2024-03-28T14:32:09Zhttp://i-rep.emu.edu.tr:8080/oai/request
oai:i-rep.emu.edu.tr:11129/19912016-01-19T00:00:14Zhdl_11129_784Validation of signaling pathways: case study of the p16-mediated pathwayAkçay, Nimet İlkeBashirov, RzaTüzmen, ŞükrüSignaling pathwayp16-mediated pathwayHybrid functional Petri netQuantitative modelingp16 is recognized as a tumor suppressor gene due to the prevalence of its genetic inactivation in all types of human cancers. Additionally, p16 gene plays a critical role in controlling aging, regulating cellular senescence, detection and maintenance of DNA damage. The molecular mechanism behind these events involves p16-mediated signaling pathway (or p16-Rb pathway), the focus of our study. Understanding functional dependence between dynamic behavior of
biological components involved in the p16-mediated pathway and aforesaid molecular-level events might suggest possible implications in the diagnosis, prognosis and treatment of human cancer. In the present work, we employ reverse-engineering approach to construct the most detailed computational model of p16-mediated pathway in higher eukaryotes. We implement experimental data from the literature to validate the model, and under various assumptions predict the dynamic behavior of p16 and other biological components by interpreting the simulation results. The quantitative model of p16-mediated pathway is created in a systematic
manner in terms of Petri net technologies.The file in this item is the post-print version of the article (author’s copy; author’s final manuscript, accepted for publication after peer-review process). Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI (with DOI: 10.1142/S0219720015500079) and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Journal of Bioinformatics and Computational Biology, World Scientific Publishing2016-01-18T10:19:36Z2016-01-18T10:19:36Z2015ArticleAkcay, Nimet Ilke, Bashirov, Rza, Tuzmen, Sukru (2015) Validation of signalling pathways: case study of the p16-mediated pathway, Journal of Bioinformatics and Computational Biology, Imperial College Press, 13(2) DOI:10.1142/S0219720015500079 (indexed in SCIE).0219-72001757-6334DOI: 10.1142/S0219720015500079http://dx.doi.org/10.1142/S0219720015500079http://hdl.handle.net/11129/1991en_US
oai:i-rep.emu.edu.tr:11129/19922016-01-18T11:15:32Zhdl_11129_784Analyzing permutation capability of multistage interconnection networks with colored Petri netsBashirov, RzaCrespi, ValentinoMultistage interconnection networkPermutation capabilityColored Petri netCPNToolsIn a multistage interconnection network (MIN) the calculation of the number of permutations of the input terminals into the output terminals is a classic difficult problem.
In this paper, we introduce an innovative technique based on Colored Petri Nets
(known as CP-nets or CPNs) that will allow us to analyze the permutation capability
of arbitrary MINs. We show how to verify whether a MIN is rearrangeable through
the state space analysis of the associated CP-net and we measure the permutation capability of non-rearrangeable MINs in terms of the permutations that can be generated. The proposed approach takes advantage of powerful existing software tools, particularly, CPNTools, which is used to explore the occurrence graphs of CP-nets and determine the set of permutations performed by the modeled MINs. This new technique is easy to use and can be efficiently applied to MINs made of cross-bar switches.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI (with DOI: 10.1016/j.ins.2005.12.012) and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Information Sciences, Elsevier2016-01-18T10:35:00Z2016-01-18T10:35:00Z2006ArticleBashirov, R., Crespi, V. (2006) Analyzing permutation capability of multistage interconnection networks with colored Petri nets, Information Sciences, Elsevier, 176, 3143-3165 (indexed in SCI).0020-0255DOI: 10.1016/j.ins.2005.12.012http://dx.doi.org/10.1016/j.ins.2005.12.012http://hdl.handle.net/11129/1992en_US
oai:i-rep.emu.edu.tr:11129/19962016-01-18T12:46:49Zhdl_11129_784Exploiting colored Petri nets to decide on permutation admissibilityBashirov, RzaKordon, FabriceLort, HüseyinPermutation admissibilityMultistage interconnection networkIn this work, we propose an innovative approach to investigate the admissibility
of permutations to multistage interconnection networks — a challenging problem of switching theory. The proposed approach is centered upon modeling of multistage interconnection networks with colored Petri nets and use of Petri net analysis tools such as the unfolding
technique and the invariants method. To assess the feasibility of the proposed approach we demonstrate that the complete unfoldings obtained in this work are polynomial in the problem size and employ an acyclic structure. The approach takes advantage of easy to use, yet extremely efficient, software tools.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI (with DOI: 10.1007/s00236-008-0084-1) and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Acta Informatica, Springer2016-01-18T12:46:37Z2016-01-18T12:46:37Z2009ArticleBashirov, R., Kordon, F., Lort, H. (2009) Exploiting colored Petri nets to decide on permutation admissibility, Acta Informatica, Springer Berlin/Heidelberg, 46, 43-55 (indexed in SCI).1432-0525 (online)0001-5903 (print)DOI: 10.1007/s00236-008-0084-1http://dx.doi.org/10.1007/s00236-008-0084-1http://hdl.handle.net/11129/1996en_US
oai:i-rep.emu.edu.tr:11129/19972016-01-19T00:00:31Zhdl_11129_784On path dependent loss and switch crosstalk reduction in optical networksBashirov, RzaOptical interconnection networkPath dependent lossSwitch crosstalkPermutation admissibilityP/T-netP-invariantsAlthough optical multistage interconnection networks (OMINs) promise to meet the ever
growing demands of communication networks and multiprocessor systems in fast communication, they suffer from challenges such as path dependent loss and switch crosstalk. In this paper, we propose an innovative approach for reducing not only the path dependent loss but also the number of switch crosstalks in OMINs. Our approach is centered upon modelling OMINs with Petri nets and using the P-invariants method to determine the minimum number of stages that is sufficient to establish requested communication patterns in variable-stage OMINs. Being composed of the smallest number of stages and consequently directional couplers (or photonic switches), mmin-stage OMIN employs minimal structure and, therefore, path dependent loss and also number of switch crosstalks reach the least possible values in the realization of requested communication patterns.
We prove that the size of Petri nets created in this work is in polynomial dependence on
the problem size which alleviates memory consumption significantly and ascertains the
fact that memory capacity and performance of modern computers are indeed sufficient
to run our task. We also show that the complexity results obtained in this research improve similar results reported in our previous paper. We carry out a series of computer experiments to confirm the effectiveness of the proposed approach.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI (with DOI: 10.1016/j.ins.2009.11.017) and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Information Sciences, Elsevier2016-01-18T13:16:31Z2016-01-18T13:16:31Z2010ArticleBashirov, R., Karanfiller, T. (2010) On path dependent loss and switch crosstalk reduction in optical networks, Information Systems, Elsevier, 180, 1040-1050 (indexed in SCI).0020-025510.1016/j.ins.2009.11.017http://dx.doi.org/10.1016/j.ins.2009.11.017http://hdl.handle.net/11129/1997en_US
oai:i-rep.emu.edu.tr:11129/19982016-01-18T13:28:07Zhdl_11129_784Rearrangeability of (2 log n N− 1)-stage networks employing a uniform connection patternBashirov, RzaMultistage interconnection networkRearrangeabilityShuffle-exchange networkIn this paper, we study the rearrangeablity of multistage networks. Although the necessity of (2 lgN −1)1 stages for rearrangeability of a shuffle-exchange network has been known, the sufficiency of (2 lgN −1) stages has never been proved. The best known upper bound for its rearrangeability
is (3 lgN−4).We prove that (2 logn N−1) stages are sufficient for the
rearrangeability of a multistage network with (n×n)-switches employing a
uniform interconnection pattern. This, in particular, implies the sufficiency
of (2 lgN−1) stages for the rearrangeability of a shuffle-exchange network.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI (with DOI: 10.1007/s100920170005) and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Calcolo, Springer2016-01-18T13:27:51Z2016-01-18T13:27:51Z2001ArticleBashirov, R. (2001) Rearrangeability of (2 log n N− 1)-stage networks employing a uniform connection pattern, Calcolo, Springer Verlag, 38, pp. 85-95 (indexed in SCIE).1126-5434 (online)0008-0624 (print)DOI: 10.1007/s100920170005http://dx.doi.org/10.1007/s100920170005http://hdl.handle.net/11129/1998en_US
oai:i-rep.emu.edu.tr:11129/28112016-06-29T06:53:27Zhdl_11129_784A splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problemDaoud S., DaoudSubaşı, DervişAdditive parallel splitting;Inverse problemParabolic equationsOne of the global approaches for solving the two dimensional inverse parabolic problem
is the predictor corrector which takes place for evaluating the pair (u,p) and adjusting
the evaluation for the desired accuracy. For general class of higher dimensional
parabolic problems the ADI or the FS methods have been considered with an advantage
of reducing or splitting the problem, in accordance to the time fractions, into one
dimensional dependent problems and they are a non-parallel type of splittings. In
1992 Lu et al. proposed an additive parallel type of splitting method such that the splitting
is defined in accordance to the spatial variables to solve multi dimensional parabolic
problem.In this work we will present a new algorithm for solving two or higher dimensional
inverse control problem. The algorithm is a parallel predictor corrector type of method
such that the solution and the predictor and corrector schemes are defined by the parallel
splitting up method. Some numerical results from the solution of two model problems
are considered to demonstrate the accuracy of the presented algorithm.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier2016-06-29T06:46:10Z2016-06-29T06:46:10Z2005-07-26articleDerviş Hasan Subaşı, Davoud Davoud, (2005) "A splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problem", Applied Mathematics and Computation, Volume 166, Issue 3, 26 July 2005, Pages 584–595.0096-3003http://dx.doi.org/10.1016/j.amc.2004.07.005http://hdl.handle.net/11129/28111663584595eng10.1016/j.amc.2004.07.005Applied Mathematics and Computationinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/28092016-06-23T12:04:47Zhdl_11129_784A Novel Fully Implicit Block Coupled Solution Strategy For The Ultimate Treatment of The Velocity–Pressure Coupling Problem in İncompressible Fluid FlowMazhar, ZekaSolution StrategyUltimate TreatmentVelocity–VressureTwo new extremely robust, fully implicit coupled solution procedures (FICS-1 and FICS-2) are presented for the ultimate solution of the notorious velocity–pressure coupling problem arising in incompressible fluid flow problems. Based on a previous idea of the author, the algebraic coupled system of equations resulting from the discretization of the momentum and mass conservation equations is taken in its primitive form. A special incomplete decomposition technique is applied to the block matrix of the algebraic system, requiring only two defect vectors in the defect matrix. With the new mechanism applied, the mass and momentum conservations are satisfied simultaneously at all points of the solution region and at each step of the solution process. In this way, the effect of any change in a dependent variable is sensed immediately at all of the points in the solution region. Contrary to the almost outdated segregated-type approaches, the new procedures do not require any explicit equation for pressure, so that the laborious tasks of formulation and solution of any Poisson-type equations are avoided. The procedures are not pressure-based. They are very simple to formulate and implement. The strong coupling preserved and the full implicitness of the algorithm involved helps in treating the nonlinearities most efficiently through a couple of overall block solutions. Tests on the two procedures presented in this work show that up to at least 20 times faster convergence rates can be achieved, compared with any of the segregatedtype procedures, which accounts for a 95% reduction in computing time. The procedures may converge even when no relaxation is applied, but they may converge faster if some optimal relaxation is applied. With these properties, the procedures presented seem to provide a breakthrough in the area of computational fluid mechanics.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Taylor & Francis (Routledge)2016-06-23T12:04:01Z2016-06-23T12:04:01Z2016-01-21articleZeka Mazhar (2016) A novel fully implicit block coupled solution
strategy for the ultimate treatment of the velocity–pressure coupling problem in
incompressible fluid flow, Numerical Heat Transfer, Part B: Fundamentals, 69:2, 130-1491040-7790 (print)1521-0626 (online)http://dx.doi.org/10.1080/10407790.2015.1093787http://hdl.handle.net/11129/2809692130149eng10.1080/10407790.2015.1093787Numerical Heat Transfer, Part B: Fundamentalsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/27972016-06-21T12:01:43Zhdl_11129_784Delay structure of wideband noises with application to filtering problemsBashirov, AgamirzaMazhar, ZekaEtikan, HüseyinErtürk, SinemWideband NoiseWhite NoiseKalman FilteringNonlinear Filtering EquationFiltering of random processes is one of the central subjects in the theory of random processes. Especially, Kalman filtering, originating from the famous works of Kalman and Bucy [1, 2], is one of the powerful methods of estimation and widely used in applications. The overwhelming majority of the results in filtering theory for linear and nonlinear systems has been obtained for a pair of independent or correlated white noises corrupting the state and observation systems in finite [3, 4] and infinite [5,6] dimensional spaces. However, real noises are only approximations to white noises.
Fleming and Rishel [7] wrote that the real noises are wideband and white noises are an ideal case of wideband noises. Whenever the parameters of white and wideband noises are sufficiently close to each other, the wideband noise can be replaced by the white noise to make the respective mathematical model simpler. Therefore, in order to get a more adequate version of the filtering equations, a method of handling and working with wideband noises must be developed. In this paper, we aim to give a mathematical background for the wideband noises. We show that under general conditions a wideband noise can be modeled as a distributed delay of a white
noise, demonstrating an important relationship between practical wideband noises and ideal white noises. We show that an equation, corrupted by a wideband noise, is indeed an infinite dimensional equation corrupted by a white noise. From this, we modify the Kalman filter and the nonlinear filtering equation for wideband-noise-driven systems.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Wiley Online Library2016-06-21T12:00:54Z2016-06-21T12:00:54Z2013articleAgamirza Bashirov, Zeka Mazhar, Hüseyin Etikan, Sinem Ertürk. ''Delay structure of wideband noises with application to filtering problems'' Optim. Control Appl. Meth. 2013; 34:69–790143-2087 (print)1099-1514 (online)http://dx.doi.org/10.1002/oca.1029http://hdl.handle.net/11129/27973416979eng10.1002/oca.1029Optimal Control Applications and Methodsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/27942016-06-21T23:00:29Zhdl_11129_784Boundary Value Problems Arising in Kalman FilteringBashirov, AgamirzaMazhar, ZekaErtürk, SinemBoundary ValueKalman FilteringProblem ArisingThe file in this item is the publisher version (published version) of the article.Hindawi Publishing Corporation2016-06-21T10:42:56Z2016-06-21T10:42:56Z2009-01-01articleAgamirza Bashirov,Zeka Mazhar,Sinem Ertürk. ''Boundary Value Problems Arising in
Kalman Filtering'' Boundary Value Problems Journal, No:1, pp.1-10, 2009.1687-2762 (print)1687-2770 (online)http://dx.doi.org/10.1155/2008/279410http://hdl.handle.net/11129/27941110eng10.1155/2008/279410Boundary Value Problemsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/29042016-09-27T23:00:37Zhdl_11129_784On asymptotical behavior of solution of Riccati equation arising in linear filtering with shifted noisesBashirov, Agamirza E.Mazhar, ZekaAsymptotical BehaviorSolution Of RiccatiEquation ArisingLinear FilteringShifted NoisesIn this paper we consider a linear signal system together with the two linear observation systems. The observation systems differ from each other by the noise processes. The noise of one of them is a constant shift in time of the signal noise. In the other one the shift is neglected. Respectively, we consider two best estimates of the signal corresponding to two different observation systems. The following problem is investigated: whether the effect of the shift on the best estimate becomes negligible as time increases. This leads to a comparison of the asymptotical behaviors of the solutions of respective Riccati equations. It is proved that under a certain relation between the parameters, the effect of the shift is not negligibleSpringer2016-09-27T10:32:58Z2016-09-27T10:32:58Z2007articleAgamirza E. Bashirov, Zeka Mazhar. ''On asymptotical behavior of solution of Riccati equation arising in linear filtering with shifted noises'' Mathematical Methods in Engineering Journal, 141–149, 2007.978-1-4020-5677-2 (Print)978-1-4020-5678-9 (Online)http://dx.doi.org/10.1007/978-1-4020-5678-9http://hdl.handle.net/11129/2904141149eng10.1007/978-1-4020-5678-9Mathematical Methods in Engineeringinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/26672016-05-21T09:27:28Zhdl_11129_784A PROCEDURE FOR THE TREATMENT OF THE VELOCITY-PRESSURE COUPLING PROBLEM IN INCOMPRESSIBLE FLUID FLOWMazhar, ZekaProcedure For The TreatmentVelocity-PressureCoupling ProblemIncompressible Fluid FlowA new block implicit procedure ( BID) is introduced which utilizes a simple incomplete
decomposition of the matrix resulting from the discretization of the momentum and mass conservation equations for incompressible uid ow problems. In contrast to the conventional methods, the new method is not of the segregated type, and does not require an explicit equation for pressure. The complete, coupled block system is solved in its primitive form. In this way, mass and momentumconservation are satis ed simultaneously at all grid points, while pressure is calculated implicitly. Only a couple of overall iterations are required for the treatment of the nonlinearities of the problem. Tests show that the new procedure converges fast for any E value ( in an E-factor formulation) , and therefore virtually the E-factor formulation is not necessaryDue to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Taylor & Francis (Routledge)2016-05-21T09:26:54Z2016-05-21T09:26:54Z2001articleZeka Mazhar (2001) ''A PROCEDURE FOR THE TREATMENT OF THE VELOCITYPRESSURE COUPLING PROBLEM IN INCOMPRESSIBLE FLUID FLOW'' Numerical Heat Transfer, Part B: Fundamentals, 39:1, 91-100,1040-7790 (Print)1521-0626 (Online)http://dx.doi.org/10.1080/104077901460704http://hdl.handle.net/11129/266739191100eng10.1080/104077901460704Numerical Heat Transfer, Part B: Fundamentalsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/28382016-07-18T08:49:24Zhdl_11129_784The highly accurate block-grid method in solving Laplace’s equation for nonanalytic boundary condition with corner singularityDosiyev, A.A.Buranay, S.C.Subaşı, DervişIntegral representation, 9-point approximation, SingularityFlux intensity factors, Block-grid method, Artificial boundaryThe highly accurate block-grid method for solving Laplace’s boundary value problems on
