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2020

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Articles 1201 - 1230 of 1326

Full-Text Articles in Mathematics

Representation Numbers Of Seven Quaternary Quadratic Forms Each In A Genus Consisting Of Only Two Classes, Ayşe Alaca, Şaban Alaca, Kenneth Williams Jan 2020

Representation Numbers Of Seven Quaternary Quadratic Forms Each In A Genus Consisting Of Only Two Classes, Ayşe Alaca, Şaban Alaca, Kenneth Williams

Turkish Journal of Mathematics

The purpose of this paper is to present some examples of positive-definite integral nondiagonal quaternary quadratic forms whose representation numbers can be determined explicitly using the theory of modular forms. Very few such examples appear in the literature. The seven forms presented were selected because they each belong to a genus containing exactly two form classes for which the single genus mate is a diagonal form whose representation number has been determined recently.

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New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra Jan 2020

New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra

Turkish Journal of Mathematics

In this paper, necessary and sufficient conditions for asymptotic behavior are established of the solutions to second-order neutral delay differential equations of the form \begin{equation} \frac{d}{d{}t}\Biggl(r(t)\biggl(\frac{d}{d{}t}[x(t)-p(t)x(\tau(t))]\biggr)^{\gamma}\Biggr)+\sum_{i=1}^{m}q_{i}(t)f_{i}\bigl(x(\sigma_{i}(t))\bigr)=0 \quad\text{for}\ t\geq{}t_{0}.\nonumber \end{equation} We consider two cases when $f_{i}(u)/u^{\beta}$ is nonincreasing for $\gamma>\beta$, and nondecreasing for $\beta>\gamma$, where $\beta$ and $\gamma$ are quotients of two positive odd integers. Our main tool is Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.

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Some Results On A System Of Multiterm Fractional Integro-Differential Equations, Shahram Rezapour, Fethi̇ye Müge Sakar, Seher Meli̇ke Aydoğan, Elahe Ravash Jan 2020

Some Results On A System Of Multiterm Fractional Integro-Differential Equations, Shahram Rezapour, Fethi̇ye Müge Sakar, Seher Meli̇ke Aydoğan, Elahe Ravash

Turkish Journal of Mathematics

In present study, we investigate the existence of solution for a multiterm fractional integro-differential system with special boundary conditions under some different conditions. In this way, we provide different results for the existence of solutions for the system and also for obtaining unique solution for the system under different conditions. We also present three numerical examplesin which by using the Legendre multiwavelet method, we approximate solutions of the system. These examples illustrate our main results.

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Generalized $\Pi$-Baer Rings, Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi Jan 2020

Generalized $\Pi$-Baer Rings, Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi

Turkish Journal of Mathematics

We call a ring $R$ generalized right $\pi$-Baer, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y^n$ is generated, as a right ideal, by an idempotent, for some positive integer $n$, depending on $Y$. In this paper, we investigate connections between the \g $\pi$-Baer rings and related classes of rings (e.g., $\pi$-Baer, generalized Baer, generalized quasi-Baer, etc.) In fact, generalized right $\pi$-Baer rings are special cases of generalized right quasi-Baer rings and also are a generalization of $\pi$-Baer and generalized right Baer rings. The behavior of the generalized right $\pi$-Baer condition is investigated with …

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Some Deformations Of The Fibred Biset Category, Laurence Barker, İsmai̇l Alperen Öğüt Jan 2020

Some Deformations Of The Fibred Biset Category, Laurence Barker, İsmai̇l Alperen Öğüt

Turkish Journal of Mathematics

We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are given by simpler formulas. Those larger categories are constructed from a partial category of subcharacters by linearizing and introducing a cocycle.

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The Relation Between The Existence Of Bounded Global Solutions Of The Differential Equations And Equations On Time Scales, Olha Karpenko, Oleksandr Stanzhytskyi, Tetiana Dobrodzii Jan 2020

The Relation Between The Existence Of Bounded Global Solutions Of The Differential Equations And Equations On Time Scales, Olha Karpenko, Oleksandr Stanzhytskyi, Tetiana Dobrodzii

Turkish Journal of Mathematics

This work is devoted to the study of existence of a bounded solution of the differential equation, defined on a family of time scales $\mathbb{T}_\lambda$, provided the graininess function $\mu_\lambda$ converges to zero as $\lambda\to 0$. We obtained the conditions, under which the existence of a bounded solution of differential equation implies the existence of a bounded solution of the corresponding equation, defined on time scales, and vice versa.

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Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n Jan 2020

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 $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.

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Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order, Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset Jan 2020

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 $F_{\mathbb{N}}.$

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Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi Jan 2020

Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi

Turkish Journal of Mathematics

An asymptotic theory is developed for a class of third-order differential equations. We identify a critical case to obtain the asymptotic form of three linearly independent solutions for large $x$.

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Pre-Markov Operators, Hülya Duru, Serkan İlter Jan 2020

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.

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4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n Jan 2020

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)

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Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er Jan 2020

Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er

Turkish Journal of Mathematics

In this paper, we introduce almost symmetric Arf partitions (for short, ASA-partitions) and using properties of partitions of positive integers, we give the number of almost symmetric Arf semigroups of genus $g$.

