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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms(De Gruyter, 2018) Lei, Antonio; Department of Mathematics; Büyükboduk, Kazım; Faculty Member; Department of Mathematics; College of Sciences; N/AThis is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Z(p)-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson-Flach elements.Publication Metadata only Semi-Markov modulated Poisson process: probabilistic and statistical analysis(Springer, 2006) Soyer, R.; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We consider a Poisson process that is modulated in such a way that the arrival rate at any time depends on the state of a semi-Markov process. This presents an interesting generalization of Poisson processes with important implications in real life applications. Our analysis concentrates on the transient as well as the long term behaviour of the arrival count and the arrival time processes. We discuss probabilistic as well as statistical issues related to various quantities of interest.Publication Metadata only Extension of one-dimensional proximity regions to higher dimensions(Elsevier, 2010) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AProximity regions (and maps) are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in various fields. The simplest of such maps is the spherical proximity map which gave rise to class cover catch digraph (CCCD) and was applied to pattern classification. In this article, we note some appealing properties of the spherical proximity map in compact intervals on the real line, thereby introduce the mechanism and guidelines for defining new proximity maps in higher dimensions. For non-spherical PCDs, Delaunay tessellation (triangulation in the real plane) is used to partition the region of interest in higher dimensions. We also introduce the auxiliary tools used for the construction of the new proximity maps, as well as some related concepts that will be used in the investigation and comparison of these maps and the resulting PCDs. We provide the distribution of graph invariants, namely, domination number and relative density, of the PCDs and characterize the geometry invariance of the distribution of these graph invariants for uniform data and provide some newly defined proximity maps in higher dimensions as illustrative examples. (C) 2010 Elsevier B.V. All rights reserved.Publication Metadata only Decay of solutions and structural stability for the coupled Kuramoto-Sivashinsky–Ginzburg-Landau equations(Taylor & Francis Ltd, 2015) Celebi, Okay A.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655We show that solutions of the initial boundary value problem for the coupled system of Kuramoto-Sivashinsky and Ginzburg-Landau (KS–GL) equations continuously depend on parameters of the system, and under some restrictions on parameters all solutions of initial boundary value problem for KS–GL equations tend to zero as with an exponential rate.Publication Metadata only Global attractors for 2D navier–stokes–voight equations in an unbounded domain(Taylor & Francis Ltd, 2009) Celebi, A. O.; Polat, M.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655We consider the 2D Navier–Stokes–Voight equation in an unbounded strip-like domain. It is shown that the semigroup generated by this equation has a global attractor in weighted Sobolev spaces.Publication Metadata only Preventing blow up by convective terms in dissipative PDE’s(Springer Basel Ag, 2016) Zelik, Sergey; N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member 0000-0002-6282-4027; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation and KdV type equations. The following common scenario is established: adding sufficiently strong (in comparison with the destabilizing nonlinearity) convective terms to equation prevents the solutions from blowing up in a finite time and makes the considered system globally well-posed and dissipative and for weak enough convective terms the finite time blow up may occur similar to the case, when the equation does not involve convective term. This kind of result has been previously known for the case of Burger's type equations and has been strongly based on maximum principle. In contrast to this, our results are based on the weighted energy estimates which do not require the maximum principle for the considered problem.Publication Metadata only Scheduling chains with identical jobs and constant delays on a single machine(Springer, 2006) Brucker, P; Knust, S; Department of Industrial Engineering; Oğuz, Ceyda; Faculty Member; Department of Industrial Engineering; College of Engineering; 6033In this paper we study the single-machine problem 1|chains(l), p j = p|∑ C j in which jobs with constant processing times and generalized precedence constraints in form of chains with constant delays are given. One has to schedule the jobs on a single machine such that all delays between consecutive jobs in a chain are satisfied and the sum of all completion times of the jobs is minimized. We show that this problem is polynomially solvable.Publication Metadata only Degenerate spin groups as semi-direct products(Springer, 2010) Kocak, Sahin; Limoncu, Murat; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358Let Q be a symmetric bilinear form on R(n)=R(p+q+r) with corank r, rank p+q and signature type (p, q), p resp. q denoting positive resp. negative dimensions. We consider the degenerate spin group Spin(Q) = Spin(p, q, r) in the sense of Crumeyrolle and prove that this group is isomorphic to the semi-direct product of the nondegenerate and indefinite spin group Spin(p, q) with the additive matrix group Mat (p + q, r)Publication Metadata only Bayesian analysis of Markov modulated Bernoulli processes(Springer, 2003) Soyer, R.; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We consider Markov Modulated Bernoulli Processes (MMBP) where the success probability of a Bernoulli process evolves over time according to a Markov chain. The MMBP is applied in reliability modeling where systems and components function in a randomly changing environment. Some of these applications include, but are not limited to, reliability assessment in power systems that are subject to fluctuating weather conditions over time and reliability growth processes that are subject to design changes over time. We develop a general setup for analysis of MMBPs with a focus on reliability modeling and present Bayesian analysis of failure data and illustrate how reliability predictions can be obtained.Publication Metadata only Modeling and simulation of metabolic networks for estimation of biomass accumulation parameters(Elsevier, 2009) Biegler, L.; Karasozen, Bülent; N/A; Department of Industrial Engineering; Kaplan, Uğur; Türkay, Metin; PhD Student; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 24956Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. TO understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses. (c) 2008 Elsevier B.V. .