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Articles 3301 - 3330 of 10319
Full-Text Articles in Physical Sciences and Mathematics
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Turkish Journal of Mathematics
In this paper, we investigate analytical and asymptotic properties of the Jost solution and Jost function of the impulsive discrete Dirac equations. We also study eigenvalues and spectral singularities of these equations. Then we obtain characteristic properties of the scattering function of the impulsive discrete Dirac systems. Therefore, we find the Jost function, point spectrum, and scattering function of the unperturbed impulsive equations.
Inclusions And The Approximate Identities Of The Generalized Grand Lebesgue Spaces, Ahmet Turan Gürkanli
Inclusions And The Approximate Identities Of The Generalized Grand Lebesgue Spaces, Ahmet Turan Gürkanli
Turkish Journal of Mathematics
Let $\left( \Omega ,\sum ,\mu \right) $ and $\left( \Omega ,\sum ,v\right) $ be two finite measure spaces and let $L^{p),\theta }\left( \mu \right) $ and $L^{q),\theta }\left( v\right) $ be two generalized grand Lebesgue spaces $\left[ 9,10\right] ,$ where $1
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Turkish Journal of Mathematics
The intersection of topological robotics and digital topology leads to us a new workspace. In this paper we introduce the new digital homotopy invariant digital topological complexity number $TC(X,\kappa)$ for digital images and give some examples and results about it. Moreover, we examine adjacency relations in the digital spaces and observe how $TC(X,\kappa)$ changes when we take a different adjacency relation in the digital spaces.
Existence And Nonexistence Of Global Solutions For Nonlinear Transmission Acoustic Problem, Akbar Aliyev, Sevda Isayeva
Existence And Nonexistence Of Global Solutions For Nonlinear Transmission Acoustic Problem, Akbar Aliyev, Sevda Isayeva
Turkish Journal of Mathematics
In this paper we consider a mixed problem for the nonlinear wave equations with transmission acoustic conditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one of which is clamped. We prove the existence of a global solution. Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.
Frequently Hypercyclic Weighted Backward Shifts On Spaces Of Real Analytic Functions, Berkay Anahtarci, Can Deha Kariksiz
Frequently Hypercyclic Weighted Backward Shifts On Spaces Of Real Analytic Functions, Berkay Anahtarci, Can Deha Kariksiz
Turkish Journal of Mathematics
We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convex spaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of these operators using dynamical transference principles and the frequent hypercyclicity criterion.
Ellipses And Similarity Transformations With Norm Functions, Ni̇hal Yilmaz Özgür
Ellipses And Similarity Transformations With Norm Functions, Ni̇hal Yilmaz Özgür
Turkish Journal of Mathematics
In this paper, we deal with a conjecture related to the images of ellipses (resp. circles) under similarities that are the special Möbius transformations. We consider ellipses (resp. circles) corresponding to any norm function (except in the Euclidean case) on the complex plane and examine some conditions to confirm this conjecture. Some illustrative examples are also given.
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.
On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar
On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar
Turkish Journal of Mathematics
Affine periodicity is a generalization of the notion of conventional periodicity and it is a symmetry property for classes of functions. This study is concerned with the existence of $(Q,T)$-affine periodic solutions of discrete dynamical systems. Sufficient conditions for the main results are proposed due to discrete exponential dichotomy and fixed point theory. Obtained results are also implemented for some economical and biological models. In particular cases, our results cover some existing results in the literature for periodic, antiperiodic, or quasiperiodic solutions of difference equations.
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Turkish Journal of Mathematics
In this paper we study the Caputo and Riemann--Liouville nabla $(q,h)$-fractional difference equation and obtain the following two main results: Assume $0
Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections, Leyla Bugay, Hayrullah Ayik
Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections, Leyla Bugay, Hayrullah Ayik
Turkish Journal of Mathematics
Let $I_{n}$ be the symmetric inverse semigroup, and let $PODI_{n}$ and $POI_{n}$ be its subsemigroups of monotone partial bijections and of isotone partial bijections on $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups $PODI_{n,r}=\{ \alpha \in PODI_{n}: \im(\alpha) \leq r\}$, $POI_{n,r}=\{ \alpha \in POI_{n}: \im(\alpha) \leq r\}$, and $E_{n,r}=\{ \id_{A}\in I_{n}:A\subseteq X_n\mbox{ and } A \leq r\}$ where $id_{A}$ is the identity map on $A\subseteq X_n$ for $0\leq r\leq n-1$.
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.
On A Class Of Kazdan--Warner Equations, Yu Fang, Mengjie Zhang
On A Class Of Kazdan--Warner Equations, Yu Fang, Mengjie Zhang
Turkish Journal of Mathematics
Let $(\small{\Si},g)$ be a compact Riemannian surface without boundary and $W^{1,2}(\Si)$ be the usual Sobolev space. For any real number $p>1$ and $\alpha\in\mathbb{R}$, we define a functional $$ J_{\alpha,8\pi}(u)=\frac{1}{2}\le( \int_\Si \nabla_g u ^2dv_g-\alpha (\int_\Si u ^pdv_g)^{2/p}\ri)-8\pi\log\int_\Si he^u dv_g $$ on a function space $\mathcal{H}=\le\{u\in W^{1,2}(\Si):\int_{\Si}u dv_{g}=0\ri\}$, where $h$ is a positive smooth function on $\Si$. Denote $$\lambda_{1,p}(\Si)=\inf_{u\in \mathcal{H},\,\int_\Si u ^p dv_g=1}\int_{\Si} \nabla_{g}u ^{2}\mathrm{d}v_{g}. $$ If $\alpha
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we mainly investigate the uniqueness problem on meromorphic functions in $\mathbb{C}^m$ sharing small functions with their difference operators or shifts, and we obtain some interesting results that act as some extensions of previous results from one complex variable to several complex variables.
Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao
Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao
Turkish Journal of Mathematics
The coefficient of $x^{-1}$ of a formal Laurent series $f(x)$ is called the formal residue of $f(x)$. Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their $q$-analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.
Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences, Nares Sawatraksa, Chaiwat Namnak
Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences, Nares Sawatraksa, Chaiwat Namnak
Turkish Journal of Mathematics
Let $T(X)$ be the full transformation semigroup on a set $X$. For two equivalence relations $E$ and $F$ on $X$ with $F \subseteq E$, let $T(X, E, F) = \{ \alpha \in T(X) : \forall x, y \in X, (x, y)\in E \Rightarrow (x\alpha, y\alpha) \in F \}. $
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 $_1F_1(x)$.
Conformal Slant Submersions From Cosymplectic Manifolds, Yilmaz Gündüzalp, Mehmet Aki̇f Akyol
Conformal Slant Submersions From Cosymplectic Manifolds, Yilmaz Gündüzalp, Mehmet Aki̇f Akyol
Turkish Journal of Mathematics
Akyol [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field $\xi$ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, and conformal antiinvariant submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, …
Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu
Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu
Turkish Journal of Mathematics
By means of the modified Abel lemma on summation by parts, we examine a class of terminating balanced $q$-series. Two transformation formulae are established that contain ten summation formulae as consequences.
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.
Second Hankel Determinant For A Subclass Of Analytic Bi-Univalent Functions Defined By Subordination, Ahmad Motamednezhad, Teodor Bulboaca, Ebrahim Analouei Adegani, Nesa Dibagar
Second Hankel Determinant For A Subclass Of Analytic Bi-Univalent Functions Defined By Subordination, Ahmad Motamednezhad, Teodor Bulboaca, Ebrahim Analouei Adegani, Nesa Dibagar
Turkish Journal of Mathematics
In this work with a different technique we obtain upper bounds of the functional $\left a_2a_4-a_3^2\right $ for functions belonging to a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. Moreover, our results extend and improve some of the previously known ones.
Quasinilpotents In Rings And Their Applications, Jian Cui
Quasinilpotents In Rings And Their Applications, Jian Cui
Turkish Journal of Mathematics
An element $a$ of an associative ring $R$ is said to be quasinilpotent if $1-ax$ is invertible for every $x\in R$ with $xa=ax$. Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.
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.
Multivariate Lucas Polynomials And Ideal Classes Inquadratic Number Fields, Ayberk Zeyti̇n
Multivariate Lucas Polynomials And Ideal Classes Inquadratic Number Fields, Ayberk Zeyti̇n
Turkish Journal of Mathematics
In this work, by using Pauli matrices, we introduce four families of polynomials indexed over the positive integers. These polynomials have rational or imaginary rational coefficients. It turns out that two of these families are closely related to classical Lucas and Fibonacci polynomial sequences and hence to Lucas and Fibonacci numbers. We use one of these families to give a geometric interpretation of the 200-year-old class number problems of Gauß, which is equivalent to the study of narrow ideal classes in real quadratic number fields.
A Nonexistence Result For Blowing Up Sign-Changing Solutions Of The Brezis-Nirenberg-Type Problem, Yessine Dammak
A Nonexistence Result For Blowing Up Sign-Changing Solutions Of The Brezis-Nirenberg-Type Problem, Yessine Dammak
Turkish Journal of Mathematics
We consider the Brezis-Nirenberg problem: $ -\triangle u= u ^{p-1}u\pm\varepsilon u\mbox{ in }\Omega;, \mbox{ with } u=0 \mbox{ on }\partial\Omega,$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^n$, $n\geq4$, $p+1=2n/(n-2)$ is the critical Sobolev exponent, and $\varepsilon > 0$ is a positive parameter. The main result of this paper shows that if $n\geq4$ there are no sign-changing solutions $u_\varepsilon$ of $(P_{-\varepsilon})$ with two positive and one negative blow up points.
A Singularly Perturbed Differential Equation With Piecewise Constant Argument Of Generalized Type, Marat Akhmet, Murathan Dauylbaev, Aziza Mirzakulova
A Singularly Perturbed Differential Equation With Piecewise Constant Argument Of Generalized Type, Marat Akhmet, Murathan Dauylbaev, Aziza Mirzakulova
Turkish Journal of Mathematics
The paper considers the extension of Tikhonov Theorem for singularly perturbed differential equation with piecewise constant argument of generalized type. An approximate solution of the problem has been obtained. A new phenomenon of humping has been observed in the boundary layer area. An illustrative example with simulations is provided.
Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Turkish Journal of Mathematics
In this paper, we study the $L^{p}$-boundedness of a class of semiclassical Fourier integral operators.
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
Turkish Journal of Mathematics
In this paper we consider the following higher-order nonlinear difference equation $$ x_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}x_{n-\left( k+l\right) }}{\beta x_{n-\left( k+l\right) }+\gamma x_{n-l}},\ n\in \mathbb{N} _{0}, $$ where $k$ and $l$ are fixed natural numbers, and the parameters $\alpha $, $ \beta $, $\gamma $, $\delta $ and the initial values $x_{-i}$, $i=\overline{ 1,k+l}$, are real numbers such that $\beta ^{2}+\gamma ^{2}\neq 0$. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case …
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.
Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib
Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib
Turkish Journal of Mathematics
In this paper we construct an explicit sequence of divergence-free vector fields $\rm{b}_{n}$ that pushes the spectral gap of the nonself-adjoint operator $A_{\rm{b}_{n}}=\Delta +\rm{b}_{n}\cdot\nabla $ to infinity. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution.
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 $\mathcal{S}(G)$.