polygons is developed for nonanalytic boundary conditions of the first kind. The quadrature
approximation of the integral representations of the exact solution around each reentrant
corner(‘‘singular’’ part) are combined with the 9-point finite difference equations on the
‘‘nonsingular’’ part. In the integral representations, and in the construction of the sixth
order gluing operator, the boundary conditions are taken into account with the help of
integrals of Poisson type for a half-plane which are computed with ε accuracy. It is proved
that the uniform error of the approximate solution is of order O(h6+ε), where h is the mesh
step. This estimation is true for the coefficients of singular terms also. The errors of p-order
derivatives (p = 0, 1, . . .) in the ‘‘singular’’ parts are O((h6 + ε)r1/αj−p
j ), rj is the distance
from the current point to the vertex in question and αjπ is the value of the interior angle
of the jth vertex. Finally, we give the numerical justifications of the obtained theoretical
results.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier2016-07-18T08:49:24Z2016-07-18T08:49:24Z2011-12-27article0898-1221http://dx.doi.org/10.1016/j.camwa.2011.12.068http://hdl.handle.net/11129/2838644616632eng10.1016/j.camwa.2011.12.068Computers and Mathematics with Applicationsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/28282016-07-18T07:26:32Zhdl_11129_784On the preconditioning conjugate gradient method for the solution of 9-point elliptic difference equationsMazhar, ZekaDaoud, D.SSubaşı, DenizPreconditioned conjugate gradient methoditerative methodself-adjoint partial differential equationThe Preconditioned Conjugate Gradient (PCG) method is implemented to solve the system with 9 diagonal entries generated from a 9-point finite difference approximation of the self-adjoint elliptic partial differential equation using an incomplete matrix decomposition. A simpler matrix decomposition for such a linear system is also proposed with a main advantage that it preserves the symmetry of the original matrix, and is easy to implement. Results of the numerical experiments and comparison with other iterative methods are presented.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier B.V2016-07-18T07:26:32Z2016-07-18T07:26:32Z1994article0020-7160(print)1029-0265(online)http://dx.doi.org/10.1080/00207169408804302http://hdl.handle.net/11129/2828523-4171183eng10.1080/00207169408804302International Journal of Computer Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/28292016-07-18T08:03:12Zhdl_11129_784Block method for problems on L-shaped domainsDosiyev, A.AMazhar, ZekaBuranay, S.CLaplace equationL-shaped domainCorner singularityBlock method; Stress intensity factor; ConvergenceAn extremely accurate, exponentially convergent solution is presented for both symmetric and non-symmetric Laplacian problems on L-shaped domains by using one-block version of the block method (BM). A simple and highly accurate formula for computing the stress intensity factor is given. Comparisons with various results in the literature are included.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationElsevier2016-07-18T08:03:12Z2016-07-18T08:03:12Z2010article1879-1778(online)http://dx.doi.org/10.1016/j.cam.2010.07.0070377-0427(print)http://hdl.handle.net/11129/28292353805816eng10.1016/j.cam.2010.07.007Journal of Computational and Applied Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/28302016-07-18T23:00:38Zhdl_11129_784Boundary Value Problems Arising in Kalman FilteringBashirov, AgamirzaMazhar, ZekaErtürk, SinemDifference and Functional Equations, Partial Differential EquationsApproximations and Expansions, Analysis, Ordinary Differential EquationsMathematics, general, APPLIED, Noise, StudiesMathematical models, Economic models, Science, QA1-939The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic) with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems. Copyright (c) 2008 Agamirza Bashirov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The file in this item is the publisher version (published version) of the article.Springer International Publishing2016-07-18T08:04:24Z2016-07-18T08:04:24Z2008article1687-2762, 1687-2770(print)1687-2770(online)http://dx.doi.org/10.1155/2008/279410http://hdl.handle.net/11129/283020081110eng10.1155/2008/279410Boundary Value Problemsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/28322016-07-18T08:09:27Zhdl_11129_784An Enhancement To The Block Implicit Procedure For The Treatment Of The Velocity-Pressure Coupling Problem In Incompressıble Fluid FlowMazhar, ZekaMECHANICSTHERMODYNAMICSThe performance of two new non-segregated, block implicit procedures; BIP and BIPEN are compared with the well known SIMPLER procedure, applied to benchmark problems of various sizes. It is demonstrated that BIP provides quicker convergence than SIMPLER by a factor of two, and BIPEN is %40 faster than BIP. In addition it is shown that both methods are extremely robust, even for large-sized problems, rendering them as a basis for a new generation of hybrid computation algorithms, for the efficient treatment of the velocity-pressure coupling problem.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Taylor & Francis2016-07-18T08:09:27Z2016-07-18T08:09:27Z2002article1040-7790(print)1521-0626(online)http://dx.doi.org/10.1080/104077902753725939http://hdl.handle.net/11129/2832415493500eng10.1080/104077902753725939Numerical Heat Transfer, Part B: Fundamentalsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/30212016-10-11T23:00:43Zhdl_11129_784q-Parametric Bleimann Butzer and Hahn OperatorsMahmudov, Nazim I.Sabancıgil, Pembeparametric generalizationMATHEMATICS, APPLIEDGENERALIZED BERNSTEIN POLYNOMIALS, CONVERGENCEWe introduce a new q -parametric generalization of Bleimann, Butzer, and Hahn operators in [superscript]C1+x*[/superscript] [0,∞) . We study some properties of q -BBH operators and establish the rate of convergence for q -BBH operators. We discuss Voronovskaja-type theorem and saturation of convergence for q -BBH operators for arbitrary fixed 0<q<1 . We give explicit formulas of Voronovskaja-type for the q -BBH operators for 0<q<1 . Also, we study convergence of the derivative of q -BBH operatorsThe file in this item is the publisher version (published version) of the article.Hindawi Publishing Corporation2016-10-11T19:08:16Z2016-10-11T19:08:16Z2008article1025-5834(print)1029-242X(online)http://dx.doi.org/10.1155/2008/816367http://hdl.handle.net/11129/30212008115eng10.1155/2008/81636Journal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/30102016-10-11T23:00:42Zhdl_11129_784q-Parametric Bleimann Butzer and Hahn OperatorsMahmudov, Nazim I.Sabancıgil, Pembeq-parametric generalizationq-BBH operators.Zeller operatorsWe introduce a new q-parametric generalization of Bleimann, Butzer, and Hahn operators in
C∗
1x0, ∞ . We study some properties of q-BBH operators and establish the rate of convergence
for q-BBH operators. We discuss Voronovskaja-type theorem and saturation of convergence for qBBH
operators for arbitrary fixed 0 <q< 1. We give explicit formulas of Voronovskaja-type for the
q-BBH operators for 0 <q< 1. Also, we study convergence of the derivative of q-BBH operators.The file in this item is the publisher version (published version) of the article.Hindawi Publishing Corporation2016-10-11T05:36:44Z2016-10-11T05:36:44Z2008article1029-242X(online)http://dx.doi.org/10.1155/2008/816367http://hdl.handle.net/11129/30102008115eng10.1155/2008/816367Journal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/30092016-10-11T05:36:07Zhdl_11129_784On path dependent loss and switch crosstalk reduction in optical networksBashirov, RzaKaranfiller, TolgaySwitch crosstalk, Optical interconnection networkP-invariants, Permutation admissibility, Path dependent lossP/T-net, CAPABILITY, COMPUTER SCIENCEINFORMATION SYSTEMS, ALGORITHM, PETRI NETSMULTISTAGE INTERCONNECTION NETWORKSAlthough optical multistage interconnection networks (OMINs) promise to meet the ever growing demands of communication networks and multiprocessor systems in fast communication, they suffer from challenges such as path dependent loss and switch crosstalk. In this paper, we propose an innovative approach for reducing not only the path dependent loss but also the number of switch crosstalks in OMINs. Our approach is centered upon modelling OMINs with Petri nets and using the P-invariants method to determine the minimum number of stages m that is sufficient to establish requested communication patterns in variable-stage OMINs. Being composed of the smallest number of stages and consequently directional couplers (or photonic switches), m -stage OMIN employs minimal structure and, therefore, path dependent loss and also number of switch crosstalks reach the least possible values in the realization of requested communication patterns. We prove that the size of Petri nets created in this work is in polynomial dependence on the problem size which alleviates memory consumption significantly and ascertains the fact that memory capacity and performance of modern computers are indeed sufficient to run our task. We also show that the complexity results obtained in this research improve similar results reported in our previous paper. We carry out a