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Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Turkish Journal of Mathematics
Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensional discrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceed to study its computational aspects as well as the inverse transform, which necessitate the development of a faster way to calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linear codes that can be assumed to be a generalization of Reed‒Solomon codes.
Field Of Values Of Perturbed Matrices And Quantum States, Madjid Khakshour, Gholamreza Aghamollaei, Alemeh Sheikhhosseini
Field Of Values Of Perturbed Matrices And Quantum States, Madjid Khakshour, Gholamreza Aghamollaei, Alemeh Sheikhhosseini
Turkish Journal of Mathematics
In this paper, the notion of the pseudofield of values of matrices is introduced and studied. The relationship between quantum states and the field of values of matrices is mentioned. The notion of the pseudopolynomial numerical hull, as a generalization of the pseudofield of values, of matrices is introduced and some properties of this notion are investigated.
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Turkish Journal of Mathematics
In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ then can we claim $T_{f}$\ or $T_{g}$\ is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space $H^{2}\left( \mathbb{D}% \right) $ is also given.
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
Turkish Journal of Mathematics
The localization theorem is known for compact $G$-spaces, where $G$ is a compact Lie group. In this study, we show that the localization theorem remains true for finite-dimensional compact group actions, and Borel's fixed point theorem holds not only for torus actions but for arbitrary finite-dimensional compact connected abelian group actions.
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Turkish Journal of Mathematics
It is well known that the transformation semigroup on a nonempty set $X$, which is denoted by $T(X)$, is regular, but its subsemigroups do not need to be. Consider a finite ordered set $X=(X;\leq)$ whose order forms a path with alternating orientation. For a nonempty subset $Y$ of $X$, two subsemigroups of $T(X)$ are studied. Namely, the semigroup $OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}$ and the semigroup $OS(X,Y)=\{\alpha\in T(X)\mid\alpha$ is order-preserving and $Y\alpha \subseteq Y\}$. In this paper, we characterize ordered sets having a coregular semigroup $OT(X,Y)$ and a coregular semigroup $OS(X,Y)$, respectively. Some characterizations of regular semigroups $OT(X,Y)$ …
The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi
The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi
Turkish Journal of Mathematics
The power graph $\mathcal{P}(G)$ is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph $\mathcal{S}(G)$ of the power graph $\mathcal{P}(G)$ is a graph with vertex set $G$ in which two elements $x, y \in G$ are joined if $o(x) o(y)$ or $o(y) o(x)$. The purpose of this paper is to study certain properties of this new graph together with the relationship between $\mathcal{P}(G)$ and $\mathcal{S}(G)$.
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Turkish Journal of Mathematics
We study plane algebraic curves defined over a field $k$ of arbitrary characteristic that are ramified coverings of the projective line $\mathbb{P}^{1}(k)$ branched over a given configuration of distinct points by their ramification type specified by a partition of $d$ the degree of the covering. We enumerate them by using the combinatorics of partitions and its connection to the representation theory of the symmetric group.
Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n
Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n
Turkish Journal of Mathematics
In the first part of this study, we characterize the compact subspaces of $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ and their relation to the vanishing Carleson measures. In the second part, we discuss the dual complement of the complex ellipsoid and give a duality result for $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ spaces in the sense of Grothendieck?K\"{o}the?da Silva.
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Turkish Journal of Mathematics
We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Björling problem by prescribing a circle or a helix as the core curve $\alpha$ and rotating with constant angular speed the unit normal vector field in the normal plane to $\alpha$. As particular cases, we exhibit new examples of timelike minimal surfaces invariant by a uniparametric group of helicoidal motions.
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Turkish Journal of Mathematics
We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Turkish Journal of Mathematics
A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions.
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Turkish Journal of Mathematics
The aim of this article is to discuss the existence of certain kinds of derivations and *-derivations that are of period 2. Moreover, we obtain the form of generalized reverse derivations and generalized left derivations of period $2$.
Relative Stable (Co)Homology, Chaoling Huang, Li Yuan
Relative Stable (Co)Homology, Chaoling Huang, Li Yuan
Turkish Journal of Mathematics
For a fixed precovering class $\mathcal{X}$ and a fixed preenveloping class $\mathcal{Y}$, we first introduce the notions of relative stable cohomology $\widetilde{Ext}_{\mathcal{X}}(-,\ -)$ and relative stable homology $\widetilde{Tor}_{\mathcal{X}\mathcal{Y}}(-,\ -)$. Then we consider their properties and, more importantly, we study the stable (co)homology under the case of $\mathcal{P}(R)$, $\mathcal{F}(R)$, and $\mathcal{I}(R)$ and the case of $\mathcal{P}_C(R)$, $\mathcal{F}_C(R)$, and $\mathcal{I}_C(R)$. Finally, we generalize relative stable (co)homology from the case of $R$-modules to the case of $R$-complexes.
