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Articles 31 - 60 of 228
Full-Text Articles in Physical Sciences and Mathematics
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
Turkish Journal of Mathematics
n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z
Henselian Discrete Valued Stable Fields, Ivan Chipchakov
Henselian Discrete Valued Stable Fields, Ivan Chipchakov
Turkish Journal of Mathematics
Let $(K, v)$ be a Henselian discrete valued field with residue field $\widehat K$ of characteristic $q \ge 0$, and Brd$_{p}(K)$ be the Brauer $p$-dimension of $K$, for each prime $p$. The present paper shows that if $p = q$, then Brd$_{p}(K) \le 1$ if and only if $\widehat K$ is a $p$-quasilocal field and the degree $[\widehat K\colon \widehat K ^{p}]$ is $\le p$. This complements our earlier result that, in case $p \neq q$, we have Brd$_{p}(K) \le 1$ if and only if $\widehat K$ is $p$-quasilocal and Brd$_{p}(\widehat K) \le 1$.
Computing Forgotten Topological Index Of Zero-Divisor Graphs Of Commutative Rings, Ari̇f Gürsoy, Necla Kircali Gürsoy, Alper Ülker
Computing Forgotten Topological Index Of Zero-Divisor Graphs Of Commutative Rings, Ari̇f Gürsoy, Necla Kircali Gürsoy, Alper Ülker
Turkish Journal of Mathematics
The main objective of this paper is to calculate the forgotten topological index of the zero-divisor graph of $\mathbb{Z}_n$. Let $p$, $q$ and $r$ be distinct prime numbers. We calculate the forgotten topological index of the ring $\Gamma(\mathbb{Z}_n)$ where $n=p^\alpha, pq, p^2q, p^2q^2, pqr$. Also, we study the forgotten topological index of the product of rings of integers modulo $n$. We construct a polynomial algorithm to compute the forgotten topological index of $\Gamma(\mathbb{Z}_n)$.
Depth And Stanley Depth Of The Quotient Rings Of Edge Ideals Of Some Lobster Trees And Unicyclic Graphs, Adnan Iqbal, Muhammad Ishaq
Depth And Stanley Depth Of The Quotient Rings Of Edge Ideals Of Some Lobster Trees And Unicyclic Graphs, Adnan Iqbal, Muhammad Ishaq
Turkish Journal of Mathematics
We compute depth and Stanley depth of the quotient rings of the edge ideals associated with different classes of graphs. These classes include some lobster trees and unicyclic graphs. We show that the values of depth and Stanley depth are equal for the classes we considered.
A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov
A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov
Turkish Journal of Mathematics
In this paper, we consider a multidimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation the Schauder principle is applied. The local existence and uniqueness results are obtained.
On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz
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 $X_{n}=\{1,2,\dots,n\}$.
Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas
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 …
On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan
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.
A Fredholm Theory On Krein Spaces And Its Application To Weyl-Type Theorems And Homogeneous Equations, Danilo Polo Ojito, Jose Sanabria, Yina Ospino Buelvas
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 …
A Characterization Of Abelian Group Codes In Terms Of Their Parameters, Fatma Altunbulak Aksu, İpek Tuvay
A Characterization Of Abelian Group Codes In Terms Of Their Parameters, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
In 1979, Miller proved that for a group $G$ of odd order, two minimal group codes in $\mathbb{F}_2G$ are $G$-equivalent if and only if they have identical weight distribution. In 2014, Ferraz-Guerreiro-Polcino Milies disproved Miller's result by giving an example of two non-$G$-equivalent minimal codes with identical weight distribution. In this paper, we give a characterization of finite abelian groups so that over a specific set of group codes, equality of important parameters of two codes implies the $G$-equivalence of these two codes. As a corollary, we prove that two minimal codes with the same weight distribution are $G$-equivalent if …
Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania
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.
A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici
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.
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 …
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
Turkish Journal of Mathematics
In this paper, we consider the existence and uniqueness for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations. By the fixed point theorem in Banach algebra, an existence theorem for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is given. Further, a uniqueness result for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is proved due to Banach's contraction principle. Further, we give three examples to verify the main results.
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.
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Turkish Journal of Mathematics
The aim of this paper is to establish conditions for the existence and uniqueness of the solution of a nonlinear integro-differential equation. Moreover, it is to propose a quadrature method in order to find an approximate solution and establish the convergence of the method. We conclude by providing the algorithm and some numerical simulation to confirm our theoretical results.
Elliptical Kinematics Of The Accretive Surface Growth, Zehra Özdemi̇r, Gül Güner
Elliptical Kinematics Of The Accretive Surface Growth, Zehra Özdemi̇r, Gül Güner
Turkish Journal of Mathematics
The stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of surface. Thus, we introduce the elliptical kinematics along an initial curve and construct some accretive surfaces with an elliptical cross-section. In fact, these surfaces are not only curves with an elliptical cross-sectional curve, but also the material points of the surface follow an elliptical trajectory during their formation. This situation can be easily explained through elliptical motion and elliptical quaternion algebra. Then, we …
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Turkish Journal of Mathematics
In this work, we establish the existence and uniqueness of solutions for a fractional stochastic differential equation driven by countably many Brownian motions on bounded and unbounded intervals. Also, we study the continuous dependence of solutions on initial data. Finally, we establish the transportation quadratic cost inequality for some classes of fractional stochastic equations and continuous dependence of solutions with respect Wasserstein distance.
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Turkish Journal of Mathematics
under circuit and forest conditions. Special number sequences and special vertex values of minimal length paths in suborbital graphs have been associated in our previous studies. In these associations, matrix connections of the special continued fractions $\mathcal K (-1/-k)$, where $k\in \mathbb{Z}^{+}, \ k\geq 2$ with the values of the special number sequences are used and new identities are obtained. In this study, by producing new matrices, new identities related to Fibonacci, Lucas, Pell, and Pell-Lucas number sequences are found by using both recurrence relations and matrix connections of the continued fractions. In addition, the farthest vertex values of the …
Minimal Generators Of Annihilators Of Even Neat Elements In The Exterior Algebra Footnotesize, Songül Esi̇n
Minimal Generators Of Annihilators Of Even Neat Elements In The Exterior Algebra Footnotesize, Songül Esi̇n
Turkish Journal of Mathematics
This paper deals with an exterior algebra of a vector space whose base field is of positive characteristic. In this work, a minimal set of generators forming the annihilator of even neat elements of such an exterior algebra is exhibited. The annihilator of some special type of even neat elements is determined to prove the conjecture established in [3]. Moreover, a vector space basis for the annihilators under consideration is calculated.
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
Turkish Journal of Mathematics
The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently Ünver and Orhan [19] have introduced the concepts of $P$-strong and $P$-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of $P$-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies $\triangle _{2}-$condition. We also get an improvement of this result by using the concept of uniform integrability.
The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko
The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko
Turkish Journal of Mathematics
For an Arens-Michael algebra $A$ we consider a class of $A$-$\hat{\otimes}$-bimodules which are invertible with respect to the projective bimodule tensor product. We call such bimodules topologically invertible over $A$. Given a Frechet-Arens-Michael algebra $A$ and a topologically invertible Frechet $A$-$\hat{\otimes}$-bimodule $M$, we construct an Arens-Michael algebra $\widehat{L}_A(M)$ which serves as a topological version of the Laurent tensor algebra $L_A(M)$. Also, for a fixed algebra $B$ we provide a condition on an invertible $B$-bimodule $N$ which allows us to explicitly describe the Arens-Michael envelope of $L_B(N)$ as a topological Laurent tensor algebra. In particular, we provide an explicit description of …
Capelli Identities On Algebras With Involution Or Graded Involution, Francesca Saviella Benanti, Angela Valenti
Capelli Identities On Algebras With Involution Or Graded Involution, Francesca Saviella Benanti, Angela Valenti
Turkish Journal of Mathematics
We present recent results about Capelli polynomials with involution or graded involution and their asymptotics. In the associative case, the asymptotic equality between the codimensions of the $T$-ideal generated by the Capelli polynomial of rank $k^2+1$ and the codimensions of the matrix algebra $M_k(F)$ was proved. This result was extended to superalgebras. Recently, similar results have been determined by the authors in the case of algebras with involution and superalgebras with graded involution.
$Gl_N$-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 $n\ge3$
Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar
Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar
Turkish Journal of Mathematics
Let $A$ be an algebra over a field $F$ with $(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition that $\Phi(x^2,x)=0 $ for all $x\in A$ implies that $\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$ for all $x,y,z\in A$. This is applicable to the question of whether $A$ is zero Lie product determined and is also used in proving that a Jordan homomorphism from $A$ onto a semiprime algebra $B$ is the sum of a homomorphism and an antihomomorphism.
Symmetric Polynomials In Free Associative Algebras, Silvia Boumova, Vesselin Drensky, Deyan Dzhundrekov, Martin Kassabov
Symmetric Polynomials In Free Associative Algebras, Silvia Boumova, Vesselin Drensky, Deyan Dzhundrekov, Martin Kassabov
Turkish Journal of Mathematics
By a result of Margarete Wolf in 1936, we know that the algebra $K\langle X_d\rangle^{Sym(d)}$ of symmetric polynomials in noncommuting variables is not finitely generated. In 1984, Koryukin proved that if we equip the homogeneous component of degree $n$ with the additional action of $Sym(n)$ by permuting the positions of the variables, then the algebra of invariants $K\langle X_d\rangle^G$ of every reductive group $G$ is finitely generated. First, we make a short comparison between classical invariant theory of finite groups and its noncommutative counterpart. Then, we expose briefly the results of Wolf. Finally, we present the main result of our …
On The Expansion Of The Multiplicity-Free Plethysms $ P_{2}[S_{(A, B)} ] $ And $ P_{2}[S_{(1^{R}, 2^{T})}] $, Luisa Carini
On The Expansion Of The Multiplicity-Free Plethysms $ P_{2}[S_{(A, B)} ] $ And $ P_{2}[S_{(1^{R}, 2^{T})}] $, Luisa Carini
Turkish Journal of Mathematics
We show how to compute the explicit expansion of the plethysm $ p_{2}[s_{\lambda}]$ of the power symmetric function $ p_{2}$ and the Schur function $ s_{\lambda}$, where $\lambda$ has either two rows or two columns, via the well known Littlewood-Richardson coefficients which occur in the decomposition of $ s^{2}_{\lambda}$.
On Nowicki's Conjecture: A Survey And A New Result, Lucio Centrone, Andre Dushimirimana, Şehmus Findik
On Nowicki's Conjecture: A Survey And A New Result, Lucio Centrone, Andre Dushimirimana, Şehmus Findik
Turkish Journal of Mathematics
The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in for polynomial algebras and in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson algebra.
Bound For The Cocharacters Of The Identities Of Irreducible Representations Of $\Mathfrak{Sl}_2(\Mathbb{C})$, Mátyás Domokos
Bound For The Cocharacters Of The Identities Of Irreducible Representations Of $\Mathfrak{Sl}_2(\Mathbb{C})$, Mátyás Domokos
Turkish Journal of Mathematics
For each irreducible finite dimensional representation of the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$ of $2\times 2$ traceless matrices, an explicit uniform upper bound is given for the multiplicities in the cocharacter sequence of the polynomial identities satisfied by the given representation.