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Articles 1141 - 1170 of 2595
Full-Text Articles in Mathematics
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Turkish Journal of Mathematics
Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $ j \leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Turkish Journal of Mathematics
The present paper aims to investigate a class of linear positive operators by combining Szász-Jain operators and Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-type results and establish Grüss-Voronovskaja-type theorem. Furthermore, we show the rate of convergence for Szász-Jain-Brenke operators to functions having derivative of bounded variation and not having derivative of bounded variation by illustrative graphics using MATLAB.
On $N$-Absorbing $\Delta$-Primary Ideals, Gülşen Ulucak, Ünsal Teki̇r, Suat Koç
On $N$-Absorbing $\Delta$-Primary Ideals, Gülşen Ulucak, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
Let $R$ be a commutative ring with nonzero identity and $n$ be a positive integer. In this paper, we study the concepts of $n$-absorbing $\delta $-primary ideals and weakly $n$-absorbing $\delta$-primary ideals, which are the generalizations of $\delta$-primary ideals and weakly $\delta$-primary ideals, respectively. We introduce the concepts of $n$-absorbing $\delta$-primary ideals and weakly $n$-absorbing $\delta$-primary ideals. Moreover, we give many properties of these new types of ideals and investigate the relations between these structures.
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper, we assume that $P$ and $Q$ are relatively prime odd positive integers and $P^{2}+4Q>0.$ We determine all indices $n$ such that $U_{n}=(P^{2}+4Q)x^{2}.$ Moreover, we determine all indices $n$ such that $(P^{2}+4Q)U_{n}=x^{2}.$ As a result, we show that the equation $V_{n}^{2}(P,1)+V_{n+1}^{2}(P,1)=x^{2}$ has solution only for $n=2,$ $P=1,$ $x=5$ and $V_{n+1}^{2}(P,-1)=V_{n}^{2}(P,-1)+x^{2}$ has no solutions. Moreover, we solve some Diophantine equations.
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Turkish Journal of Mathematics
In this paper, the authors study some subordination and superordination properties for classes of $p$-valent meromorphic, analytic, and univalent functions associated with a linear operator $\mathfrak{L}_{p,\lambda}^{m,\ell}(a,c,\mu)$ of the Erdélyi-Kober type. Connections with several earlier results are also pointed out.
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
Turkish Journal of Mathematics
We offer a new approach for determining Harnack quantities for the curve shortening flow and we show how, following this procedure, one can obtain Hamilton's Harnack inequality for this flow $\kappa_t+\frac{1}{2t}\kappa\geq\frac{\kappa_s^2}{\kappa}$, where $\kappa$ is the curvature of the curve being deformed by the flow.
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales, Congbian Ma, Ping Li, Youliang Hou
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales, Congbian Ma, Ping Li, Youliang Hou
Turkish Journal of Mathematics
In this paper, we prove the bilaterally almost uniformly convergence of bounded $L_1(\mathcal{M})$-noncommutative quasi-martingales. We also prove Gundy's decomposition for noncommutative quasi-martingales. As an application, we prove that every relatively weakly compact quasi-martingale difference sequence in $L_1(\mathcal{M},\tau)$ whose sequence of norms is bounded away from zero is 2-co-lacunary.
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Turkish Journal of Mathematics
In this paper, we prove that an orthonormal wavelet basis associated with a general isotropic expansive matrix must be an unconditional basis for all $L^{p}$(ℝ${}^{d})$ with $1$<$p$<$\infty$, provided the wavelet functions satisfy some usual conditions.
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Turkish Journal of Mathematics
Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Banach space $X$ is $J$-reflexive if every bounded operator on $X$ that leaves invariant the sets $J(T,x)$ for all $x$ is contained in the closure of $orb(T)$ in the strong operator topology. We discuss some properties of $J$-reflexive operators. We also give and prove some necessary and sufficient conditions under which an operator is $J$-reflexive. We show that isomorphisms preserve $J$-reflexivity and some examples are considered. Finally, we extend the $J$-reflexive property in terms of subsets.
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$, Hailin Liu
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$, Hailin Liu
Turkish Journal of Mathematics
A graph $\Ga$ is called $G$-basic if $G$ is quasiprimitive or bi-quasiprimitive on the vertex set of $\Ga$, where $G\leq\Aut\Ga$. In this paper, we complete the classification of $r$-valent arc-transitive basic graphs with order $4p$ or $4p^2$, where $p$ and $r$ are odd primes.
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
Turkish Journal of Mathematics
The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
Invariant Subspaces Of Operators Quasi-Similar To L-Weakly And M-Weaklycompact Operators, Erdal Bayram
Invariant Subspaces Of Operators Quasi-Similar To L-Weakly And M-Weaklycompact Operators, Erdal Bayram
Turkish Journal of Mathematics
Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
Turkish Journal of Mathematics
In this work, almost product and almost golden structures are studied. Conditions for those structures being integrable and parallel are investigated. Moreover, the harmonicity of a map between almost product or almost golden manifolds with pure or hyperbolic metric is discussed under certain conditions.
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
Turkish Journal of Mathematics
We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where $0
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
Turkish Journal of Mathematics
In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Turkish Journal of Mathematics
The reducing subspaces of Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.
Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Turkish Journal of Mathematics
Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensional discrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceed to study its computational aspects as well as the inverse transform, which necessitate the development of a faster way to calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linear codes that can be assumed to be a generalization of Reed‒Solomon codes.
Field Of Values Of Perturbed Matrices And Quantum States, Madjid Khakshour, Gholamreza Aghamollaei, Alemeh Sheikhhosseini
Field Of Values Of Perturbed Matrices And Quantum States, Madjid Khakshour, Gholamreza Aghamollaei, Alemeh Sheikhhosseini
Turkish Journal of Mathematics
In this paper, the notion of the pseudofield of values of matrices is introduced and studied. The relationship between quantum states and the field of values of matrices is mentioned. The notion of the pseudopolynomial numerical hull, as a generalization of the pseudofield of values, of matrices is introduced and some properties of this notion are investigated.
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal
Turkish Journal of Mathematics
In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ then can we claim $T_{f}$\ or $T_{g}$\ is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space $H^{2}\left( \mathbb{D}% \right) $ is also given.
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
Turkish Journal of Mathematics
The localization theorem is known for compact $G$-spaces, where $G$ is a compact Lie group. In this study, we show that the localization theorem remains true for finite-dimensional compact group actions, and Borel's fixed point theorem holds not only for torus actions but for arbitrary finite-dimensional compact connected abelian group actions.
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Turkish Journal of Mathematics
It is well known that the transformation semigroup on a nonempty set $X$, which is denoted by $T(X)$, is regular, but its subsemigroups do not need to be. Consider a finite ordered set $X=(X;\leq)$ whose order forms a path with alternating orientation. For a nonempty subset $Y$ of $X$, two subsemigroups of $T(X)$ are studied. Namely, the semigroup $OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}$ and the semigroup $OS(X,Y)=\{\alpha\in T(X)\mid\alpha$ is order-preserving and $Y\alpha \subseteq Y\}$. In this paper, we characterize ordered sets having a coregular semigroup $OT(X,Y)$ and a coregular semigroup $OS(X,Y)$, respectively. Some characterizations of regular semigroups $OT(X,Y)$ …
The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi
The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi
Turkish Journal of Mathematics
The power graph $\mathcal{P}(G)$ is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph $\mathcal{S}(G)$ of the power graph $\mathcal{P}(G)$ is a graph with vertex set $G$ in which two elements $x, y \in G$ are joined if $o(x) o(y)$ or $o(y) o(x)$. The purpose of this paper is to study certain properties of this new graph together with the relationship between $\mathcal{P}(G)$ and $\mathcal{S}(G)$.
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Turkish Journal of Mathematics
We study plane algebraic curves defined over a field $k$ of arbitrary characteristic that are ramified coverings of the projective line $\mathbb{P}^{1}(k)$ branched over a given configuration of distinct points by their ramification type specified by a partition of $d$ the degree of the covering. We enumerate them by using the combinatorics of partitions and its connection to the representation theory of the symmetric group.
Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n
Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n
Turkish Journal of Mathematics
In the first part of this study, we characterize the compact subspaces of $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ and their relation to the vanishing Carleson measures. In the second part, we discuss the dual complement of the complex ellipsoid and give a duality result for $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ spaces in the sense of Grothendieck?K\"{o}the?da Silva.
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Turkish Journal of Mathematics
We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Björling problem by prescribing a circle or a helix as the core curve $\alpha$ and rotating with constant angular speed the unit normal vector field in the normal plane to $\alpha$. As particular cases, we exhibit new examples of timelike minimal surfaces invariant by a uniparametric group of helicoidal motions.
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Turkish Journal of Mathematics
We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Turkish Journal of Mathematics
A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions.