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Articles 1 - 30 of 223
Full-Text Articles in Physical Sciences and Mathematics
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Turkish Journal of Mathematics
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Turkish Journal of Mathematics
In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.
On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei
On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei
Turkish Journal of Mathematics
Let $(M, F)$ be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds $(M_1, F_1)$ and $(M_2, F_2)$ with $F=\sqrt{f(K, H)}$ and $K=F_1^2$, $H=F_2^2$. In this paper, we prove that $(M, F)$ is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if $(M_1, F_1)$ and $(M_2, F_2)$ are both weakly Kähler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function $f$. Meanwhile, we prove that $(M, F)$ is a complex Landsberg manifold if and only if either $(M_1, F_1)$ and $(M_2, F_2)$ are both complex Landsberg manifolds and $f=c_1K+c_2H$ with …
A Generalization Of $\Pi$-Regular Rings, Peter Danchev
A Generalization Of $\Pi$-Regular Rings, Peter Danchev
Turkish Journal of Mathematics
We introduce the class of so-called { regularly nil clean rings} and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of $\pi$-regular and strongly $\pi$-regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong $\pi$-regularity that was visualized by Dischinger \cite{Dis}. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and \v{S}ter \cite{DS} and Danchev \cite{Da}.
On Distribution Of Upper Marginal Records In Bivariate Random Sequences, Gülder Kemalbay, İsmi̇han Bayramoğlu
On Distribution Of Upper Marginal Records In Bivariate Random Sequences, Gülder Kemalbay, İsmi̇han Bayramoğlu
Turkish Journal of Mathematics
The theory of record values has been extensively studied in the statistical literature. However, there are not many papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents the marginal record values and record times in extended sequence of bivariate random vectors. The joint distributions of some upper marginal records are derived. Some results on joint probability mass function of upper record time vectors and distribution function of upper record value vectors are given via copula functions. Moreover, the numerical and graphical applications of considered upper records using flood data and prediction of rainfall …
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations, Fanglei Wang, Nannan Yang
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations, Fanglei Wang, Nannan Yang
Turkish Journal of Mathematics
Using the Krasnosel'skii's fixed point theorem, we establish the existence and multiplicity of positive $\mathrm{T}$-periodic solutions of second-order semipositone system $ \left \{\begin{array}{lcr} x''(t)+a(t)x(t)=\lambda f(t,x(t)),\\ x(0)=x(\mathrm{T}),x'(0)=x'(\mathrm{T}), \end{array}\right. $ where $x=(x_1,x_2,\cdots,x_n)$, $f(t,x)=(f_1(t,x),f_2(t,x),\cdots,f_n(t,x))$ is bounded below.
The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico
The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico
Turkish Journal of Mathematics
In this paper we define and study the matrix-valued $k\times k$ numerical range of $n\times n$ matrices using the Hermitian product and the product with $n\times k$ unitary matrices $U$ (on the right with $U$, on the left with its adjoint $U^\dagger = U^{-1}$). For all $i, j=1,\dots ,k$ we study the possible $(i,j)$-entries of these $k\times k$ matrices. Our results are for the case in which the base field is finite, but the same definition works over $\mathbb {C}$. Instead of the degree $2$ extension $\mathbb {R}\hookrightarrow \mathbb {C}$ we use the degree $2$ extension $\mathbb {F} _q\hookrightarrow \mathbb …
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 $\mathbb F_q$.
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao
Turkish Journal of Mathematics
Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
Turkish Journal of Mathematics
In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
Turkish Journal of Mathematics
In this work, we determine the structure of the automorphism group of the free metabelian Leibniz algebra of rank three over a field K of characteristic zero.
On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker
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.
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
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 A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
On A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
Turkish Journal of Mathematics
The main object of the present paper is to state and prove a general nonnegativity principle in the framework of multiterm fractional differential equations, which we use to investigate some iterative monotone sequences of lower and upper solutions to a certain fractional eigenvalue problem. The obtained results can be easily extended to fractional differential equations of distributed orders since the latter are the natural extension of multiterm fractional differential equations.
Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints, Ta Quang Son, Ching Feng Wen
Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints, Ta Quang Son, Ching Feng Wen
Turkish Journal of Mathematics
In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problems that have an infinite number of constraints. The obtained results are based on the notion of weak-subdifferentials for vector functions. Some properties of weak stability for the problems are introduced. Relationships between strong duality and saddle points of the augmented Lagrange vector functions associated to the problems are investigated. Connections between weak-stability and saddle point theorems of the problems are established. An example is given.
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 $t\mid q^n-1$.
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Turkish Journal of Mathematics
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
Turkish Journal of Mathematics
In this paper we deal with the radii of starlikeness and convexity of the $q$-Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-P\'olya class of real entire functions plays a pivotal role in this investigation.
Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür
Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür
Turkish Journal of Mathematics
In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Turkish Journal of Mathematics
Let $(\beta_n)_{n\ge 2}$ be a sequence of nonnegative real numbers and $\delta$ be a positive real number. We introduce the subclass $\mathcal{A}(\beta_n,\delta)$ of analytic functions, with the property that the Taylor coefficients of the function $f$ satisfies $\sum_{n\ge2}^{\infty}\beta_n a_n \le \delta$, where $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. The class $\mathcal{A}(\beta_n,\delta)$ contains nonunivalent functions for some choices of $(\beta_n)_{n\ge 2}$. In this paper, we provide some general properties of functions belonging to the class $\mathcal{A}(\beta_n,\delta)$, such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. …
On Band Operators, Bahri̇ Turan, Kazim Özcan
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.
On Near Soft Sets, Alkan Özkan
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.
On S-Prime Submodules, Esra Şengelen Sevi̇m, Tarik Arabaci, Ünsal Teki̇r, Suat Koç
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\ …
Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez
Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez
Turkish Journal of Mathematics
In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weak antipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special case of the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
Turkish Journal of Mathematics
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t) _{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
An Inequality On Diagonal $F$-Thresholds Over Standard-Graded Complete Intersection Rings, Jinjia Li
An Inequality On Diagonal $F$-Thresholds Over Standard-Graded Complete Intersection Rings, Jinjia Li
Turkish Journal of Mathematics
In a recent paper, De Stefani and N\'{u}\~{n}ez-Betancourt proved that for a standard-graded $F$-pure $k$-algebra $R$, its diagonal $F$-threshold $c(R)$ is always at least $-a(R)$, where $a(R)$ is the $a$-invariant. In this paper, we establish a refinement of this result in the setting of complete intersection rings.
Third-Order Boundary Value Transmission Problems, Eki̇n Uğurlu
Third-Order Boundary Value Transmission Problems, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.
Trigonometric Expressions For Gaussian $_2f_1$-Series, Wenchang Chu
Trigonometric Expressions For Gaussian $_2f_1$-Series, Wenchang Chu
Turkish Journal of Mathematics
The classical Gaussian $_2F_1$-series containing two free variables $\{x,y\}$ and two integer parameters $\{m,n\}$ are investigated by the linearization method. Several closed formulae are derived in terms of trigonometric functions. Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating $_3F_2$-series.
Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu
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 $0\leq\alpha\leq1$.
Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r
Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r
Turkish Journal of Mathematics
We construct an equivalent renorming of $\ell^1$, which turns out to produce a degenerate $\ell^1$-analog Lorentz-Marcinkiewicz space $\ell_{\delta,1}$, where the weight sequence $\delta={(\delta_n)}_{n\in\N}=(2,1,1,1,\cdots)$ is a decreasing positive sequence in $\ell^\infty\backslash c_0$, rather than in $c_0\backslash\ell^1$ (the usual Lorentz situation). Then we obtain its isometrically isomorphic predual $\ell^0_{\delta,\infty}$ and dual $\ell_{\delta,\infty}$, corresponding degenerate $c_0$-analog and $\ell^\infty$-analog Lorentz-Marcinkiewicz spaces, respectively. We prove that both spaces $\ell_{\delta,1}$ and $\ell^0_{\delta,\infty}$ enjoy the weak fixed point property (w-fpp) for nonexpansive mappings yet they fail to have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric copy of $\ell^1$ and $c_0$, …