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Articles 1381 - 1410 of 10317
Full-Text Articles in Physical Sciences and Mathematics
Sparse Polynomial Interpolation With Bernstein Polynomials, Erdal İmamoğlu
Sparse Polynomial Interpolation With Bernstein Polynomials, Erdal İmamoğlu
Turkish Journal of Mathematics
We present an algorithm for interpolating an unknown univariate polynomial $f$ that has a $t$ sparse representation ($t
Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data, Ratan Kumar Giri, Debajyoti Choudhuri
Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data, Ratan Kumar Giri, Debajyoti Choudhuri
Turkish Journal of Mathematics
We study the following partial differential equation (PDE) \begin{align} \begin{split} (-\Delta)^s u + g(x,u) & = \mu\,\,\mbox{in}\,\,\Omega,\\ u & = 0\,\,\mbox{in}\,\,\mathbb{R}^N\setminus\Omega,\label{eqn_abs} \end{split} \end{align} where $(-\Delta)^s$ is the fractional Laplacian operator, $\Omega$ is a bounded domain in $\mathbb{R}^N$ with $\partial\Omega$ being the boundary of $\Omega$, $g(.,.)$ is a nonlinear function defined over $\Omega\times\mathbb{R}$. Let $(\mu_n)_n$ be a sequence of measure in $\Omega$. Assume that there exists a solution $u_n$ with data $\mu_n$, i.e. $u_n$ satisfies the equation (0.1) with $\mu=\mu_n$. We further assume that the sequence of measures weakly converges to $\mu$, while $(u_n)_n$ converges to $u$ in $L^1(\Omega)$. In general, …
Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces, Damian Maingi
Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces, Damian Maingi
Turkish Journal of Mathematics
The existence of monads on products of projective spaces $P^{a_1}\times\cdots\times\ P^{a_n}$ is nontrivial. In this paper, we construct monads over the polycyclic variety $P^{2n+1}\times\ P^{2n+1}$, we prove that cohomology vector bundle associated to these monads is simple. We also construct a monad on $P^1\times P^1\times\ P^2$. We also study the vector bundles associated to monads and prove stability and simplicity.
(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n
(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n
Turkish Journal of Mathematics
In this paper, we give categorical properties such as pullback, finite product, finite limit, coproduct, colimit and pushout in $\boldsymbol{XHom-Lie/A}$ of the category of Hom-Lie crossed modules.
Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli
Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.
The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators, Xiaoyuan Yang, Ran Li, Yufeng Lu
The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators, Xiaoyuan Yang, Ran Li, Yufeng Lu
Turkish Journal of Mathematics
In this paper, we study some conditions about invertible and Fredholm truncated Toeplitz operators which have unique symbols. For $f\in L^\infty$, if $A_f$ is a Fredholm operator, then $f _E\neq 0$ for any $E\subset \mathbb{T}$ with $ E >0$. Moreover \textnormal {ind} $(A_f)=0.$ In particular, if $A_f$ is invertible in $\mathfrak{L}(K_u^2)$, then $f$ is invertible in $L^\infty$. Besides, we give some results about the kernel spaces of truncated Toeplitz operators. For $f \in L^\infty$, we obtain the necessary and sufficient condition that the defect operator $I-A_f^*A_f$ of truncated Toeplitz operator $A_f$ meeting some conditions is compact on the model space …
Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova
Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova
Turkish Journal of Mathematics
In this paper, we consider the operator of parabolic type $$ Lu=\frac{\partial u}{\partial t}-\frac{\partial^{2}u}{\partial x^{2}}+q(x)u, $$ in the space $L_{2}(R^{2})$ with a greatly growing coefficient at infinity. The operator is originally defined on $C_{0}^{\infty}(R^{2})$, where $C_{0}^{\infty}(R^{2})$ is the set of infinitely differentiable and compactly supported functions. \noindent Assume that the coefficient $q(x)$ is a continuous function in $R=(-\infty, \infty)$, and it can be a strongly increasing function at infinity. \noindent The operator $L$ admits closure in space $L_{2}(R^{2})$, and the closure is also denoted by $L$. \noindent In the paper, we proved the bounded invertibility of the operator $L$ in …
Singular Integral Operators And Maximal Functions With Hardy Space Kernels, Ahmad Al Salman
Singular Integral Operators And Maximal Functions With Hardy Space Kernels, Ahmad Al Salman
Turkish Journal of Mathematics
In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on $L^{p},1
3-Principalization Over S_3-Fields, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili
3-Principalization Over S_3-Fields, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili
Turkish Journal of Mathematics
Let $p\equiv 1\,(\mathrm{mod}\,9)$ be a prime number and $\zeta_3$ be a primitive cube root of unity. Then $k=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$ is a pure metacyclic field with group $\mathrm{Gal}(k/\mathbb{Q})\simeq S_3$. In the case that $k$ possesses a $3$-class group $C_{k,3}$ of type $(9,3)$, the capitulation of $3$-ideal classes of $k$ in its unramified cyclic cubic extensions is determined, and conclusions concerning the maximal unramified pro-$3$-extension $k_3^{(\infty)}$, that is the $3$-class field tower of $k$, are drawn.
