The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets,
2019
TÜBİTAK
The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets, Daniel Yaqubi, Toufik Mansour, Madjid Mirzavaziri
Turkish Journal of Mathematics
Let $n$ be a nonnegative integer and $\mathbb{A}=\{a_1,\ldots,a_k\}$ be a multiset with $k$ positive integers such that $a_1\leqslant\cdots\leqslant a_k$. In this paper, we give a recursive formula for partitions and distinct partitions of positive integer $n$ with respect to a multiset $\mathbb{A}$. We also consider the extension of the twelvefold way. By using this notion, we solve the nonintersecting circles problem, which asks to evaluate the number of ways to draw $n$ nonintersecting circles in the plane regardless of their sizes. The latter also enumerates the number of unlabeled rooted trees with $n+1$ vertices.
On The Number Of $K$-Normal Elements Over Finite Fields,
2019
TÜBİTAK
On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş
Turkish Journal of Mathematics
In this article we give an explicit formula for the number of $k$-normal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of $k$-normal elements over finite fields, Finite Fields Appl 2013; 24: 170-183). Furthermore, for some cases we provide formulas that require the solutions of some linear Diophantine equations. Our results depend on the explicit factorization of cyclotomic polynomials.
Complete Flat Cone Metrics On Punctured Surfaces,
2019
TÜBİTAK
Complete Flat Cone Metrics On Punctured Surfaces, İsmai̇l Sağlam
Turkish Journal of Mathematics
We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.
On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions,
2019
TÜBİTAK
On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions, Prakash Kamble, Mallikarjun Shrigan, Şahsene Altinkaya
Turkish Journal of Mathematics
Making use of the $\lambda$-pseudo-$q$-differential operator, we aim to investigate a new, interesting class of bi-starlike functions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete--Szeg\"{o} functional for functions belonging to this class.
Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups,
2019
TÜBİTAK
Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups, İlker Savaş Yüce
Turkish Journal of Mathematics
Let $\xi$ and $\eta$ be two noncommuting isometries of the hyperbolic $3$-space $\mathbb{H}^3$ so that $\Gamma=\langle\xi,\eta\rangle$ is a purely loxodromic free Kleinian group. For $\gamma\in\Gamma$ and $z\in\hyp$, let $d_{\gamma}z$ denote the hyperbolic distance between $z$ and $\gamma(z)$. Let $z_1$ and $z_2$ be the midpoints of the shortest geodesic segments connecting the axis of $\xi$ to the axes of $\eta\xi\eta^{-1}$ and $\eta^{-1}\xi\eta$, respectively. In this manuscript, it is proved that if $d_{\gamma}z_2
Covariant Differential Calculus On ${\Cal Sp}_H^{2,
2019
TÜBİTAK
Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇
Turkish Journal of Mathematics
The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic superspaces are introduced and a covariant differential calculus on the quantum symplectic superspace ${\cal SP}_h^{2 1}$ is presented.
On Strongly Ozaki Bi-Close-To-Convex Functions,
2019
TÜBİTAK
On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this paper, we introduce and investigate a new subclass of strongly Ozaki bi-close-to-convex functions in the open unit disk. We have also found estimates for the first two Taylor-Maclaurin coefficients for functions belonging to this class. The results presented in this paper have been shown to generalize and improve the work of Brannan and Taha.
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays,
2019
TÜBİTAK
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript, we study nonself-adjoint second-order differential operators with two constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied of recovering the potential from spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved for this inverse problem.
Fuzzy Soft Topological Spaces And The Related Category Fst,
2019
TÜBİTAK
Fuzzy Soft Topological Spaces And The Related Category Fst, Tuğba Han Şi̇mşekler
Turkish Journal of Mathematics
In this paper, we consider fuzzy soft sets with a different approach where we generalize the idea initially introduced by \v{S}ostak for fuzzy sets. Subsequently, we define the fuzzy set topology categories of fuzzy soft topological spaces and give certain properties of them. Furthermore, we define the initial and the final fuzzy soft topological spaces.
Global Dynamics Of Perturbation Of Certain Rational Differenceequation,
2019
TÜBİTAK
Global Dynamics Of Perturbation Of Certain Rational Differenceequation, Sabina Hrustic, Mustafa Kulenovic, Samra Moranjkic, Zehra Nurkanovic
Turkish Journal of Mathematics
We investigate the global asymptotic stability of the difference equation of the form \begin{equation*} x_{n+1}=\frac{A x_{n}^{2}+F}{a x_{n}^{2}+e x_{n-1}}, \quad n=0,1,\ldots, \end{equation*}% with positive parameters and nonnegative initial conditions such that $x_0 + x_{-1}>0$. The map associated to this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras,
2019
TÜBİTAK
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras, Ahmet Hamal
Turkish Journal of Mathematics
In this paper we introduce derivative MV-algebras (or MV-algebras with additive derivative operators). We indicate that the derivative MV-algebras are generalizations of closure MV-algebras. Then we investigate the connection between additive derivative operators on MV-algebras and the derivative operators on the greatest Boolean subalgebras of MV-algebras. Finally, we study some properties of the derivative MV-algebras.
On Band Operators,
2019
TÜBİTAK
On Band Operators, Bahri̇ Turan, Kazim Özcan
Turkish Journal of Mathematics
Let $G$ and $H$ be Archimedean Riesz spaces. We study the properties of band operators and inverse band operators from $G$ to $H$ and investigate their relations to some well-known classes of operators. Then, we show that under some assumptions on the Riesz spaces $G$ or $H$, if $S$ is a bijective band operator from $G$ into $H$ then $S^{-1}:H\rightarrow G$ is a band operator. Additionally, we give some conditions under which a band operator becomes order bounded.
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions,
2019
TÜBİTAK
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate an analytic function class $% P_{q}(\lambda,A,B)$ that we call the class of $q-$starlike and $q-$convex functions with respect to the parameter $\lambda $. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class.
On The Divisors Of Shifted Primes,
2019
TÜBİTAK
On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai
Turkish Journal of Mathematics
Let $\tau(n)$ stand for the number of positive divisors of $n$. Given an additive function $f$ and a real number $\alpha\in [0,1)$, let $\displaystyle{h_n(\alpha):= \frac 1{\tau(n)} \sum_{d\mid n \atop \{f(d)\}
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations,
2019
TÜBİTAK
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang
Turkish Journal of Mathematics
This paper concerns the description of the entire or meromorphic solutions to two certain types of differential-difference equations under some certain conditions. The significance of our results lies in that we find the entire solutions of the second type equation with the form $f=Ae^{Bz}$, where $A,B$ are constants that are completely determined only by coefficients and correlated indices. Our results are accurate in a certain sense and are supplemented by an example. In particular, our results generalize and improve a result of Zhang and Huang, and they are closely related to recent results by Dong and Liao.
On Near Soft Sets,
2019
TÜBİTAK
On Near Soft Sets, Alkan Özkan
Turkish Journal of Mathematics
This study aims to contribute to the theoretical studies on near soft sets and near soft topological spaces. In addition, it presents basic concepts and constructs that will form the basis for a near theoretical set-up of near soft sets. These concepts and structures include near soft point, near soft interior, near soft closure, near soft neighborhood, near soft continuity, and near soft open (closed) function.
Fatou, Julia, And Escaping Sets In Holomorphic (Sub)Semigroup Dynamics,
2019
TÜBİTAK
Fatou, Julia, And Escaping Sets In Holomorphic (Sub)Semigroup Dynamics, Bishnu Hari Subedi, Ajaya Singh
Turkish Journal of Mathematics
We investigate under what conditions the Fatou, Julia, and escaping sets of a transcendental semigroup are respectively equal to the Fatou, Julia, and escaping sets of their subsemigroups. We define the partial fundamental set and fundamental set of a holomorphic semigroup, and on the basis of these sets, we prove that the Fatou and escaping sets of a transcendental semigroup $ S $ are nonempty.
The Numerical Range Of Matrices Over $\Mathbb {F}_4$,
2019
TÜBİTAK
The Numerical Range Of Matrices Over $\Mathbb {F}_4$, Edoardo Ballico
Turkish Journal of Mathematics
For any prime power $q$ and any $u = (x_1,\dots ,x_n),v = (y_1,\dots ,y_n)\in \mathbb {F} _{q^2}^n$ set $\langle u,v\rangle := \sum _{i=1}^{n} x_i^qy_i$. For any $k\in \mathbb {F} _q$ and any $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}$, the $k$-numerical range $\mathrm{Num} _k(M)$ of $M$ is the set of all $\langle u,Mu\rangle$ for $u\in \mathbb {F} _{q^2}^n$ with $\langle u,u\rangle =k$ \cite{cjklr}. Here, we study the case $q=2$, which is quite different from the case $q\ne 2$.
Conformal Changes Of Generalized Paracontact Pseudometric Structures,
2019
TÜBİTAK
Conformal Changes Of Generalized Paracontact Pseudometric Structures, Fereshteh Malek, Niloufar Hosseinpour Kashani
Turkish Journal of Mathematics
We characterize generalized almost paracontact pseudometric structures after a conformal change and investigate invariant components of these structures under conformal changes. Then we characterize the conformal changes of normal generalized paracontact pseudometric structures, generalized almost para-co-K{\"a}hler structures, and generalized para-co-K{\"a}hler structures. We also give examples of a generalized almost para-co-K{\"a}hler structure and a normal generalized paracontact pseudometric structure that remains invariant under a nonhomothety conformal change.
On S-Prime Submodules,
2019
TÜBİTAK
On S-Prime Submodules, Esra Şengelen Sevi̇m, Tarik Arabaci, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
In this study, we introduce the concepts of $S$-prime submodules and\ $S$% -torsion-free modules, which are generalizations of prime submodules and torsion-free modules. Suppose $S\subseteq R\ $is a multiplicatively closed subset of a commutative ring$\ R$, and let $M$ be a unital $R$-module. A submodule $P\ $of $M\ $with $(P:_{R}M)\cap S=\emptyset$ is called an $S$% -prime submodule if there is an $s\in S$\ such that $am\in P$ implies $% sa\in(P:_{R}M)\ $or $sm\in P.\ $Also, an $R$-module $M\ $is called $S$% -torsion-free if $ann(M)\cap S=\emptyset$ and there exists $s\in S\ $such that $am=0\ $implies $sa=0\ $or $sm=0\ $for each $a\in R\ …
