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2015

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Articles 871 - 900 of 1160

Full-Text Articles in Mathematics

Generalized Weakly Central Reduced Rings, Ying Zhou, Junchao Wei Jan 2015

Generalized Weakly Central Reduced Rings, Ying Zhou, Junchao Wei

Turkish Journal of Mathematics

A ring $R$ is called $GWCN$ if $x^2y^2=xy^2x$ for all $x\in N(R)$ and $y\in R$, which is a proper generalization of reduced rings and $CN$ rings. We study the sufficient conditions for $GWCN$ rings to be reduced and $CN$. We first discuss many properties of $GWCN$ rings. Next, we give some interesting characterizations of left min-abel rings. Finally, with the help of exchange $GWCN$ rings, we obtain some characterizations of strongly regular rings.

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Sharp Lower Bounds For The Zagreb Indices Of Unicyclic Graphs, Batmend Horoldagva, Kinkar Das Jan 2015

Sharp Lower Bounds For The Zagreb Indices Of Unicyclic Graphs, Batmend Horoldagva, Kinkar Das

Turkish Journal of Mathematics

The first Zagreb index $M_1$ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index $M_2$ is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on $M_1$ and $M_2$ among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which the bound is attained. Moreover, we obtain some relations between the Zagreb indices for unicyclic graphs.

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Uniquely Strongly Clean Triangular Matrices, Huanyin Chen, Orhan Gürgün, Handan Kose Jan 2015

Uniquely Strongly Clean Triangular Matrices, Huanyin Chen, Orhan Gürgün, Handan Kose

Turkish Journal of Mathematics

A ring $R$ is uniquely (strongly) clean provided that for any $a\in R$ there exists a unique idempotent $e\in R$ \big($e\in comm(a)$\big) such that $a-e\in U(R)$. We prove, in this note, that a ring $R$ is uniquely clean and uniquely bleached if and only if $R$ is abelian, ${\mathbb{T}}_{n}(R)$ is uniquely strongly clean for all $n\geq 1$, i.e. every $n\times n$ triangular matrix over $R$ is uniquely strongly clean, if and only if $R$ is abelian, and ${\mathbb{T}}_{n}(R)$ is uniquely strongly clean for some $n\geq 1$. In the commutative case, more explicit results are obtained.

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Split Extension Classifiers In The Category Of Precrossed Modules Of Commutative Algebras, Yaşar Boyaci, Tufan Sai̇t Kuzpinari, Enver Önder Uslu Jan 2015

Split Extension Classifiers In The Category Of Precrossed Modules Of Commutative Algebras, Yaşar Boyaci, Tufan Sai̇t Kuzpinari, Enver Önder Uslu

Turkish Journal of Mathematics

We construct an actor of a precat$^{1}$-algebra and then by using the natural equivalence between the categories of precat$^{1}$-algebras and that of precrossed modules, we construct the split extension classifier of the corresponding precrossed module, which gives rise to the representability of actions in the category of precrossed modules of commutative algebras under certain conditions.

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On Isophote Curves And Their Characterizations, Fati̇h Doğan, Yusuf Yayli Jan 2015

On Isophote Curves And Their Characterizations, Fati̇h Doğan, Yusuf Yayli

Turkish Journal of Mathematics

An isophote curve comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. The main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about the isophote curve and its axis in Euclidean 3-space. Particularly, for isophote curves lying on a canal surface other characterizations are obtained.

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Hilbert Series Of The Finite Dimensional Generalized Hecke Algebras, Zaffar Iqbal Jan 2015

Hilbert Series Of The Finite Dimensional Generalized Hecke Algebras, Zaffar Iqbal

Turkish Journal of Mathematics

It is known from the early results of Coxeter that the generalized Hecke algebras $H(Q_{m},3)$, $m\in\{2,3,4,5\}$, are finite dimensional. In this paper we compute the Hilbert series of these finite-type group algebras.

