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Full-Text Articles in Mathematics
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 $1\leq m\leq n-1$.
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
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 …
Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang
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.
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
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.
Chordality Of Graphs Associated To Commutative Rings, Ashkan Nikseresht
Chordality Of Graphs Associated To Commutative Rings, Ashkan Nikseresht
Turkish Journal of Mathematics
We investigate when different graphs associated to commutative rings are chordal. In particular, we characterize commutative rings $R$ with each of the following conditions: the total graph of $R$ is chordal; the total dot product or the zero-divisor dot product graph of $R$ is chordal; the comaximal graph of $R$ is chordal; $R$ is semilocal; and the unit graph or the Jacobson graph of $R$ is chordal. Moreover, we state an equivalent condition for the chordality of the zero-divisor graph of an indecomposable ring and classify decomposable rings that have a chordal zero-divisor graph.
Congruences Modulo 9 For Bipartitions Withdesignated Summands, Robert Xiaojian Hao, Erin Yiying Shen
Congruences Modulo 9 For Bipartitions Withdesignated Summands, Robert Xiaojian Hao, Erin Yiying Shen
Turkish Journal of Mathematics
Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of $n$ is an ordered pair of partitions $(\pi_1, \pi_2)$ with the sum of all of the parts being $n$. In this paper, we investigate arithmetic properties of bipartitions with designated summands. Let $PD_{-2}(n)$ denote the number of bipartitions of $n$ with designated summands. We establish several Ramanujan-like congruences and an infinite family of congruences modulo $9$ satisfied by $PD_{-2}(n)$.
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Turkish Journal of Mathematics
We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2(A_{k-1}-A^0_{k-1})-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\big(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big)-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ where the assumptions on $\eta,\ A_k^0$, and $A_k^1$ are motivated by some mathematics models for house burglary. Our results are based on the topological degree theory.
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
Turkish Journal of Mathematics
Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $(*)$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $(*)$ we have $\mu ({\rm in}(I))\leq 2(t(H))+1$.
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we mainly investigate the uniqueness problem on meromorphic functions in $\mathbb{C}^m$ sharing small functions with their difference operators or shifts, and we obtain some interesting results that act as some extensions of previous results from one complex variable to several complex variables.
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems, Özkan Öztürk, Raegan Higgins
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems, Özkan Öztürk, Raegan Higgins
Turkish Journal of Mathematics
In this article, we investigate the oscillatory behavior of a three-dimensional system of dynamic equations on an unbounded time scale. A time scale $\T$ is a nonempty closed subset of real numbers. An example is given to illustrate some of the results.
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Turkish Journal of Mathematics
In this paper, we study certain multilinear operators of fractional integral type defined by \[ I^{\vec{A}}_{\alpha}\vec{f}(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion (\mathbb{R} %EndExpansion ^{n})^m}\frac{f_1(y_1)\cdots f_m(y_m)}{ (x-y_1,\cdots,x-y_m) ^{mn-\alpha+\sum\limits_{i=1}^m(N_i-1)}}\prod\limits_{i=1}^mR_{N_i}(A_i;x,y_i)d\vec{y}, \] where $0< \alpha