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Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü Jan 2020

Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü

Turkish Journal of Mathematics

In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point …

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Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer Jan 2020

Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer

Turkish Journal of Mathematics

In this study, second order linear Volterra partial integro-differential equation with two- and three-dimensional are solved by collocation method based on Lerch polynomials. This method is composed of the operational matrix and collocation methods, which are based upon the matrix forms of the Lerch polynomials with the parameter $\lambda$ and Taylor polynomials, and their derivatives and integrals. The approximate solutions of the mentioned equations are investigated in terms of the Lerch polynomials the different values of $\lambda$. Also, to verify the accuracy and efficiency of the present method, an alternative convergence criterion along with error analysis depending on residual function …

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A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek Jan 2020

A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

By applying Laplace differential operator to harmonic conjugate components of the analytic functions and using Wirtinger derivatives, some identities and relations including Bernoulli and Euler polynomials and numbers are obtained. Next, using the Legendre identity, trigonometric functions and the Dirichlet kernel, some formulas and relations involving Bernoulli and Euler numbers, cosine-type Bernoulli and Euler polynomials, and sine-type Bernoulli and Euler polynomials are driven. Then, by using the generating functions method and the well-known Euler identity, many new identities, formulas, and combinatorial sums among the Fibonacci numbers and polynomials, the Lucas numbers and polynomials, the Chebyshev polynomials, and Bernoulli and Euler …

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Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki Jan 2020

Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki

Turkish Journal of Mathematics

In this paper, we consider a mixed boundary value problem to a class of quasi-linear elliptic operators containing a $p$-Laplace operator. We show the existence of a unique weak solution and an estimate. We also demonstrate the continuity of the solution on the given data. Moreover, we consider the dual problem.

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Banach Algebra Structure On Simple Extensions, Sara El Kinani Jan 2020

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.

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Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n Jan 2020

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.

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Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ Jan 2020

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.

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Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt Jan 2020

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 $L_n'$ …

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Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad Jan 2020

Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad

Turkish Journal of Mathematics

Our problem through this work is to give the existence of mild solutions for the first order class of neutral functional multivalued integro-differential evolution equations with infinite state-dependent delay using the nonlinear alternative of Frigon for multivalued contraction maps in Fréchet spaces combined with the semi-group theory.

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The Hewitt Realcompactification Of An Orbit Space, Sadik Eyi̇doğan, Mehmet Onat Jan 2020

The Hewitt Realcompactification Of An Orbit Space, Sadik Eyi̇doğan, Mehmet Onat

Turkish Journal of Mathematics

In this paper, we show that the statement in the study of Srivastava (1987) holds also for the Hewitt realcompactification. The mentioned statement showed that when the action of a finite topological group on a Tychonoff space is given, the Stone-Cech compactification of the orbit space of the action is the orbit space of the Stone-Cech compactification of the space. As an application, we show that Srivastava's result can be obtained using the main theorem of the present study.

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New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek Jan 2020

New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the …

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Introduction To $N$-Soft Algebraic Structures, Hüseyi̇n Kamaci Jan 2020

Introduction To $N$-Soft Algebraic Structures, Hüseyi̇n Kamaci

Turkish Journal of Mathematics

This paper is dedicated to two main objectives. The first of these is to develop some new operations on $N$-soft set, which is the generalization of soft set. The second is to highlight the concepts of $N$-soft group, $N$-soft ring, $N$-soft ideal, completely semiprime $N$-soft ideal, $N$-soft field and $N$-soft lattice. Moreover, in this study, it is attempted to derive certain properties for these concepts and to analyze the relations between them.

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Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir Jan 2020

Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir

Turkish Journal of Mathematics

This research article deals with novel two species of initial value problems, one of them, the fractional neutral functional integrodifferential equations, and the other one, the coupled system of fractional neutral functional integrodifferential equations, with finite delay and involving a $\psi$-Caputo fractional operator. The existence and uniqueness results are studied through Banach's contraction principle and Krasnoselskii's fixed point theorem. We also establish two various kinds of Ulam stability results for the proposed problems. Further, two pertinent examples are presented to demonstrate the reported results.

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Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak Jan 2020

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.

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$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna Jan 2020

$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna

Turkish Journal of Mathematics

In this paper, we develop the basic theory of linear $q-$ Hamiltonian systems. In this context, we establish an existence and uniqueness result. Regular spectral problems are studied. Later, we introduce the corresponding maximal and minimal operators for this system. Finally, we give a spectral resolution.

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Uniform Three-Class Regular Partial Steiner Triple Systems With Uniform Degrees, Prangya Rani Parida Jan 2020

Uniform Three-Class Regular Partial Steiner Triple Systems With Uniform Degrees, Prangya Rani Parida

Dissertations, Master's Theses and Master's Reports

A Partial Steiner Triple system (X, T) is a finite set of points C and a collection T of 3-element subsets of C that every pair of points intersect in at most 1 triple. A 3-class regular PSTS (3-PSTS) is a PSTS where the points can be partitioned into 3 classes (each class having size m, n and p respectively) such that no triple belongs to any class and any two points from the same class occur in the same number of triples (a, b and c respectively). The 3-PSTS is said to be uniform if m = n = …

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Positive Labeled And Unlabeled Learning Methods Of Meta-Path Based Functional Profiles For Predicting Drug-Disease Associations, Thitipong Kawichai Jan 2020

Positive Labeled And Unlabeled Learning Methods Of Meta-Path Based Functional Profiles For Predicting Drug-Disease Associations, Thitipong Kawichai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Drug repositioning, discovering new indications for existing drugs, is a competent strategy to reduce time, costs, and risk in drug discovery and development. Many computational methods have been developed to identify new drug-disease associations for further validation and drug development. A recent approach showing superior performance with less required data is a meta-path based approach, which derives network-based information using path patterns from drug to disease nodes. However, existing meta-path based methods discard information of intermediate nodes along paths, which are important indicators for describing relationships between drugs and diseases. With known (positive) and unknown (unlabeled) drug-disease associations, this research …

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Smooth Approximations Of Continuous Functions Definable In D-Minimal Structures, Phaphontee Yamchote Jan 2020

Smooth Approximations Of Continuous Functions Definable In D-Minimal Structures, Phaphontee Yamchote

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

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