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2022

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Articles 1051 - 1080 of 1375

Full-Text Articles in Mathematics

Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations, Georgia Irina Oros Jan 2022

Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations, Georgia Irina Oros

Turkish Journal of Mathematics

Ever since Lotfi A. Zadeh published the paper "Fuzzy Sets" in 1965 setting the basis of a new theory named fuzzy sets theory, many scientists have developed this theory and its applications. Mathematicians were especially interested in extending classical mathematical results in the fuzzy context. Such an extension was also done relating fuzzy sets theory and geometric theory of analytic functions. The study begun in 2011 has many interesting published outcomes and the present paper follows the line of the previous research in the field. The aim of the paper is to give some references related to the connections already …

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Induced Polynomial Structures On Generalized Geometry, Fernando Etayo, Pablo Gomez Nicolas, Rafael Santamaria Jan 2022

Induced Polynomial Structures On Generalized Geometry, Fernando Etayo, Pablo Gomez Nicolas, Rafael Santamaria

Turkish Journal of Mathematics

In this paper, we study different geometric structures that can be defined as section endomorphisms of the generalized tangent bundle $\mathbb TM := TM\oplus T^*M\to M$. This vector bundle admits some structures that arise canonically and other that can be induced from geometric structures defined on the manifold. We comment some well-known examples and present new structures, focusing on the polynomial structures that can be induced in the generalized tangent bundle.

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On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad Jan 2022

On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad

Turkish Journal of Mathematics

We introduce a new class of sets named, slack $2$-geodesic convex set on Riemannian manifolds and verify by a nontrivial example. We define a geodesic $E$-pseudoconvex function with a suitable example. Some properties of geodesic $E$-quasiconvex function are discussed. We establish some relationships between slack $2$-geodesic convex set, geodesic $E$-pseudoconvex function and geodesic $E$-quasiconvex function. Moreover, an application of geodesic $E$-quasiconvex function to a nonlinear programming problem is also presented.

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Formal Categorical Reasoning, Burak Eki̇ci̇ Jan 2022

Formal Categorical Reasoning, Burak Eki̇ci̇

Turkish Journal of Mathematics

In this paper, we present a category theory library developed in the proof assistant Coq. We discuss the design principles of the library in comparison with those existing out there. To explicitly demonstrate the utility of the library, we conclude with a case study in which a Coq formalized soundness proof of the intuitionistic propositional logic within a category theoretical settings is examined.

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Sequences Of Polynomials Satisfying The Pascal Property, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa Jan 2022

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 …

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On Hypersemigroups, Niovi Kehayopulu Jan 2022

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 …

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Capelli Identities On Algebras With Involution Or Graded Involution, Francesca Saviella Benanti, Angela Valenti Jan 2022

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.

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Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh Jan 2022

Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh

Turkish Journal of Mathematics

In our paper [3] we have constructed the first example of simple graded torsion-free $\mathfrak{sl}_2(\mathbb{C})$-module denoted by $ M^{C}_{λ}$. Here we examine tensor product of $ M^{C}_{λ}$ with finite dimensional simple $\mathfrak{sl}_2(\mathbb{C})$-modules.

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$Gl_N$-Invariant Functions On $M_N(\Mathcal{G})$, Alan Berele Jan 2022

$Gl_N$-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 $n\ge3$

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Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar Jan 2022

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.

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On The Expansion Of The Multiplicity-Free Plethysms $ P_{2}[S_{(A, B)} ] $ And $ P_{2}[S_{(1^{R}, 2^{T})}] $, Luisa Carini Jan 2022

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}$.

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On Nowicki's Conjecture: A Survey And A New Result, Lucio Centrone, Andre Dushimirimana, Şehmus Findik Jan 2022

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.

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Henselian Discrete Valued Stable Fields, Ivan Chipchakov Jan 2022

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$_{p}(\widehat K) \le 1$.

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Bound For The Cocharacters Of The Identities Of Irreducible Representations Of $\Mathfrak{Sl}_2(\Mathbb{C})$, Mátyás Domokos Jan 2022

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.

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Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova Jan 2022

Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova

Turkish Journal of Mathematics

Let $GL(n) = GL(n, CC)$ denote the complex general linear group and let $G \subset GL(n)$ be one of the classical complex subgroups $OO(n)$, $SO(n)$, and $Sp(2k)$ (in the case $n = 2k$). We take a finite dimensional polynomial $GL(n)$-module $W$ and consider the symmetric algebra $S(W)$. Extending previous results for $G=SL(n)$, we develop a method for determining the Hilbert series $H(S(W)^G, t)$ of the algebra of invariants $S(W)^G$. Our method is based on simple algebraic computations and can be easily realized using popular software packages. Then we give many explicit examples for computing $H(S(W)^G, t)$. As an application, we …

