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Article Citation - WoS: 3Citation - Scopus: 4Some Permutations and Complete Permutation Polynomials Over Finite Fields(Tubitak Scientific & Technological Research Council Turkey, 2019) Ongan, Pınar; Temür, Burcu GülmezIn this paper we determine $b\\in F_{q^n}^\\ast$ for which the polynomial $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a permutationpolynomial and determine $b\\in F_{q^n}^\\ast$ for which the polynominal $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a complete permutationpolynomial where $s=\\frac{q^n-1}t,\\;t\\in\\mathbb{Z}^+$ such that $\\left.t\\;\\right|\\;q^n-1$.Article Citation - WoS: 1Citation - Scopus: 1A Short Note on Some Arithmetical Properties of the Integer Part of Ap(Tubitak Scientific & Technological Research Council Turkey, 2019) Akbal, YıldırımLet $a>0$ be an irrational number. We study some of the arithmetical properties of ${\\{\\lfloor ap\\rfloor\\}}_{p=2}^\\infty$ where pdenotes a prime number and $\\lfloor x\\rfloor$ denotes the largest integer not exceeding x.Article Characterizations of the Commutators Involving Idempotents in Certain Subrings of $m_{2}(\\mathbb{z})$(2023) Gümüşel, Günseli; Özdın, TufanIn this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]$ = $E_1E_2 − E_2E_1$ involving idempotents $E_1, E_2$ in certain subrings of $M_2(Z)$.Article A Note on the Generalized Matsumoto Relation(2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, MehmetcikWe give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.Article Self-Adjoint Boundary Value Problems on Time Scales and Symmetric Green' S Functions(2005) Guseınov, Gusein Sh.In this note, higher order self-adjoint differential expressions on time scales, and associated with them self-adjoint boundary conditions, are discussed. The symmetry peoperty of the corresponding Green's functions is emphasizedArticle Solving an Initial Boundary Value Problem on Thesemiinfinite Interval(2016) Atalan, Ferihe; Guseınov, Gusein Sh.We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at t = 0 and a condition at t = ∞.Article An Exhaustive Computer Search for Finding New Curves With Many Points Among Fibre Products of Two Kummer Covers Over $\\bbb{f}_5$ and $\\bbb{f}_7$(2013) Özbudak, Ferruh; Temür, Burcu Gülmez; Yayla, OğuzIn this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F5 and F7 . At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product $y^3_1$ = $\\frac {5(x+2)(x +5)} {x}$, $y^3_2$ $\\frac {3x^2(x +5)} {x + 3}$ over F7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N7 (7) of F7 -rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Özbudak and Temür (2012) for determining the number of rational points of such curves.Article On Symmetric Monomial Curves in $\\bbb{p}^3$(2009) Şahin, MesutIn this paper, we give an elementary proof of the fact that symmetric arithmetically Cohen-Macaulay monomial curves are set-theoretic complete intersections. The proof is constructive and provides the equations of the surfaces cutting out the monomial curve.Article Number of Pseudo–anosov Elements in the Mapping Class Group of a Four–holed Sphere(2010) Ozan, Ferihe Atalan; Korkmaz, MustafaWe compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.Article An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse(2010) Faydaoğlu, Şerife; Guseınov, Gusein Sh.The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.
