Threshold Complexes And Connections To Number Theory,
2013
TÜBİTAK
Threshold Complexes And Connections To Number Theory, Jonathan Pakianathan, Troy Winfree
Turkish Journal of Mathematics
In this paper we study quota complexes (or equivalently in the case of scalar weights, threshold complexes) and how the topology of these quota complexes changes as the quota is changed. This problem is a simple ``linear\" version of the general question in Morse Theory of how the topology of a space varies with a parameter. We give examples of natural and basic quota complexes where this problem frames questions about the distribution of primes, squares and divisors in number theory and as an example provide natural topological formulations of the prime number theorem, the twin prime conjecture, Goldbach's conjecture, …
Commutants And Hyper-Reflexivity Of Multiplication Operators,
2013
TÜBİTAK
Commutants And Hyper-Reflexivity Of Multiplication Operators, Masoumeh Faghih Ahmadi, Karim Hedayatian
Turkish Journal of Mathematics
We characterize the commutants of some multiplication operators on a Banach space of analytic functions defined on a bounded domain in the plane. Under certain conditions on the symbol of a multiplication operator, we show that its commutant is a set of multiplication operators. This partially answers a question of Axler, Cuckovic and Rao. Next, the hyper-reflexivity of these multiplication operators are proved. The paper is concluded by proving the hyper-reflexivity of the multiplication operators with symbols \varphi (z) = z^k, k=1, 2,... .
Algorithm To Solve Certain Ternary Quartic Diophantine Equations,
2013
TÜBİTAK
Algorithm To Solve Certain Ternary Quartic Diophantine Equations, Laszlo Szalay
Turkish Journal of Mathematics
In this paper, we develop an algorithm to solve completely the Diophantine equation F(x,y)=z^2, where the quartic inhomogeneous polynomial F(x,y) with integer coefficients satisfies certain technical conditions. The procedure is an extension of the version of Runge's method given by Poulakis.
Nzi Rings,
2013
TÜBİTAK
Nzi Rings, Long Wang, Junchao Wei, Libin Li
Turkish Journal of Mathematics
A ring R is called NZI if for any a \in R, l(a) is an N-ideal of R. In this paper, we first study some basic properties and basic extensions of NZI rings. Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring. Then R is a strongly regular ring if and only if R is an NZI ring; (2) If R is an NZI left MC2 ring and every simple singular left R-module is nil-injective, then R is reduced; (3) Let R be an NZI ring. Then R …
Continuous Invariant Averagings,
2013
TÜBİTAK
Continuous Invariant Averagings, Djavvat Khadjiev, Abdullah Çavuş
Turkish Journal of Mathematics
Main results: For every equicontinuous almost periodic linear representation of a group in a complete locally convex space L with the countability property, there exists the unique invariant averaging; it is continuous and is expressed by using the L-valued invariant mean of Bochner and von-Neumann. An analog of Wiener's approximation theorem for an equicontinuous almost periodic linear representation in a locally convex space with the countability property is proved.
Slant Submersions From Almost Product Riemannian Manifolds,
2013
TÜBİTAK
Slant Submersions From Almost Product Riemannian Manifolds, Yilmaz Gündüzalp
Turkish Journal of Mathematics
In this paper, we define the concept of almost product Riemannian submersion between almost product Riemannian manifolds. We introduce slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations that arise from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.
A Class Of 3-Dimensional Almost Cosymplectic Manifolds,
2013
TÜBİTAK
A Class Of 3-Dimensional Almost Cosymplectic Manifolds, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
Turkish Journal of Mathematics
The main interest of the present paper is to classify the almost cosymplectic 3-manifolds that satisfy \Vert grad\lambda \Vert = const.(\neq 0) and \bigtriangledown_{\xi} h=2ah\phi.
Cartan Equivalence Problem For Third-Order Differential Operators,
2013
TÜBİTAK
Cartan Equivalence Problem For Third-Order Differential Operators, Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti
Turkish Journal of Mathematics
This article is dedicated to solving the equivalence problem for a pair of third-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. We will treat 2 versions of equivalence problems: first, the direct equivalence problem, and second, an equivalence problem to determine conditions on 2 differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.
Orthogonal Systems In L^2 Spaces Of A Vector Measure,
2013
TÜBİTAK
Orthogonal Systems In L^2 Spaces Of A Vector Measure, Eduardo Jiménez Fernández
Turkish Journal of Mathematics
Let m:\Sigma \to X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m-orthogonal system in the space L^2(m) of square integrable functions with respect to m. If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to this vector measure. On the other hand, if the vector measure is fixed, then we can obtain sequences of orthogonal functions using the Kadec-Pelczynski disjointification method.
On Quotients Of Ith Affine Surface Areas,
2013
TÜBİTAK
On Quotients Of Ith Affine Surface Areas, Chang-Jian Zhao
Turkish Journal of Mathematics
Following the volume difference function, we first introduce the notion of the affine surface area quotient function. We establish Brunn--Minkowski type inequalities for the affine surface area quotient function, which in special cases yield some well-known results.
Attractors For Parabolic Problems In Weighted Spaces,
2013
TÜBİTAK
Attractors For Parabolic Problems In Weighted Spaces, Xiaojun Li, Ying Tang
Turkish Journal of Mathematics
The purpose of this paper is to investigate the asymptotic behavior of the solutions of parabolic equations with singular initial data in weighted spaces L^r_{\delta(x)}(\Omega) where \delta(x) is the distance to the boundary. We first establish the existence of the attractor for that equation in L^r_{\delta(x)}(\Omega) and then show the existence of the exponential attractor in L^2_{\delta(x)}(\Omega). In contrast to our previous results, we get the existence of attractors in weak topology spaces.