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On The Mesyan Conjecture, Pedro Souza Fagundes, Thiago Castilho De Mello, Pedro Henrique Da Silva Dos Santos Jan 2022

On The Mesyan Conjecture, Pedro Souza Fagundes, Thiago Castilho De Mello, Pedro Henrique Da Silva Dos Santos

Turkish Journal of Mathematics

The well-known Lvov--Kaplansky conjecture states that the image of a multilinear polynomial $f$ evaluated on $n\times n$ matrices is a vector space. A weaker version of this conjecture, known as the Mesyan conjecture, states that if $m=\deg f$ and $n\geq m-1$ then its image contains the set of trace zero matrices. Such conjecture has been proved for polynomials of degree $m \leq 4$. The proof of the case $m=4$ contains an error in one of the lemmas. In this paper, we correct the proof of such lemma and present some evidence which allows us to state the Mesyan conjecture for …

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Symmetric Polynomials In The Free Metabelian Associative Algebra Of Rank 2, Şehmus Findik Jan 2022

Symmetric Polynomials In The Free Metabelian Associative Algebra Of Rank 2, Şehmus Findik

Turkish Journal of Mathematics

Let $F$ be the free metabelian associative algebra generated by $x$ and $y$ over a field of characteristic zero. We call a polynomial $f\in F$ symmetric, if $f(x,y)=f(y,x)$. The set of all symmetric polynomials coincides with the algebra $F^{S_2}$ of invariants of the symmetric group $S_2$. In this paper, we give the full description of the algebra $F^{S_2}$.

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$\Mathbb{Z}$-Graded Identities On The Infinite-Dimensional Grassmann Algebra And Arithmetic Tools: Revisited, Claudemir Fidelis Jan 2022

$\Mathbb{Z}$-Graded Identities On The Infinite-Dimensional Grassmann Algebra And Arithmetic Tools: Revisited, Claudemir Fidelis

Turkish Journal of Mathematics

The main purpose of this paper is to provide a survey of results concerning the $\mathbb{Z}$-gradings on the infinite-dimensional Grassmann algebra $E$ over a field of characteristic zero. First, we provide graded identities and central polynomials for $E$ equipped with fine gradings on $E$ by the semigroup $(\mathbb{Z}^\ast,\times)$. We also describe briefly techniques in order to illustrate some important methods to exhibit graded identities and central polynomials of $E$ for other abelian groups. In particular, over a field of characteristic zero, so-called $2$-induced gradings of full support were considered. In order to obtain these descriptions, we strongly use elementary number …

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Nonlinear Evolution Equations Related To Kac-Moody Algebras $A_R^{(1)}$: Spectral Aspects, Vladimir S. Gerdjikov Jan 2022

Nonlinear Evolution Equations Related To Kac-Moody Algebras $A_R^{(1)}$: Spectral Aspects, Vladimir S. Gerdjikov

Turkish Journal of Mathematics

We analyze three types of integrable nonlinear evolution equations (NLEE) related to the Kac-Moody algebras $A_r^{(1)}$. These are $\mathbb{Z}_h$-reduced derivative NLS equations (DNLS), multicomponent mKdV equations and 2-dimensional Toda field theories (2dTFT). We outline the basic tools of this analysis: i) the gradings of the simple Lie algebras using their Coxeter automorphisms; ii) the construction of the relevant Lax representations; and iii) the spectral properties of the Lax operators and their reduction to Riemann-Hilbert problems. We also formulate the minimal set of scattering data which allow one to recover the asymptotics of the fundamental analytic solutions to $L$ and its …

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Computing Forgotten Topological Index Of Zero-Divisor Graphs Of Commutative Rings, Ari̇f Gürsoy, Necla Kircali Gürsoy, Alper Ülker Jan 2022

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 $\Gamma(\mathbb{Z}_n)$.

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Polynomial Identities In Matrix Algebras With Pseudoinvolution, Antonio Ioppolo Jan 2022

Polynomial Identities In Matrix Algebras With Pseudoinvolution, Antonio Ioppolo

Turkish Journal of Mathematics

Let $F$ be an algebraically closed field of characteristic zero. In this paper we deal with matrix superalgebras (i.e. algebras graded by $\mathbb{Z}_2$, the cyclic group of order $2$) endowed with a pseudoinvolution. The first goal is to present the classification of the pseudoinvolutions that it is possible to define, up to equivalence, in the full matrix algebra $M_n(F)$ of $n \times n$ matrices and on its subalgebra $UT_n(F)$ of upper-triangular matrices. Along the way we shall give the generators of the $T$-ideal of identities for the algebras $M_2(F)$, $UT_2(F)$ and $UT_3(F)$, endowed with all possible inequivalent pseudoinvolutions.

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Depth And Stanley Depth Of The Quotient Rings Of Edge Ideals Of Some Lobster Trees And Unicyclic Graphs, Adnan Iqbal, Muhammad Ishaq Jan 2022

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.

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A Note On The $\Mathcal{A}$-Generators Of The Polynomial Algebra Of Six Variables And Applications, Tin Nguyen Khac Jan 2022

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 …

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On Almost S-Weakly Regular Rings, Kanchan Jangra, Dinesh Udar Jan 2022

On Almost S-Weakly Regular Rings, Kanchan Jangra, Dinesh Udar

Turkish Journal of Mathematics

An element $a$ of $R$ is called s-weakly regular (SWR) if $a\in aRa^2R$. A ring $R$ is called an almost SWR if for any $a\in R$, either $a$ or $1-a$ is SWR. In this paper, we introduce almost SWR rings as the generalization of abelian von Neumann local (VNL) rings and SWR rings. We provide various properties and characterizations of almost SWR rings. We discuss various extension rings to be almost SWR. Further, we discuss SWR group rings and almost SWR group rings.

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Spectral Theory Of B-Weyl Elements And The Generalized Weyl's Theorem In Primitive C*-Algebra, Yingying Kong, Yanxun Ren, Lining Jiang Jan 2022

Spectral Theory Of B-Weyl Elements And The Generalized Weyl's Theorem In Primitive C*-Algebra, Yingying Kong, Yanxun Ren, Lining Jiang

Turkish Journal of Mathematics

Let $\mathcal{A}$ be a unital primitive C*-algebra. This paper studies the spectral theories of B-Weyl elements and B-Browder elements in $\mathcal{A}$, including the spectral mapping theorem and a characterization of B-Weyl spectrum. In addition, we characterize the generalized Weyl's theorem and the generalized Browder's theorem for an element $a\in\mathcal{A}$ and $f(a)$, where $f$ is a complex-valued function analytic on a neighborhood of $\sigma(a)$. What's more, the perturbations of the generalized Weyl's theorem under the socle of $\mathcal{A}$ and quasinilpotent element are illustrated.

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Structure Of Annihilators Of Powers, Jongwook Baeck, Nam Kyun Kim, Tai Keun Kwak, Yang Lee Jan 2022

Structure Of Annihilators Of Powers, Jongwook Baeck, Nam Kyun Kim, Tai Keun Kwak, Yang Lee

Turkish Journal of Mathematics

We study the following two conditions in rings: (i) the right annihilator of some power of any element is an ideal, and (ii) the right annihilator of any nonzero element $a$ contains an ideal generated by some power of any right zero-divisor of the element $a$. We investigate the structure of rings in relation to these conditions; especially, a ring with the condition (ii) is called right APIP. These conditions are shown to be not right-left symmetric. For a prime two-sided APIP ring $R$ we prove that every element of $R$ is either nilpotent or regular, and that if $R$ …

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On Central Polynomials And Codimension Growth, Fabrizio Martino Jan 2022

On Central Polynomials And Codimension Growth, Fabrizio Martino

Turkish Journal of Mathematics

Let $A$ be an associative algebra over a field of characteristic zero. A central polynomial is a polynomial of the free associative algebra that takes central values of $A.$ In this survey, we present some recent results about the exponential growth of the central codimension sequence and the proper central codimension sequence in the setting of algebras with involution and algebras graded by a finite group.

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Codimensions Of Algebras With Additional Structures, Daniela La Mattina Jan 2022

Codimensions Of Algebras With Additional Structures, Daniela La Mattina

Turkish Journal of Mathematics

Let $A$ be an associative algebra endowed with an automorphism or an antiautomorphism $\varphi$ of order $\leq 2.$ One associates to $A,$ in a natural way, a numerical sequence $c^\varphi_n(A),$ $n=1, 2, \ldots$, called the sequence of $\varphi$-codimensions of $A$ which is the main tool for the quantitative investigation of the polynomial identities satisfied by $A$. In \cite{GLM} it was proved that such a sequence is eventually nondecreasing in case $\varphi$ is an antiautomorphism. Here we prove that it still holds in case $\varphi$ is an automorphism and present some recent results about the asymptotics of $c^\varphi_n(A)$.

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On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar Jan 2022

On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar

Turkish Journal of Mathematics

For any graph $G=(V,E),$ the order and size of G are $p$ and $q$. A bijection $l$ from $V(G)$ to $\{1,2,..,p\}$ is called $(a,d)$-edge local antimagic labeling if for any two adjacent edges are not received the same edge-weight (color) and the set of all edge-weights are formed an arithmetic progression $\{a,a+d,a+2d,\dots,a+(c-1)d\}$, for some integers $a,d>0$ and $c$ is the number of distinct colors used in the proper coloring.} An edge-weight (color) $w(uv)$ is the sum of two end vertices labels, $w(uv)=f(u)+f(v),uv\in E(G).$ The $(a,d)$-edge local antimagic coloring number is the least color (edge-weight) used in any $(a,d)$-edge local …

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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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