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Articles 65821 - 65850 of 294558

Full-Text Articles in Physical Sciences and Mathematics

A New Approach To Word Standardization And Some Of Its Applications, Wesam Talab Jan 2022

A New Approach To Word Standardization And Some Of Its Applications, Wesam Talab

Turkish Journal of Mathematics

In this article, we study word standardization in comparison to Young tableau standardization. We count the number of words (respectively Young tableau) standardized to a given permutation (respectively to a given standard Young tableau). We prove that both rectification and standardization applications commute and show that the standardization commutes with the insertion of Robinson--Schensted. We show that the standardizations of Knuth-equivalent two words are also Knuth equivalent. Finally, using word standardization we establish a proof for the following well-known equality: $$ \forall l \in \left\lbrace 0,1,\ldots,n-1\right\rbrace ,~~\left \langle {n\atop l} \right \rangle=d_{n,l}=a_{n,l}= \sum_{0\leq k \leq l}(-1)^k { n+1 \choose k …

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Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko Jan 2022

Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko

Turkish Journal of Mathematics

We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.

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Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk Jan 2022

Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk

Turkish Journal of Mathematics

In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed algebraically. Then, the conditions of existence for both period-doubling and Neimark--Sacker bifurcations arising from coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations. Finally, numerical simulations are performed to support the theoretical findings.

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On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane Jan 2022

On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane

Turkish Journal of Mathematics

We define in this note a natural metric over the tangent bundle $TM$ by using a vertical deformation of Sasaki metric. First we present the geometric result concerning the Levi-Civita connection and all forms of Riemannian curvature tensors of this metric. Secondly, we study the geodesics on the tangent bundle $TM$ and unit tangent bundle $T_{1}M$. Finally, we characterize the geodesic curvatures on $T_{1}M$.

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Vanishing Ideals Of Parameterized Subgroups In A Toric Variety, Esma Baran Özkan Jan 2022

Vanishing Ideals Of Parameterized Subgroups In A Toric Variety, Esma Baran Özkan

Turkish Journal of Mathematics

Let $K$ be a finite field and $X$ be a complete simplicial toric variety over $K$ with split torus $T_X\cong (K^*)^n$. We give an algorithm relying on elimination theory for finding generators of the vanishing ideal of a subgroup $Y_Q$ parameterized by a matrix $Q$ which can be used to study algebraic geometric codes arising from $Y_Q$. We give a method to compute the lattice $L$ whose ideal $I_L$ is exactly $I(Y_Q)$ under a mild condition. As applications, we give precise descriptions for the lattices corresponding to some special subgroups. We also prove a Nullstellensatz type theorem valid over finite …

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Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak Jan 2022

Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak

Turkish Journal of Mathematics

In this study, Sturm-Liouville operator was investigated on a star graph with nonequal edges. First, the behaviors of sufficiently large eigenvalues were learned, then the solution of the inverse problem was given to determine the potantial functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and obtain a constructive solution to the inverse problems of this class.

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Hermite-Hadamard-Mercer Type Inclusions For Interval-Valued Functions Via Riemann-Liouville Fractional Integrals, Hasan Kara, Muhammad Aamir Ali, Hüseyi̇n Budak Jan 2022

Hermite-Hadamard-Mercer Type Inclusions For Interval-Valued Functions Via Riemann-Liouville Fractional Integrals, Hasan Kara, Muhammad Aamir Ali, Hüseyi̇n Budak

Turkish Journal of Mathematics

In this research, we first establish some inclusions of fractional Hermite-Hadamard-Mercer type for interval-valued functions. Moreover, by special cases of our main results, we show that our main results reduce several inclusions obtained in the earlier works.

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On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert Jan 2022

On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert

Turkish Journal of Mathematics

We study the Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type \[ u_{t}-a\left(\ u\ _{L^{p}(\Omega)}^{p}\right)\sum\limits_{i=1}^{n}D_{i}\left( \left\vert u\right\vert ^{p-2}D_{i}u\right) +b\left( x,t,u\right)=f\left( x,t\right) \quad \text{in $Q_T=\Omega \times (0,T)$}, \] where $p\geq2$, $T>0$, $\Omega \subset \mathbb{R}^{n}$, $n\geq 2$, is a smooth bounded domain. The coefficient $a(\cdot)$ is real-valued function defined on $\mathbb{R}_+$ and $b(\cdot,\cdot,\tau)$ is a measurable function with variable nonlinearity in $\tau$. We prove existence of weak solutions of the considered problem under appropriate and general conditions on $a$ and $b$. Sufficient conditions for uniqueness are found and in the case $f\equiv0$ the decay rates for $\ u\ …

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On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz Jan 2022

On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz

Turkish Journal of Mathematics

Given a commutative ring $R$, the zero-divisor graph of $R$ is an undirected simple graph with vertices the nonzero zero-divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$. In [8], Redmond presented different versions of zero-divisor graphs of noncommutative rings. The main aim of this paper is to analyse these graphs for the semigroup $\mathcal{SP}_{n}$ of all strictly partial transformations on the set $X_{n}=\{1,2,\dots,n\}$.

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Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas Jan 2022

Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas

Turkish Journal of Mathematics

In this paper, we have characterized the nature and form of solutions of the following nonlinear delay-differential equation: $$f^{n}(z)+\sum_{i=1}^{n-1}b_{i}f^{i}(z)+q(z)e^{Q(z)}L(z,f)=P(z),$$ where $b_i\in\mathbb{C}$, $L(z,f)$ are a linear delay-differential polynomial of $f$; $n$ is positive integers; $q$, $Q$ and $P$ respectively are nonzero, nonconstant and any polynomials. Different special cases of our result will accommodate all the results of [J. Math. Anal. Appl., 452(2017), 1128-1144; Mediterr. J. Math., 13(2016), 3015-3027; Open Math., 18(2020), 1292-1301]. Thus our result can be considered as an improvement of all of them. We have also illustrated a handful number of examples to show that all the cases as …

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On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz Jan 2022

On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz

Turkish Journal of Mathematics

Given modules $A_{R}$ and $_{R}B$, $_{R}B$ is called absolutely $A_{R}$-pure if for every extension $_{R}C$ of $_{R}B$, $A\otimes B\rightarrow A\otimes C$ is a monomorphism. The class $\underline{\mathfrak{Fl}}^{-1}(A_{R})=$\{$_{R}B$ : $_{R}B$ is absolutely $A_{R}$-pure\} is called the absolutely pure domain of a module $A_{R}$. If $_{R}B$ is divisible, then all short exact sequences starting with $B$ is RD-pure, whence $B$ is absolutey $A$-pure for every $RD$-flat module $A_{R}$. Thus the class of divisible modules is the smallest possible absolutely pure domain of an $RD$-flat module. In this paper, we consider $RD$-flat modules whose absolutely pure domains contain only divisible modules, and we …

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Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli Jan 2022

Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli

Turkish Journal of Mathematics

In this paper, we discuss the domain of a recently defined conservative matrix, constructed by means of the Schröder numbers in the spaces of $p-$absolutely summable sequences and bounded sequences. We determine the $\beta-$duals of the Banach spaces, introduced here, and present characterization of some matrix operators. Moreover, we give the characterization of certain compact operators via the Hausdorff measure of noncompactness.

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On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky Jan 2022

On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky

Turkish Journal of Mathematics

The paper focused on the mean curvature and totally geodesic property of the Reeb vector field $\xi$ on $(\alpha,\beta)$ trans-Sasakian manifold $M$ of dimension $(2n+1)$ as a submanifold in the unit tangent bundle $T_1M$ with Sasaki metric $g_S$. We give an explicit formula for the norm of mean curvature vector of the submanifold $\xi(M)\subset (T_1M,g_S)$. As a byproduct, for the Reeb vector field, we get some known results concerning its minimality, harmonicity and the property to define a harmonic map. We prove that on connected proper trans-Sasakian manifold the Reeb vector field does not give rise to totally geodesic submanifold …

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On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m Jan 2022

On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m

Turkish Journal of Mathematics

In this study, we have introduced a generalization of Szasz-Mirakyan operators including Dunkl-Appell polynomials with help of sequences satisfying certain conditions and have derived some approximation properties of this generalization.