$Q$-Counting Hypercubes In Lucas Cubes, Eli̇f Saygi, Ömer Eğeci̇oğlu
$Q$-Counting Hypercubes In Lucas Cubes, Eli̇f Saygi, Ömer Eğeci̇oğlu
Turkish Journal of Mathematics
Lucas and Fibonacci cubes are special subgraphs of the binary hypercubes that have been proposed as models of interconnection networks. Since these families are closely related to hypercubes, it is natural to consider the nature of the hypercubes they contain. Here we study a generalization of the enumerator polynomial of the hypercubes in Lucas cubes, which $q$-counts them by their distance to the all 0 vertex. Thus, our bivariate polynomials refine the count of the number of hypercubes of a given dimension in Lucas cubes and for $q=1$ they specialize to the cube polynomials of Klavžar and Mollard. We obtain …
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan
Turkish Journal of Mathematics
In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler--Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In …
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz
Turkish Journal of Mathematics
In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection-diffusion-reaction equations. We derive the first-order optimality conditions by the \emph{optimize-then-discretize} method. After expressing the discrete optimal control problem, we obtain the stability properties of state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z
Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z
Turkish Journal of Mathematics
In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.
Reduction Formula Of A Double Binomial Sum, Wenchang Chu
Reduction Formula Of A Double Binomial Sum, Wenchang Chu
Turkish Journal of Mathematics
A class of double sums with binomial coefficients are evaluated by combining finite differences with partial fraction decompositions.
Frequency Independent Solvability Of Surface Scattering Problems, Fati̇h Ecevi̇t
Frequency Independent Solvability Of Surface Scattering Problems, Fati̇h Ecevi̇t
Turkish Journal of Mathematics
We address the problem of \emph{frequency independent solvability} of high-frequency scattering problems in the exterior of two-dimensional smooth, compact, strictly convex obstacles. Precisely, we show that if the leading term in the asymptotic expansion of the surface current is incorporated into the integral equation formulations of the scattering problem, then appropriate modifications of both the ``frequency-adapted Galerkin boundary element methods'' and the ``Galerkin boundary element methods based on frequency dependent changes of variables'' we have recently developed yield frequency independent approximations. Moreover, for any direct integral equation formulation of the scattering problem, we show that the error can be tuned …
Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak
Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak
Turkish Journal of Mathematics
The purpose of this paper is to answer a question of Fulman on the asymptotic normality of the number of inversions in riffle shuffles. We will also study asymptotics for the number of descents and the length of the longest alternating subsequences in the same shuffling scheme.
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Turkish Journal of Mathematics
Let $q\geq 3$ be a prime number and let $\overline{H}(\lambda _{q})$ be the extended Hecke group associated with $q.$ In this paper, we determine the presentation of the commutator subgroup ($H$($\lambda _{q})\alpha )^{\prime } $ of the normal subgroup $H$($\lambda _{q})\alpha $, where $H$($\lambda _{q})\alpha $ is a subgroup of index $2$ in $\overline{H}$($\lambda _{q}).$ Next we discuss the commutator subgroup ($\overline{H}_{2})^{\prime }$($% \lambda _{q})$ of the principal congruence subgroup $\overline{H}_{2}$($% \lambda _{q})$ of $\overline{H}$($\lambda _{q})$. Then we show that some quotient groups of $\overline{H}$($\lambda _{q})$ are generalized $M^{\ast }- $groups. Finally, we prove some results related to some normal …
An Explicit Formula Of The Intrinsic Metric On The Sierpinski Gasket Via Code Representation, Mustafa Saltan, Yunus Özdemi̇r, Bünyami̇n Demi̇r
An Explicit Formula Of The Intrinsic Metric On The Sierpinski Gasket Via Code Representation, Mustafa Saltan, Yunus Özdemi̇r, Bünyami̇n Demi̇r
Turkish Journal of Mathematics
The computation of the distance between any two points of the Sierpinski gasket with respect to the intrinsic metric has already been investigated by several authors. However, to the best of our knowledge, in the literature there is not an explicit formula obtained by using the code set of the Sierpinski gasket. In this paper, we obtain an explicit formula for the intrinsic metric on the Sierpinski gasket via the code representations of its points. We finally give an important geometrical property of the Sierpinski gasket with regard to the intrinsic metric by using its code representation.
