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Articles 151 - 169 of 169
Full-Text Articles in Physical Sciences and Mathematics
Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order, Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset
Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order, Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset
Turkish Journal of Mathematics
A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by Fenandes et al. in 2019. This paper deals with generating sets of the semigroup $F_{\mathbb{N}}$ of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that $F_{\mathbb{N}}$ has no minimal generating sets and present two particular infinite decreasing chains of generating sets of $F_{\mathbb{N}}.$
Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n
Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n
Turkish Journal of Mathematics
Let $p_{1},\ \cdots,\ p_{n}$ be integers where $n\geq 2$ and each $p_{i} \geq 2$. Let also $H(p_{1},\ \cdots,\ p_{n})$ be the generalized Hecke group associated to all $p_{i}\geq 2.$ In this paper, we study the commutator subgroups $H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime }(p_{1},\ \cdots,\ p_{n})$ of the generalized Hecke group $H(p_{1},\ \cdots,\ p_{n})$ and the extended generalized Hecke group $\overline{H}% (p_{1},\ \cdots,\ p_{n})$. We give the generators and the signatures of $% H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Turkish Journal of Mathematics
We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.
Pre-Markov Operators, Hülya Duru, Serkan İlter
Pre-Markov Operators, Hülya Duru, Serkan İlter
Turkish Journal of Mathematics
In operator theory characterizing extreme points has been systematically studied in a convex set of linear operators from an algebra to another. This paper presents some new characterizations. We define pre-Markov operators and identify when the second adjoint of a linear positive operator being an extreme point in the collection of all Markov operators between the unital second order duals of two unital f-algebras. Moreover a characterization of extreme points is given in the collection of all contractive operators between unital f-algebras. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, standard bases of some toric ideals associated to 4-generated pseudo symmetric semigroups with not Cohen-Macaulay tangent cones at the origin are computed. As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed. Therefore, using these standard bases, Hilbert functions are explicitly computed as a step towards the characterization of Hilbert function. In addition, when the smallest integer satisfying $k(\alpha_2+1)
Banach Algebra Structure On Simple Extensions, Sara El Kinani
Banach Algebra Structure On Simple Extensions, Sara El Kinani
Turkish Journal of Mathematics
We study the existence of Banach algebra structures on simple extensions of a unitary commutative Banach algebra. The link with the integrality of these extensions is studied. For any simple extension, a characterization of the existence of the Banach algebra norm making continuous the canonical injection is also given.
Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n
Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n
Turkish Journal of Mathematics
In this paper, we present the notion of isotropic submersions between Riemannian manifolds. We first give examples to illustrate this new notion. Then we express a characterization in terms of O'Neill's tensor field T and examine certain relations between sectional curvatures of the total manifold and the base manifold. We also study $\lambda$-isotropic submersions with pointwise planar horizontal sections.
Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ
Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ
Turkish Journal of Mathematics
We study topological games related to weak forms of the Menger property in bitopological spaces. In particular we investigate almost Menger game and its connections to games which are associated with the covering properties consisting of covers containing $G_\delta$ subsets.
Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt
Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt
Turkish Journal of Mathematics
Let $L_n$ be the free metabelian Leibniz algebra generated by the set $X_n=\{x_1,\ldots,x_n\}$ over a field $K$ of characteristic zero. This is the free algebra of rank $n$ in the variety of solvable of class $2$ Leibniz algebras. We call an element $s(X_n)\in L_n$ symmetric if $s(x_{\sigma(1)},\ldots,x_{\sigma(n)})=s(x_1,\ldots,x_n)$ for each permutation $\sigma$ of $\{1,\ldots,n\}$. The set $L_n^{S_n}$ of symmetric polynomials of $L_n$ is the algebra of invariants of the symmetric group $S_n$. Let $K[X_n]$ be the usual polynomial algebra with indeterminates from $X_n$. The description of the algebra $K[X_n]^{S_n}$ is well known, and the algebra $(L_n')^{S_n}$ in the commutator ideal $L_n'$ …
Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak
Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak
Turkish Journal of Mathematics
Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for any $j=1,...,t$. In the paper we construct, in an elementary way, a natural number B (m,f) (depending on $m$ and the function $f$) such that ≤ (m,f)$. We also discuss some applications of this result.
Polarization Of Neural Codes, Katie Christensen, Hamid Kulosman
Polarization Of Neural Codes, Katie Christensen, Hamid Kulosman
Turkish Journal of Mathematics
The neural rings and ideals as an algebraic tool for analyzing the intrinsic structure of neural codes were introduced by C. Curto, V. Itskov, A. Veliz-Cuba, and N. Youngs in 2013. Since then they were investigated in several papers, including the 2017 paper by S. Güntürkün, J. Jeffries, and J. Sun, in which the notion of polarization of neural ideals was introduced. In our paper we extend their ideas by introducing the notions of polarization of motifs and neural codes. We show that the notions that we introduce have very nice properties which allow the studying of the intrinsic structure …
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions, Şuayi̇p Yüzbaşi, Murat Karaçayir
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions, Şuayi̇p Yüzbaşi, Murat Karaçayir
Turkish Journal of Mathematics
In this paper, we present a weighted residual Galerkin method to solve linear functional differential equations. We consider the problem with variable coefficients under initial conditions. Assuming the exact solution of the problem has a Taylor series expansion convergent in the relevant domain, we seek a solution of the given problem in the form of a polynomial having degree $N$ of our choice. Substituting this polynomial with unknown coefficients in the given equation yields an expression linear in these coefficients. We then proceed as in the weighted residual method and take inner product of this expression with monomials up to …
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Turkish Journal of Mathematics
In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Turkish Journal of Mathematics
In this work, we characterize the boundedness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces. Some estimates for the essential norm of these operators are also given. As a corollary, we obtain some characterizations for the compactness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces.
Unimodality And Linear Recurrences Associated With Rays In The Delannoy Triangle, Said Amrouche, Hacene Belbachir
Unimodality And Linear Recurrences Associated With Rays In The Delannoy Triangle, Said Amrouche, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, we study the unimodality of sequences located in the infinite transversals of the Delannoy triangle. We establish recurrence relations associated with the sum of elements laying along the finite transversals of the cited triangle and we give the generating function of the established sum. Moreover, new identities for the odd and even terms of the Tribonacci sequence are given. Finally, we define a $q$-analogue for the Delannoy numbers and we propose a $q$-deformation of the Tribonacci sequence.
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Turkish Journal of Mathematics
In weighted Orlicz-type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre $K$-functionals is shown in the spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$.
Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov
Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov
Turkish Journal of Mathematics
In this work the approximation problems of the functions by matrix transforms in weighted Orlicz spaces with Muckenhoupt weights are studied.We obtain the degree of approximation of functions belonging to Lipschitz class $Lip(\alpha ,M,\omega )$ through matrix transforms $% T_{n}^{\left( A\right) }(x,f)$,$~$and Nörlund means $N_{n}\left(x,f\right) ~$of their trigonometric Fourier series.
On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Turkish Journal of Mathematics
The aim in this note is to provide a generalization of an interesting entry in Ramanujan's notebooks that relate sums involving the derivatives of a function $\varphi\left( t\right)$ evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.