Random Process Generated By The Incomplete Gauss Sums,
2015
TÜBİTAK
Random Process Generated By The Incomplete Gauss Sums, Emek Demi̇rci̇ Akarsu
Turkish Journal of Mathematics
In this paper we explore a random process generated by the incomplete Gauss sums and establish an analogue of weak invariance principle for these sums. We focus our attention exclusively on a generalization of the limit distribution of the long incomplete Gauss sums given by the family of periodic functions analyzed by the author and Marklof.
Some Identities For The Glasser Transform And Their Applications,
2015
TÜBİTAK
Some Identities For The Glasser Transform And Their Applications, Faruk Uçar
Turkish Journal of Mathematics
In the present paper we consider a new integral transform, denoted by $\mathcal{G}_{\nu}$, which may be regarded as a generalization of the well-known transform due to Glasser. Many identities involving this transform are given. By making use of these identities, a number of new Parseval--Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustrations of the results presented here.
On The Computation Of Generalized Division Polynomials,
2015
TÜBİTAK
On The Computation Of Generalized Division Polynomials, Ömer Küçüksakalli
Turkish Journal of Mathematics
We give an algorithm to compute the generalized division polynomials for elliptic curves with complex multiplication. These polynomials can be used to generate the ray class fields of imaginary quadratic fields over the Hilbert class field with no restriction on the conductor.
Existence Of Solutions For A First-Order Nonlocal Boundary Value Problem With Changing-Sign Nonlinearity,
2015
TÜBİTAK
Existence Of Solutions For A First-Order Nonlocal Boundary Value Problem With Changing-Sign Nonlinearity, Erbi̇l Çeti̇n, Fatma Serap Topal
Turkish Journal of Mathematics
This work is concerned with the existence of positive solutions to a nonlinear nonlocal first-order multipoint problem. Here the nonlinearity is allowed to take on negative values, not only positive values.
The Prime Tournaments $T$ With $\Mid\! W_{5}(T) \!\Mid = \Mid\! T \!\Mid -2$,
2015
TÜBİTAK
The Prime Tournaments $T$ With $\Mid\! W_{5}(T) \!\Mid = \Mid\! T \!\Mid -2$, Houmem Belkhechine, Imed Boudabbous, Kaouthar Hzami
Turkish Journal of Mathematics
We consider a tournament $T=(V, A)$. For $X\subseteq V$, the subtournament of $T$ induced by $X$ is $T[X] = (X, A \cap (X \times X))$. A module of $T$ is a subset $X$ of $V$ such that for $a, b\in X$ and $ x\in V\setminus X$, $(a,x)\in A$ if and only if $(b,x)\in A$. The trivial modules of $T$ are $\emptyset$, $\{x\}(x\in V)$, and $V$. A tournament is prime if all its modules are trivial. For $n\geq 2$, $W_{2n+1}$ denotes the unique prime tournament defined on $\{0,\dots,2n\}$ such that $W_{2n+1}[\{0,\dots,2n-1\}]$ is the usual total order. Given a prime tournament $T$, …
Sharp Lower Bounds For The Zagreb Indices Of Unicyclic Graphs,
2015
TÜBİTAK
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.
Generalized Weakly Central Reduced Rings,
2015
TÜBİTAK
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.
On Isophote Curves And Their Characterizations,
2015
TÜBİTAK
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.
Split Extension Classifiers In The Category Of Precrossed Modules Of Commutative Algebras,
2015
TÜBİTAK
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.
Defect Polynomials And Tutte Polynomials Of Some Asymmetric Graphs,
2015
TÜBİTAK
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.
Fiber Product Preserving Bundle Functors On Fibered-Fibered Manifolds,
2015
TÜBİTAK
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.
On The Second Homology Of The Sch\"{U}Tzenberger Product Of Monoids,
2015
TÜBİTAK
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 $T$.
Super D-Anti-Magic Labeling Of Subdivided $Kc_{5}$,
2015
TÜBİTAK
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 …
On Condition $(Pwp)_{W}$ For $S$-Posets,
2015
TÜBİTAK
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 $(PWP)_{w}$.
Generalized Chebyshev Polynomials Of The Second Kind,
2015
TÜBİTAK
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.
Existence Of Unique Solution To Switchedfractional Differential Equations With $P$-Laplacian Operator,
2015
TÜBİTAK
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.
Special Proper Pointwise Slant Surfaces Of A Locally Product Riemannian Manifold,
2015
TÜBİTAK
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.
Some Properties Of A Class Of Analytic Functions Defined Bygeneralized Struve Functions,
2015
TÜBİTAK
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.
On The Classification Of Almost Null Rings,
2015
TÜBİTAK
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.
On Metallic Riemannian Structures,
2015
TÜBİTAK
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.
