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Continuous Invariant Averagings, Djavvat Khadjiev, Abdullah Çavuş
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.
A Class Of 3-Dimensional Almost Cosymplectic Manifolds, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
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, Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti
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, Eduardo Jiménez Fernández
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, Chang-Jian Zhao
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, Xiaojun Li, Ying Tang
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.
Isoclinic Extensions Of Lie Algebras, Hamid Mohammadzadeh, Ali Reza Salemkar, Zahra Riyahi
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, Amutha Senthilkumar
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.
Labelings Of Type (1,1,1) For Toroidal Fullerenes, Martin Baca, Muhammad Numan, Ayesha Shabbir
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.
Bifurcations And Parametric Representations Of Traveling Wave Solutions For The Green--Naghdi Equations, Shengqiang Tang, Libing Zeng, Dahe Feng
Bifurcations And Parametric Representations Of Traveling Wave Solutions For The Green--Naghdi Equations, Shengqiang Tang, Libing Zeng, Dahe Feng
Turkish Journal of Mathematics
By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green--Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric representations of traveling wave solutions are constructed.
On Nearly Kenmotsu Manifolds, Behzad Najafi, Niloufar Hosseinpour Kashani
On Nearly Kenmotsu Manifolds, Behzad Najafi, Niloufar Hosseinpour Kashani
Turkish Journal of Mathematics
We prove that on a nearly Kenmotsu manifold a second-order symmetric closed recurrent tensor is a multiple of the associated metric tensor. We then find the necessary condition under which a vector field on a nearly Kenmotsu manifold will be a strict contact or Killing vector field. Finally, we prove that every \phi-recurrent nearly Kenmotsu manifold is an Einstein manifold and every locally \phi-recurrent nearly Kenmotsu manifold is a manifold of constant curvature -1 .
Marcinkiewicz-Fejer Means Of Double Conjugate Walsh-Kaczmarz-Fourier Series And Hardy Spaces, Ushangi Goginava, Karoly Nagy
Marcinkiewicz-Fejer Means Of Double Conjugate Walsh-Kaczmarz-Fourier Series And Hardy Spaces, Ushangi Goginava, Karoly Nagy
Turkish Journal of Mathematics
In the present paper we prove that for any 0 < p \leq 2/3 there exists a martingale f in H_p such that the Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series of the martingale f is not uniformly bounded in the space L_p.
On Cise-Normal Subgroups Of Finite Groups, Yong Xu, Tao Zhao, Xianhua Li
On Cise-Normal Subgroups Of Finite Groups, Yong Xu, Tao Zhao, Xianhua Li
Turkish Journal of Mathematics
A generalized normality CISE of subgroups of a finite group is introduced. Let F be a saturated formation containing the class of all supersolvable groups. We give a characterization of F by using CISE-normality of subgroups.
Note On Hilbert-Type Inequalities, Predrag Vukovic
Note On Hilbert-Type Inequalities, Predrag Vukovic
Turkish Journal of Mathematics
The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a general homogeneous kernel, thus generalizing a result obtained in [Namita Das and Srinibas Sahoo, A generalization of multiple Hardy-Hilbert's integral inequality, Journal of Mathematical Inequalities, 3(1), (2009), 139--154].
A Generalization Of Banach's Contraction Principle For Some Non-Obviously Contractive Operators In A Cone Metric Space, Yingxin Guo
Turkish Journal of Mathematics
This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend and generalize some fixed point theorems in cone metric spaces. An application to differential equations is given.
Warped Product Submanifolds Of A Kenmotsu Manifold, Siraj Uddin, Viqar Azam Khan, Khalid Ali Khan
Warped Product Submanifolds Of A Kenmotsu Manifold, Siraj Uddin, Viqar Azam Khan, Khalid Ali Khan
Turkish Journal of Mathematics
In the present paper, we study warped product semi-slant submanifolds of a Kenmotsu manifold. We obtain some results on the existence of such type warped product submanifolds of a Kenmotsu manifold with an example.
Geodesicity And Isoclinity Properties For The Tangent Bundle Of The Heisenberg Manifold With Sasaki Metric, Simona Luiza Druta, Paola Piu
Geodesicity And Isoclinity Properties For The Tangent Bundle Of The Heisenberg Manifold With Sasaki Metric, Simona Luiza Druta, Paola Piu
Turkish Journal of Mathematics
We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form \omega on the Heisenberg manifold (H_3,g) to (TH_3,g^S) are not totally geodesic, and the distributions F^H=L(E_1^H,E_2^H) and F^V=L(E_1^V,E_2^V) are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold (H_3,g), are geodesics on the tangent bundle endowed with the Sasaki metric (TH_3,g^s), if and only if the curves considered on the base manifold are …
Secrecy Logic: S-Secrecy Structures, George Voutsadakis
Secrecy Logic: S-Secrecy Structures, George Voutsadakis
Turkish Journal of Mathematics
Let S = \lan L,\vdash_S\ran be a deductive system. An S-secrecy logic is a quadruple K = \lan Fm_L(V),K,B,S\ran, where Fm_L(V) is the algebra of L-formulas, K,B are S-theories, with B \subseteq K and S \subseteq K such that S \cap B = \emptyset. K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible (or browsable) part of the knowledge base and S is a secret set, a set of sensitive or private information that the knowledge base aims at concealing from its users. To provide models for this context, the notion of …
Product Of Graded Submodules, Ameer Jaber
Product Of Graded Submodules, Ameer Jaber
Turkish Journal of Mathematics
Let \Delta be an abelian group. By considering the notion multiplication of \Delta-graded modules (see [7]) over a commutative \Delta-graded ring with unity, we introduce the notion of product of two \Delta-graded submodules which we use to characterize the \Delta-graded prime submodules of a multiplication \Delta-graded module. Finally we proved a graded version of Nakayama lemma for multiplication \Delta-graded modules.
