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2021

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Articles 25981 - 26010 of 27884

Full-Text Articles in Physical Sciences and Mathematics

Estimations On Some Hybrid Exponential Sums Related To Kloosterman Sums, Yingjie Cheng, Xiwang Cao, Liqin Qian, Jinlong Wan Jan 2021

Estimations On Some Hybrid Exponential Sums Related To Kloosterman Sums, Yingjie Cheng, Xiwang Cao, Liqin Qian, Jinlong Wan

Turkish Journal of Mathematics

In this paper, we revisit the bounds of the mixed exponential sums introduced by Lv and Zhang (2020). Moreover, we give some estimations for some new hybrid exponential sums related to Kloosterman sums over finite fields of odd characteristic by using the properties of Jacobi sums and Gaussian sums.

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T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes Jan 2021

T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes

Turkish Journal of Mathematics

In this paper, we characterize various local forms of T$_{4}$ constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T$_{4}$ constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T$_{4}$ and general T$_{4}$ constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.

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On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou Jan 2021

On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou

Turkish Journal of Mathematics

In this paper, we investigate the elements whose Moore-Penrose inverse is idempotent in a ${\ast}$-ring. Let $R$ be a ${\ast}$-ring and $a\in R^\dagger$. Firstly, we give a concise characterization for the idempotency of $a^\dagger$ as follows: $a\in R^\dagger$ and $a^\dagger$ is idempotent if and only if $a\in R^{\#}$ and $a^2=aa^*a$, which connects Moore-Penrose invertibility and group invertibility. Secondly, we generalize the results of Baksalary and Trenkler from complex matrices to ${\ast}$-rings. More equivalent conditions which ensure the idempotency of $a^\dagger$ are given. Particularly, we provide the characterizations for both $a$ and $a^\dagger$ being idempotent. Finally, the equivalent conditions under which …

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Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats' Jan 2021

Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats'

Turkish Journal of Mathematics

Let $J_{\nu}$ be the Bessel function of the first kind of index $\nu\ge 1/2$, $p\in\mathbb R$ and $(\rho_k)_{k\in\mathbb N}$ be a sequence of distinct nonzero complex numbers. Sufficient conditions for the completeness of the system $\big\{x^{-p-1}\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\mathbb N\big\}$ in the weighted space $L^2((0;1);x^{2p} dx)$ are found in terms of an entire function with the set of zeros coinciding with the sequence $(\rho_k)_{k\in\mathbb N}$.

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On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu Jan 2021

On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu

Turkish Journal of Mathematics

The definition of ordered $\Gamma$-hypersemigroups and the definitions of regular and intra-regular ordered $\Gamma$-hypersemigroups in the existing bibliography should be corrected. Care should be given to the definitions of bi-$\Gamma$-hyperideals and quasi-$\Gamma$-hyperideals as well. The main results are a characterization of minimal bi-ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of $\cal B$-simple bi-ideals of $S$ and a characterization of minimal left (resp. right) ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of left (resp. right) simple subsemigroups of $S$.

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Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu Jan 2021

Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu

Turkish Journal of Mathematics

This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-order weakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.

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Hardy-Copson Type Inequalities For Nabla Time Scale Calculus, Zeynep Kayar, Bi̇llur Kaymakçalan Jan 2021

Hardy-Copson Type Inequalities For Nabla Time Scale Calculus, Zeynep Kayar, Bi̇llur Kaymakçalan

Turkish Journal of Mathematics

This paper is devoted to the nabla unification of the discrete and continuous Hardy-Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.

