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2018

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Articles 931 - 960 of 1332

Full-Text Articles in Mathematics

The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat Jan 2018

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.

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Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai Jan 2018

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 $OT(X,Y)$ …

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The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi Jan 2018

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 $\mathcal{S}(G)$.

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Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez Jan 2018

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.

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Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n Jan 2018

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.

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Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez Jan 2018

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.

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Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r Jan 2018

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.

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Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol Jan 2018

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.

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Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel Jan 2018

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 $2$.

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Relative Stable (Co)Homology, Chaoling Huang, Li Yuan Jan 2018

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.

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$Q$-Counting Hypercubes In Lucas Cubes, Eli̇f Saygi, Ömer Eğeci̇oğlu Jan 2018

$Q$-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 …

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Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan Jan 2018

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 …

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Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz Jan 2018

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.

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Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z Jan 2018

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.

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Reduction Formula Of A Double Binomial Sum, Wenchang Chu Jan 2018

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.

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Frequency Independent Solvability Of Surface Scattering Problems, Fati̇h Ecevi̇t Jan 2018

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 …

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Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak Jan 2018

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.

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Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n Jan 2018

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 …

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An Explicit Formula Of The Intrinsic Metric On The Sierpinski Gasket Via Code Representation, Mustafa Saltan, Yunus Özdemi̇r, Bünyami̇n Demi̇r Jan 2018

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.

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Small Covers Over Products Of A Simple Polytope With A Simplex, Wei Dai, Yanying Wang Jan 2018

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 …

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Somos's Theta-Function Identities Of Level 10, Belakavadi Radhakrishna Srivatsa Kumar, Devadas Anu Radha Jan 2018

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.

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A Nonexistence Result For Blowing Up Sign-Changing Solutions Of The Brezis-Nirenberg-Type Problem, Yessine Dammak Jan 2018

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.

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Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani Jan 2018

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.

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Block Classical Gram-Schmidt-Based Block Updating In Low-Rank Matrix Approximation, Hasan Erbay, Fati̇h Varçin, Fahretti̇n Horasan, Cenker Bi̇çer Jan 2018

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 …

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Neumann Boundary Value Problems In Fan-Shaped Domains, Mohamed Akel, Mona Aldawsari Jan 2018

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.

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Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh Jan 2018

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.

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On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik Jan 2018

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 $1\leq m\leq n-1$.

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On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara Jan 2018

On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara

Turkish Journal of Mathematics

In this paper we consider the following higher-order nonlinear difference equation $$ x_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}x_{n-\left( k+l\right) }}{\beta x_{n-\left( k+l\right) }+\gamma x_{n-l}},\ n\in \mathbb{N} _{0}, $$ where $k$ and $l$ are fixed natural numbers, and the parameters $\alpha $, $ \beta $, $\gamma $, $\delta $ and the initial values $x_{-i}$, $i=\overline{ 1,k+l}$, are real numbers such that $\beta ^{2}+\gamma ^{2}\neq 0$. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case …

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Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang Jan 2018

Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang

Turkish Journal of Mathematics

In this paper we give the characterizations of Green's relations $\mathscr{R}$, $\mathscr{L}$, and $\mathscr{D}$ on the set of matrices with entries in a tropical semiring. An $m\times n$ tropical matrix $A$ is called regular if there exists an $n\times m$ tropical matrix $X$ satisfying $AXA = A$. Furthermore, we study the regular $\mathscr{D}$-classes of the semigroup of all $n\times n$ tropical matrices under multiplication and give a partition of a nonsingular regular $\mathscr{D}$-class.

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First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov Jan 2018

First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov

Turkish Journal of Mathematics

In this paper, using the Calkin-Gorbachuk method, the general form of all self-adjoint operators generated by first order linear singular multipoint quasi-differential expressions in the direct sum of weighted Hilbert spaces of vector functions has been found. Later on, the geometry of the spectrum set of these type extensions was researched.

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