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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only Counterexamples to regularity of Mane projections in the theory of attractors(Institute of Physics (IOP) Publishing, 2013) Eden, Alp; Zelik, Sergey V.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655This paper is a study of global attractors of abstract semilinear parabolic equations and their embeddings in finite-dimensional manifolds. As is well known, a sufficient condition for the existence of smooth (at least C-1-smooth) finite-dimensional inertial manifolds containing a global attractor is the so-called spectral gap condition for the corresponding linear operator. There are also a number of examples showing that if there is no gap in the spectrum, then a C-1-smooth inertial manifold may not exist. on the other hand, since an attractor usually has finite fractal dimension, by Mane's theorem it projects bijectively and Holder-homeomorphically into a finite-dimensional generic plane if its dimension is large enough. It is shown here that if there are no gaps in the spectrum, then there exist attractors that cannot be embedded in any Lipschitz or even log-Lipschitz finite-dimensional manifold. Thus, if there are no gaps in the spectrum, then in the general case the inverse Mane projection of the attractor cannot be expected to be Lipschitz or log-Lipschitz. Furthermore, examples of attractors with finite Hausdorff and infinite fractal dimension are constructed in the class of non-linearities of finite smoothness.Publication Metadata only Addendum to “On the mean square average of special values of L-functions” [J. Number Theory 131 (8) (2011) 1470–1485](Elsevier, 2011) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803Publication 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 On sums over the mobius function and discrepancy of fractions(Academic Press Inc Elsevier Science, 2013) Department of Mathematics; N/A; Alkan, Emre; Göral, Haydar; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 32803; 252019We obtain quantitative upper bounds on partial sums of the Mobius function over semigroups of integers in an arithmetic progression. Exploiting, the cancellation of such sums, we deduce upper bounds for the discrepancy of fractions in the unit interval [0, 1] whose denominators satisfy the same restrictions. In particular, the uniform distribution and approximation of discrete weighted averages over such fractions are established as a consequence.Publication Metadata only Pseudoduality and complex geometry in sigma models(World Scientific Publ Co Pte Ltd, 2013) Department of Mathematics; Sarısaman, Mustafa; Researcher; Department of Mathematics; College of Sciences; 217652We study the pseudoduality transformations in two-dimensional N = (2, 2) sigma models on Kahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti) holomorphic preserving mapping. This map requires that torsions related to individual spaces and riemann connection on pseudodual manifold must vanish. We also consider holomorphic isometries which puts additional constraints on the pseudoduality.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 Biased behavior of weighted mertens sums(World Scientific Publ Co Pte Ltd, 2020) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803Using convexity properties of reciprocals of zeta functions, especially the reciprocal of the Riemann zeta function, we show that certain weighted Mertens sums are biased in favor of square-free integers with an odd number of prime factors. We study such type of bias for different ranges of the parameters and then consider generalizations to Mertens sums supported on semigroups of integers generated by relatively large subsets of prime numbers. We further obtain a wider range for the parameters both unconditionally and then conditionally on the Riemann Hypothesis. At the same time, we extend to certain semigroups, two classical summation formulas originating from the works of Landau concerning the behavior of derivatives of the reciprocal of the Riemann zeta function at s = 1.Publication Metadata only Interior energy focusing within an elasto-plastic material(Pergamon-Elsevier Science Ltd, 1996) Tadi, M; Rabitz, H; Kim, YS; Prevost, JH; McManus, JB; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822In this paper we consider the problem of focusing acoustic energy within a subsurface volume in a solid by means of a designed surface pattern, and ask how that focusing is affected by plastic yield of the material. Surface force patterns that yield efficient subsurface acoustic focusing have been designed using optimal control theory, based on a linear elastic model of a solid. The acoustic waves generated by these forces then are propagated, via numerical algorithms, in a model solid that exhibits plastic yield. Numerical results indicate that as the amplitude of the force increases, yield begins to develop at the focus, with the formation of an expanding region of permanent plastic deformation. Despite the occurrence of yield near the focus, acoustic energy still can be delivered to the focal volume with good efficiency.