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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only On maximal partial Latin hypercubes(Springer, 2023) Donovan, Diane M.; Grannell, Mike J.; Department of Mathematics; Yazıcı, Emine Şule; Department of Mathematics; College of SciencesA lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d and order n. The result generalises and extends previous results for d= 2 (Latin squares) and d= 3 (Latin cubes). Explicit constructions show that this bound is near-optimal for large n> d . For d> n , a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2.Publication Metadata only Exactness of the first born approximation in electromagnetic scattering(Oxford Univ Press Inc, 2024) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of SciencesFor the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born approximation yields the exact expression for the scattered wave whenever the incident wavenumber k does not exceed a preassigned value alpha. We also show that under this condition the medium is omnidirectionally invisible for k <= alpha/2, i.e. it displays broadband invisibility regardless of the polarization of the incident wave.Publication Metadata only A support function based algorithm for optimization with eigenvalue constraints(Siam Publications, 2017) N/A; Department of Mathematics; Mengi, Emre; Faculty Member; Department of Mathematics; College of Sciences; 113760Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and Hermitian matrix-valued function. We propose a numerical approach based on quadratic support functions that overestimate the smallest eigenvalue function globally. the quadratic support functions are derived by employing variational properties of the smallest eigenvalue function over a set of Hermitian matrices. We establish the local convergence of the algorithm under mild assumptions and deduce a precise rate of convergence result by viewing the algorithm as a fixed point iteration. the convergence analysis reveals that the algorithm is immune to the nonsmooth nature of the smallest eigenvalue. We illustrate the practical applicability of the algorithm on the pseudospectral functions.Publication Metadata only On the anticyclotomic Iwasawa theory of CM forms at supersingular primes(European Mathematical Soc, 2015) Department of Mathematics; Büyükboduk, Kazım; Faculty Member; Department of Mathematics; College of Sciences; N/AIn this paper, we study the anticyclotomic Iwasawa theory of a CM form f of even weight w >= 2 at a supersingular prime, generalizing the results in weight 2, due to Agboola and Howard. In due course, we are naturally lead to a conjecture on universal norms that generalizes a theorem of Perrin-Riou and Berger and another that generalizes a conjecture of Rubin (the latter seems linked to the local divisibility of Heegner points). Assuming the truth of these conjectures, we establish a formula for the variation of the sizes of the Selmer groups attached to the central critical twist of f as one climbs up the anticyclotomic tower. We also prove a statement which may be regarded as a form of the anticyclotomic main conjecture (without p-adic L-functions) for the central critical twist of f.Publication Metadata only Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti- PT -symmetry(American Physical Society, 2023) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, homogenous, or passive. Unlike the traditional transfer matrices whose definition involves slicing the medium, the fundamental transfer matrix is a linear operator acting in an infinite-dimensional function space. It is given in terms of the evolution operator for a nonunitary quantum system and has the benefit of allowing for analytic calculations. In this respect it is the only available alternative to the standard Green's-function approaches to EM scattering. We use it to offer an exact solution of the outstanding EM scattering problem for an arbitrary finite collection of possibly anisotropic nonmagnetic point scatterers lying on a plane. In particular, we provide a comprehensive treatment of doublets consisting of pairs of isotropic point scatterers and study their spectral singularities. We show that identical and PT-symmetric doublets do not admit spectral singularities and cannot function as a laser unless the real part of their permittivity equals that of the vacuum. This restriction does not apply to doublets displaying anti-PT-symmetry. We determine the lasing threshold for a generic anti-PT-symmetric doublet and show that it possesses a continuous lasing spectrum.Publication Metadata only Symplectic and Lagrangian surfaces in 4-manifolds(Rocky Mt Math Consortium, 2008) Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206This is a brief summary of recent examples of isotopically different symplectic and Lagrangian surfaces representing a fixed homology class in a simply-connected symplectic 4-manifold.Publication Metadata only Number of least area planes in gromov hyperbolic 3-spaces(American Mathematical Society (AMS), 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences; N/AWe show that for a generic simple closed curve Gamma in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exists a unique least area plane Sigma in X such that partial derivative(infinity)Sigma = Gamma. This result has interesting topological applications for constructions of canonical 2-dimensional objects in Gromov hyperbolic 3-manifolds.Publication Metadata only Decomposition of lambda K-nu into kites and 4-cycles(Charles Babbage Research Centre, 2017) Milici, Salvatore; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252Given a collection of graphs H, an H-decomposition of λkv is a decomposition of the edges of λKv into isomorphic copies of graphs in Ti. A kite is a triangle with a tail consisting of a single edge. In this paper we investigate the decomposition problem when H is the set containing a kite and a 4-cycle, that is; this paper gives a complete solution to the problem of decomposing λKv into r kites and s 4-cycles for every admissible values of v, λ, r and s.Publication Metadata only Principles and performance analysis of second: a system for epidemic peer-to-peer content distribution(Academic Press Ltd- Elsevier Science Ltd, 2009) N/A; Department of Computer Engineering; Department of Mathematics; Department of Computer Engineering; Özkasap, Öznur; Çağlar, Mine; Alagöz, Ali; Faculty Member; Faculty Member; Other; Department of Mathematics; Department of Computer Engineering; College of Engineering; College of Sciences; College of Engineering; 113507; 105131; N/AWe propose and design a peer-to-peer system, SeCond, addressing the distribution of large sized content to a large number of end systems in an efficient manner. In contrast to prior work, it employs a self-organizing epidemic dissemination scheme for state propagation of available blocks and initiation of block transmissions. in order to exploit heterogeneity of peers, enhance the utilization of system resources and for the ease of deployment, scalability, and adaptivity to dynamic peer arrivals/departures, we propose mechanisms for adjusting protocol parameters dynamically according to the bandwidth usages. We describe design and analysis details of our protocol SeCond. Comprehensive performance evaluations and comparison with the BitTorrent system model have been accomplished for a wide range of scenarios. Performance results include scalability analysis for different arrival/departure patterns, flash-crowd scenario, overhead analysis, and fairness ratio. The major metrics we study include the average file download time, load on the primary seed, uplink/downlink utilization. and communication overhead. We show that SeCond is a scalable and adaptive protocol which takes the heterogeneity of the peers into account. The protocol is as fair as BitTorrent although it has no explicit strategy addressing free-riding. We also illustrate the applicability of an analytical fluid model to the behavior of SeCond.Publication Metadata only An investigation of new graph invariants related to the domination number of random proximity catch digraphs(Springer, 2012) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AProximity catch digraphs (PCDs) are a special type of proximity graphs based on proximity maps which yield proximity regions. PCDs are defined using the relative allocation of points from two or more classes in a region of interest and have applications in various fields. We introduce some auxiliary tools for PCDs and graph invariants related to the domination number of the PCDs and investigate their probabilistic properties. We consider the cases in which the vertices of the PCDs come from uniform and non-uniform distributions in the region of interest. We also provide some of the newly defined proximity maps as illustrative examples.