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Classification Of Genus-$1$ Holomorphic Lefschetz Pencils, Noriyuki Hamada, Kenta Hayano Jan 2021

Classification Of Genus-$1$ Holomorphic Lefschetz Pencils, Noriyuki Hamada, Kenta Hayano

Turkish Journal of Mathematics

In this paper, we classify relatively minimal genus-$1$ holomorphic Lefschetz pencils up to smooth isomorphism. We first show that such a pencil is isomorphic to either the pencil on $P^1\times P^1$ of bidegree $(2,2)$ or a blow-up of the pencil on $P^2$ of degree $3$, provided that no fiber of a pencil contains an embedded sphere (note that one can easily classify genus-$1$ Lefschetz pencils with an embedded sphere in a fiber). We further determine the monodromy factorizations of these pencils and show that the isomorphism class of a blow-up of the pencil on $P^2$ of degree $3$ does not …

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On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye Jan 2021

On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye

Turkish Journal of Mathematics

Self-orthogonal codes and self-dual codes, on the one hand, and matrix-product codes, on the other, form important and sought-after classes of linear codes. Combining the two constructions would be advantageous. Adding to this combination the relaxation of the underlying algebraic structures to be commutative rings instead of fields would be even more advantageous. The current article paves a path in this direction. The authors study the problem of self-orthogonality and self-duality of matrix-product codes over a commutative ring with identity. Some methods as well as special matrices are introduced for the construction of such codes. A characterization of such codes …

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Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev Jan 2021

Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev

Turkish Journal of Mathematics

In this paper,we define a class of analytic functions $F_{\left( \beta ,\lambda \right) }\left( H,\alpha ,\delta ,\mu \right) ,$ satisfying the following subordinate condition associated with Chebyshev polynomials \begin{equation*} \left\{ \alpha \left[ \frac{zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\delta }+\left( 1-\alpha \right) \left[ \frac{% zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\mu }\left[ 1+% \frac{zG^{^{\prime \prime }}\left( z\right) }{G^{^{\prime }}\left( z\right) }% \right] ^{1-\mu }\right\} \prec H\left( z,t\right) , \end{equation*}% where $G\left( z\right) =\lambda \beta z^{2}f^{^{\prime \prime }}\left( z\right) +\left( \lambda -\beta \right) zf^{^{\prime }}\left( z\right) +\left( 1-\lambda +\beta \right) f\left( z\right) ,$ $0\leq \alpha \leq 1,$ $% 1\leq \delta \leq …

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Yau-Type Ternary Hom-Lie Bialgebras, Elkadri Abdaoui, Sami Mabrouk, Abdenacer Makhlouf, Sonia Massoud Jan 2021

Yau-Type Ternary Hom-Lie Bialgebras, Elkadri Abdaoui, Sami Mabrouk, Abdenacer Makhlouf, Sonia Massoud

Turkish Journal of Mathematics

The purpose of this paper is to introduce and study $3$-Hom-Lie bialgebras, which are a ternary version of Hom-Lie bialgebras introduced by Yau (2015). We provide their properties, some key constructions and their 3-dimensional classification. Moreover we discuss their representation theory and their generalized derivations and coderivations. Furthermore, a more generalized notion called generalized $3$-Hom-Lie bialgebra is also considered.

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The $2$-Rank Of The Class Group Of Some Real Cyclic Quartic Number Fields Ii, Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini Jan 2021

The $2$-Rank Of The Class Group Of Some Real Cyclic Quartic Number Fields Ii, Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini

Turkish Journal of Mathematics

In this paper, we determine the $2$-rank of the class group of certain classes of real cyclic quartic number fields. Precisely, we consider the case in which the quadratic subfield is $\mathbb{Q}(\sqrt{\ell})$ with $\ell=2$ or a prime congruent to $1\,\pmod8$.

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Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy Jan 2021

Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy

Turkish Journal of Mathematics

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for the analytic bi-univalent function class, which we call Mocanu type bi-starlike functions, related to a shell-shaped region in the open unit disk in the complex plane. Some interesting special cases of the results are also discussed.

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A Class Of Operators Related To $M$-Symmetric Operators, Fei Zuo, Salah Mecheri Jan 2021

A Class Of Operators Related To $M$-Symmetric Operators, Fei Zuo, Salah Mecheri

Turkish Journal of Mathematics

$m$-symmetric operator plays a crucial role in the development of operator theory and has been widely studied due to unexpected intimate connections with differential equations, particularly conjugate point theory and disconjugacy. For positive integers $m$ and $k$, an operator $T$ is said to be a $k$-quasi-$m$-symmetric operator if $T^{*k}(\sum\limits_{j=0}^{m}(-1)^{j}(^{m}_{j})T^{*m-j}T^{j})T^{k}=0$, which is a generalization of $m$-symmetric operator. In this paper, some basic structural properties of $k$-quasi-$m$-symmetric operators are established with the help of operator matrix representation. In particular, we also show that every $k$-quasi-$3$-symmetric operator has a scalar extension. Finally, we prove that generalized Weyl's theorem holds for $k$-quasi-$3$-symmetric operators.

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On 2-Algebras: Crossed R-Modules And Categorical R-Algebras, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan Jan 2021

On 2-Algebras: Crossed R-Modules And Categorical R-Algebras, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan

Turkish Journal of Mathematics

In this work, we describe the category of categorical $R$-algebras and show that a categorical $R$-algebra is a category object in $\mathcal{C=}A\lg _{R}$. By using this property of categorical $R$-algebras, we can give an equivalency between the category of categorical $R$-algebras and the category of crossed $R$-modules and also the category of simplicial $R$-algebras.

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Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani Jan 2021

Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani

Turkish Journal of Mathematics

We consider strongly simple extensions of unitary commutative Banach algebras. We study these Banach algebra structure without assuming the continuity of the canonical injection. The link of the integrality with these extensions is studied. Several algebraic results are also obtained.

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The Extension Of Step-$N$ Signatures, Kistosil Fahim Jan 2021

The Extension Of Step-$N$ Signatures, Kistosil Fahim

Turkish Journal of Mathematics

In 2009, Gyurko introduced $\Pi$-rough path which extends $p$-rough path. Inspired by this work we introduce the degree-$(\Pi,N)$ signature which can be treated as the step-$N$ signature for some $\Pi$. The degree-$(\Pi,N)$ signature holds some algebraic properties which will be proven in this paper.

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Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir Jan 2021

Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir

Turkish Journal of Mathematics

In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo--Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.

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Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation, Nguyen Dat Thuc, Le Thi Phuong Ngoc, Nguyen Thanh Long Jan 2021

Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation, Nguyen Dat Thuc, Le Thi Phuong Ngoc, Nguyen Thanh Long

Turkish Journal of Mathematics

This paper is devoted to the study of the following nonlinear functional integral equation \begin{equation} f(x)=\sum\limits_{i=1}^{q}\alpha _{i}(x)f(\tau_{i}(x))+\int_{0}^{\sigma_{1}(x)}\Psi \left( x,t,f(\sigma _{2}(t)),\int_{0}^{\sigma_{3}(t)}f(s)ds\right) dt+g(x),\text{ }\forall x\in \lbrack 0,1], \tag{E} \label{E} \end{equation} where $\tau _{i},$ $\sigma _{1},$ $\sigma _{2},$ $\sigma _{3}:[0,1]\rightarrow \lbrack 0,1];$ $\alpha _{i},$ $g:[0,1]\rightarrow \mathbb{R};$ $\Psi :[0,1]\times \lbrack 0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ are the given continuous functions and $f:[0,1]\,\rightarrow \mathbb{R}$ is an unknown function. First, two sufficient conditions for the existence and some properties of solutions of Eq. (E) are proved. By using Banach's fixed point theorem, we have the first sufficient condition yielding existence, uniqueness and stability of the solution. By applying …

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Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk Jan 2021

Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk

Turkish Journal of Mathematics

In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.

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A Short Note On Generic Initial Ideals, Beki̇r Daniş Jan 2021

A Short Note On Generic Initial Ideals, Beki̇r Daniş

Turkish Journal of Mathematics

The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a …

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Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca Jan 2021

Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca

Turkish Journal of Mathematics

The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to Poisson distribution series. Several corollaries and consequences of the main results are also considered.

