık başat gengüdüm, ve bulanık Nash dengesi araştırılır.
Anahtar Kelimeler: Bulanık Mantık, Oyun Teorisi, Bulanık Işbirlikli ve Işbirliksiz Oyunlar, Bulanık Karma Gengüdüm, Bulanık Başat Gengüdüm, Bulanık Nash Dengesi.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Fuzzy decision making
Game Theory
Fuzzy Sets
Fuzzy Logic, Game Theory, Fuzzy Cooperative and Non-Cooperative Games, Fuzzy Mixed Strategy, Fuzzy Dominant Strategy, Fuzzy Nash Equilibrium
Fuzzy game theory for decision analysis
Thesis
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oai:i-rep.emu.edu.tr:11129/15932015-03-04T00:00:47Zhdl_11129_66
EMU I-REP
author
Karanfiller, Tolgay
2015-03-03T06:11:16Z
2015-03-03T06:11:16Z
2012-01
Karanfiller, Tolgay. (2012). Exploiting Petri Nets to Reduce Switch Crosstalk and Path-Dependent-Loss in Optical Interconnection Networks. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1593
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Applied Mathematics and Computer Science, 2012. Supervisor: Prof. Dr. Rza Bashirov.
ABSTRACT: Although optical communication systems promise to meet demands of communication networks and multiprocessors in fast communication, they suffer from challenges such as path dependent loss and switch crosstalk. An innovative approach proposed in the present thesis is centered upon modelling OMINs with Petri nets and using P-invariants method for determination of the minimum number of stages that is sufficient for realization of demanded communication patterns in an OMIN with variable number of stages. Being composed of stages an OMIN of the minimal structure provides the least values for the path dependent loss and switch crosstalk. Based on complexity results, we make sure about feasibility of our approach. Firstly, we prove that the P/T-nets created in the present research are in polynomial dependence on the problem size, which alleviates memory consumption significantly and reassures the fact that the task according to our approach can be completed in feasible time. Secondly, we compare P/T-nets obtained in the present reasearch with the complete unfoldings created in our previous reasearch and show that P/T-nets in the latter work are more compact in the size than the ones considered in the former research. This is improvement of the complexity results obtained in our previous work. Finally, we verify validation of our approach through performing series of computer tests and showing that the results of the computer experiments agree with known analytical results.
…………………………………………………………………………………………………………………………
ÖZ: Optik interkoneksiyon ağları, bilgisayar iletişim ağlarının ve çok işlemcili sistemlerin hızlı iletişime olan ihtiyaçlarını karşılamanın yanı sıra yola bağımlı kayıplar ve anahtarlamada hatların karışması gibi zorluklardan etkilenirler. Bu tezde önerilen yenilikçi yaklaşımın temelinde optik interkoneksiyon ağlarının Petri ağları ile modellenmesi ve P-invariantlar metodunu uygulayarak çok basamaklı optik interkoneksiyon ağlarında verilen permütasyona göre en küçük basamak sayısının bulunması yatar. En küçük basamak sayılı optik interkoneksiyon ağında yola bağımlı kayıplar ve anahtarlamada hatların karışması en küçük düzeyde seyredilir.
Önerilen metodun uygulanabilirliğinden emin olmak için bir karmaşıklık analizi yapılmıştır. Öncelikle tasarlanan P/T-ağların büyüklüğünün artış hızının polinomyal olduğu ispat edilmiştir. Bu olgu, P/T-ağ oluşumunda hafıza tüketiminin önemli ölçüde azaltarak, sıkça rastlanan “durum patlaması”ndan uzakta tutulabileceğini göstermektedir. Sonra takdim edilen çalışmada elde edilen P/T-ağlarını, bir önceki çalışmamızda tasarlanan tamamen açılmış Petri ağlarıyla kıyasladık. Sonuç olarak elde ettiğimiz Petri ağlarının daha küçük olduğu ispat edilmiştir.
Alınan analitik ve kuramsal sonuçların geçerliliği yapılan bilgisayar testleri ile kanıtlanmıştır.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics Department
Applied Mathematics and Computer Science
Exploiting Petri Nets to Reduce Switch Crosstalk and Path-Dependent-Loss in Optical Interconnection Networks
Thesis
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oai:i-rep.emu.edu.tr:11129/16042015-03-07T00:01:25Zhdl_11129_66
EMU I-REP
author
Salehi, Sara
2015-03-06T08:44:37Z
2015-03-06T08:44:37Z
2014-05
Sara, Salehi. (2014). Bayesian Probability Estimation for Reasoning Process. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1604
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Rashad Aliyev.
ABSTRACT: It is a comprehensible fact that people always desire to be able to remove or at least to decrease the level of uncertainty in real world application. In all the areas of science and technology, it is important to have an accurate measurement for evaluating the uncertainty.
Increasing accuracy of measurement includes the identification, analysis and minimization of errors, compute and estimate the result of uncertainties. A probability is the branch of science studying the quantitative inferences of uncertainty. Probability is involved in various fields such as finance, meteorology, engineering, medicine, management etc.
In this thesis, Bayesian probability estimation for reasoning process is analyzed. The conditional, joint, prior, and posterior probabilities are mentioned. The importance of the probability views based on the subjectivity and objectivity, and the properties of these two terms are considered. The Bayesian inference and the generalized Bayes’ theorem are discussed.
Keywords: Uncertainty, Bayesian method, subjective and objective probabilities, Bayesian inference, generalized Bayes’ theorem.
…………………………………………………………………………………………………………………………
ÖZ: Bilinen bir gerçektir ki insanlar farklı uygulamalarda belirsizlik derecesini yok etmeğe veya en azından küçültmeğe isteklidirler. Bilim ve teknolojinin tüm alanlarında belirsizliği değerlendirmek için hassas ölçüm gereklidir.
Hassas ölçümü yükseltmek amacı ile belirsizliğin tanımlanması, tahlili, hatanın en az olması, sonuçların hesaplanması ve değerlendirilmesi gerekir. Olasılık bir bilim dalı olarak belirsizliğin nicel çıkarımlarını öğrenir. Olasılık finans, meteroloji, mühendislik, tıp ve başka alanlarda yer alır.
Bu tezde Bayes olasılığı uslamlama işlemi için incelenir. Koşullu, bileşik, önsel, ve sonsal olasılıklardan bahsedilir. Öznellik ve nesnelliğe dayanan olasılık görünümlerinin önemi, ve bu iki kavramın özellikleri dikkate alınır. Bayes sonuç çıkarma ve genelleştirilmiş Bayes teoremi tartışılır.
Anahtar Kelimeler: Belirsizlik, Bayes yöntemi, öznel ve nesnel olasılıklar, Bayes çıkarımı, genelleştirilmiş Bayes teoremi.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Probabilities - Bayesian statistical decision theory - Proposition (Logic) - Reasoning
Uncertainty, Bayesian Method, Subjective and Objective Probabilities, Bayesian Inference, Generalized Bayes' Theorem
Bayesian Probability Estimation for Reasoning Process
Thesis
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oai:i-rep.emu.edu.tr:11129/16122015-03-07T00:01:22Zhdl_11129_66
EMU I-REP
author
Khassawneh, Bashar Suhil Jad Allah
2015-03-06T12:35:46Z
2015-03-06T12:35:46Z
2014-07
Khassawneh, Bashar Suhil Jad Allah. (2014). Credit Scoring Problem Based on Regression Analysis. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1612
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Ersin Kuset Bodur.
ABSTRACT: This thesis provides an explanatory introduction to the regression models of data mining and contains basic definitions of key terms in the linear, multiple and logistic regression models. Meanwhile, the aim of this study is to illustrate fitting models for the credit scoring problem using simple linear, multiple linear and logistic regression models and also to analyze the found model functions by statistical tools.
Keywords: Data mining, linear regression, logistic regression.
…………………………………………………………………………………………………………………………
ÖZ: Bu tez çalışması regresyon modelleri için açıklayıcı bilgiler, ayrica basit ve çoklu doğrusal regresyon modelleri ve linear lojistik regresyon modeller için temel tanımlar içermektedir. Aynı zamanda bu tezin amacı kredi sıralaması için basit, çoklu doğrusal regresyon ve linear lojistik modellemeleri kullanıp, uygun model bulmak ve bulunan model fonksiyonlarını istatistiksel yöntemlerle analiz etmektir.
Anahtar Kelimeler: Veri madenciliği, doğrusal regresyon, lojistik regresyon.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Regression analysis
Data Mining, Linear Regression, Logistic Regression
Credit Scoring Problem Based on Regression Analysis
Thesis
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KhassawnehBashar.pdf.txt
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oai:i-rep.emu.edu.tr:11129/16212015-03-11T00:01:05Zhdl_11129_66
EMU I-REP
author
Ghadaireh, Bilal Sami Mohammad
2015-03-10T08:37:37Z
2015-03-10T08:37:37Z
2014-07
Ghadaireh, Bilal Sami Mohammad. (2014). Effect of Centereing Data in Principal Component Analysis. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1621
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
ABSTRACT: In the analysis of multivariate data, the processing and extracting meaningful results becomes very difficult due large number of variables and data. Therefore, statistical techniques to deal with such data, by finding linear combinations of existing variables, such that each variable is assigned a coefficient or score that determines its contribution to that linear combination. These linear combinations are called Principal Components (PC) and the methodology used in the determination of the PCs is called Principal Component Analysis (PCA). In general the number of PCs is expected to be the same as the number of variables. However, the PCs are determined such that the great percentage of variation (usually over 90%) in the data accumulates in the first few PCs. Then, the remaining PCs become redundant, and the information contained in a large number of variables is reduced into a few new variables (PCs) that are linear combinations of original variables. Therefore, a technique used in determining the PCs is very important. In this work, theory of PCA with related mathematical background is explained and using a certain data set, various ways of the application of PCA technique is investigated, obtained results are interpreted. Keywords: Principle component analysis, data, eigenvalue, eigenvector, covariance, correlation, standardized data, centered data.
…………………………………………………………………………………………………………………………
ÖZ: Çok değişkenli veri analizinde özellikle değişken sayısının çok fazla olduğu durumlarda işlem yapıp sonuç çıkarma oldukca zordur. Bu şartlar altında veri analizini yapabilmek için geliştirilmiş istatistik teknikler, mevcut değişkenlerin lineer kombinezonlarından oluşan ve biribirinde bağımsız yeni değişkenlerin hesaplanmsını mümkün kılar. Bu değişkenlere Temel Bileşenler ve bu bileşenlerin hesaplanmasınada kullanılan yöntemlerede Temel Bileşenler Analizi denir. Hesaplanan temel bileşen sayısı, değişken sayısı kadardır. Ancak, verideki toplam değişimin çok büyük bir kısmı ilk birkaç temel bileşen tarafından temsil edilir. Sadece bunların analiz ve yorumlamada kullanılması, hesaplamalardaki yoğunluğu ciddi miktarda azaltırken, elde edilen sonuçlar tüm kitleyi 90%’ın üstünde bir temsiliyeti sahiptir. Geriye kalan ve verideki toplam değişimin çok az bir kısmını temsil eden temel bileşenler işleme sokulmaz. Böylece, çok yüksek sayıdaki veri miktari çok aza indirgenmiş olur. Bu nedenle temel bileşenlerin hesabında kullanımlan yöntemler çok önemlidir. Bu çalışmada temel bileşenler analizinin matematiksel temelleri izah edilmiş, belli bir veri seti kullanılarak metodun farklı yaklaşımlarla uygulaması yapılıp, elde edilen sonuçlar yorumlanmıştır.
Anahtar kelimeler: Temel bileşenler analizi, veri, özdeğer, özvektör, kovaryans, korelasyon, standartlaştırılmış veri, merkezileştirilmiş veri.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Statistical Mathematics
Principle Component Analysis, Data, Eigenvalue, Eigenvector, Covariance, Correlation, Standardized Data, Centered Data
Effect of Centereing Data in Principal Component Analysis
Thesis
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oai:i-rep.emu.edu.tr:11129/16422015-03-17T00:01:10Zhdl_11129_66
EMU I-REP
author
Kukul, Hande
2015-03-16T13:21:54Z
2015-03-16T13:21:54Z
2014-07
Kukul, Hande. (2014). αβ− Statistical Convergence. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1642
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Hüseyin Aktuğlu.
ABSTRACT: In this thesis we studied αβ-statistical convergence. We started with the discussion of statistical convergence. Later, we gave a brief summary of λ-statistical, lacunary statistical
and A−statistical convergences. The concept of αβ-statistical convergence which
is the main interest of this thesis has been considered in the last chapter of the thesis.
In this chapter we also show that αβ-statistical convergence is a non-trivial extension
of statistical, λ-statistical and lacunary statistical convergences. Finally, we introduced
boundedness of a sequence in the sense of αβ-statistical convergence.
Keywords: αβ−Statistical Convergence, λ−Statistical Convergence, Statistical Convergence,
A-Statistical Convergence.
…………………………………………………………………………………………………………………………
ÖZ: Bu tezde, αβ-istatistiksel yakınsaklık kavramı incelenmi¸stir. Bu kapsamda, öncelikle
istatistiksel yakınsaklık kavramı ve bu kavrama ba˘glı olarak, λ -istatistiksel, lacunary
istatistiksel ve A−istatistiksel yakınsaklık konuları hatırlatılmı¸stır. Daha sonra bu tezin
esas amacı olan αβ-istatistiksel yakınsaklık tanımı özellikleri ve λ-istatistiksel, lacunary
istatistiksel ve A−istatistiksel yakınsaklık ile ili¸skileri verilmi¸stir. Bu kapsamda
αβ-istatistiksel anlamında sınırlılık tanımı ilk kez bu çalı¸smada verilmi¸stir.
Anahtar Kelimeler: αβ−˙Istatistiksel Yakinsaklik,λ−˙Istatistiksel Yakinsaklik, ˙Istatistiksel
Yakinsaklik, A-˙Istatistiksel Yakinsaklik.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Mathematical Statistics
Gonvergence
aB - Statistical Convergence, A-Statistical Convergence
αβ− Statistical Convergence
Thesis
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oai:i-rep.emu.edu.tr:11129/16432015-03-18T00:00:45Zhdl_11129_66
EMU I-REP
author
Sayed, Hawri Hashm
2015-03-17T06:11:12Z
2015-03-17T06:11:12Z
2014-06
Sayed, Hawri Hashm. (2014).A Survey on The Methods of Spatial Statistics. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1643
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Mehmet Ali Tut.
ABSTRACT: In this thesis the kriging approach is presented for interpolating spatial data points. The mathematical model of the kriging method is mentioned first. Then a small example is provided about the steps of this approach.
ArcGIS software package is an important tool for creating maps and also for performing geostatistics about large data points. A kriging example is also tried by this package and the predicted data points are listed.
Keywords: Geostatistics, spatial data, kriging, Arcgis.
…………………………………………………………………………………………………………………………
ÖZ: Bu çalışmada, harita bilgileri (kordinatlar) üzerinde enterpolasyon uygulamalarında kullanılan kriging metodu bahsedilmektedir. Bu metodun matematiksel modeli yanında, seçilen küçük bir very örneği kullanılarak hesaplamalarla yaklaşık kestirme değerleri hesaplanmıştır. Bu analiz için geniş verilerin kullanılmasında en önemli yazılımlardan olan Arcgis paketi de kullanılarak seçilen verilerin analizi ve kestirim sonuçları eğrilerle birlikte sunulmuştur.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Spatial analysis (Statistics)
Mathematical statistics - Data processing
Geostatistics, Spatial Data, Kriging, Arcgis
A Survey on The Methods of Spatial Statistics
Thesis
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oai:i-rep.emu.edu.tr:11129/16442015-03-18T00:00:59Zhdl_11129_66
EMU I-REP
author
Ustaoğlu, Ceren
2015-03-17T06:20:47Z
2015-03-17T06:20:47Z
2014-09
Ustaoglu, Ceren. (2014). Generalized Bernstein Polynomials. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1644
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu.
ABSTRACT: This thesis consisting of three chapters is concerned with Bernstein polynomials. In the first chapter, an introduction to Bernstein polynomials is given. Then, basic properties of Bernstein polynomials are studied in the second chapter. Last chapter studies the generalized Bernstein polynomials and since it is known that generalized Bernstein
polynomials are related to q-integers, we gave basic properties of q-integers. In this chapter, convergence properties of Bernstein polynomials are also given. In addition, we introduced some probabilistic considerations of generalized Bernstein polynomials. Keywords: Bernstein polynomials; generalized Bernstein polynomials; q-integers; Convergence.
…………………………………………………………………………………………………………………………
ÖZ: Bu çalısma üç bölümden olusmaktadır. Bu tezde Bernstein polinomları çalısılmıstır. Ilk olarak Bernstein polinomlarının tanımı yapılmıs ve baslıca özellikleri incelenmistir. Ikinci bölümde genellestirilmis Bernstein polinomlari incelenmis ve bu polinomlar q-tamsayılarıyla ilgili oldugundan q-tamsayılarının baslıca özellikleri de verilmistir. Sonrasında Bernstein polinomlarının yakınsaklık özellikleri çalısılmıstır. Buna ek olarak Bernstein polinomlarının bazı olasılık metodlarıyla yakınsaklık özellikleri ele alınmıstır.
Anahtar kelimeler: Bernstein polinomları; genellestirilmis Bernstein polinomları; qtamsayıları; yakınsaklık.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Approximation theory
Bernstein Polynomials, Generalized Bernstein Polynomials, Q-Integers, Convergence
Generalized Bernstein Polynomials
Thesis
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UstaogluCeren.pdf.txt
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oai:i-rep.emu.edu.tr:11129/16512015-03-18T00:01:19Zhdl_11129_66
EMU I-REP
author
Qahraman, Yousif Ahmed
2015-03-17T08:38:25Z
2015-03-17T08:38:25Z
2014-07
Qahraman, Yousif Ahmed. (2014). Basic Iterative Methods for Solving Elliptic Partial Differential Equation. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1651
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Derviş Subaşı.
ABSTRACT: In this thesis, we studied the numerical techniques for the solution of two dimensional Elliptic partial differential equations such as Laplace's and Poisson's equations. These types of differential equations have specific applications in physical and engineering models. The discrete approximation of both equations is based on finite difference method. In this research, five points finite difference approximation is used for Laplace's and Poisson's equations. To solve the resulting finite difference approximation basic iterative methods; Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR) have been used.
Several model problems are solved by three different iterative methods and concluding remarks are presented.
Keywords: Elliptic partial differential equation, point's finite difference scheme, basic iterative methods.
…………………………………………………………………………………………………………………………
ӦZ: Yapılan bu çalışma iki boyutlu Eliptik parçalı diferansiyel denklem problemlerinin sayısal analiz teknikleri kullanılarak yaklaşık olarak çözülmesi ile ilgilidir. Eliptik parçalı diferansiyel denklemler beş noktalı sonlu farklar yöntemi kullanılarak Poisson's ve Laplace denklemlerine uygulanmış ve bu denklemler temel iteratif çözüm prosedürü olan Jacobi, Gauss Seidel ve SOR yineleme yöntemleri kullanılarak iki farklı problem üzerinde nümerik olarak çözülmüştür. Ayrıca temel iteratif çözüm prosedürü teorik olarak incelenmiştir.
Anahtar kelimeler: Eliptik parçalı diferansiyel denklem, beş noktalı sonlu farklar şeması, temel iteratif yöntemler.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Differential equations, Elliptic - Numerical solutions - Difference equations
Differential equations, Elliptic - Differential equations, Partial
Elliptic Partial Differential Equation, 5 Point's Finite Difference Scheme, Basic Iterative Methods
Basic Iterative Methods for Solving Elliptic Partial Differential Equation
Thesis
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QahramanYousif.pdf.txt
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oai:i-rep.emu.edu.tr:11129/16632015-03-21T00:00:56Zhdl_11129_66
EMU I-REP
author
Ameen, Jaafar Anwar H.
2015-03-20T12:34:43Z
2015-03-20T12:34:43Z
2014-05
Ameen, Jaafar Anwar H. (2014). Continuous Nowhere Differentiable Functions. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1663
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Agamirza Bashirov.
ABSTRACT: In this thesis four interesting points of mathematical analysis are handled. At first, some examples of continuous nowhere differentiable functions are discussed. Secondly, the Lebesgue-Cantor singular function is considered, which is continuous but the fundamental theorem of calculus is not valid for this function. Next, space-filling functions, which are continuous surjections from the interval to the square, are considered. Finally, two examples of infinitely many times differentiable functions which are not analytic are considered.
Keywords: mathematical analysis, continuous functions, differentiable functions, series, convergence.
…………………………………………………………………………………………………………………………
ÖZ: Tezde matematiksel analizin dört önemli noktası açıklanmıştır. Önce sürekli ve hiç türevi olmayan birkaç fonksiyon örneği verilmiştir. Sonra Lebesgue-Cantor singüler fonksiyonuna bakılmıştır. Bu fonksiyon sürekli olmasına rağmen analizin temel teoremi ona uygulanamamaktadır. Daha sonra uzay dolduran eğrilere bakılmıştır. Bunlar aralıktan kareye örten fonksiyonlardır. Son olarak her basamaktan türeve sahip olan fakat analitik olmayan fonksiyonlar ele alınmıştır.
Anahtar kelimeler: matematiksel analiz, sürekli fonksiyonlar, türevlenebilir fonksiyonlar, seriler, yakınsaklık.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Differentiable functions
Mathematical Analysis, Continuous Functions, Differentiable Functions, Series, Convergence
Continuous Nowhere Differentiable Functions
Thesis
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oai:i-rep.emu.edu.tr:11129/16662015-03-25T00:01:04Zhdl_11129_66
EMU I-REP
author
Abdalla, Soran Jalal
2015-03-24T06:54:28Z
2015-03-24T06:54:28Z
2014-07
Abdalla, Soran Jalal. (2014). Approximate Methods of Inverse Preconditioners for Solving the Linear Algebraic Systems. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1666
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assist. Prof. Dr. Suzan Cival Buranay.
ABSTRACT: The efficiency and robustness of iterative methods can be improved using a preconditioner that causes a change in the original matrix implicitly or explicitly. Usually preconditioners are constructed using the structure of the coefficient matrix. Therefore a preconditioner which works well for one class of matrices may fail to give good results for an other class. The focus of this study is to analyze, the efficiency of approximate inverse preconditioners for solving linear systems that arises from the discretization of the Poisson equation on a rectangle with Dirichlete boundary conditions. To realize this first, geometric construction of second order and a class of third order iterative methods for approximating a simple root of the nonlinear equation ( ) are investigated. Then by the generalization of these methods to Banach spaces, and applying them to the equation ( ) , Newton and Chebyshev iterative methods for matrix inversion are studied. These methods are applied to solve linear system of equations obtained from difference analog of Dirichlet problem of Laplace’s equation on a rectangle. The research is proceeded with the numerical results achieved and some discussions are made based on these results. Keywords: Chebyshev’s method, approximate inverse preconditioner, finite difference scheme, Laplace equation.
…………………………………………………………………………………………………………………………
ÖZ: Iteratif yöntemlerin verimlilik ve sağlamlığı kapalı veya açık olarak, orijinal matrisde bir değişime neden olan bir önkoşullandırıcı kullanılarak geliştirilebilir. Genellikle önkoşullandırıcılar katsayı matrisinin yapısı kullanılarak inşa edilir. Bu nedenle bir sınıf matrisler için iyi çalışan bir önkoşullandırıcı başka bir sınıf için iyi sonuçlar vermekte başarısız olabilir.
Bu çalışmanın odak noktası dikdörtgen üzerinde Dirichlet sınır koşullu Poisson denkleminin ayrıştırılması ile oluşan lineer sistemlerin çözümünde yaklaşık ters önkoşullandırıcıların etkinliğini analiz etmektir. Bunu ğerçekleştirmek için önce, doğrusal olmayan denklemin basit bir kökünün yaklaşımında ikinci mertebeden ve üçüncü mertebeden olan bir sınıf iteratif yöntemlerinin geometrik oluşumu incelendi. Daha sonra bu yöntemlerin Banach uzaylarına genişletilmesi ve denklemine uygulanması ile Newton ve Chebyshev iteratif yöntemleri çalışıldı. Bu yöntemler Laplace denkleminin dikdörtgen üzerinde Dirichlet sınır koşullu probleminin farklar analoğundan elde edilen lineer denklem sistemini çözmek için uygulandı. Araştırma elde edilen sonuçlar ile ilerlendirildi ve bu sonuçlara dayanarak bazı değerlendirmeler yapıldı. () 0 f x 1 () 0 FNN A
Anahtar kelimeler: Chebyshev yöntemi, yaklaşık ters önkoşollandırıcı, sonlu fark şemaları, Laplace denklemi.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Geometry, Algebraic
Chebyshev's Method, Approximate Inverse Preconditioner, Finite Difference Scheme, Laplace Equation
Approximate Methods of Inverse Preconditioners for Solving the Linear Algebraic Systems
Thesis
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oai:i-rep.emu.edu.tr:11129/16742015-03-25T00:01:11Zhdl_11129_66
EMU I-REP
author
Zangana, Zana Salahaldeen Rashid
2015-03-24T12:47:46Z
2015-03-24T12:47:46Z
2014-07
Zangana, Zana Salahaldeen Rashid. (2014). Numerical Solution of Diffusion Equation in One Dimension. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1674
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Derviş Subaşı.
ABSTRACT: In this thesis we studied the numerical techniques for the solution of one dimensional diffusion equations. The discrete approximation of the model problem is based on different finite difference schemes. These schemes are the Explicit, Implicit, Crank Nicolson and the Weighted Average schemes. For each finite difference method we studied the local truncation error, consistency and numerical results from the solution of two model problems are considered to evaluate the performance of each scheme according to the accuracy and programming efforts.
Kay word: Diffusion equation, Finite difference method, Truncation error, Stability, Consistency, Convergence.
…………………………………………………………………………………………………………………………
ÖZ: Yapılan bu çalışma tek boyutlu difüzyon differansiyel denklem problemlerinin sayısal analiz teknikleri kullanılarak çözülmesi ile ilgilidir. Bu yapılan çalışmada dört farklı sonlu farklar yöntemi problemin çözümü için kullanılmıştır. Dört farklı sonlu farklar yönteminin detaylı olarak nasıl elde edildiği, kesme hataları, stabilite şartları , yoğunluğu ve yakınsamaları detaylı olarak anlatılmıştır. Sonlu farklar metodları iki değişik problem üzerine uygulanmış ve bu metodların karşılaştırılması yapılmıştır.
Anahtar kelimeler: Difüzyon differansiyel denklem, sonlu farklar yöntemleri, kesme hatası, stabilite, yoğunluk ve yakınsama.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Mathematical models - Diffusion processes
Diffusion Equation, Finite Difference Method, Truncation Error, Stability, Consistency, Convergence
Numerical Solution of Diffusion Equation in One Dimension
Thesis
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oai:i-rep.emu.edu.tr:11129/17002015-04-13T23:00:58Zhdl_11129_66
EMU I-REP
author
Hama, Hello Ali
2015-04-13T12:04:51Z
2015-04-13T12:04:51Z
2014-05
Hama, Hello Ali. (2014). Hebb Rule Method in Neural Network for Pattern Association. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1700
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Rashad Aliyev.
ABSTRACT: In the process of the development of intelligent systems the artificial neural network plays an important role as a paradigm for pattern recognition, pattern association, optimization, prediction, and decision making problems. This master thesis focuses on analysis of Hebb rule for performing a pattern association task. The application of Hebb rule enables computing optimal weight matrix in heteroassociative feedforward neural network consisting of two layers: input layer and target output layer. The Hebb algorithm is applied to both binary and bipolar data representations. The advantages of bipolar representation of training patterns compared to binary representation of training patterns are presented. Two different ways for calculating weight matrix are used: the results of application of the Hebb algorithm, and the outer products. New input vectors which can be similar and not similar to training input vectors are tested. A new input vector differing from the training input vector in fewer components should produce the reasonable response as the same output vector.
Keywords: Neural network, Hebb rule, pattern association, binary and bipolar vectors, outer products.
…………………………………………………………………………………………………………………………
ÖZ: Yapay sinir ağı akıllı sistemlerin oluşumu sürecinde önemli rol alır ve örüntü tanıma, örüntü ilişkilendirme, optimizasyon, öngörü, ve karar verme problemlerinde paradigma olarak kullanılır.
Bu tez Hebb kuralını kullanarak örüntü ilişkilendirme görevinin incelenmesine odaklanır. Hebb kuralını uygulamakla zit ilişkili ileri beslemeli sinir ağında optimal ağırlık matrisi hesaplanır. Bu ağ iki katmandan oluşmaktadır: giriş ve hedef çıkış katmanları.
Hebb algoritması ikili ve iki kutuplu veri representasyonu için uygulanır. Eğitim örüntülerin iki kutuplu representasyonunun ikili representasyona nazaran daha avantajlı olduğu gösterilir. Ağırlık matrisinin hesaplanması iki farklı yöntemle hayata geçirilir: Hebb algoritmasının uygulanmasından elde edilen sonuçlar, ve dış çarpımlar yöntemi. Eğitim giriş vektörlerine benzer olan ve benzer olmayan yeni giriş vektörleri test edilir. Eğitim giriş vektöründen daha az bileşenle farklanan yeni giriş vektörü uygun cevap olarak aynı çıkış vektörünü üretmelidir.
Anahtar Kelimeler: Sinir ağı, Hebb kuralı, örüntü ilişkilendirme, ikili ve iki kutuplu vektörler, dış çarpımlar.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Neural Networks - Computer science
Neural Network, Hebb Rule, Pattern Association, Binary and Bipolar Vectors, Outer Products
Hebb Rule Method in Neural Network for Pattern Association
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/17142015-04-14T23:01:05Zhdl_11129_66
EMU I-REP
author
Aygören, Aysel
2015-04-14T07:42:36Z
2015-04-14T07:42:36Z
2014-07
Aygoren, Aysel. (2014). Fractional Derivative and Integral. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1714
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Hüseyin Aktuğlu.
ABSTRACT: In this thesis we studied fractional order derivative and integral. In Chapter1, a brief history on the foundation of fractional derivative and integration has been given. In the
second chapter, some definitions and theorems have been provided. Also some needed special functions such as Gamma, Beta, Mittag-Leffler and Wright function have taken place in this chapter. Properties of fractional derivative and integral are discussed in Chapter 3. We started to this chapter by the discussion of the Abel integral equation and it’s application. In the first section of Chapter 3, fractional integral in the space of integrable functions and related properties has been given. The second section is devoted to basic definitions and properties of fractional derivative and integral. Definition of fractional integral and derivative of complex order take place in the third section together with some related theorems. Fourth section contains fractional integrals of some elementary functions. In the last section of Chapter 3, we discussed fractional differentiation and integration as reciprocal operations. Keywords: Fractional Equation, Fractional Derivative, Fractional Integral.
…………………………………………………………………………………………………………………………
ÖZ: Bu tez üç bölümden olusmaktadır. Birinci bölüm giris kısmına ayrılmı¸stır. Kesirli türev ve integralin nasıl meydana getirildiginden bahsedilmistir. Ikinci bölümde bazı fonksiyon tanımlarına yer verilmistir. Ayrıca tezde kullanılacak olan bazı özel fonksiyonlar verilmistir. Bu özel fonksiyonlar Gama fonksiyonu, Beta fonksiyonu, Mittang Leffler fonksiyonu ve Wright Fonksiyonu’dur. Üçüncü bölümde genel olarak kesirli türev ve integrale giris yapılmistir, bazı özel fonksiyonlarla iliskilendirildi ve bunların özelliklerine yer verildi. Bu bölümü inceliyelim. Öncelikle Abel integral denklemi açıklanmis, özel fonksiyonlarla islemler yapılmistir. Birinci kısımda integrallenebilir fonksiyonlar uzayında kesirli integeralin çözülebilirligi bazı teoremlerle ispatlanarak açıklanmıstır. Ikinci kısımda kesirli türev ve integralin tanımları verilmis ayrıca kesirli türev ve inegralin bazı basit özelliklerinden bahsedilmistir. Üçüncü kısımda kompleks mertebeden, kesirli türev ve integral alındı ve bunlarla ilgili teoremler ispatlanarak açıklanmistir. Dördüncü kısımda bazı temel fonksiyonlarin kesirli integrali alınmis ve bunlarla ilgili islemler yapılıp istenilen temel fonksiyonlara ulasılmistir. Besinci kısımda, kesirli türev ve integral karsılıklı operatör alınarak bir takım tanımlara yer verilmis ve teoremlerle ispatlanarak açıklanmistir. Son olarak ise, yarıgrup tanımları verilmis, operatörlerin yarı gruplarla iliskisi incelenmis ve bazı uzaylarla da iliskilendirilip ispatlar yapılmistir.
Anahtar Kelimeler: Kesirli Denklemler, Kesirli Türev, Kesirli Integral.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Integral equations - Integrals, Fractional
Fractional Equation, Fractional Derivative, Fractional Integral
Fractional Derivative and Integral
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/17352015-06-24T23:00:47Zhdl_11129_66
EMU I-REP
author
Emin, Sedef Sultan
2015-06-24T10:35:53Z
2015-06-24T10:35:53Z
2015-02
Emin, Sedef Sultan. (2015). Invariants and Bestvina-Brady Groups. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1735
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Müge Saadetoğlu.
ABSTRACT: The aim of this thesis is to compute the Euler Characteristic of the Bestvina-Brady groups. First, the analytical topology, the point-set topology is introduced. Then, the
main purpose of the use of algebraic topology; the homeomorphism problem is stated.
To understand the homeomorphism problem, certain well-known topological spaces
are defined, and to solve it, the notion of topological invariants is introduced. Two
main topological invariants; Euler characteristic and the Fundamental group theories
are studied. Finally, by the use of C.T.C. Wall and the Bestvina-Brady papers, under
certain homotopic conditions the Euler Characteristic of the Bestvina-Brady groups is
computed. Keywords: Topological invariants, Euler Characteristic, Fundamental Group, Bestvina - Brady Group.
…………………………………………………………………………………………………………………………
ÖZ: Bu tezin amacı Bestvina-Brady grupların Euler karakteristiğini hesaplamaktır. İlk
olarak analitik topoloji çeşidi olan nokta-küme topolojisi tanımlanmıştır. Sonrasında,
cebirsel topolojinin başlıca amacı olan homeomorfizm problemi tanımlanmıştır. Homeomorfizm problemini anlayabilmek için, iyi bilinen bazı topolojik uzaylar tanımlanmı
ştır. Topolojik değişmezlerin tanımı verilmiş ve homeomorfizm problemini çözmede
nasıl kullanıldıkları anlatılmışstır. İki temel topolojik değişmez konusu çalışılmıştır;
bunlar Euler karaktersitik ve Fundamental grup teorileridir. Son olarak, C.T.C. Wall
ve Bestvina-Brady çalışmaları referans baz alınarak Bestvina-Brady grupların Euler
karakteristiği hesaplanmıştır. Anahtar kelimeler: Topolojik değişmezler, Euler karakteristik, Fundamental grup, Bestvina-Brady grup.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Algebraic topology
Group theory
Topological invariants, Euler Characteristic, Fundamental Group, Bestvina-Brady Group
Invariants and Bestvina-Brady Groups
Thesis
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oai:i-rep.emu.edu.tr:11129/17522015-06-25T23:00:56Zhdl_11129_66
EMU I-REP
author
Musa, Isma`il Muhammad
2015-06-25T12:27:40Z
2015-06-25T12:27:40Z
2015-02
Musa, Isma`il Muhammad. (2015). Investigation of Basic Concepts of Fuzzy Arithmetic. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1752
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
ABSTRACT: Fuzzy arithmetic is an extensively used instrument for dealing with uncertainty in a computationally competent method, recently and much better in the upcoming years. This thesis aims to investigate the basic properties of fuzzy arithmetic as its title implies. The properties of fuzzy arithmetic via definitions, examples and some figures are discussed. The methods give the picture of how fuzzy arithmetic can be flexible alongside imprecise data thereby making its applications to be handy in the modern world. This thesis investigates the properties of fuzzy sets, properties of fuzzy number, performing arithmetic operations on fuzzy number, properties of L-R fuzzy number, performing operations on L-R fuzzy number, properties of fuzzy interval and properties of L-R fuzzy interval. Also, the extension principle and fuzzy arithmetic operations using extension principle are investigated. The fuzzy equation is solved by using the method of 𝛼–cut. Keywords: Fuzzy arithmetic, Fuzzy set, Fuzzy number, Fuzzy interval, Extension principle, Fuzzy equation.
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ÖZ: Bulanık aritmetik son zamanlarda belirsizlik ile başa çıkmak için yaygın bir araç olarak kullanılan ve önümüzdeki yıllarda da sıkça kullanılacak olan çok iyi bir hesaplama yöntemidir.
Bu tezin amacı isminden de anlaşılacağı gibi bulanık aritmetik temel özelliklerini incelemektir. Tanımlar, örnekler ve bazı figürler üzerinden bulanık aritmetik özellikleri tartışılır. Kullanılan teknikler kesin olmayan bilgilerin, bulanık aritmetik kullanılarak çağdaş dünyaya uyarlılığını gösterir.
Bu tez bulanık kümelerin özelliklerini, bulanık sayı özelliklerini, bulanık sayı üzerinde aritmetik işlemleri, L-R bulanık sayı özelliklerini, L-R bulanık sayı üzerinde aritmetik işlemleri, bulanık aralığı ve bulanık aralık üzerinde işlemleri inceler.
Ayrıca, uzatma ilkesi ve bu ilkeyi kullanarak bulanık aritmetik işlemleri incelenir. Bulanık denklem, 𝛼-kesim yöntemi kullanılarak çözülür.
Anahtar Kelimeler: Bulanık aritmetik, Bulanık küme, Bulanık sayı, Bulanık aralık, Uzatma ilkesi, Bulanık denklem.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Fuzzy arithmetic
Engineering mathematics
Fuzzy numbers
Fuzzy arithmetic, Fuzzy set, Fuzzy number, Fuzzy interval, Extension principle, Fuzzy equation
Investigation of Basic Concepts of Fuzzy Arithmetic
Thesis
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oai:i-rep.emu.edu.tr:11129/17542015-06-29T23:00:27Zhdl_11129_66
EMU I-REP
author
Öneren, Afet
2015-06-29T05:23:14Z
2015-06-29T05:23:14Z
2014-10
Oneren, Afet. (2014). q-Polynomials and Location of Their Zeros. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1754
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Nazim Mahmudov.
ABSTRACT: In this thesis, we define the q-Bernoulli numbers and polynomials, q-Euler numbers and polynomials, q-Frobenius-Euler numbers and polynomials and q-Genocchi numbers and polynomials of higher order in two variables x and y, by using two q-exponential
functions. We also prove some properties and relationships of these polynomials and
q-analogue of the Srivastava and Pinter addition theorem. Furthermore, we represent
the figures of the q-Bernoulli, q-Euler and q-Genocchi numbers and polynomials. We
find the solutions of these q-polynomials, for n 2 N, x and q 2 C by using a computer
package MathematicaR ⃝ software. Finally, we discuss the reflection symmetries of these
q-polynomials.
Keywords: q-analogues of Bernoulli - Euler - Genocchi - Frobenius-Euler numbers and
Polynomials, Srivastava Pinter addition Theorems, shapes and roots of q-polynomials
…………………………………………………………………………………………………………………………
ÖZ: Bu tezde, iki q-üstel fonksiyonlarını kullanarak q-Bernoulli, q-Euler, q-Frobenius-Euler
ve q-Genocchisayıları ve polinomlari iki de˘gi¸sken x ve y yüksek düzenin polinomları
tanımlanır ve bu polinomların bazı özellikleri, ili¸skileri ve Srivastava-Pinter ilave teoremin
q-analogu kanıtlanır. Ayrıca bilgisayar kullanarak q-Bernoulli, q-Euler ve q-
Genocchi numaralarının ¸sekilleri ke¸sfedilir ve indeks n de˘gerleri için q-Bernoulli, q-
Euler ve q-Genocchi polinomların köklerinin yapısı tarif edilir.
AnahtarKelimeler: Genelle¸stirilmi¸s Bernoulli-Euler- Genocchi -Frobenius-Euler sayıları
ve Polinomları ve Srivastava - Pinter ilave teoremi, q-polinomlarının kökleri ve grafikleri.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Bernoulli polynomials
Euler polynomials
Polynomials
q-analogues of Bernoulli - Euler - Genocchi - Frobenius-Euler numbers and Polynomials, Srivastava Pinter addition Theorems, shapes and roots of q-polynomials
q-Polynomials and Location of Their Zeros
Thesis
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URL
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oai:i-rep.emu.edu.tr:11129/17702015-06-30T23:00:49Zhdl_11129_66
EMU I-REP
author
Akgün, Gülbahar
2015-06-30T07:26:42Z
2015-06-30T07:26:42Z
2015-02
Akgun, Gulbahar. (2015). Performance Analysis of Hill Cipher and Its Modifications. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1770
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rza Bashirov.
ABSTRACT: The history of cryptography goes to several thousand years back when ancient Egyptions tried to hide text by using unusual hieroglyphs instead of more ordinary ones here and there on a tablet. Although lot of cryptographic algorithms have been developed and practically used in various areas, the choice of best algorithm is still on focus of researchers. Since encryption/decryption is an expensive operation, the researchers have always tried to compromise between performance measured in terms of time-effectiveness and confidentiality (or secrecy) provided by cryptographic algorithms. The researchers have realized that the best cryptographic algorithm is determined by reasonable trade-off between performance and confidentiality of the cryptosystem. In this thesis we investigate performance of three cryptographic algorithms, namely Hill cipher, affine Hill cipher and Saeednia‟s modification. We perform comparative analysis of aforesaid cryptographic algorithms via measuring run times on different sized problems. Computer experiments are performed in MATLAB, a high-level technical computing language and interactive environment for algorithm development. Keywords: Cryptography, Hill cipher, affine Hill cipher, Saeednia‟s algorithm, linear transformation, permutation matrix.
…………………………………………………………………………………………………………………………
ÖZ: Kriptografinin tarihi birkaç bin yıl önceye antik Mısırlıların alışılmadık hiyeroglifler kullanarak tablet üzerindeki metinleri sakladıkları döneme kadar uzanır. Günümüzde çok sayıda kriptografik algoritma bulunmasına ve bu algoritmaların çeşitli alanlarda kullanılmasına rağmen, en iyi kriptografik algoritma seçimi halen araştırmacıların dikkat ettikleri konulardandır. Şifreleme/şifre çözme pahalı bir işlem olduğundan, en iyi algoritmanın seçimi için şifreleme algoritmalarının performansı ve gizlilik arasındaki bağlantı zemininde seçim yapılır. İyi kriptografik algoritmanın performans ve gizlilik arasında makul seçim yaparak belirlenmesi konusunda araştırmacılar ortak fikir belirlemişlerdir.
Bu tezde Hill şifreleme yöntemi, afin Hill şifreleme yöntemi ve Saeednia yöntemi farklı büyüklükte matrisler kullanarak çalışma sürelerinin ölçülmesi ve kıyaslanması şeklinde karşılaştırmalı olarak irdelenmiştir. Bilgisayar deneyleri için yüksek seviyeli teknik hesaplama dili ve algoritma geliştirme aracı MATLAB kullanılmıştır.
Anahtar Kelimeler: Kriptografi, Hill şifreleme yöntemi, lineer transformasyon, permütasyon matrisi.
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Performance Analysis of Hill Cipher and Its Modifications
Thesis
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oai:i-rep.emu.edu.tr:11129/17832015-07-01T23:00:36Zhdl_11129_66
EMU I-REP
author
Rashid, Pshtiwan Qader
2015-07-01T05:59:09Z
2015-07-01T05:59:09Z
2015-02
Rashid, Pshtiwan Qader. (2015). Semantic Network and Frame Knowledge Representation Formalisms in Artificial Intelligence. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/1783
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
ABSTRACT: Choosing a suitable method to represent the knowledge concerning the real world is one of the major issues involved in Artificial Intelligence.
The purpose of this research is to consider the important beneficial roles of semantic network and frame formalisms for knowledge representation in Artificial Intelligence. The basic properties of the above methods for appropriate structuring and arranging the knowledge are presented.
Some types of relationships, the conceptual graph, and the types of semantic network are described. The structure of frame-based system is given. The term class and instances are discussed. Some examples of semantic networks and frames are represented. The advantages and disadvantages of both semantic network and frame techniques are considered.
Keywords: Artificial Intelligence, Knowledge representation, Semantic networks, Frames.
…………………………………………………………………………………………………………………………
ÖZ: Gerçek dünya ile ilgili bilginin temsili için uygun bir yöntem seçme yapay zeka’nın önemli konularından biridir.
Bu araştırmanın amacı, yapay zeka bilgi gösterimi için anlamsal ağ ve çerçeve biçimciliklerinin önemli rollerinin yararını tartışmaktır. En iyi yapılanma ve bilgi düzenlenmesi için yukarıdaki yöntemlerin temel özellikleri sunulur.
Anlamsal ağda ilişkilerin bazı türleri ve kavramsal grafik tanımlanır. Çerçeve tabanlı sistemin yapısı verilir. Anlamsal ağlar ve çerçevelerin bazı örnekleri gösterilir. Anlamsal ağ ve çerçeve tekniklerinin avantajları ve dezavantajları tanımlanır.
Anahtar Kelimeler: Yapay Zeka, Bilgi gösterimi, Anlamsal ağlar, Çerçeveler .
en
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Mathematics
Applied Mathematics and Computer Science
Artificial intelligence - Data processing
Artificial intelligence - Mathematical models
Knowledge representation (Information theory)
Artificial Intelligence, Knowledge representation, Semantic networks, Frames
Semantic Network and Frame Knowledge Representation Formalisms in Artificial Intelligence
Thesis
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oai:i-rep.emu.edu.tr:11129/21662016-03-02T00:00:14Zhdl_11129_66
EMU I-REP
advisor
Tandoğdu, Yücel
author
Noupoue, Yves Yannick Yameni
2016-03-01T13:59:26Z
2016-03-01T13:59:26Z
2015-08
2015
Noupoue, Yves Yannick Yameni.(2015). Significance of the Covariance Matrix in Principal Component Analysis. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2166
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
In all the scientific fields, scientist usually deal with big data. Statistical Data Analysis is therefore used to manage data. Depending on the nature of the experiment, its output can be analyzed using univariate, bivariate or multivariate statistics. In the multivariate case when the number of variables is very large, it sometime wise to reduce the number of variable to optimize the analysis of the data. Dimension reduction is used to reduce the number of variables which is also the size of data. In this work, on method of dimension reduction called Principal Component Analysis (PCA) is discussed. The PCA is a method which is based mainly on two matrices , covariance-variance matrix and correlation coefficient matrix obtained from the data. From the mentioned matrices, using the eigenvalues and corresponding eigenvectors, linear combination of the variables called principal components (PC) are established. It is important to mentioned that for the same set of data, the PCs computed using the covariance-variance matrix are different from those computed using the correlation coefficient matrix. The core topic in this work is to studied the conditions under which it is better to use either covariance matrix or correlation coefficient matrix for the PCs computation.Öz:Bilmin hemen her dalında bilim insanları büyük verilerin analizi ile uğraşmak durumundadır. İstatistiki veri analizi verilerin değerlendirilmesinde kullanılır. Deneyin doasına bağlı olarak, elde edilen veriler, tek veya çok değişkenli istatistik yöntemlerle değerledirilebilir. Değişken sayısının çok fazla olduğu durumlarda, daha hızlı analiz imkanını elde etmek için boyut indirgemesi yapılabilir. Bu amaçla Temel Bileşenler Analizi (TBA) yöntemi kullanılır. TBA metodu verinin kovaryans veya korelasyon matrislerine bağımlı bir sistemdir. Bu matrislerin özdeğer ve özvektörlerinden yararlanarak, Temel Bileşenler (TB) denen değişkenlerin lineer kombinasyonları oluşturulur. Ancak kovaryans ve korelasyon matrisleri kullanılarak oluşturulan TB ler, bir birinden farklıdır. Bu çalışmanın temel amacı, hangi şartlar altında kovaryans veya korelasyon matrislerinin kullanılabileceğinin incelenmesidir.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Statistical Mathematics
Principal Component Analysis (PCA)
Principal Components (PCs)
Dimension Reduction
Variance - covariance matrix
Correlation Coefficient Matrix
Significance of the Covariance Matrix in Principal Component Analysis
masterThesis
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oai:i-rep.emu.edu.tr:11129/23252016-03-23T00:00:25Zhdl_11129_66
EMU I-REP
advisor
Rashad, Aliyev
author
Mzori, Bareen Haval Sadiq
2016-03-22T19:40:54Z
2016-03-22T19:40:54Z
2015-07
2015
Mzori, Bareen Haval Sadiq. (2015). Forward and Backward Chaining Techniques of Reasoning in Rule-Based Systems . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2325
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
The forward and backward chaining techniques are well-known reasoning concepts used in rule-based systems in Artificial Intelligence. The forward chaining is data-driven, and the backward chaining is goal-driven reasoning methods.
The aim of this thesis is to present the implementation of above concepts. The matching process between facts and rules, and the conflict resolution strategy in forward chaining are used. The depth-first search in both forward and backward chaining is performed. The backtracking process in backward chaining employs the Prolog programming language which is also discussed in this thesis. Some examples for better understanding the forward and backward chaining techniques are provided.
ÖZ:
İleri ve geri zincirleme teknikleri Yapay Zeka kural tabanlı sistemlerde kullanılan analiz kavramları iyi bilinmektedir. İleri zincirleme veri odaklı ve geri zincirleme hedef odaklı analiz yöntemleridir.
Bu tezin amacı, verilen kavramların uygulamasını sunmaktır. Gerçekler, kurallar ve ileri zincirleme uyuşmazlık çözümü stratejisi arasındaki eşleştirme işlemi kullanılır. İleri ve geri zincirleme derinlik öncelikli arama yapılır. Bu tezde, Geriye zincirleme olarak geriye izlemeli arama süreci de tartışılmıştır. Programlama dili olarak Prolog kullanır. İleri ve geriye zincirleme tekniklerini daha iyi anlamak için bazı örnekler verilmiştir.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
forward and backward chaining techniques
matching process
conflict resolution
depth-first search
backtracking
Prolog language
Forward and Backward Chaining Techniques of Reasoning in Rule-Based Systems
masterThesis
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oai:i-rep.emu.edu.tr:11129/23262016-03-23T00:00:13Zhdl_11129_66
EMU I-REP
advisor
Rashad, Aliyev
author
Hameed, Haifaa Hussein
2016-03-22T19:42:41Z
2016-03-22T19:42:41Z
2015-07
2015
Hameed, Haifaa Hussein. (2015).Smoothing Techniques for Time Series Forecasting. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2326
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
There are many forecasting techniques available, and selecting the appropriate technique is very important issue to achieve a good forecasting performance.
This thesis intends to present the smoothing techniques for time series forecasting. The forecasting process using simple moving average and weighted moving average methods is investigated. The exponential smoothing forecasting method is analyzed. The simple exponential smoothing method is described.
Some error measures - Mean Absolute Deviation, Mean Absolute Percentage Error, and Mean Square Error are calculated for above forecasting techniques to define the forecast accuracy of these methods.
The double exponential smoothing method is discussed.
ÖZ:
Birçok öngörü teknikleri mevcuttur ve tekniğin uygun seçilmesi iyi bir öngörü performansı elde etmek için çok önemli bir konudur.Bu tez zaman serisi öngörüsü için düzeltme teknikleri sunmayı amaçlıyor. Basit hareketli ortalama ve ağırlıklı hareketli ortalama yöntemleri kullanarak öngörü süreci incelenmiştir. Üstel düzeltme öngörü yöntemi analiz edilir. Basit üstel düzeltme tarif edilir.
Yukarıdaki tekniklerde öngörü doğruluğunu tanımlamak için bazı hata önlemleri - Ortalama Mutlak Sapma, Mutlak Yüzde Hata ortalama, ve Ortalama Hata Kare hesaplanır.Çift üstel düzeltme yöntemi tartışılır.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Time-series analysis - Data processing
Forecasting
Time series
Simple moving average
Weighted moving average
Simple exponential smoothing
Double exponential smoothing
Smoothing Techniques for Time Series Forecasting
masterThesis
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oai:i-rep.emu.edu.tr:11129/26502016-05-18T23:00:33Zhdl_11129_66
EMU I-REP
advisor
Oğurlu, Sonuç Zorlu
author
Victor, Oluwafemi Oludu
2016-05-18T19:55:21Z
2016-05-18T19:55:21Z
2015-09
2015-09
Victor, Oluwafemi Oludu . (2015). Martingale Theory . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2650
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu.
From ages to ages there had been expectation of individuals on a specific predictions and future occurrences. So also in a game, different participant that involves in those specified game have their various expectations of the results or the output of the game they are involved in. That is why we need a mathematical theory that helps in prediction of the future expectations in our day to day activities. Therefore the Martingale Theory is a very good theory that explains and dissects the expectation of a gamer in a given game of chance. So in this thesis, we shall talk about the Martingale Theory expressing the expectations of a gamer in a game of chance, and also discuss the gaming strategies so as to enlighten everyone involved in a specific game their required expectation after proper understanding of the Martingale Theory.
Keywords: Martingale, Game of chance, Random walk, Stopping time.
Eski zamanlardan günümüze kadar insanların gelecekteki oluşumlar ile ilgili belirli öngörüleri ve beklentileri olmuştur. Hatta farklı katılımcıların dahil olduğu belirli bir oyunda, oyuncunun dahil olduğu oyunun sonucuna yönelik çeşitli beklentileri vardır. Bu sebebledir ki, günlük hayatımızda gelecekle ilgili beklentiler hakkında öngörüde bulunabilmek için matematiksel Teoriye ihtiyaç duyulmaktadır. Bir şans oyununda oyuncunun beklentisini açıklamak ve incelemek için Martingale Teorisi kullanılmaktadır. Bu tezde oyuncunun beklentisi ifade etmek için Martingale Teorisi hakkında konuşacağız ve ayrıca oyun stratejilerini tartışacağız.
Anahtar kelimeler: Martingale, şans oyunu, rasgele adım, durma zamanı
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Harmonic analysis - Martingales (Mathematics)
Martingale, Game of chance, Random walk, Stopping time
Martingale Theory
masterThesis
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oai:i-rep.emu.edu.tr:11129/27502016-06-20T23:00:30Zhdl_11129_66
EMU I-REP
advisor
Akkales, Arif
author
Hamad, Sarwar
2016-06-20T05:15:17Z
2016-06-20T05:15:17Z
2015-09
2015-09
Hamad, Sarwar. (2015).The Cross Entropy Method and Its Applications. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2750
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Arif Akkeleş.
The Cross Entropy (CE) method which was initiated and developed by Reuven Rubinstein has been applied to combinatorial optimization problems with promising results. The CE method is actually a generic approach for solving combinatorial optimization. The CE method has been applied successfully to well known optimization problems such as traveling salesman, quadratic assignment problem, and the maximal cuts. In this study, the solution methodology of Traveling Salesman Problem (TSP) for different CE parameters are considered and tested.
Keywords: Travelling Salesman Problem, Genetic Algorithm, CE parameter
ÖZ:Reuven Rubinstein tarafından geliştirilen Çapraz Entropi (CE) yöntemi umut verici sonuçlar ile kombinatoryel optimizasyon problemlerine uygulanmıştır. Çapraz-Entropi (CE) yöntemi CE gibi yolculuk satıcısı, kuadratik atama problemi ve maksimal kesimler olarak optimizasyon problemleri başarıyla uygulanmış olan bir kombinasyon optimizasyonu için genel bir yaklaşımdır. Bu çalışmada, farklı CE parametreleri için Satıcı Problemi (TSP) çözüm yöntemi olarak uygulandi ve testedildi.
Anahtar Kelimeler: Gezgin Satıcı Problemi, Genetik Algoritma
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Cross-entropy method
Travelling Salesman Problem, Genetic Algorithm, CE parameter
The Cross Entropy Method and Its Applications
masterThesis
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oai:i-rep.emu.edu.tr:11129/27472016-06-20T23:00:27Zhdl_11129_66
EMU I-REP
advisor
Dosiyev, Adiguzel
author
Faris, Fahmi Sharif
2016-06-20T05:05:14Z
2016-06-20T05:05:14Z
2015-06
2015
Faris, Fahmi Sharif. (2015). Multipoint Nonlocal Problem for Ordinary Differential Equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2747
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Adiguzel Dosiyev.
Boundary value problems with nonlocal boundary conditions have been considered in numerous investigations.In this thesis different approaches are analyzed by considering nonlocal boundary conditions of the solution of second order ordinary differential equations. For the existences and uniqueness of the solution the method of contraction mapping of the multipoint nonlocal problems is applied. The finite-difference analogue of the method is also discussed. Keywords: Boundary Value Problems , Second order ordinary differential equations, multipoint nonlocal condition.
ÖZ: Yerel olmayan sınır koşulları ile Sınır değer problemleri sayısız araştırmalarda dikkate alınmıştır. Bu tez çalışmasında farklı yaklaşımlar ikinci mertebeden adi diferansiyel denklemlerin çözümünün yerel olmayan sınır koşullarını dikkate alınarak analiz edilmektedir. Çözümün varoluşunun ve teklik çoklu yerel olmayan problemlerin daralma haritalama yöntemi uygulanır. Yöntemin sonlu farklar analogu da tartışılmıştır. Anahtar Kelimeler: Sınır Değer Problemleri, İkinci mertebeden adi diferansiyel denklemler, çoklu yerel olmayan Sınır Problemleri.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Differential equations
Boundary Value Problems
Second order ordinary differential equations
multipoint nonlocal condition Remove selected
Multipoint Nonlocal Problem for Ordinary Differential Equations
masterThesis
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oai:i-rep.emu.edu.tr:11129/28372016-07-18T23:00:35Zhdl_11129_66
EMU I-REP
advisor
Dosiyev, Adiguzel
author
Omar, Haji Omar
2016-07-18T08:34:41Z
2016-07-18T08:34:41Z
2015-07
2015
Omar, Haji Omar. (2015). Error Estimation Methods for the Finite-Difference Solution for Poisson’s Equation. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2837
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Adiguzel Dosiyev.
The finite-difference method is universally used for the approximation of differential equations.
In this thesis two different approaches are reviewed for the error estimation of the approximation of the Dirichlet problem for elliptic equations, specifically Poisson’s and Laplace’s equations using various finite-difference schemes.
The first approach is based on the difference analogue of the maximum principle. Applying Gerschgorin’s majorant method to the analysis , also the order of accuracy of the proposed scheme is obtained.
The second approach uses the difference analogue of Green’s function and Green’s third identity. In order to obtain an order of approximation, Gerschgorin’s majorant method is applied in this approach also.
Both methods gave similar approximations.
Keywords: Finite-difference, maximum principle, Gerschgorin’s majorant method, Green’s function, Green’s third identity.
ÖZ:
Sonlu-farklar metodu, yakınsak çözümlemeler için evrensel olarak kullanılan bir metoddur.
Bu tezde, Poisson denklemi için Dirichlet probleminin sonlu-farklar analogu, iki farklı hata analizi yöntemi ile gözden geçirilmiştir.
Birinci yöntem, maksimum ilkesine (maximum principle) bağlıdır. Gerschgorin’in majorant metodunun da uygulanması ile sonlu farklar metodu analiz edilmiştir.
İkinci yöntemde ise, Green fonksiyonunun sonlu-farklar analogu, ve Green’in 3. denklemi analogu kullanılmıştır. Yakınsaklık derecesinin elde edilmesi için, Gerschgorin’in majorant metodu da kullanılmıştır.
İki yöntem de benzer sonuçlar vermiştir.
Anahtar kelimeler: sonlu farklar, maksimum ilkesi, Gerschgorin majorant metodu, Green fonksiyonu.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Finite differences - Difference equations
Differential equations - Numerical solutions
Finite-difference
maximum principle
Gerschgorin’s majorant method
Green’s function
Green’s third identity
Error Estimation Methods for the Finite-Difference Solution for Poisson’s Equation
masterThesis
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oai:i-rep.emu.edu.tr:11129/28392016-07-18T23:00:36Zhdl_11129_66
EMU I-REP
advisor
Rıza, Mustafa
author
Khalaf, Rifaat Zaidan
2016-07-18T09:34:33Z
2016-07-18T09:34:33Z
2015-08
2015
Khalaf, Rifaat Zaidan. (2015). Quantum Encryption Algorithm Based on Modified BB84 and Authentication DH Algorithm. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2839
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
This thesis will describe two main contributions to quantum cryptography. First of all
the well-known BB84 protocol for quantum key exchange is modified to eliminate
the originally high bit error rate completely without compromising on the security.
As the classical channel is the only place where eavesdropping could be possible, any
attempt to eavesdropping is prevented. Secondly, the Quantum Linear Feedback Shift
Register is proposed as a tool to generate the key matrix for the classical Hill-Cipher
algorithm. Finally, all proposed methods are combined in an encryption process,
proving to be secure, i.e. the resulting quantum encrypted message is less susceptible
to attacks as shown in the detailed security.
Keywords : Network security, Quantum cryptography, Quantum computing, BB84
Protocol, Quantum encryption algorithm , polarization filter, Multi-qubit Quantum
shift register matrices,.
ÖZ:
Bu tezin kuantum şifreleme sistemlerine iki ana katkısı tartışılacaktır. BB84
protokolü kuantum şifre değişiminde literatürde en tanınmış protokolü,
güvenliğinden ödün vermeden yüksek bit hata oranını ortadan kaldırmak için
değiştirilmiştir. Orijinal BB84 protokolünde tek dinleme olasılığı olan klasik hat
modifye edilmiş BB84 protokolünde ortadan kaldırılarak, tüm hatlar kuantum fizik
kurallarına tabiidir. Dolayısıyla kuantum klonlanamama (no-cloning theorem)
teoremine tabiidir. İkincisi, Kuantum Doğrusal Geri Dönüm Kayan Yazmaç
(Quantum Linear Feedback Shift Register) klasik Hill-Şifreleme algoritması için şifre
matrisini oluşturmak için bir araç olarak önerilmiştir. Son olarak, tüm önerilen
yöntemler bir şifreleme işleminde birleştirilmiştir. Ayrıntılı güvenlik analizi kuantum
şifreli mesaj saldırılarına klasik yöntemlere göre daha az duyarlı olduğu, yani güvenli
olduğunu kanıtlamaktadır.
Anahtar Kelimeler: Ağ güvenliği, Kuantum kriptografi, Kuantum hesaplama, BB84
Protokolü, Kuantum şifreleme algoritması, polarizasyon filtresi, Multi-qubit
Kuantum kayan yazmaç matrisleri.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Computer security - Network Security
Network security
Quantum cryptography
Quantum computing
BB84 Protocol
Quantum encryption algorithm
polarization filter
Multi-qubit Quantum shift register matrices
Quantum Encryption Algorithm Based on Modified BB84 and Authentication DH Algorithm
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/28352016-07-18T23:00:33Zhdl_11129_66
EMU I-REP
advisor
Bodur, Ersin Kuset
author
Abdullah, Daban Abdulsalam
2016-07-18T08:23:36Z
2016-07-18T08:23:36Z
2015-07
2015
Abdullah, Daban Abdulsalam. (2015). Association Rule Mining Using k-Map Model in Data Mining. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2835
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Ersin Kuset Bodur.
In data mining, many algorithms were suggested to define the frequent rules within
the data set. One of the problems is to choose a correct algorithm for the problem
and the determination of the efficiency of the algorithm has important role during
the investigation of hidden knowledge.
The thesis describes how to handle data set with Association Rules Analysis/ Market
Basket Analysis with the popular Apriori algorithm and k -Map algorithm of data
mining. The goal of this thesis is to find the most frequent patterns within the data
set and then using different measurements to do further investigation on the obtained
frequent patterns.
Keywords: Data Mining, Association Rules Analysis, Market-Basket Analysis
ÖZ;
Veri madenciliğinde, anlamlı kurallar tanımlamak için bir çok algoritma önerilmiştir. Doğru algoritmayı seçmek ve algoritmanın kullanırlığının kararı verinin içindeki gizli bilginin bulunması için önemli problemlerdir.
Bu tez verinin Birliktelik Kuralları Analizinde sıklıkla kullanılan Apriori algoritması ve k-Harita (Karnaugh Haritası) algoritmasının nasıl kullanılacağını tanımlar. Bu tezin amacı verinin içindeki anlamlı kuralları bulmak ve sonrasında ise farklı ölçüler kullanıp anlamlı kurallar için ileri analizler yapmaktır.
Anahtar kelimeler: Veri Madenciliği, Birliktelik Kuralları Analizi, Sepet Analizi
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Data Mining
Association Rules Analysis
Market-Basket Analysis
Association Rule Mining Using k-Map Model in Data Mining
masterThesis
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oai:i-rep.emu.edu.tr:11129/28472016-07-18T23:00:34Zhdl_11129_66
EMU I-REP
advisor
Dosiyev, Adiguzel
author
Ahmed, Ghazi Sabah
2016-07-18T12:02:06Z
2016-07-18T12:02:06Z
2015-06
2015
Ahmed, Ghazi Sabah. (2015). Schwarz's Method for Differential and Difference Equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2847
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Adiguzel Dosiyev.
Schwarz introduced a method that permits to obtain a solutions for complicated
domains by covering the domain with overlapping subdomains by realizing the
solution of the Dirichlet problem for harmonic functions on these overlapping
subdomains.
The present MS Thesis deals with analyzing the construction and justification of
Schwarz's method and Schwarz-Neumann method for partial differential and finitedifference
equations and how we can prove the convergence of them by using some
theorems and assumptions.
Keywords: Dirichlet problem, Artificial boundary, Schwarz's method, Schwarz-
Neumann method.
ÖZ:
Schwarz, bu örtüşen alt etki alanında harmonik fonksiyonlar için Dirichlet
probleminin çözümünü gerçekleştirerek alt alanları örtüşen etki kaplayarak karmaşık
alanları için bir çözüm elde etmek için izin veren bir yöntem tanıttı.
Mevcut Yüksek Lisans Tezi, kısmi diferansiyel ve sonlu fark denklemlerinin ve nasıl
bazı teoremleri ve varsayımlar kullanılarak bunların yakınsama ispat için Schwarz
yöntem ve Schwarz-Neumann yönteminin inşaat ve gerekçesini analiz ile ilgilenir.
Anahtar Kelimeler: Dirichlet problemi, Yapay sınır, Schwarz metodu, Schwarz-
Neumann yöntemi.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Differential equations
Dirichlet problem
Artificial boundary
Schwarz's method
Schwarz-Neumann method
Schwarz's Method for Differential and Difference Equations
masterThesis
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oai:i-rep.emu.edu.tr:11129/28422016-07-18T23:00:38Zhdl_11129_66
EMU I-REP
advisor
Bodur, Ersin Kuset
author
Onyejiaka, Kelechi Churchill
2016-07-18T09:54:46Z
2016-07-18T09:54:46Z
2015-05
2015
Onyejiaka, Kelechi Churchill (2015). Unsupervised Learning Method Based on Partitioning in Data Mining. . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2842
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Ersin Kuset Bodur.
This study provides the introduction of some basic definitions about clustering
method of data mining. For this purpose, it is given the methods of data mining, some
algorithms of clustering method. Meanwhile, the k -Means clustering and
Hierarchical clustering algorithms are defined.
The aim of this study is to cluster the dataset into two clusters using Hierarchical
clustering algorithm and k -Means algorithm. In order to achieve our target, two
distance formulas are used to measure the distance between the vectors in the
algorithms: the Euclidean distance and k -Nearest neighborhood distance.to compare
two methods.
Keywords: Data mining, data mining algorithms, data mining applications
ÖZ:
Bu çalışma veri madenciliği kümeleme yönteminin bazı temel tanımlarını sunar. Bu
amaçla, veri madenciliği yöntemleri, veri madenciliğinin bazı kümeleme yöntemleri
algoritmaları veriliyor. Bunun yanında, K -ortalama ve Hiyerarşik kümeleme
algoritmaları tanımlanır.
Bu çalışmanın amacı, Hirerarşik ve K -ortalama algoritmalarını kullanıp veri
kümesini iki kümeye ayırmaktır. Amacımıza ulaşmak için, vektörler arasındaki
uzaklığı ölçmek için iki tane tanım kullanılır: Öklit uzaklık ve en yakın K komşu
bağıntıları.