series of computer experiments to confirm the effectiveness of the proposed approachDue to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier2016-10-11T05:36:07Z2016-10-11T05:36:07Z2010article0020-0255(print)1872-6291(online)http://dx.doi.org/10.1016/j.ins.2009.11.017http://hdl.handle.net/11129/3009180610401050eng10.1016/j.ins.2009.11.017Information Sciencesinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/31862017-03-14T00:00:36Zhdl_11129_784Identifying targets for gene therapy of β-globin disorders using quantitative modeling approachBashirov, RzaMehraei, ManiHybrid functional Petri netQuantitative modelingCell illustratorβ-thalassemiaSickle cell diseaseFetal to adult hemoglobin switching networkSickle cell disease and β-thalassemia are well-known genetic disorders which are caused by mutations in β-globin gene. Reactivation of fetal hemoglobin in adulthood through induction of γ-globin gene expression has proven be sufficient to ameliorate sickle cell disease and β-thalassemia. In the last few decades, substantial efforts have been made to identify potential target candidates for β-globin diseases. In the present work, we propose an innovative approach for identifying novel molecular targets of β-globin diseases. Our approach is based on quantitative modeling of fetal-to-adult hemoglobin switching network with hybrid functional Petri nets. We verify the coherence of deterministic quantitative model created in this research to be sure it is consistent with qPCR data available for known siRNA- and shRNA-based strategies. Comparison of simulation results for the proposed strategy with the ones obtained for already existing RNAi-mediated treatments shows that our strategy is optimal, as it leads to the highest level of γ-globin induction. Consequently, it has potential beneficial therapeutic effect on β-globin diseases. This study also provides an innovative strategy for the target-based treatment of many other diseases.The file in this item is the post-print version of the article (author’s copy; author’s final manuscript, accepted for publication after peer-review process). Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier2017-03-13T06:36:25Z2017-03-13T06:36:25Z2017-08article0020-0255http://dx.doi.org/10.1016/j.ins.2017.02.053http://hdl.handle.net/11129/3186397-3983747engdx.doi.org/10.1016/j.ins.2017.02.053Information Sciencesinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34522017-10-23T23:00:38Zhdl_11129_784Approximate controllability of semilinear control systems in Hilbert spacesŞemi, NidaiMahmudov, Nazim I.Control theory, Approximation theoryMathematical research, Hilbert space, ResearchControl systems, ApproximationsThis paper deals with the approximate controllability of semilinear evolution systems in Hilbert spaces. Sufficient condition for approximate controllability have been obtained under natural conditions.Turkic World Mathematical Society2017-10-23T08:18:37Z2017-10-23T08:18:37Z2012articleMAHMUDOV N. I., ŞEMİ N., Approximate Controllability of
Semilinear Control Systems in Hilbert Spaces2146-1147https://search.proquest.com/docview/1561503068?pq-origsite=summonhttp://hdl.handle.net/11129/3452216774engJournal of Applied and Engineering Mathematicsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34462017-10-23T08:12:15Zhdl_11129_784Partial controllability conceptsŞemi, NidaiBashirov, AgamirzaMahmudov, Nazim I.AUTOMATION & CONTROL SYSTEMS, STOCHASTIC-SYSTEMSThe main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form. i.e., given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract Hilbert or Banach space and disturbed by a deterministic function or by a white noise process. At the same time, some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged. Respectively, the ordinary controllability conditions for them are too strong since they assume extended state space. It is reasonable to introduce partial controllability concepts, which assume original state space. In this paper, we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases.Taylor & Francis Group2017-10-23T08:12:15Z2017-10-23T08:12:15Z2007article0020-7179(print)1366-5820(online)http://dx.doi.org/10.1080/00207170600885489http://hdl.handle.net/11129/34468017eng10.1080/00207170600885489International Journal of Controlinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34382017-10-23T08:05:20Zhdl_11129_784New Korovkin Type Theorem for Non-Tensor Meyer–König and Zeller OperatorsÖzarslan, Mehmet Alipositive linear operators, Meyer–König and Zeller operators, 41A36, Korovkin type theoremgenerating function, 41A25, modulus of continuity, Mathematics, general, MathematicsIn this paper, we introduce a certain class of linear positive operators via a generating function, which includes the non-tensor MKZ operators and their non-trivial extension. In investigating the approximation properties, we prove a new Korovkin type approximation theorem by using appropriate test functions. We compute the rate of convergence of these operators by means of the modulus of continuity and the elements of modified Lipschitz class functions. Furthermore, we give functional partial differential equations for this class. Using the corresponding equations, we calculate the first few moments of the non-tensor MKZ operators and investigate their approximation properties. Finally, we state the multivariate versions of the results and obtain the convergence properties of the multivariate Meyer–König and Zeller operators.Springer International Publishing2017-10-23T08:05:20Z2017-10-23T08:05:20Z2016article1422-6383 (print)1420-9012(online)http://dx.doi.org/10.1007/s00025-015-0472-0http://hdl.handle.net/11129/3438693327343eng10.1007/s00025-015-0472-0Results in Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34312017-10-19T08:24:33Zhdl_11129_784Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operatorsÖzarslan, Mehmet AliAktuğlu, HüseyinKantorovich-Mittag-Leffler operatorsLipschitz class functionals, Bernoulli numbers, λ-statistical convergence, Szász-Mirakjan operators, statistical convergence, Lacunary statistical convergence, αβ-statistical convergenceIn this paper we introduce Kantorovich variant of the Mittag-Leffler operators including the modified Kantorovich-Szász-Mirakjan operators. We give αβ-statistical approximation theorems for these operators in various function spaces. The results include the statistical, lacunary statistical and λ-statistical cases. Moreover, we compute the rate of convergence in different Lipschitz type spaces.Springer Verlag2017-10-19T08:24:33Z2017-10-19T08:24:33Z2016articlehttp://dx.doi.org/10.1515/ms-2015-0171http://hdl.handle.net/11129/3431663695706eng10.1515/ms-2015-0171Mathematica Slovacainfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34572017-10-23T08:20:44Zhdl_11129_784Approximation Properties of Jain-Stancu OperatorsÖzarslan, Mehmet AliUNIFORM APPROXIMATION, Szasz-Mirakyan operatorsMATHEMATICS, POLYNOMIALS, Modulus of continuity, ERROR ESTIMATIONINTEGRAL TYPE OPERATORS, FAMILY, MATHEMATICS, APPLIED,MIRAKJAN TYPE OPERATORS, Jain operators,Voronovskaya-Type asymptotic formula, SZASZ, Szász-Mirakyan operatorsIn the present paper, we introduce the Stancu type Jain operators, which generalize the well-known Szasz-Mirakyan operators via Lagrange expansion. We investigate their weighted approximation properties and compute the error of approximation by using the modulus of continuity. We also give an asymptotic expansion of Voronovskaya type. Finally, we introduce a modified form of our operators, which preserves linear functions, provides a better error estimation than the Jain operators and allows us to give global results in a certain subclass of C[0, infinity). Note that the usual Jain operators do not preserve linear functions and the global results in a certain subspace of C[0, infinity) can not be given for them.UNIV NIS, FAC SCI MATH2017-10-23T08:20:43Z2017-10-23T08:20:43Z2016article0354-5180http://dx.doi.org/10.2298/FIL1604081Ohttp://hdl.handle.net/11129/345730410811088eng10.2298/FIL1604081OFILOMATinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34412017-10-23T08:06:38Zhdl_11129_784Smoothness Properties of Modified Bernstein-Kantorovich OperatorsÖzarslan, Mehmet AliDuman, Oktay41A36, modulus of continuity,Bernstein-Kantorovich operators, simultaneous approximationDitzian-Totik modulus of smoothness, 41A25, MATHEMATICS, APPLIEDPOSITIVE LINEAR-OPERATORS, APPROXIMATION PROPERTIESmodulus ofcontinuity, Ditzian-Totik modulus ofsmoothnessIn this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.Taylor & Francis2017-10-23T08:06:38Z2017-10-23T08:06:38Z2016article0163-0563 (print)1532-2467 (online)http://dx.doi.org/10.1080/01630563.2015.1079219http://hdl.handle.net/11129/344137192105eng10.1080/01630563.2015.1079219Numerical Functional Analysis and Optimizationinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34692017-10-23T08:45:35Zhdl_11129_784Korovkin type theorem for non‐tensor Balázs type Bleimann, Butzer and Hahn operatorsÖzarslan, Mehmet AliAktuğlu, Hüseyinpositive linear operators, modulus of continuity, Balázs operatorsKorovkin type theorem, Bernstein type rational functions, Bleimann, Butzer and Hahn operatorsMATHEMATICS, APPLIED, APPROXIMATION,BERNSTEIN-TYPE OPERATORS, Butzer and Hahn operators, INVERSE-BETA, CONVERGENCE, Balazs operators, Bleimann, Bleimann Butzer and Hahn operatorsIn this paper, we prove a certain Korovkin type approximation theorem by introducing new test functions. We introduce the non-tensor Balázs type Bleimann, Butzer and Hahn operators and give the approximation property by using this new Korovkin theorem. Furthermore, we obtain the rate of convergence of these operators by means of modulus of continuity. Finally, we state the multivariate version of the abovementioned Korovkin type theorem. Copyright © 2014 John Wiley & Sons, Ltd.WILEY-BLACKWELL2017-10-23T08:45:35Z2017-10-23T08:45:35Z2015article0170-4214(print)1099-1476(online)http://dx.doi.org/10.1002/mma.3204http://hdl.handle.net/11129/346938919371944eng10.1002/mma.3204Mathematical Methods in the Applied Sciencesinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34392017-10-23T23:00:33Zhdl_11129_784Chlodowsky-type q-Bernstein-Stancu-Kantorovich operatorsÖzarslan, Mehmet AliVedi, TubaMATHEMATICS, APPLIED, APPROXIMATION PROPERTIES, modulus of continuitySchurer-Stancu and Schurer-Chlodowsky operators, MATHEMATICSIn this paper, we introduce Chlodowsky-type q-Bernstein-Stancu-Kantorovich operators on the unbounded domain. We should note that this generalization includes various kinds of operators which have not been introduced earlier. We calculate the error of approximation of these operators by using the modulus of continuity and Lipschitz-type functionals. Finally, we give generalization of the operators and investigate their approximations.MSC: 41A10, 41A25, 41A36.Springer International Publishing AG2017-10-23T08:05:42Z2017-10-23T08:05:42Z2015article1029-242X, 1025-5834(print)http://dx.doi.org/10.1186/s13660-015-0610-y1029-242X(online)http://hdl.handle.net/11129/343920151191eng10.1186/s13660-015-0610-yJournal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34402017-10-23T23:00:33Zhdl_11129_784Singular integral equation involving a multivariable analog of Mittag-Leffler functionGaboury, SebastienÖzarslan, Mehmet AliFunctional Analysis, fractional integrals and derivatives, MathematicsDifference and Functional Equations, Partial Differential Equationscontour integral representation, singular integral equationMittag-Leffler function, Analysis, Ordinary Differential Equations,Mathematics, general, APPLIED, LAGUERRE-POLYNOMIALSMotivated by the recent work of the second author (Özarslan in Appl. Math. Comput. 229:350-358, 2014), we present, in this paper, some fractional calculus formulas for a mild generalization of the multivariable Mittag-Leffler function, a Schläfli's type contour integral representation, some multilinear and mixed multilateral generating functions; and, finally, we consider a singular integral equation with the function [InlineEquation not available: see fulltext.] in the kernel and we provide its solution. MSC: 26A33, 33E12.The file in this item is the publisher version (published version) of the article.Springer International Publishing2017-10-23T08:06:19Z2017-10-23T08:06:19Z2014article1687-1847, 1687-1839(print)1687-1847(online)http://dx.doi.org/10.1186/1687-1847-2014-252http://hdl.handle.net/11129/344020141110eng10.1186/1687-1847-2014-252Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34562017-10-23T23:00:39Zhdl_11129_784Chlodowsky variant of q-Bernstein-Schurer-Stancu operatorsÖzarslan, Mehmet AliVedi, TubaSchurer-Stancu and Schurer Chlodowsky operators, Lipschitz-type functionals,Analysis, Applications of Mathematics, q -Bernstein operators, modulus of continuity,Korovkin-type theorems, Mathematics, general, POLYNOMIALS, APPROXIMATION PROPERTIES, Modulus of continuity, Q-Bernstein operatorsIt was Chlodowsky who considered non-trivial Bernstein operators, which help to
approximate bounded continuous functions on the unbounded domain. In this
paper, we introduce the Chlodowsky variant of q-Bernstein-Schurer-Stancu operators.
By obtaining the first few moments of these operators, we prove Korovkin-type
approximation theorems in different function spaces. Furthermore, we compute the
error of the approximation by using the modulus of continuity and Lipschitz-type
functionals. Then we obtain the degree of the approximation in terms of the modulus
of continuity of the derivative of the function. Finally, we study the generalization of
the Chlodowsky variant of q-Bernstein-Schurer-Stancu operators and investigate their
approximationsThe file in this item is the publisher version (published version) of the article.Springer International Publishing2017-10-23T08:20:05Z2017-10-23T08:20:05Z2014article1029-242Xhttp://dx.doi.org/10.1186/1029-242X-2014-189http://hdl.handle.net/11129/345620141114eng10.1186/1029-242X-2014-189Journal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34482017-10-23T08:16:23Zhdl_11129_784A set of finite order differential equations for the Appell polynomialsÖzarslan, Mehmet AliYılmaz, BanuEXTENSIONS, Hermite polynomials, FORMULAS, Differential equation,LAGUERRE, Bernoulli polynomials, MATHEMATICS, APPLIED,QUASI-MONOMIALITY, BERNOULLI, EULER POLYNOMIALS,Appell polynomials, IDENTITIES, NUMBERS, Differential equationsLet { (x)}n=0 denote the set of Appell polynomials which includes, among others, Hermite, Bernoulli, Euler and Genocchi polynomials. In this paper, by introducing the generalized factorization method, for each kâ̂̂N, we determine the differential operator {Ln,k(x)}n=0 such that Ln,k(x)( (x))=λn, (x), where λn, =(n+k)!n!-k!. The special case k=1 reduces to the result obtained in [M.X. He, P.E. Ricci, Differential equation of Appell polynomials via the factorization method, J. Comput. Appl. Math. 139 (2002) 231-237]. The differential equations for the Hermite and Bernoulli polynomials are exhibited for the case k=2. © 2013 Elsevier B.V. All rights reserved.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier Science BV2017-10-23T08:16:23Z2017-10-23T08:16:23Z2014article0377-0427(print)1879-1778(online)http://dx.doi.org/10.1016/j.cam.2013.08.006http://hdl.handle.net/11129/3448259108116eng10.1016/j.cam.2013.08.006Journal Of Computational And Applied Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34362017-10-23T08:04:34Zhdl_11129_784On a singular integral equation including a set of multivariate polynomials suggested by Laguerre polynomialsÖzarslan, Mehmet AliMATHEMATICS, APPLIED, FAMILIES, KONHAUSER SETS, Generating functions,Mittag-Leffler function, Contour integral representation, Laplace transform,Multivariate Laguerre polynomials, Singular integral equation,Fractional integrals and derivatives, BIORTHOGONAL POLYNOMIALSIn this paper, we introduce the class of polynomials Zn1,…,nj(α)(x1,…,xj;ρ1,…,ρj) suggested by the multivariate Laguerre polynomials. We give Schläfli’s contour integral representation and calculate the fractional order integral of these polynomials. Furthermore, we obtain linear, multilinear and mixed multilateral generating functions for them. Finally, we construct a singular integral equation with Zn1,…,nj(α)(x1,…,xj;ρ1,…,ρj) in the kernel and obtain the solution in terms of multivariate analogue of the Mittag–Leffler functions.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier2017-10-23T08:04:34Z2017-10-23T08:04:34Z2014article0096-3003(print)1873-5649(online)http://dx.doi.org/10.1016/j.amc.2013.12.050http://hdl.handle.net/11129/3436229350358eng10.1016/j.amc.2013.12.050Applied Mathematics and Computationinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34632017-10-23T23:00:39Zhdl_11129_784The extended Mittag-Leffler function and its propertiesÖzarslan, Mehmet AliYılmaz, BanuMittag-Leffler extended Beta functions fractional derivative Mellin transformLaguerre polynomials Whittaker functions Wright generalized hypergeometric functionsIn this paper, we present the extended Mittag-Leffler functions by using the extended Beta functions (Chaudhry et al. in Appl. Math. Comput. 159:589-602, 2004) and obtain some integral representations of them. The Mellin transform of these functions is given in terms of generalized Wright hypergeometric functions. Furthermore, we show that the extended fractional derivative (Özarslan and Özergin in Math. Comput. Model. 52:1825-1833, 2010) of the usual Mittag-Leffler function gives the extended Mittag-Leffler function. Finally, we present some relationships between these functions and the Laguerre polynomials and Whittaker functions.The file in this item is the publisher version (published version) of the articleSpringer International Publishing2017-10-23T08:26:45Z2017-10-23T08:26:45Z2014article1029-242X(online)http://dx.doi.org/10.1186/1029-242X-2014-85http://hdl.handle.net/11129/346320141110eng10.1186/1029-242X-2014-85Journal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34592017-10-23T23:00:39Zhdl_11129_784Solvability of differential equations of order 2 < alpha <= 3 involving the p-Laplacian operator with boundary conditionsÖzarslan, Mehmet AliAktuğlu, HüseyinMATHEMATICS, APPLIED, fractional derivative, MATHEMATICSCaputo fractional derivative, EXISTENCE, p-Laplacian operators,Caputo fractional boundary value problem, boundary value problem, anti-periodic boundary value problemFractional integral, Boundary value problemIn this paper, we study the existence of solutions for non-linear fractional differential
equations of order 2 < α ≤ 3 involving the p-Laplacian operator with various
boundary value conditions including an anti-periodic case. By using the Banach
contraction mapping principle, we prove that, under certain conditions, the
suggested non-linear fractional boundary value problem involving the p-Laplacian
operator has a unique solution for both cases of 0 < p < 1 and p ≥ 2. Finally, we
illustrate our results with some examples.The file in this item is the publisher version (published version) of the articleSpringer International Publishing AG2017-10-23T08:21:36Z2017-10-23T08:21:36Z2013article1687-1847, 1687-1839(print)http://dx.doi.org/10.1186/1687-1847-2013-358http://hdl.handle.net/11129/34591358371eng10.1186/1687-1847-2013-358Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34422017-10-23T23:00:34Zhdl_11129_784q-Bernstein-Schurer-Kantorovich OperatorsÖzarslan, Mehmet AliVedi, Tubaq-analysis; q-integral operator; positive linear operatorsq-Bernstein operators; modulus of continuityIn the present paper, we introduce the q-Bernstein-Schurer-Kantorovich operators.