Oscillation Of Solutions Of A Neutral Pantograph Equation With Impulsive Perturbations,
2013
TÜBİTAK
Oscillation Of Solutions Of A Neutral Pantograph Equation With Impulsive Perturbations, Kaizhong Guan
Turkish Journal of Mathematics
Some sufficient conditions are established on the oscillation of all solutions of a class of neutral pantograph equations with impulsive perturbations of the form \{\begin{array}{l}\frac{d}{dt}[x(t)-C(t)x(\gamma t)]+ \frac{P(t)}{t}x(\alpha t)-\frac{Q(t)}{t}x(\beta t)=0,~~ t\geq t_{0}>0,~~ t\neq t_{k}, x(t^{+}_{k})=b_{k}x(t_{k}), k=1,2,... . \end{array}\right.
Erratum To: ``Null Mannheim Curves In The Minkowski 3-Space E_1^3'',
2013
TÜBİTAK
Erratum To: ``Null Mannheim Curves In The Minkowski 3-Space E_1^3'', Handan Özteki̇n, Mahmut Ergüt
Turkish Journal of Mathematics
In this paper, Theorem 3.2 and Proposition 3.2 in the paper which is cited in the title are corrected.
Isoclinic Extensions Of Lie Algebras,
2013
TÜBİTAK
Isoclinic Extensions Of Lie Algebras, Hamid Mohammadzadeh, Ali Reza Salemkar, Zahra Riyahi
Turkish Journal of Mathematics
In this article we introduce the notion of the equivalence relation, isoclinism, on the central extensions of Lie algebras, and determine all central extensions occurring in an isoclinism class of a given central extension. We also show that under some conditions, the concepts of isoclinism and isomorphism between the central extensions of finite dimensional Lie algebras are identical. Finally, the connection between isoclinic extensions and the Schur multiplier of Lie algebras are discussed.
Bbm Equation With Non-Constant Coefficients,
2013
TÜBİTAK
Bbm Equation With Non-Constant Coefficients, Amutha Senthilkumar
Turkish Journal of Mathematics
In this article, a model for the propagation of long waves over an uneven bottom is considered. We provide both theoretical and numerical results for this model. We also discuss the changes which occur in a solitary wave solution of the BBM equation as it travels through a channel of decreasing depth.
Radical Operations On The Multiplicative Lattice,
2013
TÜBİTAK
Radical Operations On The Multiplicative Lattice, Esra Şengelen Sevi̇m
Turkish Journal of Mathematics
The purpose of this paper is to introduce interesting and useful properties of quasi-radical and radical operations on the elements of a multiplicative lattice.
A Characterization Of Auslander Category,
2013
TÜBİTAK
A Characterization Of Auslander Category, Juxiang Sun
Turkish Journal of Mathematics
In this paper, we discuss the Bass class and the Auslander class with respect to a semidualizing module over an associative ring. Let _SC_R be a semidualizing module, we proved that the Bass class B_C (R) is a right orthogonal subcategory of some right R-module; and that the Auslander class A_C (S) is a left orthogonal subcategory of the character module of some left S-module. As an application, we introduce the notion of the minimal semidualizing module, and get a one to one correspondence between the isomorphism classes of minimal semidualizing R-modules and maximal classes among coresolving preenvelope classes of …
Morphism Classes Producing (Weak) Grothendieck Topologies, (Weak) Lawvere--Tierney Topologies, And Universal Closure Operations, Seyed Naser Hosseini, Mehdi Nodehi
Turkish Journal of Mathematics
In this article, given a category X, with \Omega the subobject classifier in Set^{X^{op}, we set up a one-to-one correspondence between certain (i) classes of X-morphisms, (ii) \Omega-subpresheaves, (iii) \Omega-automorphisms, and (iv) universal operators. As a result we give necessary and sufficient conditions on a morphism class so that the associated (i) \Omega-subpresheaf is a (weak) Grothendieck topology, (ii) \Omega-automorphism is a (weak) Lawvere--Tierney topology, and (iii) universal operation is an (idempotent) universal closure operation. We also finally give several examples of morphism classes yielding (weak) Grothendieck topologies, (weak) Lawvere--Tierney topologies, and (idempotent) universal closure operations.
Remarks On The Paper ``On Some New Inequalities For Convex Functions\\" By M. Tunç,
2013
TÜBİTAK
Remarks On The Paper ``On Some New Inequalities For Convex Functions\\" By M. Tunç, Alfred Witkowski
Turkish Journal of Mathematics
In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed.
Labelings Of Type (1,1,1) For Toroidal Fullerenes,
2013
TÜBİTAK
Labelings Of Type (1,1,1) For Toroidal Fullerenes, Martin Baca, Muhammad Numan, Ayesha Shabbir
Turkish Journal of Mathematics
In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene H_m^n with mn hexagons by the consecutive integers from 1 up to V(H_m^n) + E(H_m^n) + F(H_m^n) in such a way that the set of face-weights of 6-sided faces forms an arithmetic progression with common difference d, where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face. The paper examines the existence of such labelings for several differences d.
