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The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul
The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul
Turkish Journal of Mathematics
In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.
Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan
Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan
Turkish Journal of Mathematics
The subject of this paper is the Zariski topology on a multiplication module $M$ over a commutative ring $R$. We find a characterization for the radical submodule $rad_{M}(0)$ and also show that there are proper ideals $I_{1},...,I_{n}$ of $R$ such that $rad_{M}(0)=rad_{M}(\left( I_{1}...I_{n}\right) M)$. Finally, we prove that the spectrum $Spec(M)$ is irreducible if and only if $M$ is the finite sum of its submodules, whose $ \mathcal{T}$-radicals are prime in $M$.
Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan
Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan
Turkish Journal of Mathematics
We consider new kinds of max and min matrices, $\left[ a_{\max(i,j)}\right] _{i,j\geq1}$ and $\left[ a_{\min(i,j)}\right] _{i,j\geq1},$ as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence $\left\{ a_{n}\right\} $ have been studied. We derive their $LU$ and Cholesky decompositions and their inverse matrices as well as the $LU$-decompositions of their inverses. Some interesting corollaries will be presented.
A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt
A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt
Turkish Journal of Mathematics
Let$\ X$ be a locally compact and noncompact$\ G-$space with a compact group $G$. In this paper, we give some useful description of a compactification of the orbit space $X/G$ when it is an orbit space of a $G-$compactification of $X$. As an application, we show that the closed bounded interval $[a,b]$ is homeomorphic to the space of maximal ideals with Stone topology of uniformly continuous even functions subring of $\ C^{\ast }(\mathbb{R})$.
Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu
Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu
Turkish Journal of Mathematics
In this paper, we investigate approximation properties of the Stancu type generalization of the $\alpha$-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.
On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi
On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi
Turkish Journal of Mathematics
We completely characterize a subclass of Drazin inverses by means of tripotents and nilpotents. We prove that an element $a$ in a ring $R$ has Hirano inverse if and only if $a^2\in R$ has strongly Drazin inverse, if and only if $a-a^3$ is nilpotent. If $\frac{1}{2}\in R$, we prove that $a\in R$ has Hirano inverse if and only if there exists $p^3=p\in comm^2(a)$ such that $a-p\in N(R)$, if and only if there exist two idempotents $e,f\in comm^2(a)$ such that $a+e-f\in N(R)$. Multiplicative and additive results for this generalized inverse are thereby obtained.
Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa
Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa
Turkish Journal of Mathematics
We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between two categorified group-sets is given by a particular equivalence between the underlying categories. We also exhibit some of the differences between the old Burnside theory and the new one. Lastly, we briefly explain how to extend these new techniques and concepts to the context of groupoids, employing the categories of (right) groupoid-sets, aiming by this to give an alternative approach to the classical Burnside ring …
On Ps-Drazin Inverses In A Ring, Huanyin Chen, Tuğçe Çalci
On Ps-Drazin Inverses In A Ring, Huanyin Chen, Tuğçe Çalci
Turkish Journal of Mathematics
An element $a$ in a ring $R$ has a ps-Drazin inverse if there exists $b\in comm^2(a)$ such that $b=bab, (a-ab)^k\in J(R)$ for some $k\in {\Bbb N}$. Elementary properties of ps-Drazin inverses in a ring are investigated here. We prove that $a\in R$ has a ps-Drazin inverse if and only if $a$ has a generalized Drazin inverse and $(a-a^2)^k\in J(R)$ for some $k\in {\Bbb N}$. We show Cline's formula and Jacobson's lemma for ps-Drazin inverses. The additive properties of ps-Drazin inverses in a Banach algebra are obtained. Moreover, we completely determine when a $2\times 2$ matrix $A\in M_2(R)$ over a local …
The Boundedness Of $H$-Admissible Fourier Integral Operators On Bessel Potential Spaces, Omar Farouk Aid, Abderrahmane Senoussaoui
The Boundedness Of $H$-Admissible Fourier Integral Operators On Bessel Potential Spaces, Omar Farouk Aid, Abderrahmane Senoussaoui
Turkish Journal of Mathematics
The aim of this work is to study the boundedness of $h$-admissible Fourier integral operators. These operators are bounded on the Bessel potential spaces if the weight of the amplitude is bounded.