Anahtar kelimeler: Veri madenciliği teknikleri, veri madenciliği algorimaları, veri
madenciliği uygulamaları
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Cluster analysis - Data mining
Data mining
data mining algorithms
data mining applications
Unsupervised Learning Method Based on Partitioning in Data Mining
masterThesis
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OnyejiakaKelechi Churchill.pdf.txt
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oai:i-rep.emu.edu.tr:11129/28542016-07-26T23:00:19Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Rza
author
Krivdic, Alma
2016-07-26T07:02:50Z
2016-07-26T07:02:50Z
2015-09
2015-09
Krivdic, Alma. (2015). Mathematical and Computational Models of Cell Cycle in Higher Eukaryotes. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2854
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rza Bashirov.
The cell cycle is an ordered sequence of coordinated biological processes that enable cells to grow and divide, to check for certain abnormalities whenever it is appropriate, to regulate the different stages of growth and division in the predefined order, and to respond to DNA damage and other dysfunctions by arresting progression through the cell cycle so that to allow the regulators to repair DNA damage and recover from dysfunction before DNA is completely replicated. Understanding the detailed structure of cell cycle regulation is of practical importance in biotechnology, medicine, and pharmacology. Since a detailed analysis of cellular mechanisms behind of cell cycle regulation is too complex to be preformed intuitively, mathematical and computational modeling of involved processes is essential part of the research in this field. The main idea behind this approach is to create the closest approximation of a biological system based on wet lab results, and predict its dynamic behavior through measuring the amounts of biological components. Mathematical and computational approaches implemented to cell cycle regulation have the following benefits. Firstly, it makes possible to provide a detailed qualitative and quantitative structure of the biological system describing the cell cycle regulation. Secondly, modeling allows us to conjecture a hypothesis regarding the biological system and then check consistency of the hypothesis to desired deep by extrapolating the parameters involved into the model.
Keywords: cell cycle, mathematical model, computational model, Petri nets
ÖZ:
Canlı hücrelerin büyümesi, bölünmesi, hücre içi belirli anormalliklerin aşamalı kontrolü, DNA hasarı, DNA hasarının giderilmesi gibi ardışık süreçler dizisine hücre döngüsü denir. Hücre döngüsünün detaylı yapısal düzenini anlamak biyoteknoloji, tıp ve farmakolojideki uygulamalar açısından pratik önem arz etmektedir. Hücre döngüsünü oluşturan moleküler mekanizmalar çok karmaşık olmanın yanı sıra sezgisel olarak incelenmeleri olanaksız görünmektedir. Bu bakımdan matematiksel ve bilgisayar ortamında oluşturulan modeller hücre döngüsü ve bileşenlerini anlamak için bu alan kullanılan önemli araştırma yöntemidir.Matematiksel ve bilgisayar ortamında sayısal simülasyon biyolojik sistemleri keşfetmek için uygulanan verimli bir yaklaşımdır. Bu yaklaşımın ana fikiri laboratuvar sonuçlarına göre biyolojik sistemin olabilecek kadar gerçekçi modelinin oluşturulması ve biyolojik bileşenlerin miktarlarını ölçerek dinamik davranışların tahmin etmektir. Hücre döngüsünün düzenlenmesi için uygulanan matematiksel ve sayısalın modeller ilk önce hücre döngüsünün olabilecek kadar detaylı nicel ve nitel yapısını oluşturma, hücre içi molekuler süreçleri anlama, varsayımlar veya hipotezler öne sürme, ve bu varsayım veya hipotezlerin tutarlılığını kontrol etmenizi sağlar.
Anahtar Kelimeler: Hücre döngüsü, matematiksel model, hesaplama modeli, Petri ağları
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Eukaryotic cells
Cell cycle, mathematical model, computational model, Petri nets
Mathematical and Computational Models of Cell Cycle in Higher Eukaryotes
masterThesis
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oai:i-rep.emu.edu.tr:11129/28622016-08-18T23:00:36Zhdl_11129_66
EMU I-REP
advisor
Aliyev, Rashad
author
Mraiziq, Derar Atallah Talal
2016-08-18T07:14:42Z
2016-08-18T07:14:42Z
2015-07
2015
Mraiziq, Derar Atallah Talal. (2015).Computation and Reasoning with Z-Numbers. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2862
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
In most cases the information relevant to the real-world decision is partially reliable. This can be explained by the unreliability of the source of information, misinterpretation, inexperience etc. Z-numbers-based formalization of information (Z-information) represents a Natural Language (NL)-based value of a variable of interest in line with the related NL-based reliability. The necessary point that needs to be considered is that a Z-information generally represents the imperfect information specific to real-world, but at the same time a Z-information has a powerful description from perception point of view of human compared to fuzzy number.
In this thesis two conversion methods are given to convert the Z-number into the fuzzy number and also, to convert the fuzzy number into the crisp number.
An approach to decision making under Z-information based on direct computation over Z-numbers is presented. This approach utilizes the expected utility paradigm and is applied to a benchmark decision problem in the field of economics.
Keywords: Z-numbers, Fuzzy number, Discrete Z-numbers, Discrete fuzzy number, Utility value, Defuzzification, Decision making, Expected utility
ÖZ:
Bir çok durumda gerçek dünyadaki kararlarla ilgili bilgiler kısmen güvenilirdir. Bu durum, bilginin elde edildiği kaynağın kısmen güvenilir olması, yanlış yorumlama, deneyimsizlik vb. ile izah edilebilir. Bilginin Z-sayılara dayalı biçimselleştirilmesi (Z-bilgi) Doğal Dil tabanlı güvenilirliği doğrultusundaki bir değişkenle ilgili Doğal Dil tabanlı değerini temsil eder. Dikkate alınması gereken bir nokta ise Z-bilginin genellikle gerçek dünyaya özgü eksik bilgiyi temsil etmesidir. Aynı zamanda, Z-bilgi bulanık sayı ile kıyaslandığı zaman insan bakış algısı açısından güçlü bir açıklamaya sahip olmasıdır.
Bu tezde iki dönüşüm yöntemi verilmektedir: Z-sayıyı bulanık sayıya dönüştürmek ve bulanık sayıyı belirgin (crisp) sayıya dönüştürmek.
Z-sayılar üzerinde doğrudan hesaplamaya dayalı Z-bilgi altında bir karar verme yaklaşımı sunulmuştur. Bu yaklaşım beklenen fayda paradigmasını kullanır ve ekonomi alanında karşılaştırmalı değerlendirme (benchmark) karar problemine uygulanır.
Anahtar kelimeler: Z-sayılar, Bulanık sayı, Ayrık Z-sayılar, Ayrık bulanık sayı, Fayda değeri, Durulaştırma, Karar kabulü, Beklenen fayda
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Fuzzy sets
Fuzzy numbers
Fuzzy arithmetic Index term
Z-numbers
Discrete Z-numbers
Discrete
Utility value
Defuzzification
Decision making
Expected utility
Computation and Reasoning with Z-Numbers
doctoralThesis
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URL
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oai:i-rep.emu.edu.tr:11129/28762016-08-18T23:00:35Zhdl_11129_66
EMU I-REP
advisor
Tut, Mehmet Ali
author
Babalola, Ademola Ezekiel
2016-08-18T11:32:36Z
2016-08-18T11:32:36Z
2016-02
2016
Babalola, Ademola Ezekiel. (2016). A Regression Analysis on the Flow of EMU Library USERS. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2876
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Mehmet Ali Tut.
This paper highlights the importance of statistics in everyday life in this 21st century. Statistics which is based on collecting, managing, processing and disseminating information, it applications are seen in Banks, Airports, information technology and schools.
This research presents a simple linear regression model, its derivation and how it is used to analyse data’s obtained from the school library. The data’s which defines the average population of students who use the library yearly. The model obtained is used to predict future use of the library by students, as well as an estimate of students that used the library before 2007. A statistical software application, called SPSS was used in the analysis.
The result obtained from this research shows about 33% of data can be analyze which makes our model somewhat a good fit for the data; however a non-linear model would be best to describe the library data.
Keywords: linear regression models, Sample data, correlation coefficient, influential point, SPSS.
ÖZ:
Bu yazıda, bu 21. yüzyılda gündelik hayatın istatistiğin önemini vurgulamaktadır. Toplama, yönetme, işlenmesi ve bilginin yayılmasından dayanmaktadır İstatistik, bu uygulamalar Bankalar, Havaalanları, bilgi teknolojileri ve okullarda görülür.
Bu araştırma, basit bir doğrusal regresyon modeli, kendi türetme sunar ve okul kütüphanesinden elde edilen veriler 's analiz nasıl kullanılır. Yıllık kütüphane kullanımı öğrencilerin ortalama nüfus tanımlayan veri en. Elde edilen model, gelecek öğrenciler tarafından kütüphane kullanımı yanı sıra analizde kullanılan SPSS denilen 2007. istatistik programı uygulamadan önce kütüphaneyi kullanılan öğrenciler bir tahmin, tahmin etmek için kullanılır.
Bu araştırmada elde edilen sonuç verilerinin yaklaşık% 33 modelimizi verileri için biraz iyi bir uyum kılan analiz olabilir göstermektedir; Ancak doğrusal olmayan bir model kütüphanesi verilerini açıklamak için iyi olurdu.
Anahtar Kelimeler: Doğrusal regresyon modelleri, örnek veriler, korelasyon katsayısı, etkili nokta, SPSS.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Statistics
Mathematical statistics - Data processing
Eastern mediterranean University Library - Usage Statistics
linear regression models
Sample data
correlation coefficient
influential point
SPSS
A Regression Analysis on the Flow of EMU Library USERS
masterThesis
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oai:i-rep.emu.edu.tr:11129/29242016-09-30T23:01:08Zhdl_11129_66
EMU I-REP
advisor
Özarslan, Mehmet Ali
author
Baran, Gizem
2016-09-30T08:00:04Z
2016-09-30T08:00:04Z
2016-02
2016
Baran, Gizem. (2016). Exponential Operators and Hermite Type Polynomials. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2924
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Prof. Dr. Mehmet Ali Özarslan.
This thesis consists of five Chapters. Chapter 1 is devoted to the Introduction. We
investigate some basic properties of the exponential operators, in Chapter 2. Chapter
3, gives the proves of some exponential operator identities such as Weyl, Sack, Hausdorff
and Crofton identities. In Chapter 4, we study the monomiality principle and its
properties.
Finally in the last chapter, as an application to Chapters 3 and 4, we investigate some
properties of Hermite polynomials in two variables, Hermite-Kampe de Feriet polynomials,
Laguerre polynomials in two variables and Hermite-Based Appell polynomials.
Keywords: Exponential operators,Weyl, Sack, Hausdorff and Crofton identities, Monomiality
principle,Hermite-Kampe de Feriet polynomials, Laguerre polynomials in two
variables.
ÖZ:
Bu tez be¸s bölümden olu¸smaktadır. Birinci bölüm giri¸s kısmına ayrılmı¸stır. ˙Ikinci
bölümde üstel operatörlerin bazı özellikleri incelenmi¸stir. Üçüncü bölümde Weyl,
Sack, Hausdorff ve Crofton özde¸slikleri ispatlanmı¸stır. Dördüncü bölümde tek terimlilik
prensipleri çalı¸sılmı¸stır. Son bölümde ise üçüncü ve dördüncü bölümün uygulamaları
yapılmı¸s, iki de˘gi¸skenli Hermite polinomları, Hermite-Kampe de Feriet polinomları,
iki de˘gi¸skenli Laguerre polinomları ve Hermite-Based Appell polinomları
gösterilmi¸stir.
Anahtar Kelimeler: Üstel operatörler,Weyl, Sack, Hausdorff ve Crofton özde¸slikleri,
Monomiallik prensipleri, Hermite-Kampe de Feriet polinomları, iki de˘gerli Laguerre
polinomları
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Operator theory (Mathematics)
Exponential operators
Weyl
Sack
Hausdorff and Crofton identities
Monomiality principle
Hermite-Kampe de Feriet polynomials
Laguerre polynomials in two variables
Exponential Operators and Hermite Type Polynomials
masterThesis
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oai:i-rep.emu.edu.tr:11129/29262016-09-30T23:00:56Zhdl_11129_66
EMU I-REP
advisor
Tut, Mehmet Ali
author
Eduiyovwiri, Ogheneovo Mclarry
2016-09-30T08:33:13Z
2016-09-30T08:33:13Z
2016-02
2016
Eduiyovwiri, Ogheneovo Mclarry. (2016). A Statistical Analysis on the Visits to EMU Health Center by the Students. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2926
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Mehmet Ali Tut.
There are different statistical techniques in estimating and predicting future events or
outcome given a set of independent factors influencing such an event. Regression
analysis is one of the modern statistical tools used for such purpose. Knowing the
outcome of an event given a set of independent variable will help make proper
decisions regarding the scenario. Here, regression analysis was used to predict the
number of visitors visiting some key department of the Eastern Mediterranean
University Health Center. This will help the school management to know the area
where the health center is shorting man power and to also carry out a research or
study on the reason why visitors are faced with such illness relating to the
department they visit often. A solution has been detected and discussed to help in the
prediction of the number of visitors visiting some key department of the school
health center. A regression analysis has been carried out on the data set of the visitors
who visited the health center in the past 22 months (January, 2014 to October, 2015)
this involves the number of visitors in each month and the department they visited.
This is done by the use of statistical software called SPSS. It is use for regression,
and prediction measure especially when one is dealing with large numbers.
Keywords: Estimating, Department, Health Center, Predicting, Regression Analysis,
SPSS, Statistical Techniques
ÖZ:
Gerçek hayat olaylarında (uygulamalarında) bilinmeyen (var olmayan) parametre
değerlerini kestirimini yapabilmek için istatiksel metodlardan Regresyon analizi
önemli bir rol oynamaktadır.Bağımsız parametre değeri kullanılarak bilinmeyen
değer bulunan regresyon fonksiyonu yardımıyla bulunabilmektedir.
Yapılan bu çalışmada DAÜ Sağlık merkezine başvuran hastaların hangi ünite(branş)
üzerinde yoğunlaştıkları Eregrasyon analizi yardımıyla modellenerek gelecek aylarda
beklenen ziyaretçi sayıları kestirilmesiyle çalışılmıştır. Yapılan kestirimlerde
üniversitesinin yoğunluk yaşayacağı söylenebilir.
Anahtar kelimeler : Bağımsız değişken , Bağımlı değişken , Kestirme, Öngörme
,regresyon analizi ,SPSS
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Statistics
Mathematical statistics - Data processing
Estimating
Department
Health Center
Predicting
Regression Analysis
SPSS
Statistical Techniques
A Statistical Analysis on the Visits to EMU Health Center by the Students
masterThesis
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oai:i-rep.emu.edu.tr:11129/29212016-09-30T23:01:02Zhdl_11129_66
EMU I-REP
advisor
Aliyev, Rashad
author
Hasan, Zewar Fadhlulddin
2016-09-30T07:47:45Z
2016-09-30T07:47:45Z
2015-07
2015
Hasan, Zewar Fadhlulddin. (2015). Implementation of Strategies for Solving Constraint Satisfaction Problems. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2921
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Rashad Aliyev.
This thesis investigates the different strategies for solving constraint satisfaction problems. The basic properties of constraint satisfaction problems are discussed. The different types of constraints are given. The constraint graph and cryptarithmetic constraint satisfaction problems are discussed. Such search techniques as backtracking search, local search, and constraint propagation for solving constraint satisfaction problems are presented. The forward checking in constraint satisfaction problems is used. Some constraint satisfaction problems such as map-coloring problem, cryptarithmetic problem, n-queens problems and Sudoku problem are solved.
Keywords: Constraint satisfaction problem, Constraint graph, Backtracking search, n-queens problem, Local search, Constraint propagation, Forward checking
ÖZ:
Bu tez kısıtlama memnuniyeti sorunlarını çözmek için farklı stratejiler araştırıyor. Ayrıca, kısıtlama memnuniyeti problemlerinin temel özellikleri tartışılır. Bunun yanında, kısıtlamaların farklı türleri verilmiştir. Kısıtlama grafiği ve cryptarithmetic kısıtlama memnuniyeti sorunları tartışılır. Geriye arama, yerel arama ve kısıtlama memnuniyeti problemlerinin çözümü için kısıtlama yayılma gibi arama teknikleri sunulmuştur. Kısıtlama memnuniyeti problemlerinde ileri kontrol yöntemi kullanılır. Harita renklendirme problemi, cryptarithmetic problemi, n-vezir problemi gibi bazı kısıtlama memnuniyeti problemleri ve Sudoku problemi çözülür.
Anahtar Kelimeler: Kısıtlama memnuniyeti sorunu, Kısıtlama grafiki, Geri İzleme arama, n-vezir problemi, Yerel arama, Kısıtlama yayılımı, İleri kontrol
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Constraint programming (Computer science)
Constraint satisfaction problem
Constraint graph
Backtracking search
n-queens problem
Local search
Constraint propagation
Forward checking
Implementation of Strategies for Solving Constraint Satisfaction Problems
masterThesis
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oai:i-rep.emu.edu.tr:11129/29092016-09-27T23:01:31Zhdl_11129_66
EMU I-REP
advisor
Tandoğdu, Yücel
author
Karim, Shagul Faraj
2016-09-27T11:07:52Z
2016-09-27T11:07:52Z
2016-02
2016
Karim, Shagul Faraj (2016) . Fyuzzy Logic and Principal Components Analysis . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2909
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
Data analysis is the process of collecting and processing data with the aim of extracting significant and sound results to aid in decision making in almost every field where data collection is possible. However, when the number of variables involved in a process increase, processing of such data becomes more difficult. One way of alleviating such problems, is to reduce the number of variables to be processed in such a way that, the reduced version still represents great part of the variation in the data. This is achieved by the technique named Principal Component Analysis (PCA).
One other aspect considered in this study is the case when the interpretation of data is not very easy, as some data values may not definitely be assigned to a sub group of interest. Handling such situations is becoming possible through the theory of fuzzy logic. This enables the partial assignment of data to different sub groups, through the use of fuzzy membership functions. Using different fuzzy membership functions, it is possible to generate different membership data sets. Application of PCA to such data produced some interesting results that can be handy in selecting the type of the membership functions.
Keywords: Fuzzy logic, fuzzy set, fuzzy membership, covariance matrix, correlation matrix, principal component analysis.
ÖZ:
Veri analizi, veri toplama, değerlendirme ve elde edilen sonuçların karar verme işlemlerinde kullanılması amacı ile veri elede edilebilecek her alanda kullanılan bir işlemdir. Ancak bir işlemde kullanılan değişken sayısı arttıkca, veri analizi daha zor hale gelir. Bu zorluğun üstesinden gelmenin bir yoluda, işlemi kontrol eden değişken sayısının, işlemdeki varyansın çok yüksek bir oranda temsil eileceği daha düşük bir boyuta indirgenmesidir. Bu amaca yönelik boyut indirgemesi Temel Bileşenler analizi yöntemi ile elde edilebilir.
Bu tezde üzerinde çalışılan diğer bir konu, bazı verilerin veri setini oluşturan alt kümelerden herhangi birine kesin tayininin mümkün olmadığı durumlardır. Kesin olmayan kümeler kuramı ile bu tür durumların çözümünde büyük ilerlemeler sağlanmıştır. Bu kuram çerçevesinde üyelik fonksiyonları kullanılarak verilerin farklı alt kümelere kısmi tayini yapılabilmektedir. Farklı üyelik fonksiyonları kullanılarak, farklı üyelik veri kümeleri üretmek mümküdür. Bu şekilde elde edilen veri kümelerinde temel bileşenler analizi yöntemleri uygulanmış ve tatmin edici sonuçlara ulaşılmıştır.
Anahtar kelimeler: Kesin olmayan mantık, kesin olmayan küme, kesin olmayan üyelik, kovaryans matrisi, korelasyon matrisi, temel bileşenler analizi.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Fuzzy Logic
fuzzy set
fuzzy membership
covariance matrix
correlation matrix
principal component analysis
Fuzzy Logic and Principal Components Analysis
masterThesis
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URL
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oai:i-rep.emu.edu.tr:11129/29512016-10-06T23:00:43Zhdl_11129_66
EMU I-REP
advisor
Oğurlu, Sonuç Zorlu
author
Ogunbayo, Segun
2016-10-06T07:03:21Z
2016-10-06T07:03:21Z
2016-02
2016
Ogunbayo, Segun. (2016). Markov Chains and Markov Processes. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/2951
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu.
Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict our expectation for the future. In this thesis we specifically talk about Markov Chains and how it has been processed, the gaming tactics which gives us a clue in a game that requires expectation. Also, we gave some applications of Markov chains such as Random walk, Games of chance, Queuing chain etc.
Keywords: Stochastic Process, Conditional Expectation, Markov chain, Random Walk, Birth and Death Chains
ÖZ:
Andrew Markov’dan sonra adlandırılan Markov zinciri durumlar arası geçişleri çalışan matematiksel bir modeldir. Gerçek hayatta birçok olay belirsizlik içerir. Bu çalışma Markov zincirinin temel fikrini anlamaya yardımcı olmayı ve günlük yaşamdaki kullanımını belirtmeyi amaçlamaktadır. Farklı oyunlarda farklı beklentiler veya sonuçlar yer almaktadır. Gelecek için yapılacak tahminlerde Markov zincirleri önem taşımaktadır. Bu tezde özellikle Markov Zincirlerinin tanım ve özellikleri, oyun taktikleri, ayrıca Rastgele yürüyüş, şans oyunu, kuyruk zinciri gibi Markov zincirlerinin bazı uygulamaları çalışılmıştır.
Anahtar Kelimeler: Stokastik Süreç, Koşullu Beklenti, Markov Zinciri, Rasgele Yürüyüş, Doğum ve Ölüm Zincirleri
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Markov processes - Mathematics
Stochastic Process
Conditional Expectation
Markov chain
Random Walk
Birth and Death Chains
Markov Chains and Markov Processes
masterThesis
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ogunbayosegun.pdf.txt
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http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F2951/1/ogunbayosegun.pdf
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MD5
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ogunbayosegun.pdf
oai:i-rep.emu.edu.tr:11129/32292017-04-24T23:00:34Zhdl_11129_66
EMU I-REP
advisor
Kara, Mustafa
author
Aşçıoğlu, Didem
2017-04-24T08:25:03Z
2017-04-24T08:25:03Z
2015-09
2015
Aşçıoğlu, Didem. (2015).The Generalized Incomplete Gamma Functions. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3229
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Mustafa Kara.
Engineering and physics demand a through knowledge of applied mathematics and a
good understanding of special functions. These functions commonly arise in such
areas of applications as heat conduction, communication systems, electro-optics,
approximation theory, probability theory, and electric circuit theory, among others.
The subject of special functions is quite rich and expanding continuously with the
emergence of new problems in the areas of applications in engineering and applied
sciences. We investigate generalized gamma function, digamma function, the
generalized incomplete gamma function, extended beta function. Also, some
properties of these functions are taken into hand.
