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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 Stabilization of solutions of marine riser equations(Wiley, 2024) Ahmedov, S. Z.; Namazov, A. A.; Department of Mathematics; Kalantarov, Varga; Department of Mathematics; College of SciencesWe study the problem of stabilization to zero stationary state of nonlinear fourth-order wave equation with nonlinear damping term modelling dynamics of marine riser by feedback control terms that employ finitely many Fourier modes. Additionally, we demonstrate that the corresponding equation with linear damping, which represents the dynamics of pipes conveying fluids, can be exponentially stabilized by a feedback controller employing a finite number of Fourier modes.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 characterization of heaviness in terms of relative symplectic cohomology(Wiley, 2024) Mak, Cheuk Yu; Sun, Yuhan; Department of Mathematics; Varolgüneş, Umut; Department of Mathematics; College of SciencesFor a compact subset K$K$ of a closed symplectic manifold (M,omega)$(M, \omega)$, we prove that K$K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.Publication Metadata only Can Nth order Born approximation be exact?(IOP Publishing Ltd, 2024) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of SciencesFor the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the Nth order Born approximation gives the exact solution of the scattering problem for some N >= 1.Publication Metadata only Orthogonal cycle systems with cycle length less than 10(John Wiley and Sons Inc, 2024) Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Department of Mathematics; College of SciencesAn H-decomposition of a graph G is a partition of the edge set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of G is a set of kH-decompositions of G such that any two copies of H in distinct H-decompositions intersect in at most one edge. When G = K-v, we call the H-decomposition an H-system of order v. In this paper, we consider the case H is an l-cycle and construct a pair of orthogonal l-cycle systems for all admissible orders when l is an element of {5, 6, 7, 8, 9}, except when l = v.Publication Metadata only Complex vs. convex Morse functions and geodesic open books(World Scientific, 2024) Dehornoy, Pierre; Department of Mathematics; Özbağcı, Burak; Department of Mathematics; College of SciencesSuppose that Sigma is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of Sigma, having complex, contact and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on Sigma. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on Sigma. Moreover, we observe that if Sigma has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages.Publication Metadata only QC-LDPC codes from difference matrices and difference covering arrays(IEEE-Inst Electrical Electronics Engineers Inc, 2023) Donovan, Diane M.; Rao, Asha; Üsküplü, Elif; Department of Mathematics; Yazıcı, Emine Şule; Department of Mathematics; ; College of Sciences;We give a framework that generalizes LDPC code constructions using transversal designs or related structures such as mutually orthogonal Latin squares. Our constructions offer a broader range of code lengths and codes rates. Similar earlier constructions rely on the existence of finite fields of order a power of a prime, which significantly restricts the functionality of the resulting codes. In contrast, the LDPC codes constructed here are based on difference matrices and difference covering arrays, structures that are available for any order a, resulting in LDPC codes across a broader class of parameters, notably length a(a - 1), for all even a. Such values are not possible with earlier constructions, thus establishing the novelty of these new constructions. Specifically the codes constructed here satisfy the RC constraint and for a odd, have length a(2) and rate 1 - (4a - 3)/a(2), and for a even, length a(2) - a and rate at least 1 - (4a - 6)/(a(2 )- a). When 3 does not divide a, these LDPC codes have stopping distance at least 8. When a is odd and both 3 and 5 do not divide a, our construction delivers an infinite family of QC-LDPC codes with minimum distance at least 10. We also determine lower bounds for the stopping distance of the code. Further we include simulation results illustrating the performance of our codes. The BER and FER performance of our codes over AWGN (via simulation) is at least equivalent to codes constructed previously.Publication Metadata only Uniform syndeticity in multiple recurrence(CAMBRIDGE UNIV PRESS, 2024) Pan, Minghao; Department of Mathematics; Jamneshan, Asgar; Department of Mathematics; College of SciencesThe main theorem of this paper establishes a uniform syndeticity result concerning the multiple recurrence of measure-preserving actions on probability spaces. More precisely, for any integers d, l >= 1 and any epsilon > 0, we prove the existence of delta > 0 and K >= 1 (dependent only on d, l, and epsilon) such that the following holds: Consider a solvable group Gamma of derived length l, a probability space (X, mu), and d pairwise commuting measure-preserving Gamma-actions T-1, & mldr;, T-d on (X, mu). Let E be a measurable set in X with mu(E) >= epsilon. Then, K many (left) translates of {gamma is an element of Gamma: mu (T-1(gamma-1 )(E)boolean AND T-2(gamma-1)degrees T-1(gamma-1 )(E) boolean AND center dot center dot center dot boolean AND T-d(gamma-1 )degrees T-d-1(gamma-1 )degrees center dot center dot center dot degrees T-1(gamma-1 )(E)) >= delta} cover Gamma. This result extends and refines uniformity results by Furstenberg and Katznelson. As a combinatorial application, we obtain the following uniformity result. For any integers d, l >= 1 and any epsilon>0, there are delta>0 and K >= 1 (dependent only on d, l, and epsilon) such that for all finite solvable groups G of derived length l and any subset E subset of G(d) with m(circle times d)(E) >= epsilon (where m is the uniform measure on G), we have that K-many (left) translates of {g is an element of G:m(circle times d)({(a(1), & mldr;, a(n)) is an element of G(d): (a(1), & mldr;, a(n)), (ga(1), a(2), & mldr;, a(n)), & mldr;, (ga(1), ga(2), & mldr;, ga(n)) is an element of E}) >= delta} cover G. The proof of our main result is a consequence of an ultralimit version of Austin's amenable ergodic Szemeredi theorem.Publication Metadata only Consistent treatment of quantum systems with a time-dependent Hilbert space(MDPI, 2024) Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of SciencesWe consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product. © 2024 by the author.