Fibonacci And Lucas Numbers As Products Of Two Repdigits, Fati̇h Erduvan, Refi̇k Keski̇n
Fibonacci And Lucas Numbers As Products Of Two Repdigits, Fati̇h Erduvan, Refi̇k Keski̇n
Turkish Journal of Mathematics
In this study, it is shown that the largest Fibonacci number that is the product of two repdigits is $F_{10}=55=5\cdot 11=55\cdot 1$ and the largest Lucas number that is the product of two repdigits is $L_{6}=18=2\cdot 9=3\cdot 6.$
Some Permutations And Complete Permutation Polynomials Over Finite Fields, Pinar Ongan, Burcu Gülmez Temür
Some Permutations And Complete Permutation Polynomials Over Finite Fields, Pinar Ongan, Burcu Gülmez Temür
Turkish Journal of Mathematics
In this paper we determine $b\in\F_{q^n}^*$ for which the polynomial $f(x)=x^{s+1}+bx\in\F_{q^n}[x]$ is a permutation polynomial and determine $b\in\F_{q^n}^*$ for which the polynomial $f(x)=x^{s+1}+bx\in\F_{q^n}[x]$ is a complete permutation polynomial where $s=\frac{q^n-1}{t}, t\in \mathbb{Z}^+$ such that $t\mid q^n-1$.
Positivity Of Continuous Time Irregular Linear Descriptor Systems, Mahmoud Mansouri, Kameleh Nassiri
Positivity Of Continuous Time Irregular Linear Descriptor Systems, Mahmoud Mansouri, Kameleh Nassiri
Turkish Journal of Mathematics
The positivity of continuous-time irregular linear descriptor systems is investigated in this study. The present method is introduced based on Weierstrass decomposition. We obtain necessary and sufficient conditions for the positivity of the linear irregular descriptor systems. The conditions are investigated by two examples with Simulink/MATLAB.
$(P,Q)$-Lucas Polynomial Coefficient Inequalities Of Thebi-Univalent Function Class, Arzu Akgül
$(P,Q)$-Lucas Polynomial Coefficient Inequalities Of Thebi-Univalent Function Class, Arzu Akgül
Turkish Journal of Mathematics
Recently, Lucas polynomials and other special polynomials gained importance in the field of geometric function theory. In this study, by connecting these polynomials, subordination, and the Al-Oboudi differential operator, we introduce a new class of bi-univalent functions and obtain coefficient estimates and Fekete-SzegÖ inequalities for this new class.
Extending Self-Orthogonal Codes, Alp Bassa, Nesri̇n Tutaş
Extending Self-Orthogonal Codes, Alp Bassa, Nesri̇n Tutaş
Turkish Journal of Mathematics
In this short note we give an exact count for the number of self-dual codes over a finite field $\mathbb F_q$ of odd characteristic containing a given self-orthogonal code. This generalizes an analogous result of MacWilliams, Sloane, and Thompson over the field $\mathbb F_2$ to arbitrary odd finite fields $\mathbb F_q$.
Approximation By Generalized Complex Szasz--Mirakyan Operators In Compact Disks, Döne Karahan, Sevi̇lay Kirci Serenbay, Aydin İzgi̇
Approximation By Generalized Complex Szasz--Mirakyan Operators In Compact Disks, Döne Karahan, Sevi̇lay Kirci Serenbay, Aydin İzgi̇
Turkish Journal of Mathematics
In this study, the generalized complex Szasz-Mirakyan operators are introduced and the approximation properties of these operators are studied. Voronovskaya's theorem with a quantitative estimate for these operators attached to an analytic function is achieved on compact disks.
Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim
Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim
Turkish Journal of Mathematics
We study the longest increasing subsequences in random involutions that avoid the patterns of length three under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes.
Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz
Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz
Turkish Journal of Mathematics
In this paper we investigate the Volterra difference equation of the form $ \D(r_n\D x_n)=b_n+\sum_{k=1}^{n}K(n,k)f(x_k). $ We establish sufficient conditions for the existence of a solution $x$ of the above equation with the property $ x_n=y_n+\o(n^s), $ where $y$ is a given solution of the equation $\D(r_n\D y_n)=b_n$ and $s$ is nonpositive real number. We also obtain sufficient conditions for the existence of asymptotically periodic solutions.
A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar
A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar
Turkish Journal of Mathematics
In the present study, by using the Horadam Polnomials and $q-$analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.
Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo
Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo
Turkish Journal of Mathematics
In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $\map(F(\br^m,k),\bs^n)$ and $\map^*(F(\br^m,k),\bs^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.
On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli
On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli
Turkish Journal of Mathematics
$\left(M_{2n},g^w,D\right)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $\left(M_{2n},g^w\right)$ of signature $(++--$) (or neutral), which is admitted a field of null 2-plane. In this paper, we consider bi-Hermitian structures $({\varphi }_1,{\ \varphi }_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the bi-Kahler forms are symplectic.
Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al
Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al
Turkish Journal of Mathematics
In this paper, the general form of all normal differential operators generated by first-order linear singular differential expressions in the weighted Hilbert spaces of vector-functions on right semiaxis has been found. Later on, the spectrum set of these type extensions is investigated. Finally, the asymptotical behavior of the singular numbers of any normal extension is studied.
Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar
Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar
Turkish Journal of Mathematics
One of the useful generalization of extending notion is $FI$-extending property. A module is called $FI$-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak $FI$-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak $FI$-extending. We obtain that $FI$-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak $FI$-extending modules.
An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek
An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the spirit of probabilistic distributions. By applying generating functions methods, we derive miscellaneous novel identities and formulas involving the Chu--Vandermonde-type convolution formulas, combinatorial sums, Bernstein basis functions, and the other well-known special numbers and polynomials. Moreover, we provide a computational algorithm which returns special values of these numbers and polynomials. In addition, we show that our new identities and formulas are connected with the interpolation …
A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol
A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol
Turkish Journal of Mathematics
Motivated by the Ronning-starlike class [Proc Amer Math Soc {\bf118}, no. 1, 189-196, 1993], we introduce new class $\mathcal{S}^*_c$ includes of analytic and normalized functions $f$ which satisfy the inequality $$ {\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\}\geq\left \frac{f(z)}{z}-1\right \quad( z 1/2$ in $ z
On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov
On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov
Turkish Journal of Mathematics
We study reducible projective unitary representations $(U_g)_{g\in G}$ of a compact group $G$ in separable Hilbert spaces $H$. It is shown that there exist the projections $Q$ and $P$ for which ${\mathcal V}=\overline {span(U_gQU_g^*,\ g\in G)}$ is the operator system and $P{\mathcal V}P=\{{\mathbb C}P\}$. As an example, a bipartite Hilbert space $H={\mathfrak {H}}\otimes {\mathfrak {H}}$ is considered. In this case, the action of $(U_g)_{g\in G}$ has the property of transforming separable vectors to entangled.
On The $J$-Reflexive Sequences, Parviz Sadat Hosseini, Bahmann Yousefi
On The $J$-Reflexive Sequences, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
We call a sequence $\mathcal{T}=(T_n)_n$ of bounded operators on a Banach space $X$, $J$-reflexive if every bounded operator on $X$ that leaves invariant, the $J$-sets of $\mathcal{T}$ is contained in the closure of $\{I, T_1, T_2, ... \}$ in the strong operator topology. We discuss some properties of $J$-reflexive sequences. We also give and prove some sufficient conditions under which an operator sequence is $J$-reflexive. Some examples are considered. Indeed, weakly $J^{mix}$-reflexivity is also defined. Finally, we extend the $J$-reflexive property in terms of subsets.
Unpredictable Solutions Of Linear Differential And Discrete Equations, Marat Akhmet, Mehmet Onur Fen, Madina Tleubergenova, Akylbek Zhamanshin
Unpredictable Solutions Of Linear Differential And Discrete Equations, Marat Akhmet, Mehmet Onur Fen, Madina Tleubergenova, Akylbek Zhamanshin
Turkish Journal of Mathematics
The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincaré chaos. Simulations illustrating the chaos are provided.
Quasi-Idempotent Ranks Of Some Permutation Groups And Transformation Semigroups, Leyla Bugay
Quasi-Idempotent Ranks Of Some Permutation Groups And Transformation Semigroups, Leyla Bugay
Turkish Journal of Mathematics
Let $S_{n}$, $A_{n}$, $I_{n}$, $T_{n}$, and $P_{n}$ be the symmetric group, alternating group, symmetric inverse semigroup, (full) transformations semigroup, and partial transformations semigroup on $X_{n}=\{1,\dots ,n\}$, for $n\geq 2$, respectively. A non-idempotent element whose square is an idempotent in $P_{n}$ is called a quasi-idempotent. In this paper first we show that the quasi-idempotent ranks of $S_{n}$ (for $n\geq 4$) and $A_{n}$ (for $n\geq 5$) are both $3$. Then, by using the quasi-idempotent rank of $S_{n}$, we show that the quasi-idempotent ranks of $I_{n}$, $T_{n}$, and $P_{n}$ (for $n\geq 4$) are $4$, $4$, and $5$, respectively.
On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader
On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader
Turkish Journal of Mathematics
In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of $\Gamma _{0}(m)$ in $PSL(2,\mathbb{R})$. We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties.