On Hypercyclic Fully Zero-Simple Semihypergroups,
2019
TÜBİTAK
On Hypercyclic Fully Zero-Simple Semihypergroups, Mario De Salvo, Domenico Freni, Giovanni Lo Faro
Turkish Journal of Mathematics
Let $\mfI$ be the class of fully zero-simple semihypergroups generated by a hyperproduct. In this paper we study some properties of residual semihypergroup $(H_+, \star)$ of a semihypergroup $(H,\circ)\in \mfI$. Moreover, we find sufficient conditions for $(H,\circ)$ and $(H_+, \star)$ to be cyclic.
Some Results Related To The Berezin Number Inequalities,
2019
TÜBİTAK
Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu
Turkish Journal of Mathematics
In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of $A^{\alpha}XB^{\alpha}$ and $A^{\alpha}XB^{1-\alpha}$ for the case when $0\leq\alpha\leq1$.
An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order,
2019
TÜBİTAK
An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order, Anar Assanova
Turkish Journal of Mathematics
An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The …
The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
$(P,Q)$-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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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,
2019
TÜBİTAK
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.