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Turkish Journal of Mathematics
In this paper, a second-order mock theta function $\mathfrak{D}_5(q)$ given by Hikami [11] is studied. By using basic hypergeometric transformation formulae, we attain some new representations of Hikami's mock theta function $\mathfrak{D}_5(q)$. Meanwhile, dual nature of bilateral series associated to mock theta function $\mathfrak{D}_5(q)$ is also discussed.
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
Turkish Journal of Mathematics
In this paper, we study the magnetic Schrödinger operator in a three-dimensional layer. We obtain an estimate for the number of eigenvalues of this operator lying to the left of the essential spectrum threshold. We show that the magnetic Schrödinger operator to the left of the continuous spectrum threshold can have only a finite number of eigenvalues of infinite multiplicity.
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Turkish Journal of Mathematics
Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular …
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …
Diameter Estimate For A Class Of Compact Generalized Quasi-Einstein Manifolds, Deng Yihua
Diameter Estimate For A Class Of Compact Generalized Quasi-Einstein Manifolds, Deng Yihua
Turkish Journal of Mathematics
In this paper, we discuss the lower diameter estimate for a class of compact generalized quasi-Einstein manifolds which are closely related to the conformal geometry. Using the Bochner formula and the Hopf maximum principle, we get a gradient estimate for the potential function of the manifold. Based on the gradient estimate, we get the lower diameter estimate for this class of generalized quasi-Einstein manifolds.
Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek
Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The main purpose of this paper is to obtain computational identities and formulas for a certain class of combinatorial-type numbers and polynomials. By the aid of the generating function technique, we derive a recurrence relation and an infinite series involving the aforementioned class of combinatorial-type numbers. By applying the Riemann integral to the combinatorial-type polynomials with multivariables, we present some integral formulas for these polynomials, including the Bernoulli numbers of the second kind. By the implementation of the $p$-adic integral approach to the combinatorial-type polynomials with multivariables, we also obtain formulas for the Volkenborn integral and the fermionic $p$-adic integral …
Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker
Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker
Turkish Journal of Mathematics
Let $\mathcal P_{n}$ be the partial transformation semigroup on $X_{n}=\{1,2,\ldots ,n\}$. In this paper, we find the left zero-divisors, right zero-divisors and two sided zero-divisors of $\mathcal P_{n}$, and their numbers. For $n \geq 3$, we define an undirected graph $\Gamma(\mathcal P_{n})$ associated with $\mathcal P_{n}$ whose vertices are the two sided zero-divisors of $\mathcal P_{n}$ excluding the zero element $\theta$ of $\mathcal P_{n}$ with distinct two vertices $\alpha$ and $\beta$ joined by an edge in case $\alpha\beta=\theta =\beta\alpha$. First, we prove that $\Gamma(\mathcal P_{n})$ is a connected graph, and find the diameter, girth, domination number and the degrees of …
Finite Groups With Three Non-Abelian Subgroups, Bijan Taeri, Fatemeh Tayanloo Beyg
Finite Groups With Three Non-Abelian Subgroups, Bijan Taeri, Fatemeh Tayanloo Beyg
Turkish Journal of Mathematics
We characterize finite groups with exactly two nonabelian proper subgroups. When $G$ is nilpotent, we show that $G$ is either the direct product of a minimal nonabelian $p$-group and a cyclic $q$-group or a $2$-group. When $G$ is nonnilpotent supersolvable group, we obtain the presentation of $G$. Finally, when $G$ is nonsupersolvable, we show that $G$ is a semidirect product of a $p$-group and a cyclic group.
Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim
Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim
Turkish Journal of Mathematics
This paper is concerned with the existence and blow-up of solutions to the following linear parabolic equation: $ ~~ u_t - \Delta u +u = 0 \quad \text{ in } \Omega \times (0,T) $, under nonlinear boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^n $, $n \geq 1$, with smooth boundary. We obtain a threshold result for the global existence of solutions, next we shall prove the existence time $T$ of solution is finite when the initial energy satisfies certain condition.
Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian
Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian
Turkish Journal of Mathematics
In the present work it is shown that on a Finslerian space, a forward complete gradient shrinking Ricci soliton has finite topological type, provided either the Ricci scalar is bounded above or the Ricci scalar is bounded from below and injectivity radius is bounded away from zero.
Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu
Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu
Turkish Journal of Mathematics
We perform an opportunistic search for cubic surfaces over small fields of characteristic two. The starting point of our work is a list of surfaces complied by Dickson over the field with two elements. We consider the nonsingular ones arising in Dickson' s work for the fields of larger orders of characteristic two. We investigate the properties such as the number of lines, singularities and automorphism groups. The problem of determining the possible numbers of lines of a nonsingular cubic surface over the fields of $\mathbb{C}, \mathbb{R}, \mathbb{Q}, \mathbb{F}_q$ where q odd, $\mathbb{F}_2$ was considered by Cayley and Salmon, Schlafli, …
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an extension of the classical Eilenberg-MacLane higher order cohomology theories of abelian groups to presheaves of commutative monoids (and of abelian groups, then) over an arbitrary small category. These high-level cohomologies enjoy many desirable properties and the paper aims to explore them. The results apply directly in several settings such as presheaves of commutative monoids on a topological space, simplicial commutative monoids, presheaves of simplicial commutative monoids on a topological space, commutative monoids or simplicial commutative monoids on which a fixed monoid or group acts, and so forth. As a main application, we state and prove a precise …
On The Distribution Of Coefficients Of Half-Integral Weight Modular Forms And The Bruinier-Kohnen Conjecture, İlker İnam, Zeynep Demi̇rkol Özkaya, Eli̇f Tercan, Gabor Wiese
On The Distribution Of Coefficients Of Half-Integral Weight Modular Forms And The Bruinier-Kohnen Conjecture, İlker İnam, Zeynep Demi̇rkol Özkaya, Eli̇f Tercan, Gabor Wiese
Turkish Journal of Mathematics
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete
On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete
Turkish Journal of Mathematics
The aim of the article is to study the Betti numbers of the tangent cone of Gorenstein monomial curves in affine 4-space. If $C_S$ is a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen--Macaulay, we show that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).
On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş
On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş
Turkish Journal of Mathematics
In this paper, we establish new Lyapunov-type inequalities for $\left(n+1\right)$st order nonlinear differential equation including $p$-relativistic operator and $q$-prescribed curvature operator under the antiperiodic boundary conditions.
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Turkish Journal of Mathematics
Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G)=0$ if $G$ has no such generating sets). This paper investigates $d_k(G)$ when $G$ is a finite Coxeter group either of type $B_n$ or $D_n$, or of exceptional type. Together with the work of Garzoni and Yu, this determines $d_k(G)$ for all finite irreducible Coxeter groups $G$ when $2 \leq k \leq (G)$ ($(G)+1$ when $G$ is of type A$_{n}$).
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces, Wanyu Wu, Jiang Zhou
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces, Wanyu Wu, Jiang Zhou
Turkish Journal of Mathematics
In this paper, we establish the two-weight norm inequalities for fractional maximal functions and fractional integral operators related to Schrödinger differential operator on weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Turkish Journal of Mathematics
We propose and analyze a modified weak Galerkin finite element method (MWG-FEM) for solving singularly perturbed problems of convection-dominated type. The proposed method is constructed over piecewise polynomials of degree $k\geq1$ on interior of each element and piecewise constant on the boundary of each element. The present method is parameter-free and has less degrees of freedom compared to the classical weak Galerkin finite element method. The method is shown uniformly convergent for small perturbation parameters. An uniform convergence rate of $\mathcal {O}((N^{-1}\ln N)^k)$ in the energy-like norm is established on the piecewise uniform Shishkin mesh, where $N$ is the number …
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
Turkish Journal of Mathematics
In this paper, we obtain an important inequalities for coordinated convex functions and as a result of these inequalities we give the extension of Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral and logarithmic integral. The inequalities obtained in this study provide generalizations of some result given in earlier works.
Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi
Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi
Turkish Journal of Mathematics
The purpose of this paper is to provide a more general Cameron-Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process $\mathcal Z_k$ on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions $a(t)$ and $b(t)$ on $[0,T]$. As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley-Wiener-Zygmund stochastic integrals.
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
Turkish Journal of Mathematics
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.