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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only The triangle intersection problem for K4 - E designs(Utilitas Mathematica Publishing Inc., 2007) Billington, Elizabeth J.; Lindner, C. C.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432An edge-disjoint decomposition of the complete graph Kn into copies of K4 - e, the simple graph with four vertices and five edges, is known to exist if and only if n ≡ 0 or 1 (mod 5) and n ≥ 6 (Bermond and Schönheim, Discrete Math. 19 (1997)). The intersection problem for K4 - e designs has also been solved (Billington, M. Gionfriddo and Lindner, J. Statist. Planning Inference 58 (1997)); this problem finds the number of common K4 - e blocks which two K4 - e designs on the same set may have. Here we answer the question: how many common triangles may two K4 - e designs on the same set have? Since it is possible for two K4 - e designs on the same set to have no common K4 - e blocks and yet some positive number of common triangles, this problem is largely independent of the earlier K4 - e intersection result.Publication Metadata only Time-dependent diffeomorphisms as quantum canonical transformations and the time-dependent harmonic oscillator(Iop Publishing Ltd, 1998) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a previously unknown class of exactly solvable time-dependent harmonic oscillators. The Caldirola-Kanai oscillator belongs to this class. For a general time-dependent harmonic oscillator, it is shown that choosing the dilatation parameter to satisfy the classical equation of motion, one obtains the solution of the Schrodinger equation. A simple generalization of this result leads to the reduction of the Schrodinger equation to a second-order ordinary differential equation whose special case is the auxiliary equation of the Lewis-Riesenfeld invariant theory. The time-evolution operator is expressed in terms of a positive red solution of this equation in a closed form, and the time-dependent position and momentum operators are calculated.Publication Metadata only Continuous dependence for the convective brinkman–forchheimer equations(Taylor & Francis, 2005) Çelebi, A.O.; Ugurlu, D.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655In this article, we have considered the convective Brinkman–Forchheimer equations with Dirichlet's boundary conditions. The continuous dependence of solutions on the Forchheimer coefficient in H 1 norm is proved.Publication Metadata only Asymptotic behavior of the irrational factor(Springer, 2008) Ledoan, A. H.; Zaharescu, Alexandru; Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803We study the irrational factor function I(n) introduced by Atanassov and defined by I(n) = Pi(k)(k=1)p(v)(1/alpha v), where n = Pi(k)(v=1) p(v)(alpha v) is the prime factorization of n. We show that the sequence {G(n)/n}(n >= 1), where G(n) = Pi(n)(v=1) I(v)(1/n), is covergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).Publication Metadata only Propagation of electromagnetic waves in linear media and pseudo-hermiticity(EPL Association, European Physical Society, 2008) Loran, F.; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We express the electromagnetic field propagating in an arbitrary time-independent non-dispersive medium in terms of an operator that turns out to be pseudo-Hermitian for Hermitian dielectric and magnetic permeability tensors (epsilon) over left right arrow and (mu) over left right arrow. We exploit this property to determine the propagating field. In particular, we obtain an explicit expression for a planar field in an isotropic medium with (epsilon) over left right arrow = epsilon(1) over left right arrow and mu = mu(1) over left right arrow varying along the direction of the propagation. We also study the scattering of plane waves due to a localized inhomogeneity.Publication Metadata only Z(n)-graded topological generalizations of supersymmetry and orthofermion algebra(Iop Publishing Ltd, 2003) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We review various generalizations of supersymmetry and discuss their relationship. in particular, we show how supersymmetry, parasupersymmetry, fractional supersymmetry, orthosupersymmetry, and the Z(n)-graded topological symmetries are related.Publication Metadata only Statistical origin of pseudo-Hermitian supersymmetry and pseudo-hermitian fermions(Iop Publishing Ltd, 2004) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N = 2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (nonequivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multifermion systems.Publication Metadata only Surgery diagrams for horizontal contactstructures(Springer, 2008) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We describe Legendrian surgery diagrams for some horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. As an application we determine Millior fillable contact structures on some Milnor fillable 3-manifolds.Publication Metadata only An analytical model based on G/M/1 with self-similar input to provide end-to-end QoS in 3G networks(Association for Computing Machinery (ACM), 2006) Iftikhar, M.; Landfeldt, B.; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131The dramatic increase in demand for wireless Internet access has lead to the introduction of new wireless architectures and systems including 3G, Wi-Fi and WiMAX. 3G systems such as UMTS and CDMA2000 are leaning towards an all-IP architecture for transporting IP multimedia services, mainly due to its scalability and promising capability of inter-working heterogeneous wireless access networks. During the last ten years, substantial work has been done to understand the nature of wired IP traffic and it has been proven that IP traffic exhibits self-similar properties and burstiness over a large range of time scales. Recently, because of the large deployment of new wireless architectures, researchers have focused their attention towards understanding the nature of traffic carried by different wireless architecture and early studies have shown that wireless data traffic also exhibits strong long-range dependency. Thus, the classical tele-traffic theory based on a simple Markovian process cannot be used to evaluate the performance of wireless networks. Unfortunately, the area of understanding and modeling of different kinds of wireless traffic is still immature which constitutes a problem since it is crucial to guarantee tight bound QoS parameters to heterogeneous end users of the mobile Internet. In this paper, we make several contributions to the accurate modeling of wireless IP traffic by presenting a novel analytical model that takes into account four different classes of self-similar traffic. The model consists of four queues and is based on a G/M/1 queueing system. We analyze it on the basis of priority with no preemption and find exact packet delays. To date, no closed form expressions have been presented for G/M/1 with priority.Publication Metadata only Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras(Institute of Mathematics of the Polish Academy of Sciences, 2007) Kaniuth, Eberhard; Lau, Anthony To-Ming; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism phi : A -> B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and phi) axe given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.