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Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo Jan 2022

Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo

Turkish Journal of Mathematics

In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.

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Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh Jan 2022

Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh

Turkish Journal of Mathematics

In this paper, we obtain the classification of topological dynamical systems with a discrete action. The equicontinuity and sensitivity for amenable discrete countable semigroup action are shown by the left Følner sequence. We consider the notion of uniquely ergodic and mean equicontinuous on amenable discrete countable semigroup action and develop the notion of density with respect to the Følner sequence on equicontinuous and sensitivity.

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$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus Jan 2022

$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus

Turkish Journal of Mathematics

In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.

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The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang Jan 2022

The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang

Turkish Journal of Mathematics

In this paper, the authors obtain the continuity of a class of linear operators on variable anisotropic Hardy--Lorentz spaces. In addition, the authors also obtain that the dual space of variable anisotropic Hardy-Lorentz spaces is the anisotropic BMO-type spaces with variable exponents. This result is still new even when the exponent function $p(\cdot)$ is $p$.

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On The Solutions Of Fractional Integro-Differential Equations Involving Ulam-Hyers-Rassias Stability Results Via $\Psi$-Fractional Derivative With Boundary Value Conditions, Kulandhivel Karthikeyan, Gobi Selvaraj Murugapandian, Özgür Ege Jan 2022

On The Solutions Of Fractional Integro-Differential Equations Involving Ulam-Hyers-Rassias Stability Results Via $\Psi$-Fractional Derivative With Boundary Value Conditions, Kulandhivel Karthikeyan, Gobi Selvaraj Murugapandian, Özgür Ege

Turkish Journal of Mathematics

In this paper, we study boundary value problems for the impulsive integro-differential equations via $\psi$-fractional derivative. The contraction mapping concept and Schaefer's fixed point theorem are used to produce the main results. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam-Hyers-Rassias stability of the solution to the proposed system.

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A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda Jan 2022

A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda

Turkish Journal of Mathematics

The primary aim of this article is to discuss and prove fixed point results using the operator type condensing map, and to obtain the existence of solution of Erdelyi-Kober bivariate fractional integral equation in a Banach space. An instance is given to explain the results obtained, and we construct an iterative algorithm by sinc interpolation to find an approximate solution of the problem with acceptable accuracy.

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Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki Jan 2022

Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki

Turkish Journal of Mathematics

In this work a new functional expansion-compression fixed point theorem of Leggett--Williams type is developed for a class of mappings of the form $T+F,$ where $(I-T)$ is Lipschitz invertible map and $F$ is a $k$-set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem.

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Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev Jan 2022

Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev

Turkish Journal of Mathematics

In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.

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Globally Unsolvability Of Integro-Differential Diffusion Equation And System With Exponential Nonlinearities, Meiirkhan Borikhanov Jan 2022

Globally Unsolvability Of Integro-Differential Diffusion Equation And System With Exponential Nonlinearities, Meiirkhan Borikhanov

Turkish Journal of Mathematics

In this paper, the Cauchy problem for an integro-differential diffusion equation and a system with nonlocal nonlinear sources are considered. The results on the existence of local integral solutions and the nonexistence of global weak solutions to the nonlinear integro-differential diffusion equation and system are presented.

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On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan Jan 2022

On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan

Turkish Journal of Mathematics

We introduce a certain type of warped-twisted product submanifolds which is called warped-twisted product hemislant submanifolds of the form $_{f_2}M^{\bot}\times_{f_1}M^{\theta}$ with warping function $f_2$ on $M^\theta$ and twisting function $f_1$, where $M^\bot$ is a totally real and $M^\theta$ is a slant submanifold of a globally conformal Kaehler manifold. We prove that a warped-twisted product hemislant submanifold of a globally conformal Kaehler manifold is a locally doubly warped product. Then we establish a general inequality for doubly warped product mixed geodesic hemislant submanifolds and get some results for such submanifolds by using the equality sign of the general inequality.