Keywords: Approximation, Circuit, Gamma, Beta, Digamma
ÖZ:
Mühendislik ve fizik, uygulamalı matematiğin derinlemesine bilinmesini ve özel
fonksiyonların iyi anlaşılmasını istemektedir. Bu fonksiyonlar genellikle ısı iletimi,
iletişim sistemleri, elektro-optik, yaklaşıklık teorisi, olasıklık teorisi, elektrik aksam
teorisi ve diğerleri alanlarında uygulama bulur. Özel fonksiyonlar konusu oldukça
zengin ve genişlemeye açık bir alan bunun sebebi ise mühendislik ve uygulamalı
bilimler alanlarındaki yeni problem doğuşlarıdır. Biz genelleştirilmiş gama
fonksiyonu, digamma fonksiyonu, genişletilmiş beta fonksiyonu ve bu
fonksiyonların bazı özelliklerini inceledik.
Anahtar Kelimeler: Yaklaşıklık, Aksam, Gamma, Beta, Digamma
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Gamma functions
Approximation
Circuit,
Gamma
Beta
Digamma
The Generalized Incomplete Gamma Functions
masterThesis
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URL
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ascioguludidem.pdf.txt
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oai:i-rep.emu.edu.tr:11129/32452017-05-15T23:00:51Zhdl_11129_66
EMU I-REP
advisor
Dosiyev, Adıgüzel
author
Çeliker, Emine
2017-05-15T11:19:55Z
2017-05-15T11:19:55Z
2014-12
2014
Çeliker, Emine. (2014).The Block-Hexagonal Grid Method for Laplace’s Equation with Singularities. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3245
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Adıgüzel Dosiyev.
A fourth order accurate matching operator is constructed on a hexagonal grid, for the
interpolation of the mixed boundary value problem of Laplace’s equation, by using
the harmonic properties of the solution. With the application of this matching operator
for the connection of the subsystems, the Block-Grid method (BGM), which is
a difference-analytical method, has been analysed on a hexagonal grid, for the solution
of both the Dirichlet and mixed boundary value problems of Laplace’s equation
with singularities. First of all, BGM is considered on staircase polygons and it is justified
that when the boundary functions outside the finite neighbourhood of the singular
points are from the Hölder classes C6;l ; 0 < l < 1; the error of approximation has
an accuracy of O
���
h4
; where h is the mesh size. The analysis of this method is extended
to special polygons whose interior angles are a jp; a j 2
1
3 ; 2
3 ;1;2
; and for
the Dirichlet problem of Laplace’s equation it is proved that, with the application of
BGM, it is possible to lower the smoothness requirement on the boundary functions
to C4;l ; 0 < l < 1; outside the finite neighbourhood of the singular points, in order
to obtain an accuracy of O
���
h4
. For the demonstration of the theoretical results on
staircase polygons, BGM has been applied on an L-shaped domain for two examples,
which has a singularity at the vertex with an interior angle of 3p
2 ; where Dirichlet and
mixed boundary conditions are assumed respectively. The slit problem, which has the
strongest singularity due to the interior angle of 2p at the vertex of the slit, has been
considered on a parallelogram with a slit, in order to illustrate the results obtained on
polygons with interior angles of a jp; a j 2
1
3 ; 2
3 ;1;2
: The second example on a parallelogram
demonstrates the application of BGM on a domain with two singularities as
it is assumed that the vertices with interior angles of 2p
3 are singular points. Solutions
of the numerical examples are consistent with the theoretical results obtained.
Keywords: Hexagonal grids, Laplace’s equation, singularity problem, block-grid method.
ÖZ
Laplace denklemi sınır problemleri için, dördüncü derece hata payı olan birless¸tirme (matching)
operatörü petek düg˘ ümleri üzerinde kurulmuss¸tur. Bu enterpolasyon oper- atörünün kurulumu için
çözümün harmonik özellikleri kullanılmıss¸tır. Alt sistemlerin birless¸tirilmesinde uygulanan
matching operatörü ile Block-Grid metodu (BGM), petek ag˘ lar üzerinde analiz edilmiss¸tir. Bu
metod, tekillig˘ i olan Laplace denkleminin Dirich- let ve karıss¸ık (mixed) sınır problemlerine
uygulanmıss¸tır.
˙Ilk önce BGM, iç açıları α j π , α j ∈ { 1 , 1, 3 , 21 olan çokgenler üzerinde incelenmiss¸tir.
2 2
Tekil noktalardan belli bir uzaklıkta olan sınır üzerindeki fonksiyonlar C6,λ , 0 < λ < 1,
Hölder gruplarından oldug˘ u zaman yakınsaklık hatasının O (h4) oldug˘ u kanıtlanmıs¸tır
(h ag˘ aralıg˘ ıdır).
˙Il˙lalaveten, BGM’nin analizi özel çokgenler üzerine genisss¸letilmisss¸tir. Bu özel çokgenlerin
iç açıları α
j
j , α
j ∈
{
{ 3 , 2 , 1, 2
21
iç açıları α j , α j ∈ { 3 , 2 , 1, 21 , olarak verilmisssssssssss¸tir. Laplace’ın Dirichlet
probleminin
yaklasssssssssss¸ık çözümü için, bu çokgenler üzerinde, tekil noktalardan belli bir uzaklıkta olan
sınır fonksiyonlarının C4,λ , 0 < λ < 1, Hölder grubundan olması ve BGM metodunun
uygulanması ile hata payının yine O (h4) oldug˘ u kanıtlanmısssssssssss¸tır.
Teorik sonuçların nümerik çözümlemesi için BGM, iç açılarından biri 3π
olan L-
s¸ekilli (L-shaped) çokgende uygulanmıs¸tır. Açıları α j π , α j ∈ { 1 , 2 , 1, 21 , olan çok-
3 3
genler üzerinde BGM’nin uygulanmasını göstermek üzere, iç açısı 2π oldug˘ undan dolayı en güçlü
tekillig˘ e sahip olan kesik problemi (slit problem), paralelkenar üz- erinde çözülmüs¸tür. Yine
paralelkenar üzerinde, 2π iç açılı kenarların ikisinde de tekil- lik oldug˘ u varsayılarak BGM ile
Laplace sınır problemi çözümlenmis¸tir. Elde edilen
v
sayısal çözümlerin teorik sonuçlarla uyumlu oldug˘ u sergilenmis¸tir.
Anahtar Kelimeler: Laplace denklemi, tekil problemi, Block-Grid metodu, petek
ag˘ lar.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Hexagonal grids
Laplace’s equation
singularity problem
block-grid method
The Block-Hexagonal Grid Method for Laplace’s Equation with Singularities
doctoralThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F3245/3/celemi.pdf.txt
File
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celemi.pdf.txt
URL
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oai:i-rep.emu.edu.tr:11129/32422017-05-15T23:00:46Zhdl_11129_66
EMU I-REP
advisor
Mahmudov, Nazim
author
Kara, Mustafa
2017-05-15T11:04:47Z
2017-05-15T11:04:47Z
2013-02
2013
Kara, Mustafa. (2013). Approximation by kantorovich type operators. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3242
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Prof. Dr. Nazim Mahmudov.
In this thesis, new type q-Bernstein - Kantorovich polynomials and
complex q-Szász-Kantorovich operators are introduced. In additon, The
exact order of approximation, quantitative Voronovskaja-type theorems,
simultaneous approximation properties for complex q-Bernstein - Kantorovich
polynomials , complex Szász-Kantorovich and complex q-Szász-
Kantorovich operators are studied.
ÖZET:
Bu tezde, yeni tip karmaşık q-Bernstein - polinomları ve karmaşık q-
Szasz-Kantorovich operatörleri tanımlanmıştır. Buna ek olarak, karmaşık q-
Bernstein-Kantorovich polinomlarının , karmaşık Szász-Kantorovich
operatörünün ve karmaşık q-Szász-Kantorovich operatörünün yakınsaklık
oranları, yakınsaklık özellikleri ve Voronovskaja tipi teoremler incelenmiştir.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Mathematical Operators
Q-Bernstein Kantorovich Polynomials
Q-Szasz Kantorovich Operator
Complex Szasz Kantorovich Operator
Q-Szasz Kantorovich Operator
Approximation by kantorovich type operators
doctoralThesis
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File
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oai:i-rep.emu.edu.tr:11129/33012017-06-28T23:01:03Zhdl_11129_66
EMU I-REP
advisor
Nagy, Benedek
author
Awe, Samson Ayodeji
2017-06-28T05:23:34Z
2017-06-28T05:23:34Z
2015-02
2015
Awe, Samson Ayodeji. (2015). 2-Head Pushdown Automata. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3301
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assoc. Prof. Dr. Benedek Nagy.
ÖZ:
Sonlu otomata düzenli dilleri tanır ve metin işleme, derleyiciler ve donanım tasarımı icin kullanilabilir. Iki basli sonlu otomata doğrusal bağlamsiz dilleri kabul eder, ve ters otomata programlama dilleri ve yapay zeka konularinda kullanilabilen baglamsiz dilleri tanir. Sonlu otomat iki basli sonlu otomata ve asagi suruklemeli otomata’da oldugu gibi deterministik ve deterministik olmayan versiyonlara sahiptir. Bu otomata’larin deterministik versiyonlarinda hareket etme secimi yapilamaz iken, deterministik olmayan versiyonlarda hareket seçimi yapmak mumkundur. Bu tezde ters otomata’dan daha güçlü olan bunun yani sira bazi baglamli dilleri de tanimakta olan 2-basli asagi suruklemeli otomata tarif edilmiştir. Bu çalışmalar sırasında, temel olarak yapilan is bu otomata’lari karakterize etmektir.
Anahtar Kelimeler: 2-basli asagi suruklemeli otomata, bağlamli serbest diller, deterministik otomata, deterministik olmayan otomata.
Finite state automata recognize regular languages which can be used in text processing, compilers, and hardware design. 2-head finite automata accept linear context-free languages. In addition, pushdown automata are able to recognize context-free languages which can be used in programming languages and artificial intelligence. We distinguish between deterministic and nondeterministic finite automata, 2-head automata and also pushdown automata. The deterministic version of these machines is such that there is no choice of move in any situation while the non-deterministic version may have a choice of move. The present thesis describes 2-head pushdown automata which is more powerful than the pushdown automata and it is able to recognize some non-context-free languages as well. Throughout the thesis we try to focus on characterization of aforementioned machines.
Keywords: 2-head pushdown automata, non-context-free languages, deterministic automata, non-deterministic automata.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Machine theory - Formal languages - Computer programming
2-head pushdown automata
non-context-free languages
deterministic automata
non-deterministic automata
2-Head Pushdown Automata
masterThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F3301/3/AweSamson.pdf.txt
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AweSamson.pdf.txt
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oai:i-rep.emu.edu.tr:11129/34942017-11-01T00:01:36Zhdl_11129_66
EMU I-REP
advisor
Aktuğlu, Hüseyin
author
Gezer, Halil
2017-10-31T08:59:52Z
2017-10-31T08:59:52Z
2013-01
2013
Gezer, Halil. (2013). Equistatistical convergence . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3494
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Huseyin Aktuglu.
In this thesis, we focus on di↵erent types of equistatistical convergences. We define
some new type of convergences such as lacunary equistatistical convergence,
!-equistatistical convergence, A-equistatistical convergence, B-equistatistical convergence
and ↵#-equistatistical convergence. We also study properties of these
new types of convergences. We construct examples for each case, to show that equistatistical
convergence lies between point wise and uniform convergences. Moreover,
we prove Korovkin type approximation theorems via lacunary equistatistical
convergence, !-equistatistical convergence, A-equistatistical convergence, Bequistatistical
convergence and ↵#-equistatistical convergence. In the last chapter
we introduce ↵#- statistical convergence of order $ and we prove Korovkin type
approximation theorems in the sense of ↵#- statistical convergence.
Keywords: Statistical convergence, lacunarystatistical convergence, A-statistical
convergence, !-statistical convergence, equistatistical convergence, Korovkin type
approximation theorem.
ÖZ:
Bu tezde esas olarak eşistatistiksel yakınsaklık kavramı ele alınacaktır. Eşistatistiksel
yakınsaklık noktasal istatistiksel yakınsaklık ile düzgün istatistiksel yakınsaklık
arasında yer alan bir yakınsama çeşididir. Bu doktora tezindeki esas amaç lacunary
eşistatistiksel, A-eşistatistiksel, !-eşistatistiksel, ℬ-eşistatistiksel ve !"-
eşistatistiksel yakınsaklık kavramlarını vermek ve herbiri için Korovkin Tipli
Teoremler ispat etmektir. Bunun yanında bu yakınsama türlerinin daha anlaşılır
olması için belli başlı özellikleride incelenecektir. Bu yakınsama türleri için elde
edilecek Korovkin Tipli Teoremlerin Mevcut Korovkin Tipli Teoremlerle ilişkileri
de verilecektir.
Anahtar Kelimeler: İstatistiksel yakınsaklık, lacunary istatistiksel yakinsaklik, Aistatistiksel
yakınsaklık, !-istatistiksel yakınsaklık, eşistatistiksel yakınsaklık,
Korovkin Tipli Teorem.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Mathematical Statistics.
Convergence.
Statistical Convergence.
Equistatistical Convergence
Korovkin Type Approximation Theorem
Lacunary Statistical Convergence
Equistatistical Convergence
Equistatistical convergence
doctoralThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F3494/3/Gezer.pdf.txt
File
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URL
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oai:i-rep.emu.edu.tr:11129/34852017-11-01T00:01:29Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Agamirza
author
Belaghi, Mahmoud Jafari
2017-10-31T08:29:54Z
2017-10-31T08:29:54Z
2013-01
2013
Belaghi, Mahmoud Jafari. (2013). On continued fractions. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3485
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Prof. Dr. Agamirza Bashirov.
In this thesis we concern two problems related to continued fractions.
Euler's differential method: we apply Euler's differential method, which was not
used by mathematicians for a long time, to derive a new formula for a certain kind
continued fraction depending on a parameter. This formula is in the form of the ratio
of two integrals. In case of integer values of the parameter, the formula reduces to the
ratio of two finite sums. Asymptotic behavior of this continued fraction is
investigated numerically and it is shown that it increases in the same rate as the root
function.
Bauer-Muir transform: we define a transformation of a certain kind of continued
fractions to the same kind of continued fractions. This transformation is obtained by
multiple application of the Bauer-Muir transform and then using the limiting process.
It is shown that a double application of this transformation is the identity
transformation. The obtained result is applied to some classic continued fractions due
to Euler and Ramanujan. As a result a new transformation was found which in some
special cases infinite continued fraction can be transformed to finite continued
fraction.
Keywords: Continued fractions, Euler’s differential method, Bauer-Muir transform
ÖZ:
Bu tezde sürekli kesirlerle alakalı iki konu çalışıldı.
Euler’in differensiyel metodu: Matematikçilerin uzun zamandır kullanmadığı Euler
diferensiyel metodunu kullanarak, bir parametreye bağlı sürekli kesirler için yeni bir
formül bulundu. Bu formül iki integralin oranı formundadır. Parametrelerin tam sayı
olduğu durumlarda bu formül iki sonlu toplamın oranı şeklinde değişir. Bu sürekli
kesirlerin asimptotik davranışları üzerinde yapılan sayısal çalışmalar sonunda, kök
fonksiyonu ile aynı oranda büyüdükleri görüldü.
Bauer-Muir dönüşümü: Belirli bir türden olan sürekli kesirleri yine aynı türe
çeviren bir dönüşüm tanımlandı. Bu dönüşüm, birçok kez Bauer-Muir dönüşümü ve
daha sonra limit işlemleri uygulanarak bulundu. Dönüşümün iki kez uygulandığı
durumlarda birim dönüşüm elde edildiği görüldü. Elde edilen dönüşüm Euler ve
Ramanujan’ın sürekli kesirlerine uygulandı. Sonuç olarak, belirli parametreler için
sonsuz sürekli kesirleri sonlu sürekli kesirlere çeviren bir dönüşüm bulundu.
Anahtar Kelimeler: Sürekli kesirlerle, Euler diferensiyel metodunu, Bauer-Muir
dönüşümü
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Fractions
Continued Fractions
Euler's Differential Method
Bauer-Muir Transform
On continued fractions
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/36182018-04-13T23:01:00Zhdl_11129_66
EMU I-REP
advisor
Nagy, Benedek
author
Saadat, MohammadReza
2018-04-13T07:37:15Z
2018-04-13T07:37:15Z
2016-02
2016-02
Saadat, Mohammad Reza. (2016). Cellular Automata in the Triangular Grid. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3618
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assoc. Prof. Dr. Benedek Nagy.
Cellular automata are parallel computing devices working on a discrete timescale. Each cell of a regular grid has a finite number of states and the state in the next time instant depends only on the actual state of the cell itself and the states of its neighbor cells. When every cell could have exactly two states, they can be identified as “live” and “dead” states.
“Game of Life” is a very popular type of cellular automata on the square grid based on the 8 neighborhood of the cells. There are various initial configuration that leads to periodic or growing or moving patterns, etc. Triangular Grid which also called an isometric grid, is a grid generated by tiling the plane regularly with equilateral triangles. In the thesis, life like cellular automata are analyzed in the triangular gird based on 3-neighborhood relation that is the next state of a cell depends only on its actual state and the states of its closest neighbor cells.
There are 2 sets of conditions. The first set is called “Birth” or “B” which shows the number of live cells needed in the neighborhood of a dead cell to make it alive. The second set is called “Stay alive” or “S” which shows the number of live cells needed in the neighborhood of a live cell to keep it alive. Various B/S models are analyzed. While some can generate patterns like snowflake or etc, some can be used for noise removal in image processing.
Keywords: Cellular Automata, Game of Life, Triangular Grid
ÖZ :
Hücresel otomatlar ayrık zaman çizelgesi üzerinde çalışan paralel hesaplama araçlarıdır. Düzenli kılavuzun her hücresinin sonlu sayıda „durum‟ u vardır ve gelecek zamandaki durum ancak hücrenin ve komşu hücrelerin şu anki durumlarına bağlıdır. Hücrenin sadece iki durumu bulunduğunda, bunlar „canlı‟ ve „ölü‟ olarak adlandırılırlar.
„Hayat Oyunu‟ kare kılavuz üzerinde, hücrelerin 8 komşuluğuna dayalı çok popüler bir hücresel otomat çeşididir. Dönemli, büyüyen, veya hareket eden kalıpları yaratan değişik başlangıç ayarlamaları bulunur. Ügensel kılavuz, ya da farklı bir adıyla „eş‟ kılavuz, düzlemi düzenli şekilde eşkenar üçgenlerle döşeyerek elde edilir. Bu tezde 3‟lü komşuluk bağıntısına dayalı üçgensel kılavuz yaşam tarzı hücresel otomatlar analiz edilir. Öyle ki hücrenin bir sonraki durumu sadece kendisinin ve en yakınındaki komşu hücrelerin şu anki durumuna bağlıdır.
Toplam 2 sonuç kümesi vardır. İlk kümenin adı „Doğum‟ ya da kısaca „D‟ dir ve bu küme ölü hücreyi canlandırmak için komşuluğunda ihtiyaç duyulan canlı hücre sayısını gösterir. İkinci kümenin adı ise „Hayatta Kal‟ veya kısaca „K‟ olmakla beraber, bu küme de canlı hücreyi canlı tutmak için gerekli olan komşuluğundaki canlı hücre sayısını temsil eder. Farklı D/K modelleri analiz edilir. Bunların bazıları kartanesi gibi desenler üretirken, bazıları da görüntü işleme alanında gürültü gidermek için kullanılır.
Anahtar Kelimeler: Hücresel Otomatlar, Hayat Oyunu, Ügensel kılavuz
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Cellular automata
Cellular Automata
Game of Life
Triangular Grid
Cellular Automata in the Triangular Grid
masterThesis
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oai:i-rep.emu.edu.tr:11129/35882018-04-12T23:01:18Zhdl_11129_66
EMU I-REP
advisor
Rıza, Mustafa
author
Alizadeh, Yashar
2018-04-12T07:58:49Z
2018-04-12T07:58:49Z
2016-09
2016-09
Alizadeh, Yashar. (2016). Quantum Error Correction Methods . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3588
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
This study surveys the mathematical structure of a quantum error correcting codes and
the way they are developed through certain stages of error correction. In particular, the
families of Calderbank-Shor-Steane codes (CSS) and the stabilizer codes are discussed
and through elaborative examples it will be shown that the CSS codes are in the family
of the stabilizer codes. Since the study of the CSS codes depends on a firm knowledge
of classical coding theory, a rigorous mathematical review of the linear codes is done
separately. Analysing the structure of the stabilizer formalism is highly depended on
the effective use of some group theoretic notions. This structure is discussed in more
detail and examples will be given. As the ultimate application of the quantum error
correction the rules of the fault-tolerant quantum computing is explored and finding
the threshold condition of an example will be done.
Keywords: QEC, Coding theory, Stabilizer formalism, CSS codes, Fault-tolerant quantum
computing, Threshold condition
OZ :
Bu c¸alıs¸ma kuantum hata d¨uzeltimin kodlarının matematiksel yapısını ve belli hata
d¨uzeltilim evrelerinden nasıl gec¸ti˘gini incelemektedir. ¨ozellikle, Calderbank-Shor-
Steane (CSS) kod ailesi ve stabilizat¨or kodları ele alınarak, ve ayrıca ayrıntılı ¨ornekler
ile CSS kodları stabilizat¨or kodlar ailesinden oldu˘gunu g¨osterilmektedir. CSS kodları
klasik kodlama teorisine dayandı˘gı ic¸in, matematiksel ayrıntılı bir s¸ekilde lineer kodlar
g¨ozden gec¸irilmis¸tir. Stabilizat¨or bic¸imcili˘gin str¨ukt¨ur¨un¨un analizi gurup teorisi tabanında
yapılmıs¸tır. Bu bic¸imcilik detaylı s¸ekilde tartıs¸ılacaktır ve ¨orneklerle desteklenecektir.
Kuantum hata d¨uzeltimi kurallarının en uc¸ uygulaması kusura dayanıklı
kuantum hesaplamaları incelenmis¸tir ve bir ¨ornekte es¸ik seviyesinin nasıl bulundu˘gu
g¨osterilecektir.
Anahtar Kelimeler:Kuantum Hata D¨uzeltme, Kodlama teorisi, Stabiliz¨or bic¸imcili˘gi,
CSS kodları, hata d¨uzeltimi kuantum hesaplamalar, es¸ik seviyesi s¸artı
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Quantum computers - Error - correcting codes (Information theory)
QEC
Coding theory
Stabilizer formalism
CSS codes
Fault-tolerant quantum computing
Threshold condition
Quantum Error Correction Methods
masterThesis
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oai:i-rep.emu.edu.tr:11129/36112018-04-13T23:00:36Zhdl_11129_66
EMU I-REP
advisor
Saadetoğlu, Müge
author
Avkan, Aydın
2018-04-13T06:52:45Z
2018-04-13T06:52:45Z
2016-08
2016-08
Avkan, Aydın. (2016). Irreducible Representations of Some Finite Groups. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3611
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Müge Saadetoğlu.
In this thesis we compute the irreducible representations and the characters of some certain finite groups. We first provide the necessary overview on linear algebra, group theory and the representations theory. Then, we compute the irreducible representations of finite cyclic groups, smaller symmetric groups and the direct products of the two groups. Finally, we give a general method to compute the irreducible representations of 𝑆����𝑛���� by using Young diagrams and provide the Frobenius formula to obtain the characters for these irreducible representations. Keywords: Representation, Character, Cyclic groups, Symmetric groups, Young diagram, Frobenius formula.
ÖZ :
Bu tezde sonlu grupların indirgenemez reprezantasyonları ve karakterleri
hesaplanmıştır.
İlk olarak Cebir, grup teorisi ve reprezantasyon teorileri hakkında ön bilgi verilmiştir.
Daha sonra devirli ve simetrik grupların ve bunların direkt çarpımlarının indirgenemez
reprezantasyonları hesaplanmıştır.
Son olarak simetrik grup 𝑆���𝑛��� için genelleştirilmiş indirgenemez reprezantasyon metodu
Young şeması kullanılarak verilmiş ve Frobenius formülüyle bu reprezantasyonların
karakterleri bulunmuştur.
Anahtar Kelimeler: Reprezantasyon, Karakter, Devirli grup, Simetrik grup,
Young şeması, Frobenius formülü
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Algebras and Groups
representations of groups - Finite groups
Group theory
Representation
Character
Cyclic groups
Symmetric groups
Young diagram
Frobenius formula
Irreducible Representations of Some Finite Groups
masterThesis
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URL
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avkanaydin.pdf.txt
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oai:i-rep.emu.edu.tr:11129/37372018-05-31T23:00:58Zhdl_11129_66
EMU I-REP
advisor
Subaşı, Derviş
author
Ibrahim, Kabiru Garba
2018-05-31T10:51:49Z
2018-05-31T10:51:49Z
2016-07
2016
Ibrahim, Kabiru Garba. (2016). Determination of an Unknown Diffusion Coefficient in a Parabolic Inverse Problem. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3737
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assoc. Prof. Dr. Derviş Subaşı.
In this thesis we studied the finite difference approximation for the solution of one dimensional parabolic inverse problem of finding the function ( ) and the unknown positive coeffient ( ) . The Backward time centered space (BTCS) which is unconditionally stable is studied and it’s convergent is proved using application of discrete maximum principle. Error estimates for ( ) and ( ) is studied and to give clear overview of the methodology several model problems are solved numerically. According to the experimental numerical results the concluding remark are presented.
Keywords: finite difference methods, parabolic inverse problem, convergence, Error estimates, maximum principle.
ÖZ :
Bu tez tek boyutlu parabolik ters problemlerinin sayısal analiz tekniği kullanılarak çözülmesi ile ilgilidir. Çözüm esnasında klasik geri zaman merkezli sonlu farklar tekniği kullanılarak ( ) fonksiyonu ve yayılma katsayısı ( ) hesplanmıştır. Kullanılan sonlu farklar tekniğinin yakınsaması ayrık maksimum prensibi ile hesplanmış ayrıca ( ) ve ( ) bilinmeyenlerinin hata tahminleri çalışılmıştır. Sayısal analiz hesaplarında iki farklı denklem üzerinde çalışılmış ve sonuçlar ile düşünceler yazılmıştır.
Anahtar kelimeler: sonlu fark yöntemleri, parabolik ters problemi sorun, yakınsama, hata tahminleri, maksimum ilkesi.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Finite difference methods
parabolic inverse problem
convergence
Error estimates
maximum principle
Determination of an Unknown Diffusion Coefficient in a Parabolic Inverse Problem
masterThesis
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oai:i-rep.emu.edu.tr:11129/37492018-05-31T23:00:50Zhdl_11129_66
EMU I-REP
advisor
Buranay, Suzan Cival
author
Adekanmbi, Damilola Victoria
2018-05-31T12:09:00Z
2018-05-31T12:09:00Z
2016-06
2016
Adekanmbi, Damilola Victoria. (2016). On A Comparative Study of Direct Solution Methods of the Discrete Poisson’s Equation on A Rectangle. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3749
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Suzan Cival Buranay.
The solution of systems of algebraic equations arising from the 5-point discretization
of Poisson’s equation on a rectangle with Dirichlet boundary conditions is analyzed
by direct solution methods. Special emphasis is given for block direct methods, such
as block elimination, block decomposition and block cyclic reduction methods. For
this purpose block elimination algorithms, orthogonal block decomposition
algorithms, cyclic odd even reduction method, (CORF) algorithm and Buneman
version of the CORF algorithm is also studied. A test problem is constructed for the
Laplace equation and solved by these block methods for the mesh size
1
4
h .
Comparisons are given based on the computational complexity of the methods.
Keywords: Block elimination methods, block cyclic reduction method, block
decomposition methods, Thomas algorithm, discrete Poisson’s equation, 5-point
scheme.
ÖZ :
Poisson denkleminin dikdörtgen üzerindeki Dirichlet sınır değer probleminin 5-nokta
çözümlemesi ile elde edilen cebirsel denklem takımlarının çözümü doğrudan
yöntemler ile incelendi. Blok yoketme yöntemleri, blok ayrıştırma yöntemleri, ve blok
döngüsel indirgeme yöntemleri gibi blok doğrudan yöntemlere özel önem verildi. Bu
amaç doğrultusunda blok yoketme algorithmaları, dik blok ayrıştırma algorithmaları,
tek çift döngüsel indirgeme metodu, (CORF) algorithması ve Buneman versiyonu
çalışıldı. Laplace denklemi için bir test proplemi oluşturuldu ve adım büyüklüğü
1
4
h
için verilen yöntemler ile çözüldü. Karşılaştırmalar yöntemlerin hesaplama
karmaşasına göre verildi.
Anahtar kelimeler: Blok yoketme yöntemi, blok döngüsel indirgeme yöntemi, blok
ayrıştırma yöntemi, Thomas algorıthması, Poisson denklemi, 5-nokta şeması.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Algebraic Equations - Solutions Systems
Equations - Numerical solutions
Block elimination methods
block cyclic reduction method
block decomposition methods
Thomas algorithm
discrete Poisson’s equation
5-point scheme
On A Comparative Study of Direct Solution Methods of the Discrete Poisson’s Equation on A Rectangle
masterThesis
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oai:i-rep.emu.edu.tr:11129/36482018-05-17T23:01:21Zhdl_11129_66
EMU I-REP
advisor
Oğurlu, Sonuç Zorlu
author
Ali, Kawa Sardar Mohammad
2018-05-17T12:21:03Z
2018-05-17T12:21:03Z
2016-06
2016-06
Ali, Kawa Sardar Mohammad. (2016). Bernstein-Type Operators. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3648
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Prof. Dr. Sonuç Zorlu Oğurlu.
In this work we are interested in the approximation of some type of operators called
Bernstein-type. For this purpose, the operator , 0, n L f x f C called the
Bernstein-type approximation operator is considered. The aim is to use some
probabilistic properties to improve and sharp to operator defined above. Also, the rates
of convergence as well as the continuity of the operator are studied. Various methods
of approaching the problem are evaluated in this study.
Keywords: Bernstein type operator, probabilistic approach, binomial distribution,
rates of convergence.
ÖZ :
Bu çalışmada Bernstein - tipi operatörlerin yaklaşımlarıyla ilgilenilimiştir.Bunun için
, 0, n L f x f C olarak belirtilen Bernstein tipi yaklaşım operatörü ele
alınmıştır. Yukarıda verilen operatör için bazı olasılıksal metodlar kullanılarak
yaklaşım özellikleri çalışılmıştır. Ayrıca, yakınsama hızı yanı sıra operatörün
sürekliliği incelenmiş olup farklı yöntemlerle yaklaşım problemi de bu çalışmada
değerlendirilmiştir.
Anahtar kelimeler: Bernstein tipi operatörler, olasılıksal yaklaşım, binom dağılımı,
yaklaşım hızı.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Mathematical Operators
Bernstein type operator
probabilistic approach
binomial distribution
rates of convergence
Bernstein-Type Operators
masterThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F3648/3/alikawa.pdf.txt
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alikawa.pdf.txt
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alikawa.pdf
oai:i-rep.emu.edu.tr:11129/37332018-05-31T23:00:33Zhdl_11129_66
EMU I-REP
advisor
Dosiyev, Adıgüzel
author
Sadeghi, Hamid Mir Mohammad
2018-05-31T10:41:59Z
2018-05-31T10:41:59Z
2016-06
2016-06
Sadeghi, Hamid Mir Mohammad. (2016). High Order Accurate Approximation of the First and Pure Second Derivatives of the Laplace Equation on a Rectangle and a Rectangular Parallelepiped. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3733
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Prof. Dr. Adıgüzel Dosiyev.
In thisthesis,wediscusstheapproximationofthefirstandpuresecondorderderiva-
tivesforthesolutionoftheDirichletproblemforLaplace’sequationonarectangular
domain andinarectangularparallelepiped.Inthecasewhenthedomainisarectangle,
the boundaryvaluesonthesidesoftherectanglearesupposedtohavesixthderivatives
satisfying theHöldercondition.Onthevertices,besidesthecontinuity,thecompat-
ibility conditions,whichresultfromtheLaplaceequation,forthesecondandfourth
derivativesoftheboundaryfunctions,givenontheadjacentsides,arealsosatisfied.
Under theseconditionsauniformapproximationoforder O
����
h4
(h is thegridsize),is
obtained forthesolutionoftheDirichletproblemonasquaregrid,itsfirstandpure
second derivatives,byasimpledifferenceschemes.
In thecasearectangularparallelepiped,weproposeandjustifydifferenceschemes
for thefirstandpuresecondderivativesapproximationofthesolutionoftheDirichlet
problem for3DLaplace’sequtation.Theboundaryvaluesonthefacesoftheparal-
lelepiped areassumedtohavethesixthderivativessatisfyingtheHöldercondition.
Theyarecontinuousontheedges,andtheirsecondandfourthorderderivativessatisfy
the compatibilityconditionswhichresultsfromtheLaplaceequation.Itisprovedthat
the solutionsoftheproposeddifferenceschemesconvergeuniformlyonthecubicgrid
with order O(h4), where h is thegridstep.Forbothcasesnumericalexperimentsare
demonstrated tosupporttheanalysismade.
Keywords: Finite differencemethod,approximationofderivatives,uniformerror,
Laplace equation.
ÖZ :
Bu tezde,LaplaceDenkleminindikdörtgenselbölgedevedikdörtgenlerprizmasıüz-
erinde Dirichletproblemininçözümüiçinbirincimertebedenvepürikincimertebeden
türevlerininyakla¸sımıtartı¸sılır.Tanımbölgesinindikdörtgenoldu˘gu durumdadikdört-
genin kenarlarındaverilensınırfonksiyonlarınınaltıncıtürevlerininHölder¸sartını
sa˘gladıkları kabuledildi.Kö¸selerdesüreklilik¸sartınınyanındaLaplacedenkleminden
sonuçlanan kö¸selerinkom¸sukenarlarındaverilensınırde˘ger fonksiyonlarınınikinci
vedördüncütürevleriicinuyumluluk¸sartlarıdasa˘glandı. Bu¸sartlaraltındaDirich-
let problemininkareızgaraüzerindeçözümüiçinveçözümünbirincivepürikinci
türevleriiçin O(h4) (h adım uzunlu˘gu) düzgünyakla¸sımısadebirfark¸semasıileelde
edildi.
˙Ikinci durumdatanımbölgesidikdörtgenlerprizmasıoldu˘gunda Laplacedenkleminin
Dirichlet problemininçözümününbirincivepürikincitürevlerininyakla¸sımıiçinfark
¸semalarıönerilirvesa˘glanır.Prizmanınyüzeylerindeverilensınırde˘gerlerinin altıncı
türevlerininHölderko¸sulunusa˘gladı˘gı kabuledildi.Kö¸selerdesüreklidirlerveonların
ikinci vedördüncümertebedentürevleriLaplacedenklemlerindensonuçlananuyum-
luluk ko¸sulunusa˘glar.Önerilenfark¸semalarınınçözümününküpızgaralarüzerindeh
ızgarauzunlu˘gu oldu˘gunda O(h4) mertebesinden düzgünyakınsadı˘gı ispatlandı.Her
iki durumiçinsayısalörnekleryapılananalizleridesteklemekiçinverildi.
Anahtar Kelimeler: Sonlu farkmetodu,türevlerinyaklasımı,düzgünhata,Laplace
denklemi.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Laplace Functions - Mathematics
Finite differencemethod
approximationofderivatives
uniformerror
Laplace equation
High Order Accurate Approximation of the First and Pure Second Derivatives of the Laplace Equation on a Rectangle and a Rectangular Parallelepiped
doctoralThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F3733/3/sadeghihamid.pdf.txt
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sadeghihamid.pdf.txt
URL
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oai:i-rep.emu.edu.tr:11129/36832018-06-19T10:32:10Zhdl_11129_66
EMU I-REP
advisor
Tüzmen, Şükrü (Co-Supervisor)
advisor
Bashirov, Rza (Supervisor)
author
Mehraei, Mani
2018-05-24T11:32:21Z
2018-05-24T11:32:21Z
2016-07
2016-07
Mehraei, Mani. (2016). Exploiting Hybrid Functional Petri Nets to Investigate Transcriptional Activity of Hemoglobin Switching. Thesis (Ph.D.). Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3683
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Co-Supervisor: Assoc. Prof. Dr. Şükrü Tüzmen, Supervisor: Prof. Dr. Rza Bashirov.
β-thalassemia, SCD and other human β-globin gene related diseases are the major sources of mortality in the world. Bone marrow transplantation, gene therapy and supporting care with transfusion of red blood cells are possible treatments of human β-globin gene related diseases. However, none of these treatments has progressed to the level of worldwide efficient clinical therapy. Reactivation of γ-globin gene in affected adults is known to be an efficient measure to ameliorate the severity of β-thalassemia and SCD.
In this study, we propose new strategies for β-globin disorders. These approaches are centered upon induction of γ-globin gene expression. We use Cell Illustrator software tool to create HFPN model of hemoglobin switching network, validate the model with available qPCR data and perform simulations to compare the efficiency of the proposed strategies with the existing drug and RNAi-mediated therapies. Simulation results show that our drug and RNAi-mediated strategies have been postulated to lead to the potential induction of γ-globin gene expression.
Keywords: Quantitative modeling, hybrid functional Petri net, β-thalassemia, hemoglobin switching network
ÖZ :
β-talasemi ve diğer β-globin geni ile ilgili anomalilerden oluşan hastalıklar dünyada mortalitenin en yüksek olduğu önemli bir halk sağlığı sorunudur. Kemik iliği nakli, gen terapisi ve kırmızı kan hücrelerinin nakli ile destekleyici bakım, β-globin geni ile ilgili anomalilerden oluşan hastalıkların olası tedavileri arasında yer almaktadır. Fakat bu tedavilerin hiçbiri dünya genelinde yeterli klinik tedavi seviyesine ulaşmış değildir. Ancak γ-globin geninin reaktivasyonu, β-talasemi hastalığının şiddetini iyileştirmek için etkin önlem olarak önerilebilir.
Bu tezde, β-globin geni ile ilgili anomalilerden oluşan bozuklukları çalışmak için γ-globin gen ekspresyonunun reaktivasyon olgusuna dayanan yeni stratejiler önerilmiştir. “Hemoglobin Switching”, HFPN modeli oluşturarak mevcut qPCR verileri ile, mevcut ilaç ve RNAi metodu kullanılan tedavilerle ve önerilen stratejilerin etkinliğini karşılaştırmak koşulu ile, “Cell Illustrator” yazılımı kullanılarak in silico simülasyonlar gerçekleştirilmiştir. Simülasyon sonuçları, bizim önerdiğimiz ilaç ve RNAi aplikasyonlarının γ-globin gen ekspresyonunun yüksek indüklenmesine neden olabilecek potansiyel stratejiler olabileceğini göstermektedir.
Anahtar kelimeler: Kantitatif modelleme, hibrid fonksiyonel Petri net, β-talasemi, hemoglobin anahtarlamalı ağ
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Petri nets - Computer science - Mathematics
Computational biology Petri nets
Quantitative modeling
hybrid functional Petri net
β-thalassemia
hemoglobin switching network
Exploiting Hybrid Functional Petri Nets to Investigate Transcriptional Activity of Hemoglobin Switching
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/36602018-05-18T23:01:19Zhdl_11129_66
EMU I-REP
advisor
Nagy, Benedek
author
Mujahed, Hamzeh Abdel Hamid
2018-05-18T10:50:27Z
2018-05-18T10:50:27Z
2016-06
2016-06
Mujahed, Hamzeh Abdel Hamid. (2016). Graph Indices on Grids. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3660
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assoc. Prof. Dr. Benedek Nagy.
The Wiener index of a graph, known as the “sum of distances” of a connected graph,
is the first topological index used in chemistry to sum the distances between all
unordered pairs of vertices of a graph. Wiener index, or sometimes called Wiener
number, of a molecular graph correlates physical and chemical characteristics of
graphs, and has been studied for various kinds of graphs. In this thesis, we derived
mathematical formulas to compute Wiener index and hyper-Wiener index for bodycentered
cubic grid and face-centered cubic grid. In the body-centered cubic graph,
the lines of unit cells of the body-centered cubic grid are used. These graphs contain
center points of the unit cells and other vertices, called border vertices. Closed
formulas are obtained to calculate the sum of shortest distances between pairs of
border vertices, between border vertices and centers and between pairs of centers.
Based on these formulas, their sum, the Wiener index and hyper-Wiener index of
body-centered cubic grid with unit cells connected in a row are computed. Some
relationships between formulas and integer sequences are also presented.
In face-centerd cubic grid, the graphs of lines of unit cells of the face-centered cubic
grid are investigated. The face-centered cubic unit cell is a cube (all sides have the
same length and all faces are perpendicular to each other) with an atom at each
corner of the unit cell called border points and an atom situated in the middle of each
face of the unit cell called face central points. Closed formulas are obtained to
calculate the sum of shortest distances between pairs of border points, between
border points and centrals and between pairs of centrals. Based on these formulas,
their sum, the Wiener index and hyper-Wiener index of face-centered cubic grid with
unit cells connected in a row graph is computed.
Keywords: Wiener index, body-centered cubic grid, face-centered cubic grid, hyper-
Wiener index, shortest paths, non-traditional grids, combinatorics.
ÖZ :
Bir grafın mesafeler toplamı olarak bilinen Wiener indeksi, kimdaya sırasız düğüm
çiftleri arasındaki mesafeler toplamını hesaplamak için kullanılan ilk topolojik
indekstir. Moleküler grafın bir çok graf türü için irdelenmiş olan ve Wiener sayısı
olarak da bilinen Wiener indeksi grafın fiziksel ve kimyasal özelliklerini
ilişkilendirir. Bu tezde gövde-merkezli grafın birim hücrelerinin kenarlarını
kullanarak gövde-merkezli ve yüzey-merkezli kübik grafın Wiener indeksi ve hiper-
Wiener indeksinin hesaplanması için formül geliştirilmiştir. Bunun yanı sıra yüzeymerkezli
kübik şebekelerde birim hücre dizileri biçiminde olan graflar irdelenmiştir.
Yüzey-merkezli kübik birim hücre, köşeleri sınır noktaları da denilen çekirdeklerden
oluşan bir küpdür. Sözkonusu graflar birim hücreleri merkez düğümlerini ve sınır
düğümlerini içermektedir. Bu bağlamda önerilen formüller uygulanarak sınır
düğümleri çiftleri, sinir ve merkez düğüm çiftleri ve merkez düğüm çiftleri
arasındaki en kısa yollar toplamı hesaplanabilmektedir. Sözkonusu formüller ve
tamsayı dizileri arasında bazı ilişkiler de bu tezde irdelenmiştir.
Anahtar Kelimeler: Wiener endeksi, gövde-merkezli kübik grid, yüzey-merkezli
kübik grid, hiper-Wiener endeksi, kısa yollar, Geleneksel olmayan grid,
kombinatoriks.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Wiener index
body - centered cubic grid
face - centered cubic grid
hyper - Wiener index
shortest paths
non - traditional grids
combinatorics
Graph Indices on Grids
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/37132018-05-30T23:01:31Zhdl_11129_66
EMU I-REP
advisor
Nagy, Benedek
author
Basbous, Raed Yousef Mohammed
2018-05-30T11:25:24Z
2018-05-30T11:25:24Z
2016-06
2016-06
Basbous, Raed Yousef Mohammed. (2016). Strategies to Fast Evaluation of Expression Trees . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3713
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assoc. Prof. Dr. Benedek Nagy.
Expression trees are well-known tools to visualize the syntactical structure of the
expressions. They are helpful also in evaluations, e.g., decision trees are widely used.
Games and game theory form an important field in Artificial Intelligence and it has
several connections to Business and Economy. Short circuit, short cut, or by other
name, lazy evaluations play important roles in various fields of computer science
including logic, hardware design, programming, decision making.
In this thesis, different types of trees are considered including extensions of game
trees using operations, e.g., multiplication, (constrained) addition and the usual
minimum and maximum, and three of the best known and used fuzzy logic systems,
(Gödel, Lukasiewicz, and product logics).
The evaluation of lots of formulae can be speeded up by various pruning techniques
by discovering which remaining part of the formulae has no influence on the final
result for various reasons. The presented techniques can be seen as generalizations of
short circuit evaluations in Boolean logic and also of alpha-beta pruning of game
trees. Simulation results show the efficiency of the presented techniques.
Keywords: expression trees, game trees, formula trees, fast evaluation, fuzzy logic,
many valued logic, pruning techniques, short circuit evaluation, lazy evaluations.
ÖZ :
İfade ağaçları, ifadelerin sözdizimsel yapılarını görselleştirmek için kullanılan
araçlardır. Onlar değerlendirmede oldukça yardımcıdırlar, örneğin, karar ağaçları
yaygın olarak kullanılanlardandır. Oyun ve oyun teorisi yapay zekada önemli bir alan
olup, işletme ve ekonomide çeşitli bağlantılara sahiptir. Kısa devre, kısa yol, ya da
diğer bir adıyla tembel değerlendirmeler mantık, donanım tasarımı, programlama,
karar verme gibi bilgisayar bilimlerinin çeşitli alanlarında önemli rol oynar.
Bu tezde, oyun ağaçlarının uzantıları dahil farklı ağaç modelleri düşünülmüştür.
Örneğin, çarpma, toplama(sınırlandırılmış) ve olağan minimum ve maksimum
işlemleri ile, en iyi bilinen ve en çok kullanılan bulanık mantık sistemlerinden üç
tanesi, çarpma mantığı işlenmiştir.
Anahtar kelimeler: ifade ağaçları, oyun ağaçları, formül ağaçları, hızlı
hesaplamalar, bulanık mantık, birçok değerli mantık, budama teknikleri, kısa devre
hesaplamaları, tembel hesaplamalar.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Artificial Intelligence - Expression Trees
Computer logic - Artificial intelligence
Expression trees
game trees
formula trees
fast evaluation
fuzzy logic
many valued logic
pruning techniques
short circuit evaluation
lazy evaluations
Strategies to Fast Evaluation of Expression Trees
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/36502018-05-18T23:01:20Zhdl_11129_66
EMU I-REP
advisor
Mahmudov, Nazım
author
Avcı, İbrahim
2018-05-18T07:16:34Z
2018-05-18T07:16:34Z
2014-09
2014-09
Avcı, İbrahim. (2014). Numerical Solutions of Fractional Differential Equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3650
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Nazım Mahmudov.
Fractional analysis has almost the same history as classical calculus. Fractional analysis
did not attract enough attention for a long time. However, in recent decades,
fractional analysis and fractional differential equations become very popular because
of its powerful applications. A large number of new differential models that involve
fractional calculus are developed. For most fractional differential equations we can not
provide methods to compute the exact solutions analytically. Therefore it is necessary
to revert to numerical methods.
The structure of this thesis is arranged in the following way. We begin by recalling
some classical facts from calculus. Partically, we recall definition and some properties
of gamma, beta and Mittag-Leffler function. Then, in Chapter 3, we introduce the fundamental
concepts and definitions of fractional calculus. This includes, in particular,
some basic results concerning Riemann–Liouville differentiation and integration, and
basic properties of Caputo derivative. In Chapter 4 we discuss fractional variant of the
classical second-order Adams–Bashforth–Moulton method. It has been introduced by
K. Diethelm, A.D. Freed, and discussed in book by K. Diethelm.
Keywords: R-L Fractional Derivative, Caputo Fractional Derivative, Adams-Bashforth-
Moulton Method, Fractional Differential Equations
ÖZ :
Kesirli analiz, klasik kalkülüs ile hemen hemen aynı tarihe sahiptir. Kesirli analiz uzun
bir süre dikkat çekmemesine ra˘gmen son yıllarda güçlü uygulama alanları oldu˘gu ortaya
çıktıktan sonra kesirli diferansiyel denklemler ile birlikte en popüler çalı¸sma alanları
olmu¸stur. Bununla birlikte kesirli kalkülüsü de kapsayan çok sayıda diferansiyel
model geli¸stirilmi¸stir. Birçok kesirli diferansiyel denklemlerin kesin çözümleri için
analitik metodlar yetersiz kalmaktadır. Bu nedenle sayısal yöntemlere dönmek gerekmektedir.
Bu tezin yapısı ¸su ¸sekilde düzenlenmi¸stir: Öncelikle klasik kalkülüsün bazı özellikleri
hatırlatılacaktır. ˙Ikinci kısımda gamma, beta, mittag-leffler gibi bazı özel fonksiyonların
tanım ve bazı özellikleri hatırlanacaktır. Daha sonra üçüncü bölümde kesirli
analizin tanım ve temel kavramları tanıtılacaktır. Bu kısım Abel integral denkleminin
çözüm ko¸sullarını, Riemann-Liouville kesirli integral ve türevinin temel sonuçlarını
ve Caputo kesirli türevinin tanım ve bazı temel özelliklerini içermektedir. Dördüncü
bölümde ise ikinci dereceden klasik Adams-Bashford-Moulton metodunun kesirli varyantını
tartı¸sıp, hata analizini yapılacaktır. Bu method K. Diethelm ve A.D. Freed tarafından
tanıtılmı¸s ve K. Diethelm tarafından yazılan kitapta bahsedilmi¸stir.
Anahtar kelimeler: R-L Kesirli Turev, Caputo Kesirli Turev, Adams-Bashforth-Moulton
Metodu, Kesirli Diferensiyel Denklemler.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Fractional calculus - Differential equations
Differential equations - Numerical solutions
R-L Fractional Derivative
Caputo Fractional Derivative
Adams-Bashforth-Moulton Method
Fractional Differential Equations Moulton Method
Fractional Differential Equations
Numerical Solutions of Fractional Differential Equations
masterThesis
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URL
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oai:i-rep.emu.edu.tr:11129/36592018-05-18T23:01:24Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Agamirza
author
Duranay, Recep
2018-05-18T10:48:22Z
2018-05-18T10:48:22Z
2014-09
2014-09
Duranay, Recep. (2014). Riemann Type Integration for Functions of One Real Variable . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3659
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Agamirza Bashirov.
In this thesis, process of Riemann integral is tackled. Firstly, theorems and their proofs
of Proper Riemann integral are explained. After that, improper Riemann integral with
the same proof techniques is handled. Riemann Steiltjes integral with examples and
theorems of continuous linear function in Riesz Representation theorem is explained.
Finally, Kurzweil-Henstock and Lebesgue integrals are handled with theorems and
proofs.
Keywords: Riemann Integral, Riemann Steiltjes Integral, Riesz Representation Theorem,
Kurzweil-Henstock and Lebesgue Integral
ÖZ :
Bu tezde Riemann integralinin ba¸slangıcından geli¸simin günümüze kadar olan süreci
i¸slenmi¸stir. ˙Ilk olarak teoremler ve ispatlarıyla has Riemann integrali açıklanmı¸stır.
Aynı ispat tekni˘gi ile sınırsız alanda has olmayan Riemann ˙Integrali ele alınmı¸stır.
Sürekli linear fonksiyonların Riesz gösteriminden yardım alarak Riemann Steiltjes integrali
anlatılmı¸stır. Son olarak Kurzweil-Henstock ve Lebesgue’nin uygulamarıyla
tezde amaçlanan hedefe ula¸sılmı¸stır.
Anahtar kelimeler: Riemann ˙Integral’i, Riemann Steiltjes ˙Integral’i, Riesz Gösterimi,
Kurzweil-Henstock ve Lebesgue˙Integral’i
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Integrals
Riemann Integral
Riemann Steiltjes Integral
Riesz Representation Theorem
Kurzweil-Henstock and Lebesgue Integral
Riemann Type Integration for Functions of One Real Variable
masterThesis
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URL
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oai:i-rep.emu.edu.tr:11129/38452018-06-20T23:01:50Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Agamirza
author
Azeez, Twana Yousif
2018-06-20T11:23:14Z
2018-06-20T11:23:14Z
2014-06
2014-06
Azeez, Twana Yousif. (2014). Euler Integrals. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3845
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Agamirza Bashirov.
Euler’s integral are two functions, called Beta and Gamma functions. They play
important role in mathematics and its applications. These functions are defined through
improper integrals and their properties depend on properties of improper integrals
depending on parameter. In this thesis, proper and improper integrals are reviewed,
Beta and Gamma functions are defined and their properties are presented.
Keywords: Euler integrals, Riemann integral, improper integral, Gamma function,
Beta function
Öz: Euler integralları Beta ve Gamma fonksyonlarıdır. Bunlar matematik ve onun
uygulamalarında önemli rol alırlar. Bu fonksiyonlar belirsiz integrallar olarak
tanımlanırlar ve özelliklerini parametreye bağlı belirsız integralların özelliklernden
alırlar. Bu tezde belirli ve belirsiz integrallar incelenmidir, Beta ve Gamma
fonksiyonları tanımlanmış ve özellikleri verilmelidir.
Anahtar Kelimeler: Euler integrallar, Riemann integralı, belirsiz integrallar, Gamma
fonksiyonu, Beta fonksiyonu.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Integrals
Numerical Integration
Gamma functions
Beta functions
Euler integrals
Riemann integral
improper integral
Euler Integrals
masterThesis
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oai:i-rep.emu.edu.tr:11129/38992018-07-27T23:00:57Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Agamirza
author
Jneid, Maher
2018-07-27T08:21:47Z
2018-07-27T08:21:47Z
2014-07
2014-07
Jneid, Maher. (2014). Partial Complete Controllability of Semilinear Control Systems. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3899
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Prof. Dr. Agamirza Bashirov.
This work is devoted to examining the partially complete controllability for deterministic
semilinear systems in Hilbert spaces. Besides reviewing briefly some existing
results of controllability concepts, two main sets of sufficient conditions for partial
controllability concepts are proved. The strategy in both results is based on the contraction
mapping principle which has played an effective role as the cornerstone of
studying controllability concepts for semilinear system, provided that the corresponding
linear system is partially complete controllable. The first one is simply obtained
by contraction mapping theorem. However, the second result uses the generalized
contraction mapping theorem. In the first part, we study the partially complete controllability
of deterministic semilinear systems for any positive time. The benefit of
this result is demonstrated on some appropriate examples. In the second part, we deal
with the same kind of deterministic semilinear systems but with additional condition
on the nonlinear part. By this technique, we can defeat the improper integral which
arises when we select a suitable control operator by which a generalized contraction
mapping theorem can be applied.
Keywords: Contraction mapping principle, complete controllability, partial controllability,
semilinear system.
Öz: Bu çalı¸sma, ayrılabilir Hilbert uzaylarında, deterministik yarı-lineer sistemler için, kısmen
tam kontrol edilebilirligi inceler. Bu tür kontrol edilebilirlik için, iki temel set ˘
yeterlilik ko¸sulu ispatlanmı¸stır. Her iki sonuçtaki strateji, yarı-lineer sistemlerde kontrol
edilebilirlik durumlarının incelenmesinde önemli rol oynayan büzülme dönü¸süm
esasına dayanmaktadır. ˙Ilk sonuç sadece büzülme dönü¸süm teoremi ile elde edilmi¸stir.
Ancak, ikinci sonuç genelle¸stirilmi¸s büzülme dönü¸süm teoremini kullanır. ˙Ilk kısımda,
herhangi bir pozitif zaman dilimi için, deterministik yarı-lineer sistemlerin kısmen tam
kontrol edilebilirligi incelenmi¸stir. Bu sonucun yararı, bazı uygun örnekler üzerinde ˘
gösterilmi¸stir. ˙Ikinci bölümde ise, deterministik yarı-lineer sistemlerin farklı bir türü,
lineer olmayan terimleri, zamana baglı bir yardımcı terimle çarpılarak incelenmi¸stir. ˘
Bu teknik ile, 1’den küçük Lipschitz katsayısını elde edebilmek için, ardarda integral
alımında ortaya çıkan, improper integral ortadan kaldırılmı¸s olur.
Anahtar kelimeler: Daralma e¸sleme özelligi, tam kontrol edilebilirlik, kısmi kontrol ˘
edilebilirlik , yarı- lineer sistem.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Hilbert space
Contraction mapping principle
complete controllability
partial controllability
semilinear system
Partial Complete Controllability of Semilinear Control Systems
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/37672018-06-14T23:01:21Zhdl_11129_66
EMU I-REP
advisor
Şemi, Nidai
author
Houag, Jean Martin
2018-06-14T06:30:09Z
2018-06-14T06:30:09Z
2016-12
2016-12
Houag, Jean Martin. (2016). Stochastic Processes and Markov Chain. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3767
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Nidai Şemi.
Andrey Andreyevich Markov is the founder of the Markov Chain. The Markov
Chain is a stochastic process involving modeling over time and space. In sciences or
randomize sciences in particular, it is usually important to predict an outcome based
on the acquired or previous knowledge of a process. There exits various random
processes. The Markov Chain appears as a key technique to deal and model such
processes.
Keywords: Stochastic Matrix, Probability Vector, Markov Chain.
Öz: Bu çalışmada, öncelikle ıstokastik süreçler tanımlanarak özellikleri verilmiş,
sonrasında da örneklerle ve uygulamalarla konu pekiştirilmeye çalışılmıştır. Daha
sonra da, Markov Zinciri tanımlanmış ve uygulama alanları verilmiş ve örneklerle
desteklenerek konu anlatılmıştır.
Anahtar kelimeler: Istokastik Matris, Olasılık Vektörü, Markov Zinciri.
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Stochastic Processes
Stochastic Matrix
Probability Vector
Markov Chain
Stochastic Processes and Markov Chain
masterThesis
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URL
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oai:i-rep.emu.edu.tr:11129/38352018-06-20T23:01:36Zhdl_11129_66
EMU I-REP
advisor
Oğurlu, Sonuç Zorlu
author
Arshad, Nouman
2018-06-20T10:08:13Z
2018-06-20T10:08:13Z
2017-02
2017-02
Arshad, Nouman. (2017). Fractional Mixed Volttera - Fredhol Integrodifferential Equation. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/3835
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Prof. Dr. Sonuç Zorlu Oğurlu.
In mathematics, an integrodifferential equation is an equation that involves both
integral and derivative of a function. These equations model many situation ranging
from science and engineering. A particular rich source is electrical circuit analysis.
Different techniques have been evolved for finding the solution of these differential
equations under certain conditions. One of them is to prove the existence and
uniqueness of mixed Volteraa-Fredholm type integral equation with the integral
boundary conditions in Banach Space. This has been worked on by some authors
such as S A Murad from Iraq, H J Zekri from Iraq, S Hadid from UAE.
Keywords: fixed point theorems; sequential fractional derivative; integral boundary
conditions; fractional differential equation
Öz: Matematikte integrodifferansiyel denklem, bir fonksiyonun hem integralini hem de
türevini içeren bir denklemdir. Bu denklemler birçok durumu bilim ve
mühendislikten modüle eder. Bu diferansiyel denklemlerin belirli koşullar altında
çözümünün bulunması için farklı teknikler geliştirilmiştir. Bunlardan biri, karışık
Volteraa-Fredholm tipi integral denkleminin Banach Uzayındaki integral sınır
koşullarıyla varlığını ve tekliğini kanıtlamaktır. Bu, Irak'tan S A Murad, yine Irak'tan
H J Zekri, Birleşik Arap Emirliği’nden S. Hadid gibi bazı yazarlarca çalışılmıştır.
Anahtar Kelimeler: sabit nokta teoremleri, kesirli türev, integral sınır koşulları,
integrodiferansiyel kesirli denklemler
eng
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Integro-differential equations
Fixed Point Theorems
Sequential Fractional Derivative
Integral Boundary Conditions
Fractional Differential Equation
Fractional Mixed Volttera - Fredhol Integrodifferential Equation
masterThesis
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oai:i-rep.emu.edu.tr:11129/40412019-04-26T05:14:37Zhdl_11129_66
EMU I-REP
advisor
Mahmudov, Nazim I.
author
Keleshteri, Marzieh Eini
2019-04-25T12:47:44Z
2019-04-25T12:47:44Z
2015-07
2015
Keleshteri, Marzieh Eini (2015). A Comprehensive Study on the Class of q-Appell Polynomials . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4041
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Nazim Mahmudov.
This thesis is aimed to study the q-analogue of the class of so called Appell polynomials
from different aspects and using various algebraic as well as analytic approaches. To
achieve this aim, not only many new results are found based on a proposed general
generating function for all members belonging to the aforementioned family of polynomials,
but also various relations between famous members of this family are derived. 2D q-Appell
polynomials as the q-Appell polynomials in two variables can be considered as another new
achievement of this thesis. In addition to the definition of the class of q-Appell polynomials
by means of their generating function, a determinantal representation, for the first time, is
proposed for indicating different members of the class of q-Appell polynomials. Moreover,
it is shown that how easy some results can be proved by using the new proposed linear
algebraic indication and applying basic properties of determinant. In the sequel, this family
of q-polynomials are studied also from q-umbral point of view and many interesting results
are found based on this algebraic approach.
Keywords: q-Appell, q-Calculus, Determinatal, q-Umbral, q-Polynomilas, q-Apostol, q-
Bernoulli, q-Euler, q-Genocchi, q-Hermite.
Öz:Bu tez farklı açılardan ve çeşitli cebirsel yanı sıra analitik yaklaşımlar kullanarak q-Appell
polinomların sınıfının incelenmesini amaçlanmaktadır. Bu amaca ulaşmak için, yukarıda
belirtilen q-Appell polinomlar ailesine ait tüm üyeler üyeleri arasında çeşitli ilişkiler elde
edilmektedir. İki değişkenli q-Appell polinomları olarak 2D q-Appell polinomları bu tezin
yeni bir başarı olarak kabul edilebilir. Ayrıca, bazı sonuçlar yeni önerilen lineer cebirsel
gösterge kullanılarak ve determinantın temel özelliklerini uygulanarak ispat edilebilir.
Ayrıca, bu tezde q-polinomların birçok ilginç özellikleri q-umbral açısından da
incelenmiştir.
Anahtar Kelimeler: q-Appell, q-Matematik, q-Umbral, q-Polynomlar, q-Apostol, q-
Bernoulli, q-Euler, q-Genocchi, q-Hermite.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
q-Appell
q-Umbral
q-Polynomilas
q-Apostol
q-Bernoulli
q-Euler
q-Genocchi
q-Hiteerm
Determinatal
q-Calculus
A Comprehensive Study on the Class of q-Appell Polynomials
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/40392019-04-25T23:01:46Zhdl_11129_66
EMU I-REP
advisor
Mahmudov, Nazım
author
Khaleel, Hogir Ageed
2019-04-25T12:28:34Z
2019-04-25T12:28:34Z
2015-09
2015
Khaleel, Hogir Ageed. (2015).On Fractional Differential Equations . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4039
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Nazım Mahmudov.
In this thesis, we collect some results on sufficient conditions for the existence and unique of solutions for various classes of initial and boundary value problem for fractional differential equations involving the Caputo fractional derivative. Although the tools of fractional calculus have been available and applicable to various fields of study, the investigation of the theory of fractional differential equations has only been started quite recently. The differential equations involving Caputo differential operators of fractional order, appear to be important in modeling several physical phenomena and therefore seem to deserve an independent study of their theory parallel to the well-known theory of ordinary differential equations.
In this thesis, we shall study systematically the basic theory of fractional differential equations involving Caputo differential operators. We follow the method of deducing the basic existence and uniqueness results from the fixed point theory.
Keywords: Boundary Value Problems, Fractional Differential Equation, Fractional Calculus
ÖZ:
Bu tezde, Caputo fraksiyonel türevli fraksiyonel diferansiyel denklemler için başlangıç ve sınır değer probleminin çeşitli sınıflar için varlığı ve tekliği araştırılmıştır. Kesirli analizin araçları, çalışmanın çeşitli alanlarda kullanılabilir ve uygulanabilir olmasına rağmen, fraksiyonel diferansiyel denklemlerin teorisi sadece çok yakın zamanda araştırılmaya başlanmıştır. Fraksiyonel düzenin Caputo diferansiyel operatörleri kapsayan diferansiyel denklemler, çeşitli fiziksel olguları modelleme de önemli gibi görünmektedir ve bu nedenle adi diferansiyel denklemlerin tanınmış teoriye kendi teorisi paralel bağımsız bir çalışma yı haketmekte gibi görünüyor.
Bu tezde, sistematik olarak Caputo diferansiyel operatörleri kapsayan fraksiyonel diferansiyel denklemlerin temel teorisini incelenecektir.
Anahtar Kelimeler: Sınır değer problemi, Fraksiyonel diferansiyel denklemler, Fraksiyonel kalkulus
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Fractional calculus-Differential equations
Differential equations-Numerical solutions
Boundary Value Problems
Fractional Differential Equation
Fractional Calculus
On Fractional Differential Equations
masterThesis
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oai:i-rep.emu.edu.tr:11129/41122019-05-03T23:01:43Zhdl_11129_66
EMU I-REP
advisor
Mahmudov, Nazim
author
Jangeer, Abdullah Hasan
2019-05-03T06:58:56Z
2019-05-03T06:58:56Z
2015-09
2015
Jangeer, Abdullah Hasan. (2015). Integral Type Fractional Gronwall Inequalities. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4112
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Nazim Mahmudov.
The current research involves the ideas and principles about integral inequalities of Gronwall type. It deals with the possibilities that we mathematicians use in order to solve equations in various ways. The first case we adopted to solve equations is Linear Generalization. The latter deals with equations that are different from those treated with Non-Linear Generalization.
The research we conduct overlaps to study the relation between fractional and Gronwall inequalities by analyzing how Gronwall inequalities are included and used in fractional inequalities.
Keywords: Gronwall inequalities, Fractional inequalities, Linear generalizations and Non-Linear generalizations.
ÖZ:
Mevcut araştırma Gronwall Çeşidi integral eşitsizlikler hakkında fikir ve ilkeleri içermektedir. Biz matematikçiler çeşitli şekillerde denklemleri çözmek için kullanmak olasılıklar ile ilgilenir. Biz denklemleri çözmek için kabul edilen ilk vaka Doğrusal Genelleme olduğunu. Doğrusal Olmayan Genelleme ile tedavi farklıdır denklemler ile ikinci fırsatlar.
Yaptığımız araştırmalar Gronwall eşitsizlikler dahil ve fraksiyonel eşitsizliklerin nasıl kullanıldığını analiz ederek fraksiyonel ve Gronwall eşitsizlikler arasındaki ilişkiyi incelemek için örtüşür.
Anahtar Kelimeler: Gronwall eşitsizlikler, Fraksiyonel eşitsizlikler, lineer genellemeler ve Doğrusal Olmayan genellemeler.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Gronwall inequalities
Gronwall inequalities
Fractional inequalities
Linear generalizations and Non-Linear generalizations
Integral Type Fractional Gronwall Inequalities
masterThesis
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oai:i-rep.emu.edu.tr:11129/41142019-05-03T23:00:56Zhdl_11129_66
EMU I-REP
advisor
Rıza, Mustafa
author
Aktöre, Hatice
2019-05-03T07:10:59Z
2019-05-03T07:10:59Z
2015-09
2015
Aktöre, Hatice. (2015). Numerical Approximation Methods using Multiplicative Calculus . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4114
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
In this thesis, the 2nd, 3rd and 4th order multiplicative Runge-Kutta Methods are developed
in analogy to the classical Runge-Kutta Method. The error analysis is only
carried out for the 4th order multiplicative Runge-Kutta method based on the convergence
and stability analysis. The convergence behaviour of the developed multiplicative
Runge-Kutta method is analysed by examining examples of initial value problems
with closed form solutions, as well as problems without closed form solutions. The
obtained results are also compared to the results obtained from the solutions of the
classical Runge-Kutta method for the same examples. The error analysis shows that
the solutions of the multiplicative Runge-Kutta methods give better results especially
when the solution has an exponential nature. The modified quadratic Lorenz attractor
is developed to examine the applicability of the proposed multiplicative Runge-Kutta
method on the chaotic systems. The chaotic system is analysed numerically for its
chaotic behaviour. Finally, the chaotic system is transformed into the corresponding
system in terms of multiplicative calculus and the analysis are also done based on the
rules of the multiplicative calculus. The results of the analysis show that the multiplicative
Runge-Kutta method is also applicable to multiplicative chaotic systems.
Keywords: Multiplicative calculus, complex multiplicative calculus, Runge-Kutta,
differential equations, numerical approximation, dynamical systems.
ÖZ:
Bu tezde, 2. ,3. ve 4. derece Runge-Kutta metodları temelinde çarpımsal analiz kuralları
kullanılarak 2. ,3. ve 4. dereceden çarpımsal Runge-Kutta yöntemleri bulunmu¸s
ve incelenmi¸stir. Bulunan yöntemlerin hata analizleri, yakınsaklık ve istikrarlılık analizleri
temel alınarak yapılmı¸stır. Bulunan metodların yakınsaklık özellikleri, çözümleri
bilinen ve bilinmeyen diferansiyel denklemler çözülerek gösterilmi¸stir. Çözümleri
bilinen adi diferansiyel denklemler, çarpımsal Runge-Kutta ve Runge-Kutta yöntemleri
kullanılarak çözülmü¸s ve hata analizleri yapılmı¸stır. Bu sonuçlara göre, özellikle
çözümü eksponensiyel olan denklemlerde, çarpımsal Runge-Kutta metodunun bilinen
Runge-Kutta metoduna göre daha iyi sonuçlar verdi˘gi görülmü¸stür. Son olarak da
çarpımsal Runge-Kutta metodlarının karma¸sık sistemler üzerinde uygulanabildi˘gini
göstermek için karma¸sık bir sistem bulunmu¸s ve numerik olarak incelenmi¸stir. Daha
sonra bulunan sistem çarpımsal analiz kurallarına göre düzenlenmi¸s ve çarpımsal Runge-
Kutta yöntemleri kullanılarak çözülmü¸stür. Elde edilen sonuçlar bulunan yöntemlerin
karma¸sık sistemler üzerinde de kullanılabilece˘gini göstermi¸stir.
AnahtarKelimeler: Çarpımsal analiz, kompleks çarpımsal analiz, Runge-Kutta, diferansiyel
denklemler, numerik yakınsama, dinamik sistemler.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Multiplicative calculus
complex multiplicative calculus
Runge-Kutta
differential equations
numerical approximation
dynamical systems
Numerical Approximation Methods using Multiplicative Calculus
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/41192019-05-03T23:01:38Zhdl_11129_66
EMU I-REP
advisor
Rıza, Mustafa
author
Eminağa, Buğçe
2019-05-03T09:23:22Z
2019-05-03T09:23:22Z
2015-09
2015
Eminağa, Buğçe. (2015). Bigeometric Taylor Theorem and its Application to the Numerical Solution of Bigeometric Differential Equations . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4119
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Assist. Prof. Dr. Mustafa Rıza.
Many studies in the field of Bigeometric Calculus are based on an approximation to the
Bigeometric Taylor series, as the correct version is not known. The Bigeometric Taylor
Series introduced in this research, is derived and proven explicitly. As an application
of the Bigeometric Taylor Series, the Bigeometric Runge-Kutta method is derived in
analogy to the classical Runge-Kutta method. The stability, as well as the convergence
analysis is given explicitly for Bigeometric Runge-Kutta method. Application of the
Bigeometric Runge-Kutta method to problems with known closed form solutions show
the advantage of this method for a certain family of problems compared to the classical
Runge-Kutta Method.
Keywords: Bigeometric calculus, Runge-Kutta, differential equations, numerical approximation,
dynamical systems,electirical circuits.
ÖZ:
Bigeometrik alanında yapılan birçok çalı¸smada Bigeometrik Taylor serisi do˘gru analiz
edilmeden kullanılmı¸stır. Bu çalı¸smada Bigeometrik Taylor Serisinin ispatı açık olarak
verilmi¸stir. Bigeometrik Taylor Serisinin bir uygulaması olarak, Bigeometric Runge-
Kutta yöntemi nümerik analizde bilinen Runge-Kutta yöntemi baz alınarak çıkarılmı¸stır.
Ayrıca Bigeometric Runge-Kutta yöntemi için yakınsak ve kararlılık testleri de analiz
edilmi¸stir. Yöntem dinamik sistemler, bioloji ve elektrik devrelerinde uygulanmı¸s ve
Bigeometrik Runge Kutta ile elde edilen sonuçlar nümerik analizde bilinen Runge-
Kutta yöntemi ile kar¸sıla¸stırılmı¸stır.
Anahtar Kelimeler: Çarpımsal analiz„ Runge-Kutta, diferansiyel denklemler, numerik
yakınsama, dinamik sistemler, elektrik devreleri.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Bigeometric calculus
Runge-Kutta
differential equations
numerical approximation
dynamical systems
electirical circuits
Bigeometric Taylor Theorem and its Application to the Numerical Solution of Bigeometric Differential Equations
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/41252019-05-03T23:04:14Zhdl_11129_66
EMU I-REP
advisor
Özarslan, Mehmet Ali
author
Vedi, Tuba
2019-05-03T11:07:51Z
2019-05-03T11:07:51Z
2015-09
2015
Vedi, Tuba. (2015). Approximation Properties of Schurer Type q-Bernstein Operators. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4125
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Mehmet Ali Özarslan.
This thesis consist of five chapters. In the first chapter, the introduction is given. In the
second chapter, we consider the Chlodowsky variant of q-Bernstein-Schurer-Stancu
operators. We state the Korovkin type approximation theorem and obtain the error of
approximation by using modulus of continuity and Lipschitz-type functionals. Moreover,
we obtain the rate of approximation in terms of the first derivative of the function
and we examine the generalization of the operators.
In the third chapter, we define Chlodowsky type q-Bernstein-Stancu-Kantorovich operators.
Many properties and results of these polynomials, such as Korovkin type approximation
and the rate of convergence of these operators in terms of Lipschitz class
functional are given.
In the fourth chapter, we introduce and study Chlodowsky-Durrmeyer type q-Bernstein-
Schurer-Stancu operators. We state the Korovkin-type approximation theorem and obtain
the order of convergence of the operators.
In the last chapter, we define two dimensional Chlodowsky type of q-Bernstein-Schurer-
Stancu operators. We study Korovkin-type approximation theorem and state the error
of approximation by using full and partial modulus of continuity. Finally, we define
the generalization of the operators and investigate their approximation properties in
weighted space.
Keywords: Chlodowsky variant of q-Bernstein-Schurer-Stancu operators, Chlodowsky
type q-Bernstein-Stancu-Kantorovich, Chlodowsky-type q-Durrmeyer operators.
ÖZ:
Bu tez be¸s bölümden olu¸smaktadır. Birinci bölüm giri¸s kısmına ayrılmı¸stır. ˙Ikinci
bölümde, Chlodowsky tipli q-Bernstein-Schurer-Stancu Operatörleri tanımlanmı¸stır.
Korovkin tipli teorem yakla¸sımı ispatlanmı¸s ve fonksiyonun yakınsaklı˘gındaki hatalar
süreklilik modülü yardımıyla ve Lipschitz sınıfındaki yakınsaklı˘gı incelenmi¸stir.
Üçüncü bölümde Chlodowsky tipli q-Bernstein-Stancu-Kantorovich Operatörleri tanımlanmı
¸stır. Bu operatörlerin Korovkin tipli yakla¸sım teoremi ve Lipschitz tipli fonksiyonların
yakınsaklık hızları gibi özellikler incelenmi¸stir.
Dördüncü bölümde, Chlodowsky-Durrmeyer tipli q-Bernstein-Schurer-Stancu Operatörleri
tanımlanmı¸stır. Korovkin tipli yakınsaklık teoremi verilmi¸s ve yakınsamanın
yakınsaklık derecesi incelenmi¸stir.
Be¸sinci bölümde, iki de˘gi¸skenli Chlodowsky tipli q-Bernstein-Schurer-Stancu Operatörleri
tanımlanmı¸stır. Korovkin tipli yakınsaklık teoremi verilmi¸s, fonksiyonun süreklilik
modülü ve kısmi süreklilik modülü yardımıyla yakınsama hızları hesaplanmı¸stır. Son
olarak, operatörlerin bir genelle¸stirilmesi verilmi¸s ve onların a˘gırlıklı uzaydaki yakla
¸sım özellikleri inclenmi¸stir.
AnahtarKelimeler: Chlodowsky tip q-Bernstein-Schurer-Stancu Operatörleri, Chlodowsky
tip q-Bernstein-Stancu-Kantorovich Operatörleri, Chlodowsky Tip q-Durrmeyer Operatörleri.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Chlodowsky variant of q-Bernstein-Schurer-Stancu operators
Chlodowsky type q-Bernstein-Stancu-Kantorovich
Chlodowsky-type q-Durrmeyer operators
Approximation Properties of Schurer Type q-Bernstein Operators
doctoralThesis
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URL
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oai:i-rep.emu.edu.tr:11129/41272019-05-03T23:04:14Zhdl_11129_66
EMU I-REP
advisor
Bashirov, Agamirza
author
Ghahramanlou, Noushin Houshyar
2019-05-03T11:29:13Z
2019-05-03T11:29:13Z
2015-09
2015
Ghahramanlou, Noushin Houshyar. (2015). Partial Approximate Controllability of Semilinear Control Systems. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4127
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Agamirza Bashirov.
Most of the controllability concepts are for first ordered differential equations, while
not all the control systems are of this kind; but by increasing the dimension of the
state space, one can rewrite the control system in the form of first ordered differential
equations. Therefore, it seems useful to define partial controllability concepts which
maintain the original state space. In this thesis, a sufficient condition for partial approximate
controllability of semilinear deterministic control systems is proved with a
technique which is completely different from the methods using fixed point theorems.
More specifically, the partial S-controllability has been weakened for partially observable
semilinear stochastic systems and a sufficient condition is provided. The results
obtained are demonstrated within examples.
Keywords: Controllability, approximate controllability, exact controllability, partial
controllability, semilinear systems, stochastic systems.
ÖZ:
Kontrol edilebilirlik kavramlarının ço˘gu, birinci dereceden diferansiyel denklemlerı
içeren kontrol sistemleri için formüle edilmi¸stir. Do˘gadaki bütün diferansiyel denklem
sistemleri bu tür de˘gildir, ama alanın boyutunu geni¸sleterek bu formda yazılmı¸s
olabilir. Bu nedenle, orijinal alanı korumak kısmi kontrol edilebilirlik kavramları
tanımlamak yararlı görünüyor. Bu tezde, yarı-lineer deterministik kontrol sistemlerinin
kısmi yakla¸sık kontrol edilebilirlik için yeterli bir ko¸sul, sabit nokta teoremleri
yöntemlerinden tamamen farklı bir teknik ile kanıtlanmı¸stır. Dahası, kısmen gözlemlenebilir
yarı-lineer stokastik sistemleri için zayıflatılmı¸s kısmi S-kontrol edilebilirlik
incelenmi¸s ve bu kontrol edilebilirlik kavramı için yeterli bir ko¸sul sa˘glanmı¸stır. Elde
edilen sonuçlar, örneklerle gösterilmi¸stir.
Anahtar Kelimeler: Kontrol edilebilirlik, yakla¸sık kontrol edilebilirlik, tam kontrol
edilebilirlik, kısmi kontrol edilebilirlik, yarı-lineer sistemler, stokastik sistemler.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Mathematics
Applied Mathematics and Computer Science
Controllability
approximate controllability
exact controllability
partial controllability
semilinear systems
stochastic systems
Partial Approximate Controllability of Semilinear Control Systems
doctoralThesis
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GhahramanlouNoushin Houshyar.pdf.txt
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oai:i-rep.emu.edu.tr:11129/41802019-10-22T23:02:39Zhdl_11129_66
EMU I-REP
advisor
Tandoğdu, Yücel
author
Shabir, Ahmad
2019-10-22T11:46:23Z
2019-10-22T11:46:23Z
2017-09
2017
Ahmad, Shabir. (2017). Relationship between Principal Component Analysis and Factor Analysis. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4180
Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Assist. Prof. Dr. Yücel Tandoğdu.
In every field of scientific research and application, where the masses of data is available in multivariate form, the use of multivariate statistical analysis techniques can be implemented to achieve proper statistical inferences. The statistical modeling of data is the essential part of the multivariate analysis. The model might be the linear combinations of the original data, which can be created though the relationship between Principal Component Analysis (PCA) and Factor Analysis (FA). Such process of converting the entire data into the set of few clusters or linear models is called dimension reduction. Before applying FA, the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy test for FA is used (12). Initial factor loadings and the variamx rotated factor loadings are computed via PCA approach. The estimated factor models generated by ordinary least square method, are further used for statistical control charts. Finally the generation of the uncorrelated statistical models using the relationship between PCA and FA is carried out to enable the estimation of the future outcomes.
Keywords: Correlation matrix, KMO test, Reducible Eigen space, dimension reduction, varimax rotation, uncorrelated statistical models, OLS estimated factor scores, statistical control charts.
ÖZ:
Bilimsel araştırma ve uygulamanın her alanında, çok değişkenli verilerin var olduğu durumlarda, en uygun sonuçlar çok değişkenli istatistik analiz yöntemleri ile elde edilebilir. Verilerin istatistikslel modellemesi çok değişkenli analizin temel unsurudur. Bu modelleme Temel Bileşenler Analizi (TBA) ve Faktör Analizi (FA) arasındaki ilişkiden yararlanarak veriler arasında doğrusal kombinasyonların oluşturulması şeklinde olabilir. Verilerin alt gruplara veya doğrusal modellere dönüştürülmesine boyut indirgeme denir. FA yapılmadan önce, verilerin FA’ya uygunluğunun saptanması için Kaiser-Meyer-Olkin (KMO) ölçüm hesabı yapılır. İlk faktör yükleri ve varimax metodu ile dönüşümü yapımış faktör yükleri TBA yaklaşımı ile hesaplanır. Minimum kareler yöntemi ile tahmin edilmiş faktör modeli istatistiksel control grafiklerinin oluşturulmasında kullanıldı. Son olarak TBA ve FA arasındaki ilişki kullanılarak ileriki oluşumların tahmininde kullanılmak üzere bağımsız istatistiksel modeller oluşturulmuştur.
Anahtar kelimeler: Korelasyon matrisi, KMO test, indirgenebilir Eigen uzayı, boyut indirgeme, varimaks döndürümü, enküçük kareler metodu ile tahmin edilmiş faktör skorları, istatistiki Kontrol grafikleri.
eng
Eastern Mediterranean University EMU
info:eu-repo/semantics/openAccess
Principal components analysis
Correlation matrix
KMO test
Reducible Eigen space
dimension reduction
varimax rotation
uncorrelated statistical models
OLS estimated factor scores
statistical control charts
Mathematics
Relationship between Principal Component Analysis and Factor Analysis
masterThesis
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URL
http://i-rep.emu.edu.tr:8080/xmlui/bitstream/11129%2F4180/3/ahmadshabir.pdf.txt
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oai:i-rep.emu.edu.tr:11129/42202019-12-26T00:02:14Zhdl_11129_66
EMU I-REP
advisor
Özarslan, Mehmet Ali
author
Kürt, Cemaliye
2019-12-25T12:55:43Z
2019-12-25T12:55:43Z
2017-09
2017
Kürt, Cemaliye. (2017). Some Results on Laguerre Type and Mittag-Leffler Type Functions. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4220
Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Prof. Dr. Mehmet Ali Özarslan.
This thesis includes four chapters. In the first chapter, we give general information and
some preliminaries that is used throughout the thesis.
In Chapter 2, by defining a new class of 2D-Mittag-Leffler functions E(a;b;h;x ;l)
g;k (x;y)
and 2D-Laguerre polynomials L(a;b;g;h;x )
n;m (x;y), the two-dimensional fractional integral
and two-dimensional fractional derivative properties are derived for them. Moreover,
linear generating function for L(a;b;g;h;x )
n;m (x;y) in terms of E(a;b;h;x ;l)
g;k (x;y) is
obtained. Also, the double Laplace transform of these classes are investigated. A general
singular integral equation containing L(a;b;g;h;x )
n;m (x;y) in the kernel is considered
and the solution is obtained in terms of E(a;b;h;x ;l)
g;k (x;y). Lastly, we obtain the image
of E(a;b;h;x ;l)
g;k (x;y) under the action of Marichev-Saigo-Maeda integral operators and
some consequences are also exhibited.
In Chapter 3, linear and mixed multilateral generating functions for the general class
of 2D-Laguerre polynomials L(a;b;g;h;x )
n;m (x;y) are derived. Furthermore, a finite summation
formula for L(a;b;g;h;x )
n;m (x;y) is obtained. Moreover, series relation between
L(a;b;g;h;x )
n;m (x;y) and product of confluent hypergeometric functions is derived with
the help of two-dimensional fractional derivative operator.
In Chapter 4, new classes of bivariate Mittag-Leffler functions E(g)
a;b;k (x;y) and 2DKonhauser-
Laguerre polynomials kL(a;b)
n (x;y) are introduced. Some of them associated
with fractional calculus are given. Also, a convolution type integral equation with
the polynomials kL(a;b)
n (x;y) in the kernel is considered and the solution is obtained
by means of E(g)
a;b;k (x;y). Furthermore, a double linear generating function is obtained
for the polynomials kL(a;b)
n (x;y) in terms of E(g)
a;b;k (x;y). Finally, some miscellaneous
properties of E(g)
a;b;k (x;y) and kL(a;b)
n (x;y) are exhibited.
Keywords: Mittag-Leffler functions, Laguerre and Konhauser polynomials, Laplace
transform, fractional integrals and derivatives, generating functions, convolution integral
equation, singular integral equation
ÖZ:
Bu tez 4 bölümden olu¸smaktadır. Birinci bölümde tez ile ilgili genel bilgiler ve tezde
kullanılan tanımlar hakkında bilgiler verilmi¸stir.
˙Ikinci bölümde, 2D-Mittag-Leffler fonksiyonları E(a;b;h;x ;l)
g;k (x;y) ve 2D-Laguerre polinomları
L(a;b;g;h;x )
n;m (x;y) tanımlanarak, yukarıda belirtilen sınıfların kesirli integral ve
türevleri hesaplanmı¸stır. Buna ek olarak, 2D-Laguerre polinomları L(a;b;g;h;x )
n;m (x;y)
için 2D-Mittag-Leffler fonksiyonlarını E(a;b;h;x ;l)
g;k (x;y) içeren linear do˘gurucu fonksiyon
elde edilmi¸stir. Ayrıca, bu sınıfların iki boyutlu Laplace dönü¸sümleri de hesaplanmı¸stır.
Çekirde˘ginde L(a;b;g;h;x )
n;m (x;y) bulunan tekil integral denklemi ele alınmı¸s ve çözümü
E(a;b;h;x ;l)
g;k (x;y) cinsinden verilmi¸stir. Son olarak, E(a;b;h;x ;l)
g;k (x;y) fonksiyonlarının
Marichev-Saigo-Maeda integral operatörü altındaki görüntüleri elde edilmi¸s ve bazı
sonuçlar gösterilmi¸stir.
Üçüncü bölümde, 2D-Laguerre polinomları olarak tanımlanan L(a;b;g;h;x )
n;m (x;y) için
linear ve multi-linear do˘gurucu fonksiyonlar elde edilmi¸stir. Buna ek olarak,
L(a;b;g;h;x )
n;m (x;y) polinomları için sonlu toplam formülü elde edilmi¸stir. Bunun yanında,
kesirli türev operatörü kullanarak, L(a;b;g;h;x )
n;m (x;y) ve birbirine karı¸san hipergeometrik
fonksiyon arasındaki seri ili¸skisi gösterilmi¸stir.
Dördüncü bölümde, 2D-Konhauser-Laguerre polinomları kL(a;b)
n (x;y) ve yeni tanımlanan
iki de˘gi¸skenli Mittag-Leffler fonksiyonları E(g)
a;b;k (x;y) ele alınarak, onların kesirli
türev ve integrallerle ilgili bazı sonuçları hesaplanmı¸stır. Ayrıca çekirde˘ginde
kL(a;b)
n (x;y) içeren konvolüsyon integral denklemi ele alınmı¸s ve çözümü E(g)
a;b;k (x;y)
v
cinsinden elde edilmi¸stir. Bunun yanında kL(a;b)
n (x;y) polinomları için E(g)
a;b;k (x;y)
içeren linear do˘gurucu fonksiyon elde edilmi¸stir. Son olarak ise, E(g)
a;b;k (x;y) fonksiyonları
ve kL(a;b)
n (x;y) polinomları ile ilgili bir takım özellikler gösterilmi¸stir.
Anahtar Kelimeler: Mittag-Leffler fonksiyonları, Laguerre ve Konhauser polinomları,
Laplace dönü¸sümleri, kesirli integraller ve türevler, üreten fonksiyonlar, konvolüsyon
integral denklemi, tekil integral denklemi
eng
Eastern Mediterranean University EMU - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Mittag-Leffler functions
Laguerre and Konhauser polynomials
Laplace transform
fractional integrals and derivatives
generating functions
convolution integral equation
singular integral equation
Some Results on Laguerre Type and Mittag-Leffler Type Functions
doctoralThesis
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oai:i-rep.emu.edu.tr:11129/42752020-01-28T00:02:38Zhdl_11129_66
EMU I-REP
advisor
Oğurlu, Sonuç Zorlu
author
Mohamed, Ahmed
2020-01-27T13:11:16Z
2020-01-27T13:11:16Z
2017-07
2017
Mohamed, Ahmed. (2017). Quantum Calculus on Finite Intervals and Applications to Impulsive Difference Equations. Thesis (M.S.), Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, Famagusta: North Cyprus.
http://hdl.handle.net/11129/4275
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Prof. Dr. Sonuç Zorlu Oğurlu.
In Mathematics, quantum calculus is a version of calculus in which limits are not
taken. This type of calculus plays important role both in theoretical and practical
areas of mathematics. In quantum calculus, derivatives are differences and anti
derivatives are sums. Quantum calculus is a theory where smoothness is no more
needed. In this work, we study finite intervals in quantum calculus. We review and
study the -derivative and -integral of a function and demonstrate their properties.
We apply this concept to provide existence and uniqueness results for the initial
value problems, namely for first and second order impulsive -difference equations.
Keywords: -derivative, - integral, impulsive -difference equation, existence,
uniqueness.
ÖZ :
Matematikte q-Kalkülüs, Kalkülüsda limitlerin alınmadığı bir versiyonudur. Bu tür
matematik birçok teorik ve pratik alanda önemli rol oynamaktadır. Kuantum
Kalkülüsda türevler fark ve integral ise toplam olarak tanımlanır. Kuantum Kalkülüs
düzgünlüğün gerekli olmadığı bir teoridir. Bu çalışmada, kuantum Kalkülüsın sınırlı
aralıkları dikkate alınmıştır. Ayrıca, bu tezde bir fonksiyonun türevini ve
integralini inceleyip özellikleri verilmiştir. Bu kavram, baslangıç-değer
problemlerinin varlık ve teklik sonuçları üzerinde uygulanmıştır. Özelde birinci ve
ikinci dereceden impulsif -fark denklemleri dikkate alınmıştır.
Anahtar Kelimeler: varlık, teklik, -türev, - integral, impulsive -fark denklemi
eng
Eastern Mediterranean University EMU - Doğu Akdeniz Üniversitesi (DAÜ)
info:eu-repo/semantics/openAccess
Mathematics
Calculus-Mathematics
qj-derivative
qj- integral
impulsive qj-difference equation
existence
uniqueness
Quantum Calculus on Finite Intervals and Applications to Impulsive Difference Equations
masterThesis
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0001-01-01T00:00:00Z/9999-12-31T23:59:59Z/hdl_11129_66/mets/100