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Fundamental Group Of Galois Covers Of Degree 5 Surfaces, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu Jan 2021

Fundamental Group Of Galois Covers Of Degree 5 Surfaces, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu

Turkish Journal of Mathematics

Let $X$ be an algebraic surface of degree $5$, which is considered a branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental groups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.

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Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou Jan 2021

Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou

Turkish Journal of Mathematics

In this paper, some characterizations for boundedness, essential norm and compactness of generalized Stevic-Sharma type operators from Hardy spaces into $n$th weighted type spaces are given.

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B-Property Of Sublattices In Vector Lattices, Ömer Şafak Alpay, Svetlana Gorokhova Jan 2021

B-Property Of Sublattices In Vector Lattices, Ömer Şafak Alpay, Svetlana Gorokhova

Turkish Journal of Mathematics

We study $b$-property of a sublattice (or an order ideal) $F$ of a vector lattice $E$. In particular, $b$-property of $E$ in $E^\delta$, the Dedekind completion of $E$, $b$-property of $E$ in $E^u$, the universal completion of $E$, and $b$-property of $E$ in $\hat{E}(\hat{\tau})$, the completion of $E$.

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Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri Jan 2021

Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri

Turkish Journal of Mathematics

In this paper, fractional Sturm--Liouville problems of high-order are studied. A simple and efficient approach is presented to determine more eigenvalues and eigenfunctions than other approaches. Existence and uniqueness of solutions of a fractional high-order differential equation with initial conditions is addressed as well as the convergence of the proposed approach. This class of eigenvalue problems is important in finding solutions to linear fractional partial differential equations (LFPDE). This method is illustrated by three examples to signify the efficiency and reliability of the proposed numerical approach.

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Logarithmic Dimension And Bases In Whitney Spaces, Alexander Goncharov, Yasemi̇n Şengül Tezel Jan 2021

Logarithmic Dimension And Bases In Whitney Spaces, Alexander Goncharov, Yasemi̇n Şengül Tezel

Turkish Journal of Mathematics

We give a formula for the logarithmic dimension of the generalized Cantor-type set $K$. In the case when the logarithmic dimension of $K$ is smaller than $1$, we construct a Faber basis in the space of Whitney functions $\mathcal{E}(K)$.

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On Congruences Related To Trinomial Coefficients And Harmonic Numbers, Neşe Ömür, Si̇bel Koparal, Laid Elkhiri Jan 2021

On Congruences Related To Trinomial Coefficients And Harmonic Numbers, Neşe Ömür, Si̇bel Koparal, Laid Elkhiri

Turkish Journal of Mathematics

In this paper, we establish some congruences involving the trinomial coefficients and harmonic numbers. For example, for any prime $p>3,$ \begin{equation*} \sum\limits_{k=0}^{p-1}\left( -1\right) ^{k}\binom{p-1}{k}_{2}H_{k}\equiv 0 \ \pmod {p}. \end{equation*}

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Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik Jan 2021

Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik

Turkish Journal of Mathematics

The purpose of this paper is to study some additional relations between lines and points in the configuration of six lines tangent to the common conic. One of the most famous results concerning with this configuration is Brianchon theorem. It says that three diagonals of a hexagon circumscribing around conic are concurrent. They meet in the so called Brianchon point. In fact, by relabeling the vertices of hexagon, we obtain $60$ distinct Brianchon points. We prove, among others, that, in the set of all intersection points of six tangents to the same conic, there exist exactly $10$ sextuples of points …

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A Refinement Of The Bergström Inequality, Gülteki̇n Tinaztepe, İlknur Yeşi̇lce, Gabi̇l Adi̇lov Jan 2021

A Refinement Of The Bergström Inequality, Gülteki̇n Tinaztepe, İlknur Yeşi̇lce, Gabi̇l Adi̇lov

Turkish Journal of Mathematics

In this paper, the Bergstrom inequality is studied, and a refinement of this inequality is obtained by performing the optimality conditions based on abstract concavity. Some numerical experiments are given to illustrate the efficacy of the refinement.

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