We give the Korovkin-type approximation theorem and obtain the rate of
convergence of this approximation by means of the first and the second modulus of
continuity. Moreover, we compute the order of convergence of the operators in terms
of the elements of Lipschitz class functions and the modulus of continuity of the
derivative of the function.The file in this item is the publisher version (published version) of the articleSpringer International Publishing2017-10-23T08:07:02Z2017-10-23T08:07:02Z2013article1029-242Xhttp://dx.doi.org/10.1186/1029-242X-2013-444http://hdl.handle.net/11129/34422013115eng10.1186/1029-242X-2013-444Journal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34732017-10-23T23:00:33Zhdl_11129_784Two-parameter Srivastava polynomials and several series identitiesKaanoğlu, CemÖzarslan, Mehmet AliLaguerre, Jacobi, Bessel and Lagrange polynomials.olynomials two-parameter Srivastava polynomials.In the present paper, we introduce two-parameter Srivastava polynomials in one, two and three variables by inserting new indices, where in the special cases they reduce to (among others) Laguerre, Jacobi, Bessel and Lagrange polynomials. These polynomials include the family of polynomials which were introduced and/or investigated in (Srivastava in Indian J. Math. 14:1-6, 1972; González et al. in Math. Comput. Model. 34:133-175, 2001; Altin et al. in Integral Transforms Spec. Funct. 17(5):315-320, 2006; Srivastava et al. in Integral Transforms Spec. Funct. 21(12):885-896, 2010; Kaanoglu and Özarslan in Math. Comput. Model. 54:625-631, 2011). We prove several two-sided linear generating relations and obtain various series identities for these polynomials. Furthermore, we exhibit some illustrative consequences of the main results for some well-known special polynomials which are contained by the two-parameter Srivastava polynomials.The file in this item is the publisher version (published version) of the articleSpringer Science & Business Media2017-10-23T08:46:56Z2017-10-23T08:46:56Z2013article1687-1839http://dx.doi.org/10.1186/1687-1847-2013-81http://hdl.handle.net/11129/34732013119eng10.1186/1687-1847-2013-81Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34532017-10-23T08:18:58Zhdl_11129_784Local approximation properties for certain King type operatorsÖzarslan, Mehmet AliAktuğlu, HüseyinBaskakov operators, Lipschitz type space, Szász-Mirakjan operators,Post-Widder operators, Positive linear operators, Stancu operators, Modulus of continuity,MIRAKJAN TYPE OPERATORS, LINEAR-OPERATORS, modulus of continuity, ERROR ESTIMATIONIn this paper, we consider a certain King type operators which includes general families of Szasz-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, which provides global approximation for the above mentioned operators, we obtain the rate of convergence of this class. Furthermore, we give local approximation results by using the first and the second modulus of continuity.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.UNIV NIS, FAC SCI MATH2017-10-23T08:18:58Z2017-10-23T08:18:58Z2013article0354-5180http://dx.doi.org/10.2298/FIL1301173Ohttp://hdl.handle.net/11129/3453271173181eng10.2298/FIL1301173OFilomatinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34492017-10-23T23:00:38Zhdl_11129_784Quantitative global estimates for generalized double Szasz-Mirakjan operatorsÖzarslan, Mehmet AliAktuğlu, HüseyinMATHEMATICS, APPLIED, PRESERVING X, APPROXIMATIONLINEAR-OPERATORS, ERROR ESTIMATION,Topological spaces, Mathematical research, Research, Operator theoryConvergence (Mathematics), QA1-939, MathematicsWe introduce the generalized double Szász-Mirakjan operators in this paper. We obtain several quantitative estimates for these operators. These estimates help us to determine some function classes (including some Lipschitz-type spaces) which provide uniform convergence on the whole domain .The file in this item is the publisher version (published version) of the article.HINDAWI PUBLISHING CORPORATION2017-10-23T08:17:00Z2017-10-23T08:17:00Z2013article1110-757X, 1687-0042(print)1687-0042(online)http://dx.doi.org/10.1155/2013/613258http://hdl.handle.net/11129/3449201318eng10.1155/2013/613258Journal of Applied Mathematicsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34642017-10-23T23:00:39Zhdl_11129_784Differential equations for the extended 2D Bernoulli and Euler polynomialsÖzarslan, Mehmet AliYılmaz, Banugeneralized heat equation, Functional Analysis, 2 D Appell Polynomials,Mathematics, Difference and Functional Equations, Partial Differential Equations, AnalysisOrdinary Differential Equations, Hermite-Kampé de Fériet (or Gould-Hopper) polynomials,2 D Euler polynomials, Mathematics, general, differential equations, EXTENSIONS,Partial, Fixed point theory, Euler angles, UsageIn this paper, we introduce the extended 2D Bernoulli polynomials by t(alpha)/(e(t) - 1)(alpha) c(xt+ytj) = Sigma(infinity)(n=0) B-n((alpha,j)) (x,y,c) t(n)/n! and the extended 2D Euler polynomials by 2(alpha)(e(t) + 1)(alpha) c(xt+ytj) = Sigma(infinity)(n=0) E-n((alpha,j)) (x,y,c) t(n)/n!, where c > 1. By using the concepts of the monomiality principle and factorization method, we obtain the differential, integro-differential and partial differential equations for these polynomials. Note that the above mentioned differential equations for the extended 2D Bernoulli polynomials reduce to the results obtained in (Bretti and Ricci in Taiwanese J. Math. 8(3): 415-428, 2004), in the special case c = e, alpha = 1. On the other hand, all the results for the second family are believed to be new, even in the case c = e, alpha = 1. Finally, we give some open problems related with the extensions of the above mentioned polynomials.The file in this item is the publisher version (published version) of the article.Springer International Publishing AG2017-10-23T08:42:23Z2017-10-23T08:42:23Z2013article1687-1847, 1687-1839(print)1687-1847(online)http://dx.doi.org/10.1186/1687-1847-2013-107http://hdl.handle.net/11129/346420131116eng10.1186/1687-1847-2013-107Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34502017-10-23T23:00:38Zhdl_11129_784Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomialsÖzarslan, Mehmet AliHermite-based Apostol-Genocchi polynomials, Difference and Functional Equationsgeneralized sum of alternative integer powers, Hermite-based Apostol-Bernoulli polynomialsMathematics, SYMMETRY, MATHEMATICS, EXTENSIONS, GENERATING-FUNCTIONSHIGHER-ORDER, FORMULAS, MATHEMATICS, APPLIED,Generalized sum of alternative integer powers, Generalized sum of integer powers, Usage, Gaussian processes, Euler anglesIn this paper, we introduce a unified family of Hermite-based Apostol-Bernoulli, Euler and Genocchi polynomials. We obtain some symmetry identities between these polynomials and the generalized sum of integer powers. We give explicit closed-form formulae for this unified family. Furthermore, we prove a finite series relation between this unification and 3d-Hermite polynomials.The file in this item is the publisher version (published version) of the article.Springer International Publishing AG2017-10-23T08:17:21Z2017-10-23T08:17:21Z2013articlehttp://dx.doi.org/10.1186/1687-1847-2013-116http://hdl.handle.net/11129/345020131113eng10.1186/1687-1847-2013-116Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34352017-10-23T23:00:32Zhdl_11129_784Unified Bernstein and Bleimann-Butzer-Hahn basis and its propertiesÖzarslan, Mehmet AliBozer, MehmetEuler polynomials, generating function, Functional Analysis, Bernstein polynomials,Mathematics, Difference and Functional Equations, Bernoulli polynomials,Partial Differential Equations, Stirling numbers of the second kind, Analysis, Ordinary Differential EquationsGenerating function, Functions, Continuous, Inequalities (Mathematics), Difference equations, Euler angles, UsageIn this paper we introduce the unification of Bernstein and Bleimann-Butzer-Hahn basis via the generating function. We give the representation of this unified family in terms of Apostol-type polynomials and Stirling numbers of the second kind. More generating functions of trigonometric type are also obtained to this unification. MSC: 11B65, 11B68, 41A10, 30C15.The file in this item is the publisher version (published version) of the article.Springer International Publishing AG2017-10-23T08:03:54Z2017-10-23T08:03:54Z2013article1687-1847, 1687-1839http://dx.doi.org/10.1186/1687-1847-2013-55http://hdl.handle.net/11129/343520131114tur/10.1186/1687-1847-2013-55Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34622017-10-23T08:26:24Zhdl_11129_784New families of generating functions for certain class of three-variable polynomialsÖzarslan, Mehmet AliKaanoğlu, CemMultiple Laguerre polynomials, Generating functions, Multilateral generating functions,Srivastava polynomials, Lagrange polynomials, Hypergeometric transformations,Lagrange–Hermite polynomials, Lagrange-Hermite polynomialsMATHEMATICS, APPLIED, HYPERGEOMETRIC POLYNOMIALS, VARIABLES, FamilyRecently, Srivastava, Özarslan