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Articles 1051 - 1080 of 10317
Full-Text Articles in Physical Sciences and Mathematics
A Variant Of Rosset's Approach To The Amitsur-Levitzki Theorem And Some $\Mathbb{Z}_{2}$-Graded Identities Of $\Mathrm{M}_{N}(E)$, Szilvia Homolya, Jen Szigeti
A Variant Of Rosset's Approach To The Amitsur-Levitzki Theorem And Some $\Mathbb{Z}_{2}$-Graded Identities Of $\Mathrm{M}_{N}(E)$, Szilvia Homolya, Jen Szigeti
Turkish Journal of Mathematics
In the spirit of Rosset's proof of the Amitsur-Levitzki theorem, we show how the standard identiy (for matrices over a commutative base ring) and the addition of external Grassmann variables can be used to derive a certain $\mathbb{Z}_{2}$-graded polynomial identity of $\mathrm{M}_{n}(E)$.
Nature And Crystallization Stages Of Spherulites Within The Obsidian: Acıgöl (Cappadocia- Nevşehir, Turkey), Bahatti̇n Güllü, Kiymet Deni̇z
Nature And Crystallization Stages Of Spherulites Within The Obsidian: Acıgöl (Cappadocia- Nevşehir, Turkey), Bahatti̇n Güllü, Kiymet Deni̇z
Turkish Journal of Earth Sciences
The study area comprises a part of the Central Anatolian Cenozoic volcanism within the Cappadocia Volcanic Province (CVP). Obsidian, perlite rhyolite flows, and volcanic ashes are observed in the study area and the spherulites within the obsidian are the objects of this study. The spherulites occupied within the obsidian in the form of round nodules 0.5-10 cm in diameter. The confocal Raman spectra of feldspar minerals within the spherulites are characterized by T-O-T and M-O lattice modes in the range of 100-250 cm-1, O-T-O deformation and T-O-T lattice modes in the range of 250-350 cm-1, and …
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we establish a new second main theorem for meromorphic mappings from $M$ into $\mathbb{P}(V)$ intersecting moving targets $g_{j}:M\rightarrow\mathbb{P}(V^{\ast}),\ 1\leq j\leq q,$ where $M$ is a parabolic manifold and $V$ is a Hermitian vector space. As an application, we prove the algebraic dependence problem for meromorphic mappings with moving targets in general position.
Boundedness For Variable Fractional Integral Operators And Their Commutators On Herz-Hardy Spaces With Variable Exponent, Yinping Xin
Turkish Journal of Mathematics
Let $E\subset\mathbb{R}^n$ be a bounded open set. In this paper, we establish the boundedness of variable fractional integral operators and their commutators on variable Herz-Hardy spaces $H\dot{K}^{\alpha(\cdot),q(\cdot)}_{p(\cdot)}(E)$ with three variable exponents by using the atomic decomposition.
Global Differential Invariants Of Nondegenerate Hypersurfaces, Yasemi̇n Sağiroğlu, Uğur Gözütok
Global Differential Invariants Of Nondegenerate Hypersurfaces, Yasemi̇n Sağiroğlu, Uğur Gözütok
Turkish Journal of Mathematics
Let $\{g_{ij}(x)\}_{i, j=1}^n$ and $\{L_{ij}(x)\}_{i, j=1}^n$ be the sets of all coefficients of the first and second fundamental forms of a hypersurface $x$ in $R^{n+1}$. For a connected open subset $U\subset R^{n}$ and a $C^{\infty }$-mapping $x:U\rightarrow R^{n+1}$ the hypersurface $x$ is said to be $d$-\textit{nondegenerate}, where $d\in \left\{1, 2, \ldots n\right\}$, if $L_{dd}(x)\neq 0$ for all $u\in U$. Let $M(n)=\{F:R^{n}\longrightarrow R^{n}\mid Fx=gx+b, \; g\in O(n), \; b\in R^{n}\}$, where $O(n)$ is the group of all real orthogonal $n\times n$-matrices, and $SM(n)=\{F\in M(n)\mid g\in SO(n)\}$, where $SO(n)=\left\{g\in O(n)\mid \det(g)=1\right\}$. In the present paper, it is proved that the set $\left\{g_{ij}(x), …
Globally Unsolvability Of Integro-Differential Diffusion Equation And System With Exponential Nonlinearities, Meiirkhan Borikhanov
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.
The Interior-Boundary Strichartz Estimate For The Schrödinger Equation On The Half-Line Revisited, Bi̇lge Köksal, Türker Özsari
The Interior-Boundary Strichartz Estimate For The Schrödinger Equation On The Half-Line Revisited, Bi̇lge Köksal, Türker Özsari
Turkish Journal of Mathematics
In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interior-boundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with …
Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin
Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin
Turkish Journal of Mathematics
American options represent an important financial instrument but are notoriously difficult to price, especially when the volatility is not constant. We explore the conditions required to apply Malliavin calculus to price American options when the volatility follows a general stochastic differential process, and develop the expressions to compute the continuation value at any time before the expiration date, given the current asset price and volatility. The developed methodology can then be applied to price American options.
Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban
Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban
Turkish Journal of Mathematics
Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Any positive operator $A$ induces a semiinner product on $\mathcal{H}$ defined by $\left\langle x,y\right\rangle _{A}:=\left\langle Ax,y\right\rangle _{\mathcal{H}},$ $\forall x,y\in\mathcal{H}.$ For any $T\in\mathcal{B}\left( \mathcal{H}\left( \Omega\right) \right) $, its $A$-Berezin symbol $\widetilde{T}^{_{A}}$ is defined on $\Omega$ by $\widetilde{T}^{_{A}% }:=\left\langle T\widehat{K}_{\lambda},\widehat{K}_{\lambda}\right\rangle _{A},$ $\lambda\in\Omega,$where $\widehat{K}_{\lambda}$ is the normalized reproducing kernel of $\mathcal{H}$. In this paper, we introduce the notions $\left( A,r\right) $-adjoint of operators and $A$-Berezin number of operators on the reproducing kernel Hilbert space and prove some upper and lower bounds of the $A$-Berezin numbers of operators. In …
New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa
New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $T$ be the class of analytic functions in the open unit disc $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1.$ For $f(z)\in T,$ the Alexander integral operator $A_{-1}f(z),$ the Libera integral operator $L_{-1}f(z)$ and the Bernardi integral operator $B_{-1}f(z)$ were considered before. Using $A_{-1}f(z)$ and $L_{-1}f(z),$ a new integral operator $F_{\lambda}f(z)$ is considered. After discuss some properties of dominant for $F_{\lambda}f(z),$ another new integral operator $O_{-1}f(z)$ of $f(z)\in T$ is discussed. The object of the present paper is to discuss the dominant of new integral operators $F_{\lambda}f(z)$ and $O_{-1}f(z)$ concerning with some starlike functions and convex functions in $\mathbb{U}.$
Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan
Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan
Turkish Journal of Mathematics
We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz $\varphi$-variation. Our aim is to get more powerful approximation results with the help of summability methods. In this study, we use $\varphi$-absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitable Lipschitz class of continuous functions. A general characterization theorem for $\varphi $-absolutely continuous functions is also obtained. We also give some examples of kernels in order to verify our approximations. At the end, we indicate our approximations in figures together with some numerical computations.
Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş
Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş
Turkish Journal of Mathematics
In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in GAP and classify crossed modules by using this function.
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Turkish Journal of Mathematics
In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1
Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao
Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao
Turkish Journal of Mathematics
Though infinite-dimensional characteristic is the natural property of nabla fractional order systems and it is the foundation of stability analysis, controller synthesis and numerical realization, there are few research focusing on this topic. Under this background, this paper concerns the diffusive representation of nabla fractional order systems. Firstly, several variants are developed for the elementary equality in frequency domain, i.e. $\frac{1}{s^\alpha} = \int_0^{ + \infty } {\frac{{{\mu _\alpha }( \omega )}}{{s + \omega }}{\rm{d}}\omega }$. Afterwards, the limited frequency band diffusive representation and the unit impulse response are derived for a series of nabla fractional order transfer functions. Finally, an …
Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan
Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan
Turkish Journal of Mathematics
In this paper, we construct a new $SEIR$ epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number $% \mathcal{R}_{0}$ by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number $\mathcal{R}_{0}$ is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to $% \mathcal{R}_{0}.$ Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov …
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
Turkish Journal of Mathematics
In this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.
On Stability And Oscillation Of Fractional Differential Equations With A Distributed Delay, Limei Feng, Shurong Sun
On Stability And Oscillation Of Fractional Differential Equations With A Distributed Delay, Limei Feng, Shurong Sun
Turkish Journal of Mathematics
In this paper, we study the stability and oscillation of fractional differential equations \begin{equation*} ^cD^\alpha x(t)+ax(t)+\int_0^1x(s+[t-1])dR(s)=0. \end{equation*} We discretize the fractional differential equation by variation of constant formula and semigroup property of Mittag-Leffler function, and get the difference equation corresponding to the integer points. From the equivalence analogy of qualitative properties between the difference equations and the original fractional differential equations, the necessary and sufficient conditions of oscillation, stability and exponential stability of the equations are obtained.
The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal
The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal
Turkish Journal of Mathematics
The error functions play very important roles in science and technology. In this investigation, the error functions in the complex plane will be introduced, then comprehensive results together with several nonlinear implications in relation to the related complex functions will be indicated, and some possible special results of them will be next presented. Furthermore, various interesting or important suggestions will be also made for the scientific researchers who are interested in this topic.
On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat
On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat
Turkish Journal of Mathematics
In this note, we consider a fourth-order semilinear pseudoparabolic differential equation including a strong damping term together with a nonlocal source term. The problem is considered under the periodic boundary conditions and a finite time blow-up result is established. Also a lower bound estimate for the blow-up time is obtained.
$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee
$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee
Turkish Journal of Mathematics
In [6], [8] and [10], the authors studied the generalized Fibonacci numbers. Also, in [7], the author found a class of bipartite graphs whose number of $1$-factors is the $n$th $k$-Lucas numbers. In this paper, we give a new relationship between $g_n^{(k)}$ and $l_n^{(k)}$ and the number of $1$-factors of a bipartite graph.
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Turkish Journal of Mathematics
This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
Turkish Journal of Mathematics
By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class $S_{\vartheta }$ of $\vartheta $-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes.
Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar
Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar
Turkish Journal of Mathematics
In this article, we define Clairaut semi-invariant Riemannian maps (CSIR Maps, In short) from almost Hermitian manifolds onto Riemannian manifolds and investigate fundamental results on such maps. We also obtain conditions for totally geodesicness on distributions defined in the introduced notion. Moreover, we provide an explicit example of CSIR map.
Sequences Of Polynomials Satisfying The Pascal Property, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa
Sequences Of Polynomials Satisfying The Pascal Property, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa
Turkish Journal of Mathematics
Since one of the most important properties of binomial coefficients is the Pascal's triangle identity (referred to as the Pascal property) and since the sequence of binomial polynomials forms a regular basis for integer-valued polynomials, it is natural to ask whether the Pascal property holds in some more general setting, and what types of integer-valued polynomials possess the Pascal property. After defining the general Pascal property, a sequence of polynomials which satisfies the Pascal property is characterized with the classical case as an example. In connection with integer-valued polynomials, characterizations are derived for a sequence of polynomials which satisfies the …
On Hypersemigroups, Niovi Kehayopulu
On Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
This is from the paper "Hypergroupes canoniques values et hypervalues" by J. Mittas in Mathematica Balkanica 1971: "The concept of hypergroup introduced by Fr. MARTY in 1934 [Actes du Congres des Math. Scand. Stocholm 1935, p. 45] is as follows: "A hypergroup is a nonempty set $H$ endowed with a multiplication $xy$ such that, for every $x,y,z\in H,$ the following hold: (1) $xy\subseteq H$; (2) $x(yz)=(xy)z$ and (3) $xH=Hx=H$. The first condition expresses that the multiplication is an hyperoperation on $H$, in other words, the composition of two elements $x,y$ of $H$ is a subset of $H$. It is very …
$Gl_N$-Invariant Functions On $M_N(\Mathcal{G})$, Alan Berele
$Gl_N$-Invariant Functions On $M_N(\Mathcal{G})$, Alan Berele
Turkish Journal of Mathematics
We describe the $GL_n(F)$-invariant functions on $M_n(\mathcal{G})$ (where $\mathcal{G}$ is the infinite dimensional Grassmann algebra) and show that not all of them are trace polynomials, if $n\ge3$
A Note On The $\Mathcal{A}$-Generators Of The Polynomial Algebra Of Six Variables And Applications, Tin Nguyen Khac
A Note On The $\Mathcal{A}$-Generators Of The Polynomial Algebra Of Six Variables And Applications, Tin Nguyen Khac
Turkish Journal of Mathematics
Let $ \mathcal P_{n}:=H^{*}((\mathbb{R}P^{\infty})^{n}) \cong \mathbb Z_2[x_{1},x_{2},\ldots,x_{n}]$ be the polynomial algebra of $n$ generators $x_1, x_2, \ldots, x_n$ with the degree of each $x_i$ being 1. We investigate the Peterson hit problem for the polynomial algebra $ \mathcal P_{n},$ regarded as a module over the mod-$2$ Steenrod algebra, $ \mathcal{A}.$ For $n>4,$ this problem remains unsolvable, even with the aid of computers in the case of $n=5.$ In this article, we study the hit problem for the case $n=6$ in degree $d_s=6(2^s -1)+3.2^s,$ with $s$ an arbitrary nonnegative integer. By considering $ \mathbb Z_2$ as a trivial $ \mathcal …
Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko
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.
On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç
On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is a multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion of an $S$-prime submodule which is a generalization of a prime submodule and used them to characterize certain classes of rings/modules such as prime submodules, simple modules, torsion free modules,\ $S$-Noetherian modules and etc. Afterwards, in \cite{AnArTeKo}, Anderson et al. defined the concepts of $S$-multiplication modules and $S$-cyclic modules which are $S$-versions of multiplication and cyclic modules and extended many results on multiplication and cyclic modules to …
Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk
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.