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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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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 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 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 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 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.Publication Metadata only Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms(De Gruyter, 2018) Lei, Antonio; Department of Mathematics; Büyükboduk, Kazım; Faculty Member; Department of Mathematics; College of Sciences; N/AThis is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Z(p)-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson-Flach elements.Publication Metadata only The structure of power bounded elements in Fourier-Stieltjes algebras of locally compact groups(Elsevier Science Bv, 2013) Kaniuth, Eberhard; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be an arbitrary locally compact group and B(G) its Fourier-Stieltjes algebra. An element u of B(G) is called power bounded if sup(n is an element of N) parallel to u(n)parallel to < infinity. We present a detailed analysis of the structure of power bounded elements of B(G) and characterize them in terms of sets in the coset ring of G and w*-convergence of sequences (v(n))(n is an element of N), v is an element of B(G).Publication Metadata only Contact open books with exotic pages(Springer Basel Ag, 2015) van Koert, Otto; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity symplectomorphism. We show that the resulting infinitely many contact 5-manifolds are all diffeomorphic but pairwise non-contactomorphic. Moreover, we explicitly determine these contact 5-manifolds.Publication Metadata only Trigonometric series and special values of L-functions(Academic Press Inc Elsevier Science, 2017) 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; 252019Inspired by representations of the class number of imaginary quadratic fields, in this paper, we give explicit evaluations of trigonometric series having generalized harmonic numbers as coefficients in terms of odd values of the Riemann zeta function and special values of L-functions subject to the parity obstruction. The coefficients that arise in these evaluations are shown to belong to certain cyclotomic extensions. Furthermore, using best polynomial approximation of smooth functions under uniform convergence due to Jackson and their log-sine integrals, we provide approximations of real numbers by combinations of special values of L-functions corresponding to the Legendre symbol. Our method for obtaining these results rests on a careful study of generating functions on the unit circle involving generalized harmonic numbers and the Legendre symbol, thereby relating them to values of polylogarithms and then finally extracting Fourier series of special functions that can be expressed in terms of Clausen functions.