The Character Variety Of A Class Of Rational Links, Khaled Qazaqzeh
The Character Variety Of A Class Of Rational Links, Khaled Qazaqzeh
Turkish Journal of Mathematics
Let G_n be the fundamental group of the exterior of the rational link C(2n) in Conway's normal form, see [7]. A presentation for G_n is given by \langle a, b (ab)^n = (ba)^n\rangle [3, Thm. 2.2]. We study the character variety in SL(2, C) of the group G_n. In particular, we give the defining polynomial of the character variety of G_n. As an application, we show a well-known result that G_n and G_m are isomorphic only when n = m. Also as a consequence of the main theorem of this paper, we give a basis of the Kauffman bracket skein …
Weakly Normal Rings, Junchao Wei̇, Libin Li
Weakly Normal Rings, Junchao Wei̇, Libin Li
Turkish Journal of Mathematics
A ring R is defined to be weakly normal if for all a, r \in R and e \in E(R), ae = 0 implies Rera is a nil left ideal of R, where E(R) stands for the set of all idempotent elements of R. It is proved that R is weakly normal if and only if Rer(1-e) is a nil left ideal of R for each e \in E(R) and r \in R if and only if T_n(R, R) is weakly normal for any positive integer n. And it follows that for a weakly normal ring R (1) R is …
A Homotopy For A Complex Of Free Lie Algebras, Michele Vergne
A Homotopy For A Complex Of Free Lie Algebras, Michele Vergne
Turkish Journal of Mathematics
Using the Guichardet construction, we compute the cohomology groups of a complex of free Lie algebras introduced by Alekseev and Torossian
On Cosets In Coxeter Groups, Sarah B. Hart, Peter J. Rowley
On Cosets In Coxeter Groups, Sarah B. Hart, Peter J. Rowley
Turkish Journal of Mathematics
In this paper the notion of Coxeter length for a subset of a Coxeter group, as introduced in [9], is investigated for various subsets of a Coxeter group. Mostly cosets of various subgroups are examined as well as the associated idea of X-posets, which is a vast generalization of the Bruhat order.
On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids, Karim Ahmadidelir, Hossein Doostie
On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids, Karim Ahmadidelir, Hossein Doostie
Turkish Journal of Mathematics
This paper investigates the automorphism group of monogenic [4] semigroups (or monoids) to find its relationship with the automorphism group of cyclic groups. Then, by considering a presentation related to the direct product of monogenic semigroups, verify the relationship between the automorphism group of These and the automorphism group of the group presented by the same presentation. This study gives us some [4]explicit formulas for computing the order of automorphism groups of these algebraic structures.
Best Simultaneous Approximation In Function And Operator Spaces, Eyad Abu-Sirhan
Best Simultaneous Approximation In Function And Operator Spaces, Eyad Abu-Sirhan
Turkish Journal of Mathematics
Let Z be a Banach space and G be a closed subspace of Z. For f_1,f_2 \in Z, the distance from f_1,f_2 to G is defined by d(f_1,f_2,G) = \underset{f \in G}{\inf} max { f_1-f , f_2-f }. An element g^{\ast} \in G satisfying max { f_1-g^{\ast } , f_2-g^{\ast } } = \underset{f \in G}{\inf } max { f_1-f , f_2-f } is called a best simultaneous approximation for f_1,f_2 from G. In this paper, we study the problem of best simultananeous approximation in the space of all continuous X-valued functions on a compact Hausdorff space S; C(S,X), and …
Banach Limit And Some New Spaces Of Double Sequences, Mohammad Mursaleen, Syed Abdul Mohiuddine
Banach Limit And Some New Spaces Of Double Sequences, Mohammad Mursaleen, Syed Abdul Mohiuddine
Turkish Journal of Mathematics
In this paper, we define and study the Banach limit for double sequences and introduce some new spaces related to the concept of almost and strong almost convergence for double sequences. We characterize these spaces through some sublinear functionals and we also establish some inclusion relations.
Approximate Groups Iii: The Unitary Case, Emmanuel Breuillard, Ben Green
Approximate Groups Iii: The Unitary Case, Emmanuel Breuillard, Ben Green
Turkish Journal of Mathematics
By adapting the classical proof of Jordan's theorem on finite subgroups of linear groups, we show that every approximate subgroup of the unitary group U_n(C) is almost abelian.
An Oscillation Theorem For Second-Order Nonlinear Differential Equations Of Euler Type, Asadollah Aghajani, Vahid Roomi
An Oscillation Theorem For Second-Order Nonlinear Differential Equations Of Euler Type, Asadollah Aghajani, Vahid Roomi
Turkish Journal of Mathematics
We consider the nonlinear equation t^2x'' + g(x) = 0, where g(x) satisfies xg(x) > 0 for x \ne 0, but is not assumed to be sublinear or superlinear. We study the problem whether all nontrivial solutions of the equation are oscillatory in some critical cases.
On Injective And Subdirectly Irreducible S-Acts Over Left Zero Semigroups, Gholamreza Moghaddasi
On Injective And Subdirectly Irreducible S-Acts Over Left Zero Semigroups, Gholamreza Moghaddasi
Turkish Journal of Mathematics
The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups. Also we compute the number of such acts and specify cogenerators acts over left zero semigroups. To do these we first take another look at the description of injective hulls of the separated S-acts over left zero semigroups.