and Kaanoglu have introduced certain families of three and two variable polynomials, which include Lagrange and Lagrange-Hermite polynomials, and obtained families of two-sided linear generating functions between these families [H.M. Srivastava, M.A. Özarslan, C. Kaanoglu, Some families of generating functions for a certain class of three-variable polynomials, Integr. Transform. Spec. Funct. iFirst (2010) 1-12]. The main object of this investigation is to obtain new two-sided linear generating functions between these families by applying certain hypergeometric transformations. Furthermore, more general families of bilinear, bilateral, multilateral finite series relationships and generating functions are presented for themDue to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationElsevier ınc2017-10-23T08:26:24Z2017-10-23T08:26:24Z2011article0096-3003(print)1873-5649(online)http://dx.doi.org/10.1016/j.amc.2011.01.083http://hdl.handle.net/11129/34622183836842eng10.1016/j.amc.2011.01.083Applied Mathematics and Computationinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34662017-10-23T08:43:02Zhdl_11129_784Extension of gamma, beta and hypergeometric functionsÖzergin, EmineÖzarslan, Mehmet AliAltın, AbdullahBeta function, Confluent hypergeometric function,Mellin transform, Gamma function, MATHEMATICS, APPLIEDThe main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new generalizations.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationElsevier B.V2017-10-23T08:43:02Z2017-10-23T08:43:02Z2011article0377-0427(print)1879-1778(online)http://dx.doi.org/10.1016/j.cam.2010.04.019http://hdl.handle.net/11129/34662351646014610eng10.1016/j.cam.2010.04.019Journal of Computational and Applied Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34512017-10-23T08:17:59Zhdl_11129_784Local approximation results for Szász-Mirakjan type operatorsÖzarslan, Mehmet AliDuman, Oktaypositive linear operators, 41A36, local approximation, the second modulus of smoothness,Szász-Mirakjan operators, 41A25, Petree’s K -functional, Mathematics,general, Mathematics, The second modulus of smoothnessPetree's K-functional, Positive linear operators, Local approximation,Szasz-Mirakjan operators, MATHEMATICS, POSITIVE LINEAR-OPERATORSIn this study, motivating our earlier work [O. Duman and M.A. Ozarslan, Szasz-Mirakjan type operators providing a better error estimation. Appl. Math. Lett. 20, 1184--1188 (2007)], we investigate the local approximation properties of Szasz-Mirakjan type operators. The second modulus of smoothness and Petree's K-functional are considered in proving our results.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationSP Birkhäuser Verlag Basel2017-10-23T08:17:59Z2017-10-23T08:17:59Z2008article0003-889X(print)http://dx.doi.org/10.1007/s00013-007-2354-51420-8938(online)http://hdl.handle.net/11129/3451902144149eng10.1007/s00013-007-2354-5Archiv der Mathematikinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34452017-10-23T08:11:38Zhdl_11129_784Korovkin type approximation theorem for BBH type operators via J-convergenceÖzarslan, Mehmet AliAktuğlu, Hüseyinpositive linear operators, STATISTICAL CONVERGENCE,MATHEMATICS, BBH operators, POSITIVE LINEAR-OPERATORS,I-convergence, Korovkin theorem, A-statistical convergenceThis paper provides a Korovkin type approximation theorem for a class of positive linear operators including Bleimann-Butzer and Hahn operators via J-convergence.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Versıta2017-10-23T08:11:38Z2017-10-23T08:11:38Z2010article0139-9918(print)1337-2211(online)http://dx.doi.org/10.2478/s12175-010-0053-3http://hdl.handle.net/11129/3445606865876eng10.2478/s12175-010-0053-3Mathematica Slovacainfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34582017-10-23T08:21:15Zhdl_11129_784Rates of Ideal Convergence for Approximation OperatorsÖzarslan, Mehmet AliDuman, Oktaypositive linear operators, Secondary 41A25, Korovkin-type approximation theory,A -statistical convergence, Primary 41A10, {\mathcal {I}}$$ -convergenceMathematics, general, Mathematics, I-convergence, Positive linear operators,A-statistical convergence, MATHEMATICS, APPLIED,STATISTICAL CONVERGENCE, MATHEMATICS,In this paper, we study a general Korovkin-type approximation theory by using the notion of ideal convergence which includes many convergence methods, such as, the usual convergence, statistical convergence, A-statistical convergence, etc. We mainly compute the rate of ideal convergence of sequences of positive linear operators.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.SP Birkhäuser Verlag Basel2017-10-23T08:21:15Z2017-10-23T08:21:15Z2010article1660-5446(print)1660-5454(online)http://dx.doi.org/10.1007/s00009-010-0031-6http://hdl.handle.net/11129/345871111121eng10.1007/s00009-010-0031-6Mediterranean Journal of Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34542017-10-23T08:19:19Zhdl_11129_784Families of linear generating functions for polynomials in two variablesÖzarslan, Mehmet AliAltın, AbdullahErkuş, EsraHermite-Kampé de Fériet polynomials, Generating functions, Lagrange-Hermite polynomials,Jacobi polynomials, Lagrange polynomials, Pochhammer symbol, MATHEMATICS,APPLIED, MATHEMATICS, HYPERGEOMETRIC POLYNOMIALS,generating functions, Hermite-Kampe de Feriet polynomialsIn the present paper, we derive various families of linear, mixed multilateral and multilinear generating functions for a class of polynomials in two variables. Some further results of the above types are also discussed.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Taylor & Francis2017-10-23T08:19:19Z2017-10-23T08:19:19Z2006article1065-2469(print)1476-8291(online)http://dx.doi.org/10.1080/10652460600568162http://hdl.handle.net/11129/3454175315320eng10.1080/10652460600568162Integral Transforms and Special Functionsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34612017-10-23T08:25:50Zhdl_11129_784q-Szász operators which preserve x 2Mahmudov, Nazim I.modulus of continuity, q-Szász-Mirakjan operators, Voronovskaja type theoremIn the present paper we construct q-Szász operators that preserve the third test function e 2. Rate of global convergence is obtained in the frame of weighted spaces. Furthermore, we obtain a Voronovskaja type theorem for these operators.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Springer Verlag2017-10-23T08:25:50Z2017-10-23T08:25:50Z2013article0139-9918(print)1337-2211(online)http://dx.doi.org/10.2478/s12175-013-0155-9http://hdl.handle.net/11129/346163510591072eng10.2478/s12175-013-0155-9Mathematica Slovacainfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34552017-10-23T23:00:38Zhdl_11129_784On a class of generalized q-Bernoulli and q-Euler polynomialsMahmudov, Nazim I.Keleshteri, M EiniDifference and Functional Equations, Partial Differential Equations, Ordinary Differential EquationsAnalysis, Functional Analysis, Mathematics, general, Mathematics APOSTOL-BERNOULLI,ANALOGS,ORDER, ZETA, Q-EXTENSIONS, L-SERIES, NUMBERS, Functions, Exponential, Usage, Euler anglesThe main purpose of this paper is to introduce and investigate a new class of generalized q-Bernoulli and q-Euler polynomials. The q-analogues of well-known formulas are derived. A generalization of the Srivastava-Pintér addition theorem is obtained.The file in this item is the publisher version (published version) of the article.Springer International Publishing AG2017-10-23T08:19:42Z2017-10-23T08:19:42Z2013article1687-1847, 1687-1839(print)http://dx.doi.org/10.1186/1687-1847-2013-115http://hdl.handle.net/11129/345520131110eng10.1186/1687-1847-2013-115Advances in Difference Equationsinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34712017-10-23T08:46:17Zhdl_11129_784Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integersMahmudov, Nazim I.q-Baskakov-Kantorovich operators, 41A36, Weighted space, 41A30, 41A25,Weighted modulus of smoothness, Number Theory, Mathematics, Topological Groups, Lie Groups,Algebra, q-Baskakov operators, Geometry, q-integers, Mathematics, general,Probability Theory and Stochastic Processes, ZELLER OPERATORS, MATHEMATICS,In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.SP Versita2017-10-23T08:46:17Z2017-10-23T08:46:17Z2010article1895-1074(print)1644-3616(online)http://dx.doi.org/10.2478/s11533-010-0040-5http://hdl.handle.net/11129/347184816826eng10.2478/s11533-010-0040-5Central European Journal of Mathematicsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34602017-10-23T08:23:57Zhdl_11129_784The moments for q-Bernstein operators in the case 0 < q < 1Mahmudov, Nazim I.Central moment, Algebra, Computer Science, Positive linear operator, Numeric Computing,Algorithms, q -derivative, Mathematics, general, Theory of Computation, q -Bernstein operator,q -Bernstein polynomials, q-derivative, q-Bernstein polynomials, q-Bernstein operator,MATHEMATICS, APPLIED, POLYNOMIALS, CONVERGENCE, OMEGAIn this note we give the estimates of the central moments for q-Bernstein operators (0 < q < 1) which can be used for studying the approximation properties of the operators.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationSpringer US2017-10-23T08:23:57Z2017-10-23T08:23:57Z2010article1017-1398(print)1572-9265(online)http://dx.doi.org/10.1007/s11075-009-9312-1http://hdl.handle.net/11129/3460534439450eng10.1007/s11075-009-9312-1Numerical Algorithmsinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34752017-10-23T08:47:38Zhdl_11129_784On modeling with multiplicative differential equationsTandoğdu, YücelBashirov, AgamirzaMısırlı, EmineÖzyapıcı, AliGompertz function, 97M10, exponential arithmetic, elasticity, 93A30, multiplicative calculus,Applications of Mathematics, 00A71, Mathematics, general, growth, Mathematics, MATHEMATICS, APPLIED, CALCULUSThis work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts..Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publicationSP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities2017-10-23T08:47:38Z2017-10-23T08:47:38Z2011article1005-1031(print)1993-0445(online)http://dx.doi.org/10.1007/s11766-011-2767-6http://hdl.handle.net/11129/3475264425438eng10.1007/s11766-011-2767-6Applied Mathematics-A Journal of Chinese Universitiesinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34652017-10-23T08:42:42Zhdl_11129_784Synthesis and photophysical properties of N,N′-bis(4-cyanophenyl)-3,4,9,10-perylenebis(dicarboximide) and N,N′-bis(4-cyanophenyl)-1,4,5,8-naphthalenediimideUzun, DuyguÖzser, Mustafa E.Yüney, KıvançIcil, HuriyeDemuth, MartinN, N′-Bis(4-cyanophenyl)-3,4,9,10-perylenebis(dicarboximide), N, N′-Bis(4-cyanophenyl)-1,4,5,8-naphthalenediimide,Aggregation, Organic solar cells, Electron transfer reactions,N,N′-Bis(4-cyanophenyl)-3,4,9,10-perylenebis(dicarboximide), N,N′-Bis(4-cyanophenyl)-1,4,5,8-naphthalenediimide,PERYLENE, SOLAR-CELLS, DERIVATIVES, CHEMISTRY, PHYSICAL,N,N′-Bis(4-cyanophenyl)-1,4,5,8-naphthalenediimide (CN-NDI) and N,N′-bis(4-cyanophenyl)-3,4,9,10-perylenebis(dicarboximide) (CN-PDI) have been synthesized under special conditions in high yield. The compounds are characterized by UV-Vis, IR, NMR, MS, DSC, TGA and CV measurements. The fluorescence lifetimes, quantum yields and singlet-state energies are presented. CN groups at the phenyl moieties improve the thermal stability of the compounds. The LUMO energy values, −3.91 eV (CN-NDI in solution) and −3.96 eV (CN-NDI and CN-PDI at solid state), are determined by cyclic voltammetry. Whereas CN-NDI shows two reversible (−0.89 and −1.34 V) reduction steps (vs. Fc) in solution, CN-NDI and CN-PDI exhibit only one reversible wave at −0.48 V vs. Ag/AgCl at solid state, assigned to the one-electron reduction. Formation of aggregates shifts the UV absorption spectrum of CN-PDI to shorter wavelengths and its lifetime is measured as 4.6 ns at 580 nm. CN-PDI may be a promising dye for organic solar cells.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Elsevier B.V2017-10-23T08:42:42Z2017-10-23T08:42:42Z2003letter1873-2666(online)1010-6030(print)http://dx.doi.org/10.1016/S1010-6030(02)00436-7http://hdl.handle.net/11129/346515614554eng10.1016/S1010-6030(02)00436-7Journal of Photochemistry & Photobiology, A: Chemistryinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34302017-10-19T08:23:43Zhdl_11129_784New Singular and Nonsingular Colliding Wave Solutions in Einstein-Maxwell-Scalar TheoryGürtuğ, ÖzayHalilsoy, MustafaSakallı, İzzetEinstein-Maxwell-Scalar Theory, Physics, Mathematical and Computational Physics,Relativity and Cosmology, Differential Geometry, Colliding waves, ASTRONOMY & ASTROPHYSICS, FIELD,Einstein-Maxwell-scalar theory, PHYSICS, MULTIDISCIPLINARY, PLANE-WAVES,A technique is given to generate coupled scalar field solutions in colliding Einstein-Maxwell (EM) waves. By employing the Bell-Szekeres solution as seed and depending on the chosen scalar field, it is possible to construct nonsingular solutions. If the original EM solution is already singular, addition of scalar fields does not make the physics any better. In particular, scalar field solution that is transformable to spherical symmetry is plagued with singularities.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Kluwer Academic Publishers-Plenum Publishers2017-10-19T08:23:43Z2017-10-19T08:23:43Z2003article0001-7701 (Online)1572-9532 (Print)http://dx.doi.org/10.1023/A:1027349606694http://hdl.handle.net/11129/3430351221592170eng10.1023/A:1027349606694General Relativity and Gravitationinfo:eu-repo/semantics/closedAccess
oai:i-rep.emu.edu.tr:11129/34682017-10-23T23:00:39Zhdl_11129_784Effect of sources on the inner horizon of black holesGürtuğ, ÖzayHalilsoy, Mustafasingle pulse regular horizon extrapolates spacelikeA single pulse of null dust and colliding null dust both transform a regular horizon into a spacelike singularity
in the space of colliding waves. The local isometry between such space-times and black holes extrapolates
these results to the realm of black holes. However, the inclusion of particular scalar fields instead of null
dust creates null singularities rather than spacelike ones on the inner horizons of black holes.The file in this item is the publisher version (published version) of the article.The American Physcial Society2017-10-23T08:44:20Z2017-10-23T08:44:20Z2001article0556-2821(print)1089-4918(online)http://dx.doi.org/10.1103/PhysRevD.64.084023http://hdl.handle.net/11129/346864817eng10.1103/PhysRevD.64.084023Physical Review Dinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34702017-10-23T23:00:33Zhdl_11129_784Reflection of electromagnetic waves from mixtures of plane gravitational and scalar wavesGürtuğ, ÖzayHalilsoy, MustafaÜnver, Özlemhybrid mixtures of electromagnetic, gravitational, and scalar waves. Irrespective of the scalar field,multiple reflection of an electromagnetic wave,Coulomb-like component 2 vanishesWe consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational, and
scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational
wave. Some reflection processes are given for different choice of packets in which the Coulomb-like
component 2 vanishes. Exact solution for multiple reflection of an electromagnetic wave from
successive impulsive gravitational waves is obtained in a closed form. It is shown that a successive
sign flip in the Maxwell spinor arises as a result of encountering with an impulsive train (i.e. the Dirac’s
comb curvature) of gravitational waves. Such an observable effect may be helpful in the detection of
gravitational wave bursts.The file in this item is the publisher version (published version) of the article.American Physical Soc2017-10-23T08:45:56Z2017-10-23T08:45:56Z2006article1550-7998 (Online)1550-2368 (Print)http://dx.doi.org/10.1103/PhysRevD.74.044020http://hdl.handle.net/11129/347074418eng10.1103/PhysRevD.74.044020Physical Review Dinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34322017-10-19T23:00:37Zhdl_11129_784Search for gravitational waves through the electromagnetic Faraday rotationHalilsoy, MustafaGürtuğ, ÖzayFaraday rotation in the polarization vector of the electromagnetic field. Remove selectedA method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly nonlinear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field.The file in this item is the publisher version (published version) of the article.AMER PHYSICAL SOC2017-10-19T08:24:51Z2017-10-19T08:24:51Z2007article1550-7998 (Online)1550-2368 (Print)http://dx.doi.org/10.1103/PhysRevD.75.124021http://hdl.handle.net/11129/3432751214eng10.1103/PhysRevD.75.124021Physical Review D - Particles, Fields, Gravitation and Cosmologyinfo:eu-repo/semantics/openAccess
oai:i-rep.emu.edu.tr:11129/34722017-10-23T08:46:36Zhdl_11129_784Colliding Wave Solutions in a Symmetric Non-Metric TheoryGürtuğ, ÖzayHalilsoy, MustafaPhysics, Physics, general, Mathematical and Computational Physics, Colliding gravitational waves, Torsion waves, Quantum Physics, Elementary Particles, Quantum Field Theory,A method is given to generate the non-linear interaction (collision) of linearly polarized gravity coupled torsion waves in a non-metric theory. Explicit examples are given in which strong mutual focussing of gravitational waves containing impulsive and shock components coupled with torsion waves does not result in a curvature singularity. However, the collision of purely torsion waves displays a curvature singularity in the region of interaction.Due to copyright restrictions, the access to the publisher version (published version) of this article is only available via subscription. You may click URI and have access to the Publisher Version of this article through the publisher web site or online databases, if your Library or institution has subscription to the related journal or publication.Springer US2017-10-23T08:46:36Z2017-10-23T08:46:36Z2009article0020-7748 (Online)1572-9575 (Print)http://dx.doi.org/10.1007/s10773-008-9789-8http://hdl.handle.net/11129/3472481139149eng10.1007/s10773-008-9789-8International Journal of Theoretical Physicsinfo:eu-repo/semantics/closedAccess