Small Covers Over Products Of A Simple Polytope With A Simplex, Wei Dai, Yanying Wang
Small Covers Over Products Of A Simple Polytope With A Simplex, Wei Dai, Yanying Wang
Turkish Journal of Mathematics
This paper proves that the number of small covers over products of a simple polytope with a $n$-simplex, up to D-J equivalence, is a polynomial in the variable $2^n$. A similar result holds for orientable small covers. We also provide a new way of computation, namely computing the finite number of representatives and interpolating polynomially. The ratio between the number of orientable small covers and the number of small covers is given. As an application, by interpolation, we determine the polynomials related to small covers and orientable small covers over products of a prism with a simplex up to D-J …
Somos's Theta-Function Identities Of Level 10, Belakavadi Radhakrishna Srivatsa Kumar, Devadas Anu Radha
Somos's Theta-Function Identities Of Level 10, Belakavadi Radhakrishna Srivatsa Kumar, Devadas Anu Radha
Turkish Journal of Mathematics
Somos discovered about 6277 theta-function identities of different levels using a computer and offered no proof for them, and these identities closely resemble Ramanujan's recordings. The purpose of this paper is to prove some of his theta-function identities of level 10 and to establish certain partition identities for them.
A Nonexistence Result For Blowing Up Sign-Changing Solutions Of The Brezis-Nirenberg-Type Problem, Yessine Dammak
A Nonexistence Result For Blowing Up Sign-Changing Solutions Of The Brezis-Nirenberg-Type Problem, Yessine Dammak
Turkish Journal of Mathematics
We consider the Brezis-Nirenberg problem: $ -\triangle u= u ^{p-1}u\pm\varepsilon u\mbox{ in }\Omega;, \mbox{ with } u=0 \mbox{ on }\partial\Omega,$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^n$, $n\geq4$, $p+1=2n/(n-2)$ is the critical Sobolev exponent, and $\varepsilon > 0$ is a positive parameter. The main result of this paper shows that if $n\geq4$ there are no sign-changing solutions $u_\varepsilon$ of $(P_{-\varepsilon})$ with two positive and one negative blow up points.
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Turkish Journal of Mathematics
In this article, the extended form of Laguerre-Appell polynomials is introduced by means of generating function and operational definition. The corresponding results for the extended Laguerre-Bernoulli and Laguerre-Euler polynomials are obtained as applications. Further, the determinant forms of these polynomials are established by using operational techniques.
Block Classical Gram-Schmidt-Based Block Updating In Low-Rank Matrix Approximation, Hasan Erbay, Fati̇h Varçin, Fahretti̇n Horasan, Cenker Bi̇çer
Block Classical Gram-Schmidt-Based Block Updating In Low-Rank Matrix Approximation, Hasan Erbay, Fati̇h Varçin, Fahretti̇n Horasan, Cenker Bi̇çer
Turkish Journal of Mathematics
Low-rank matrix approximations have recently gained broad popularity in scientific computing areas. They are used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncated singular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applications such as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrix is subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULV decomposition. Herein, we propose a BLAS-3 compatible block …
Neumann Boundary Value Problems In Fan-Shaped Domains, Mohamed Akel, Mona Aldawsari
Neumann Boundary Value Problems In Fan-Shaped Domains, Mohamed Akel, Mona Aldawsari
Turkish Journal of Mathematics
n this article we give the solvability conditions and the integral representations of the solutions of the Neumann boundary value problem for the Cauchy-Riemann operator and the Beltrami operator with constant coefficient in a disc sector with angle $\vartheta=\frac{\pi}{n},\,n\in\mathbb N$. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part is studied. Classical results of complex analysis are used to obtain the expressions of the solvability conditions and the integral representations for the solutions explicitly.
Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh
Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh
Turkish Journal of Mathematics
We obtain several inequalities of approximation by integral functions of finite degree in generalized Lebesgue spaces with variable exponent defined on the real axis. Among them are direct, inverse, and simultaneous estimates of approximation by integral functions of finite degree in $L^{p\left( \cdot \right)}.$ An equivalence of modulus of continuity with Peetre's $K$ -functional is established. A constructive characterization of Lipschitz class is also obtained.
On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik
On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik
Turkish Journal of Mathematics
Let $T_{n}$ and $S_{n}$ be the full transformation semigroup and the symmetric group on $X_{n}=\{1,\ldots,n\}$, respectively. For $n,m\in \mathbb{Z}^{+}$ with $m\le n-1$ let $$T_{(n,m)}=\{ \alpha \in T_{n} : X_{m} \alpha = X_{m}\} .$$ In this paper we research generating sets and the rank of $T_{(n,m)}$. In particular, we prove that $$rank(T_{(n,m)})=\left\{ \begin{array}{lll} 2 & \mbox{ if }\, (n,m)=(2,1) \mbox{ or }(3,2)\\ 3 & \mbox{ if }\, (n,m)=(3,1) \mbox{ or } 4\leq n \mbox{ and } m=n-1\\ 4 & \mbox{ if }\, 4\leq n \mbox{ and } 1\leq m\leq n-2. \end{array}\right. $$ for $1\leq m\leq n-1$.