TR-Dizin

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/21

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Characterizations of the Commutators Involving Idempotents in Certain Subrings of $m_{2}(\\mathbb{z})$
(2023) Gümüşel, Günseli; Özdın, Tufan; Department of Social Sciences for University wide Courses; 02. School of Arts and Sciences; 01. Atılım University
In 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 $M_2(Z)$.
Citation - WoS: 1
Citation - Scopus: 2
A Convergent Two-Level Linear Scheme for the Generalized Rosenau–kdv–rlw Equation
(Tubitak Scientific & Technological Research Council Turkey, 2019) Aydın, Ayhan; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A new convergent two-level finite difference scheme is proposed for the numerical solution of initial valueproblem of the generalized Rosenau–KdV–RLW equation. The new scheme is second-order, linear, conservative, andunconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solutionis studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence ofthe scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating thesolitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically.Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term.Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulatesthe solitary waves for a long time.
Citation - WoS: 6
Citation - Scopus: 6
Exact and Nonstandard Finite Difference Schemes for the Burgers Equation B(2, 2)
(Tubitak Scientific & Technological Research Council Turkey, 2021) Köroğlu, Canan; Aydın, Ayhan; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we consider the Burgers equation B(2, 2) . Exact and nonstandard finite difference schemes(NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equationB(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. Thesetwo NSFD schemes are compared with a standard finite difference (SFD) scheme. Numerical results show that the NSFDschemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We seethat although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results forlong time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.
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, Oğuz; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse
(2010) Faydaoğlu, Şerife; Guseınov, Gusein Sh.; 01. Atılım University
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.
Fedja’s Proof of Deepti’s Inequality
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.
Citation - Scopus: 2
Field Extensions Having the Unique Subfield Property, and G-Cogalois Extensions
(2002) Albu,T.; 01. Atılım University
We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the unique subfield property, and prove that these extensions are precisely the simple G-Cogalois extensions with a cyclic Kneser group. © TÜBİTAK.
A Note on the Generalized Matsumoto Relation
(2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, Mehmetcik; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We 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.
Number fields and divisible groups via model theory
(Tubitak Scientific & Technological Research Council Turkey, 2021) CELIK, Sermin C. A. M.; GORAL, Haydar; 01. Atılım University
In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.
Number of Pseudo–anosov Elements in the Mapping Class Group of a Four–holed Sphere
(2010) Ozan, Ferihe Atalan; Korkmaz, Mustafa; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We 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.
On a Class of Permutation Trinomials Over Finite Fields
(Tubitak Scientific & Technological Research Council Turkey, 2024) Temür, Burcu Gülmez; Özkaya, Buket; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we study the permutation properties of the class of trinomials of the form f (x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and suﬀicient conditions on λ1 and λ2 such that f (x) permutes Fq2 , where q is odd and q = 22k+1, k ∈
Citation - WoS: 1
Citation - Scopus: 1
On Some Permutation Trinomials in Characteristic Three
(Hacettepe Univ, Fac Sci, 2025) Temür, Burcu Gülmez; Özkaya, Buket; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we determine the permutation properties of the polynomial x3 +xq+2 −x4q−1 over the finite field Fq2 in characteristic three. Moreover, we consider the trinomials of the form x4q−1 + x2q+1 ± x3. In particular, we first show that x3 + xq+2 − x4q−1 permutes Fq2 with q = 3m if and only if m is odd. This enables us to show that the suﬃcient condition in [34, Theorem 4] is also necessary. Next, we prove that x4q−1 + x2q+1 − x3 permutes Fq2 with q = 3m if and only if m ̸≡ 0 (mod 4). Consequently, we prove that the suﬃcient condition in [20, Theorem 3.2] is also necessary. Finally, we investigate the trinomial x4q−1 + x2q+1 + x3 and show that it is never a permutation polynomial of Fq2 in any characteristic. All the polynomials considered in this work are not quasi-multiplicative equivalent to any known class of permutation trinomials.
On Strongly Autinertial Groups
(Tubitak Scientific & Technological Research Council Turkey, 2018) Onur, Cansu Betin; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A subgroup X of G is said to be inert under automorphisms (autinert) if |X : $X^\\alpha$ ∩ X| is finite for allα ∈ Aut(G) and it is called strongly autinert if | < X, $X^\\alpha$ >: X| is finite for all α ∈ Aut(G). A group is calledstrongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. Wecharacterize such groups for a finitely generated case. Namely, we prove that a finitely generated group G is stronglyautinertial if and only if one of the following hold:i) G is finite;ii) G = ⟨a⟩ ⋉ F where F is a finite subgroup of G and ⟨a⟩ is a torsion-free subgroup of G.Moreover, in the preliminary part, we give basic results on strongly autinert subgroups.
On Symmetric Monomial Curves in $\\bbb{p}^3$
(2009) Şahin, Mesut; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Self-Adjoint Boundary Value Problems on Time Scales and Symmetric Green' S Functions
(2005) Guseınov, Gusein Sh.; 01. Atılım University
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 emphasized
Citation - WoS: 1
Citation - Scopus: 1
A Short Note on Some Arithmetical Properties of the Integer Part of Ap
(Tubitak Scientific & Technological Research Council Turkey, 2019) Akbal, Yıldırım; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Let $a>0$ 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.
Solving an Initial Boundary Value Problem on Thesemiinfinite Interval
(2016) Atalan, Ferihe; Guseınov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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 = ∞.
Citation - WoS: 3
Citation - Scopus: 4
Some Permutations and Complete Permutation Polynomials Over Finite Fields
(Tubitak Scientific & Technological Research Council Turkey, 2019) Ongan, Pınar; Temür, Burcu Gülmez; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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 $\\left.t\\;\\right|\\;q^n-1$.
Transmission Eigenvalues Problem of a Schrödinger Equation
(Tubitak Scientific & Technological Research Council Turkey, 2024) Yıldırım, Emel; Baıramov, Elgiz; 01. Atılım University
In this paper, transmission eigenvalues of a Schrödinger equation have been studied by constructing a new inner product and using Weyl theory. Necessary conditions for these eigenvalues to be negative, real, and finite have been examined. This method has provided a new framework related to transmission eigenvalue problems and the investigation of their properties. The conclusions have been verified for the special case of the problem.

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