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Approximation By Sampling Kantorovich Series In Weighted Spaces Of Functions, Tuncer Acar, Osman Alagöz, Ali̇ Aral, Dani̇lo Costarelli̇, Meti̇n Turgay, Gianluca Vinti Jan 2022

Approximation By Sampling Kantorovich Series In Weighted Spaces Of Functions, Tuncer Acar, Osman Alagöz, Ali̇ Aral, Dani̇lo Costarelli̇, Meti̇n Turgay, Gianluca Vinti

Turkish Journal of Mathematics

This paper studies the convergence of the so-called sampling Kantorovich operators for functions belonging to weighted spaces of continuous functions. This setting allows us to establish uniform convergence results for functions that are not necessarily uniformly continuous and bounded on $\mathbb{R}$. In that context we also prove quantitative estimates for the rate of convergence of the family of the above operators in terms of weighted modulus of continuity. Finally, pointwise convergence results in quantitative form by means of Voronovskaja type theorems have been also established.

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A Fredholm Theory On Krein Spaces And Its Application To Weyl-Type Theorems And Homogeneous Equations, Danilo Polo Ojito, Jose Sanabria, Yina Ospino Buelvas Jan 2022

A Fredholm Theory On Krein Spaces And Its Application To Weyl-Type Theorems And Homogeneous Equations, Danilo Polo Ojito, Jose Sanabria, Yina Ospino Buelvas

Turkish Journal of Mathematics

In this paper, we review the approach presented by An and Heo on the study of Weyl-type theorems for self-adjoint operators on Krein spaces and show that this approach is not appropriate due to a fallacy. Motivated by this fact, we define a new modification of the kernel of a bounded linear operator on a Krein space, namely $J$-kernel, which allows us to successfully introduce a Fredholm theory in this context and study some variations of Weyl-type theorems for bounded linear operators defined on these spaces. In addition, we will describe the $J$-index in terms of solution sets of homogeneous …

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Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania Jan 2022

Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania

Turkish Journal of Mathematics

A Cauchy problem for a modification of the Swift-Hohenberg equation in $R^{N}$ with a mildly integrable potential is considered. Applying the dissipative mechanism of fourth order parabolic equations in unbounded domains, it is shown that the equation generates a semigroup of global solutions possessing a global attractor in the scale of Bessel potential spaces and in $H^2(R^{N})$ in particular.

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On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu Jan 2022

On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu

Turkish Journal of Mathematics

The modular group $\Gamma=PSL(2, \mathbf{Z})$ is isomorphic to the free product of two cyclic groups of orders $2$ and $3$. In this paper, we give a necessary and sufficient condition for the existence of elliptic and parabolic elements in $\Gamma$ with a given cusp point. Then we give an algorithm to obtain such elements in words of generators using continued fractions and paths in the Farey graph.

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Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak Jan 2022

Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak

Turkish Journal of Mathematics

In this paper, we consider an initial value problem (IVP) for three dimensional elasticity system in a transversely isotropic inhomogeneous media. We will rewrite the problem in the form of Fourier images by means of Fourier transform method. After some arrangements, the problem is reduced to integral equations in the vector form. Using the properties of the vector integral equation and successive approximations method, an explicit formula for the solution of the IVP in transversely isotropic inhomogeneous media is constructed, and existence and uniqueness of the solution is stated. By a computational example, we illustrate the robustness of the method.

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A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici Jan 2022

A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici

Turkish Journal of Mathematics

A compact set $K\subset \mathbb C^n$ is called Bernstein set if, for some constant $M>0$, the following inequality $$ D^{\alpha}P _K\leq M^{ \alpha }(\deg P)^{ \alpha } P _K $$ is satisfied for every multiindex $\alpha\in \mathbb N^n$ and for every polynomial $P$. We provide here a lower bound for the transfinite diameter of Bernstein sets by using generalized extremal Leja points.

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