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Publication Open Access 2D hybrid meshes for direct simulation Monte Carlo solvers(Institute of Physics (IOP) Publishing, 2013) Şengil, Nevsan; Department of Mathematics; Şengil, Uluç; Master Student; Department of Mathematics; College of SciencesThe efficiency of the direct simulation Monte Carlo (DSMC) method decreases considerably if gas is not rarefied. In order to extend the application range of the DSMC method towards non-rarefied gas regimes, the computational efficiency of the DSMC method should be increased further. One of the most time consuming parts of the DSMC method is to determine which DSMC molecules are in close proximity. If this information is calculated quickly, the efficiency of the DSMC method will be increased. Although some meshless methods are proposed, mostly structured or non-structured meshes are used to obtain this information. The simplest DSMC solvers are limited with the structured meshes. In these types of solvers, molecule indexing according to the positions can be handled very fast using simple arithmetic operations. But structured meshes are geometry dependent. Complicated geometries require the use of unstructured meshes. In this case, DSMC molecules are traced cell-by-cell. Different cell-by-cell tracing techniques exist. But, these techniques require complicated trigonometric operations or search algorithms. Both techniques are computationally expensive. In this study, a hybrid mesh structure is proposed. Hybrid meshes are both less dependent on the geometry like unstructured meshes and computationally efficient like structured meshes.
Publication Metadata only A chain-binomial model for pull and push-based information diffusion(IEEE, 2006) Department of Mathematics; Department of Computer Engineering; Çağlar, Mine; Özkasap, Öznur; Faculty Member; Faculty Member; Department of Mathematics; Department of Computer Engineering; College of Sciences; College of Engineering; 105131; 113507We compare pull and push-based epidemic paradigms for information diffusion in large scale networks. Key benefits of these approaches are that they are fully distributed, utilize local information only via pair-wise interactions, and provide eventual consistency, scalability and communication topology-independence, which make them suitable for peer-to-peer distributed systems. We develop a chain-Binomial epidemic probability model for these algorithms. Our main contribution is the exact computation of message delivery latency observed by each peer, which corresponds to a first passage time of the underlying Markov chain. Such an analytical tool facilitates the comparison of pull and push-based spread for different group sizes, initial number of infectious peers and fan-out values which are also accomplished in this study. Via our analytical stochastic model, we show that push-based approach is expected to facilitate faster information spread both for the whole group and as experienced by each member.Publication Metadata only A characterization of the closed unital ideals of the Fourier-Stieltjes algebra B(G) of a locally compact amenable group G(Elsevier, 2003) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be a locally compact amenable group, B(G) its Fourier–Stieltjes algebra and I be a closed ideal of it. In this paper we prove the following result: The ideal I has a unit element iff it is principal. This is the noncommutative version of the Glicksberg–Host–Parreau Theorem. The paper also contains an abstract version of this theorem.Publication Metadata only A characterization of the invertible measures(Polish Acad Sciences Inst Mathematics, 2007) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be a locally compact abelian group and M(G) its measure algebra. Two measures mu and lambda are said to be equivalent if there exists an invertible measure pi such that pi * mu = lambda. The main result of this note is the following: A measure mu is invertible iff vertical bar(mu) over cap vertical bar >= epsilon on (G) over cap for some epsilon > 0 and mu is equivalent to a measure lambda of the form lambda = a + theta, where a is an element of L-1(G) and theta is an element of M(G) is an idempotent measure.Publication Open Access A class of Banach algebras whose duals have the Schur property(TÜBİTAK, 1999) Mustafayev, H.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of SciencesCall a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).Publication Metadata only A direct method for the inversion of physical systems(Institute of Physics (IOP) Publishing, 1994) Caudill, Lester F.; Rabitz, Herschel; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.Publication Open Access A generalization of the Hardy-Littlewood conjecture(Colgate University, 2022) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803A famous conjecture of Hardy and Littlewood claims the subadditivity of the prime counting function, namely that ?(x+y) ? ?(x)+?(y) holds for all integers x, y ? 2, where ?(x) is the number of primes not exceeding x. It is widely believed nowadays that this conjecture is not true since Hensley and Richards stunningly discovered an incompatibility with the prime k-tuples conjecture. Despite this drawback, here we generalize the subadditivity conjecture to subsets of prime numbers possessing a rich collection of preassigned structures. We show that subadditivity holds in this extended manner over certain ranges of the parameters which are wide enough to imply that it holds in an almost all sense. Under the prime k-tuples conjecture, very large values of convex combinations of the prime counting function are obtained infinitely often, thereby indicating a strong deviation of ?(x) from being convex, even in a localized form. Finally, a Tauberian type condition is given for subsets of prime numbers which in turn implies an extension of a classical phenomenon, originally suggested by Legendre, about the asymptotically best fit functions to ?(x) of the shape x/(log x ? A).Publication Metadata only A Hamiltonian formulation of the Pais-Uhlenbeck oscillator that yields a stable and unitary quantum system(Elsevier Science Bv, 2010) NA; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 105131We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a Hermitian operator with a positive spectrum, i.e., the quantum system is both stable and unitary. Furthermore it yields the classical Pais-Uhlenbeck oscillator in the classical limit. A consistent description of the degenerate case based on a Hamiltonian that is quadratic in momenta requires its analytic continuation into a complex Hamiltonian system possessing a generalized PT-symmetry (an involutive antilinear symmetry). We devise a real description of this complex system, derive an integral of motion for it, and explore its quantization.Publication Metadata only A long-range dependent workload model for packet data traffic(Inst Operations Research Management Sciences, 2004) Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131We consider a probabilistic model for workload input into a telecommunication system. It captures the dynamics of packet generation in data traffic as well as accounting for long-range dependence and self-similarity exhibited by real traces. The workload is found by aggregating the number of packets, or their sizes, generated by the arriving sessions. The arrival time, duration, and packet-generation process of a session are all governed by a Poisson random measure. We consider Pareto-distributed session holding times where the packets are generated according to a compound Poisson process. For this particular model, we show that the workload process is long-range dependent and fractional Brownian motion is obtained as a heavy-traffic limit. This yields a fast synthesis algorithm for generating packet data traffic as well as approximating fractional Brownian motion.Publication Metadata only A note on contact surgery diagrams(World Scientific Publishing, 2005) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We prove that for any positive integer k, the stabilization of a 1/k-surgery curve in a k contact surgery diagram induces an overtwisted contact structure.