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Quadratic Recursive Towers Of Function Fields Over $\Mathbb{F}_2$, Henning Stichtenoth, Seher Tutdere Jan 2015

Quadratic Recursive Towers Of Function Fields Over $\Mathbb{F}_2$, Henning Stichtenoth, Seher Tutdere

Turkish Journal of Mathematics

Let $\FF=(F_n)_{n\geq 0}$ be a quadratic recursive tower of algebraic function fields over the finite field $\F_2$, i.e. $\FF$ is a recursive tower such that $[F_n:F_{n-1}]=2$ for all $n\geq 1$. For any integer $r\geq 1$, let $\beta_r(\FF):=\lim_{n\to \infty} B_r(F_n)/g(F_n)$, where $B_r(F_n)$ is the number of places of degree $r$ and $g(F_n)$ is the genus, respectively, of $F_n/\F_2$. In this paper we give a classification of all rational functions $f(X,Y)\in \F_2(X,Y)$ that may define a quadratic recursive tower $\FF$ over $\F_2$ with at least one positive invariant $\beta_r(\FF)$. Moreover, we estimate $\beta_1(\FF)$ for each such tower.

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Defect Polynomials And Tutte Polynomials Of Some Asymmetric Graphs, Eunice Mphako-Banda, Toufik Mansour Jan 2015

Defect Polynomials And Tutte Polynomials Of Some Asymmetric Graphs, Eunice Mphako-Banda, Toufik Mansour

Turkish Journal of Mathematics

We give explicit expressions of the Tutte polynomial of asymmetric complete flower graph and asymmetric incomplete flower graph. We then express these Tutte polynomials as generating functions and decode some valuable information about the asymmetric complete flower graph and asymmetric incomplete flower graph. Furthermore, we convert the Tutte polynomials into coboundary polynomials and give explicit expressions of the $k$-defect polynomials of these structures. Finally, we conclude that nonisomorphic graphs in this class have the same Tutte polynomials, the same chromatic polynomials, and the same defect polynomials.

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Fiber Product Preserving Bundle Functors On Fibered-Fibered Manifolds, Wlodzimierz M. Mikulski Jan 2015

Fiber Product Preserving Bundle Functors On Fibered-Fibered Manifolds, Wlodzimierz M. Mikulski

Turkish Journal of Mathematics

We introduce the concept of modified vertical Weil functors on the category $\F_2\M_{m_1,m_2}$ of fibered-fibered manifolds with $(m_1,m_2)$-dimensional bases and their local fibered-fibered maps with local fibered diffeomorphisms as base maps. We then describe all fiber product preserving bundle functors on $\F_2\M_{m_1,m_2}$ in terms of modified vertical Weil functors.

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$R$-Ideals In Commutative Rings, Rostam Mohamadian Jan 2015

$R$-Ideals In Commutative Rings, Rostam Mohamadian

Turkish Journal of Mathematics

In this article we introduce the concept of $r$-ideals in commutative rings (note: an ideal $I$ of a ring $R$ is called $r$-ideal, if $ab\in I$ and ${\rm Ann}(a)=(0)$ imply that $b\in I$ for each $a,b\in R$). We study and investigate the behavior of $r$-ideals and compare them with other classical ideals, such as prime and maximal ideals. We also show that some known ideals such as $z^\circ$-ideals are $r$-ideals. It is observed that if $I$ is an $r$-ideal, then so too is a minimal prime ideal of $I$. We naturally extend the celebrated results such as Cohen's theorem for …

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Super D-Anti-Magic Labeling Of Subdivided $Kc_{5}$, Muhammad Hussain, Ali Tabraiz Jan 2015

Super D-Anti-Magic Labeling Of Subdivided $Kc_{5}$, Muhammad Hussain, Ali Tabraiz

Turkish Journal of Mathematics

A graph $(G=(V,E,F))$ admits labeling of type $(1,1,1)$ if we assign labels from the set $ \{1, 2, 3, . . . , V (G) + E(G) + F(G) \}$ to the vertices, edges, and faces of a planar graph $G$ in such a way that each vertex, edge, and face receives exactly one label and each number is used exactly once as a label and the weight of each face under the mapping is the same. Super $d$-antimagic labeling of type $(1,1,1)$ on snake $kC_{5}$, subdivided $kC_{5}$ as well as ismorphic copies of $kC_{5}$ for string $(1,1,...,1)$ and string …

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Classification Of Metallic Shaped Hypersurfaces In Real Space Forms, Ci̇han Özgür, Ni̇hal Yilmaz Özgür Jan 2015

Classification Of Metallic Shaped Hypersurfaces In Real Space Forms, Ci̇han Özgür, Ni̇hal Yilmaz Özgür

Turkish Journal of Mathematics

We define the notion of a metallic shaped hypersurface and give the full classification of metallic shaped hypersurfaces in real space forms. We deduce that every metallic shaped hypersurface in real space forms is a semisymmetric hypersurface.

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On The Second Homology Of The Sch\"{U}Tzenberger Product Of Monoids, Melek Yağci, Leyla Bugay, Hayrullah Ayik Jan 2015

On The Second Homology Of The Sch\"{U}Tzenberger Product Of Monoids, Melek Yağci, Leyla Bugay, Hayrullah Ayik

Turkish Journal of Mathematics

For two finite monoids $S$ and $T$, we prove that the second integral homology of the Sch\"{u}tzenberger product $S\Diamond T$ is equal to $$H_{2}(S\Diamond T)=H_{2}(S)\times H_{2}(T)\times (H_{1}(S)\otimes _{\mathbb Z} H_{1}(T)) $$ as the second integral homology of the direct product of two monoids. Moreover, we show that $S\Diamond T$ is inefficient if there is no left or right invertible element in both $S$ and $T$.

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On Condition $(Pwp)_{W}$ For $S$-Posets, Xingliang Liang, Yanfeng Luo Jan 2015

On Condition $(Pwp)_{W}$ For $S$-Posets, Xingliang Liang, Yanfeng Luo

Turkish Journal of Mathematics

Golchin and Rezaei (Commun Algebra 2009; 37: 1995--2007) introduced the weak version of Condition $(PWP)$ for $S$-posets, called Condition $(PWP)_{w}$. In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the $S$-poset $A(I)$ satisfies Condition $(PWP)_{w}$. Furthermore, we characterize pomonoids $S$ over which all cyclic (Rees factor) $S$-posets satisfy Condition $(PWP)_{w}$, and pomonoids $S$ over which all Rees factor $S$-posets satisfying Condition $(PWP)_{w}$ have a certain property. Finally, we consider direct products of $S$-posets satisfying Condition $(PWP)_{w}$.

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Jacobi-Spectral Method For Integro-Delay Differential Equations With Weakly Singular Kernels, Ishtiaq Ali Jan 2015

Jacobi-Spectral Method For Integro-Delay Differential Equations With Weakly Singular Kernels, Ishtiaq Ali

Turkish Journal of Mathematics

We present a numerical solution to the integro-delay differential equation with weakly singular kernels with the delay function $\theta (t)$ vanishing at the initial point of the given interval $[0, T]$ ($\theta (t) = qt, 0 < q < 1)$. In order to fully use the Jacobi orthogonal polynomial theory, we use some function and variable transformation to change the intergro-delay differential equation into a new equation defined on the standard interval $[-1, 1]$. A Gauss--Jacobi quadrature formula is used to evaluate the integral term. The spectral rate of convergence is provided in infinity norm under the assumption that the solution of the given equation is sufficiently smooth. For validation of the theoretical exponential rate of convergence of our method, we provide some numerical examples.

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Generalized Chebyshev Polynomials Of The Second Kind, Mohammad A. Alqudah Jan 2015

Generalized Chebyshev Polynomials Of The Second Kind, Mohammad A. Alqudah

Turkish Journal of Mathematics

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the paper with some results concerning integrals of the generalized Chebyshev-II and Bernstein polynomials.

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Existence Of Unique Solution To Switchedfractional Differential Equations With $P$-Laplacian Operator, Xiufeng Guo Jan 2015

Existence Of Unique Solution To Switchedfractional Differential Equations With $P$-Laplacian Operator, Xiufeng Guo

Turkish Journal of Mathematics

In this paper, we study a class of nonlinear switched systems of fractional order with $p$-Laplacian operator. By applying a fixed point theorem for a concave operator on a cone, we obtain the existence and uniqueness of a positive solution for an integral boundary value problem with switched nonlinearity under some suitable assumptions. An illustrative example is included to show that the obtained results are effective.

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T-Spaces, Hassan Maleki, Mohammadreza Molaei Jan 2015

T-Spaces, Hassan Maleki, Mohammadreza Molaei

Turkish Journal of Mathematics

In this paper, using generalized groups and their generalized actions, we define and study the notion of $T$-spaces. We study properties of the quotient space of a $T$-space and we present the conditions that imply the Hausdorff property for it. We also prove some essential results about topological generalized groups. As a main result, we show that for each positive integer $n$ there is a topological generalized group $T$ with $n$ identity elements. Moreover, we study the maps between two $T$-spaces and we consider the notion of $T$-transitivity.

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The Iteration Digraphs Of Finite Commutative Rings, Yangjiang Wei, Gaohua Tang Jan 2015

The Iteration Digraphs Of Finite Commutative Rings, Yangjiang Wei, Gaohua Tang

Turkish Journal of Mathematics

For a finite commutative ring $S$ (resp., a finite abelian group $S$) and a positive integer $k\geqslant2$, we construct an iteration digraph $G(S, k)$ whose vertex set is $S$ and for which there is a directed edge from $a\in S$ to $b\in S$ if $b=a^k$. We generalize some previous results of the iteration digraphs from the ring $\mathbb{Z}_n$ of integers modulo $n$ to finite commutative rings, and establish a necessary and sufficient condition for $G(S, k_1)$ and $G(S, k_2)$ to be isomorphic for any finite abelian group $S$.

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A Note On The Unit Distance Problem For Planar Configurations With $\Mathbb{Q}$-Independent Direction Set, Mark Herman, Jonathan Pakianathan Jan 2015

A Note On The Unit Distance Problem For Planar Configurations With $\Mathbb{Q}$-Independent Direction Set, Mark Herman, Jonathan Pakianathan

Turkish Journal of Mathematics

Let $T(n)$ denote the maximum number of unit distances that a set of $n$ points in the Euclidean plane $\mathbb{R}^2$ can determine with the additional condition that the distinct unit length directions determined by the configuration must be $\mathbb{Q}$-independent. This is related to the Erd\"os unit distance problem but with a simplifying additional assumption on the direction set that holds ``generically''. We show that $T(n+1)-T(n)$ is the Hamming weight of $n$, i.e. the number of nonzero binary coefficients in the binary expansion of $n$, and find a formula for $T(n)$ explicitly. In particular, $T(n)$ is $\Theta(n log(n))$. Furthermore, we describe …

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Special Proper Pointwise Slant Surfaces Of A Locally Product Riemannian Manifold, Mehmet Gülbahar, Erol Kiliç, Semra Saraçoğlu Çeli̇k Jan 2015

Special Proper Pointwise Slant Surfaces Of A Locally Product Riemannian Manifold, Mehmet Gülbahar, Erol Kiliç, Semra Saraçoğlu Çeli̇k

Turkish Journal of Mathematics

The structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise slant surfaces of a locally product manifold are introduced. A relation involving the squared mean curvature and the Gauss curvature of pointwise slant surface of a locally product manifold is proved. Two examples of proper pointwise slant surfaces of a locally product manifold, one of which is special and the other one is not special, are given.

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On The Classification Of Almost Null Rings, Ryszard Andruszkiewicz, Karol Pryszczepko Jan 2015

On The Classification Of Almost Null Rings, Ryszard Andruszkiewicz, Karol Pryszczepko

Turkish Journal of Mathematics

An almost null ring is a ring $R$ in which for all $a,b\in R$, $a^3=0$, $Ma^2=0$ for some square-free integer $M$ that depends on $a$ and $ab= ka^{2}=l b^{2}$ for some integers $k,l$. This paper is devoted to the classification of the almost null rings.

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Optimality Criteria For Sum Of Fractional Multiobjective Optimization Problem With Generalized Invexity, Deepak Bhati, Pitam Singh Jan 2015

Optimality Criteria For Sum Of Fractional Multiobjective Optimization Problem With Generalized Invexity, Deepak Bhati, Pitam Singh

Turkish Journal of Mathematics

The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. The branch and bound methods/algorithms are developed in the literature for this problem as a single objective problem. The theoretical and algorithmic development for sums of fractional programming problems is restricted to single objective problems. In this paper, some new optimality conditions are proposed for the sum of a fractional multiobjective optimization problem with generalized invexity. The optimality conditions are obtained by using …

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On Metallic Riemannian Structures, Aydin Gezer, Çağri Karaman Jan 2015

On Metallic Riemannian Structures, Aydin Gezer, Çağri Karaman

Turkish Journal of Mathematics

The paper is devoted to the study of metallic Riemannian structures. An integrability condition and curvature properties for these structures by means of a $\Phi $-operator applied to pure tensor fields are presented. Examples of these structures are also given.

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Some Properties Of A Class Of Analytic Functions Defined Bygeneralized Struve Functions, Mohsan Raza, Ni̇hat Yağmur Jan 2015

Some Properties Of A Class Of Analytic Functions Defined Bygeneralized Struve Functions, Mohsan Raza, Ni̇hat Yağmur

Turkish Journal of Mathematics

The aim of this paper is to define \ a new operator by using the generalized Struve functions $\sum\limits_{n=0}^{\infty }\frac{\left( -c/4\right) ^{n}}{\left( 3/2\right) _{n}\left( k\right) _{n}}z^{n+1}$ with $% k$ $=p+$ $\left( b+2\right) /2\neq 0,-1,-2,\ldots $ and $b,c,k\in \mathbb{C} $. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius problems, and some other interesting properties related to this operator.

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Some Concrete Operators And Their Properties, Mehmet Gürdal, Mubariz T. Garayev, Suna Saltan Jan 2015

Some Concrete Operators And Their Properties, Mehmet Gürdal, Mubariz T. Garayev, Suna Saltan

Turkish Journal of Mathematics

We consider integration and double integration operators, the Hardy operator, and multiplication and composition operators on Lebesgue space $L_{p}\left[ 0,1\right] $ and Sobolev spaces $W_{p}^{\left( n\right) }\left[ 0,1\right] $ and $W_{p}^{\left( n\right) }\left( \left[ 0,1\right] \times\left[ 0,1\right] \right) ,$ and we study their properties. In particular, we calculate norm and spectral multiplicity of the Hardy operator and some multiplication operators, investigate its extended eigenvectors, characterize some composition operators in terms of the extended eigenvectors of the Hardy operator, and calculate the numerical radius of the integration operator on the real $L_{2}\left[ 0,1\right] $ space. The main method for our investigation …

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Approximation Properties Of Szász Type Operators Based On Charlier Polynomials, Arun Kajla, Purshottam Narain Agrawal Jan 2015

Approximation Properties Of Szász Type Operators Based On Charlier Polynomials, Arun Kajla, Purshottam Narain Agrawal

Turkish Journal of Mathematics

In the present paper, we study some approximation properties of the Sz\'{a}sz type operators involving Charlier polynomials introduced by Varma and Ta\c{s}delen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

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Magnetic Curves On Flat Para-K\"Ahler Manifolds, Mohamed Jleli, Marian Ioan Munteanu Jan 2015

Magnetic Curves On Flat Para-K\"Ahler Manifolds, Mohamed Jleli, Marian Ioan Munteanu

Turkish Journal of Mathematics

In this paper we prove that spacelike and timelike magnetic trajectories corresponding to the para-K\"ahler 2-form on a para-K\"ahler manifold $(M,\p,g)$ are circles on $M$. We then classify all para-K\"ahler magnetic curves in pseudo-Euclidean spaces ${\mathbb{E}}^{2n}_n$.

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Dynamic Behavior Of A Second-Order Nonlinearrational Difference Equation, Yacine Halim, Nouressadat Touafek, Yasi̇n Yazlik Jan 2015

Dynamic Behavior Of A Second-Order Nonlinearrational Difference Equation, Yacine Halim, Nouressadat Touafek, Yasi̇n Yazlik

Turkish Journal of Mathematics

This paper deals with the global attractivity of positive solutions of the second-order nonlinear difference equation \begin{equation*} x_{n+1}=\frac{ax_{n}^{k}+b\displaystyle\sum_{j=1}^{k-1}x_{n}^{j}x_{n-1}^{k-j}+cx_{n-1} ^{k}}{Ax_{n}^{k}+B\displaystyle\sum_{j=1}^{k-1}x_{n}^{j}x_{n-1}^{k-j}+Cx_{n-1}^{k}},\ k=3,4,...,\,n=0,1,...,\label{eq1} \end{equation*} where the parameters $a$, $b$, $c$, $A$, $B$, $C$ and the initial values $x_{0}$, $x_{-1}$ are arbitrary positive real numbers.

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Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov Jan 2015

Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov

Department of Mathematics: Faculty Publications

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …

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