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Full-Text Articles in Mathematics

\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş Jan 2014

\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş

Turkish Journal of Mathematics

Almost semiinvariant \xi^{\perp}-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant \xi^{\perp}-submanifolds and semiinvariant \xi^{\perp}-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant \xi^{\perp}-submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-\textit{CR}-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant \xi^{\perp} -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.


A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz Jan 2014

A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz

Turkish Journal of Mathematics

We consider transformations preserving asymptotic directions of surfaces in Minkowski 3-space and show that a transformation preserves the asymptotic directions of a surface if only if it is the projective one. Therefore, we obtain a characterization of the projective transformation.


A Cohen Type Inequality For Laguerre--Sobolev Expansions With A Mass Point Outside Their Oscillatory Regime, Edmundo José Huertas Cejudo, Francisco Marcellán Espanol, María Francisca Pérez Valero, Yamilet Quintana Jan 2014

A Cohen Type Inequality For Laguerre--Sobolev Expansions With A Mass Point Outside Their Oscillatory Regime, Edmundo José Huertas Cejudo, Francisco Marcellán Espanol, María Francisca Pérez Valero, Yamilet Quintana

Turkish Journal of Mathematics

Let consider the Sobolev type inner product \langle f, g\rangle_S = \int_0^{\infty} f(x)g(x)d \mu (x) + Mf(c)g(c) + Nf^{\prime}(c) g^{\prime}(c), where d\mu (x) = x^{\alpha} e^{-x}dx, \alpha > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order \delta in terms of this kind of Laguerre--Sobolev polynomials.


Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir Jan 2014

Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir

Turkish Journal of Mathematics

We investigate here the connected graphs with the property that any pair of vertices are missed by some longest paths (or cycles), embeddable in n-dimensional lattices L^n where L denotes the set of integers.


On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇ Jan 2014

On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇

Turkish Journal of Mathematics

The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that a^{m+r}=a^m, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T_n, which we call transformations of index 1.


On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç Jan 2014

On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç

Turkish Journal of Mathematics

We study biharmonic Legendre curves in S-space forms. We find curvature characterizations of these special curves in 4 cases.


On The Maximal Operators Of Vilenkin-Fejéer Means, George Tephnadze Jan 2013

On The Maximal Operators Of Vilenkin-Fejéer Means, George Tephnadze

Turkish Journal of Mathematics

The main aim of this paper is to prove that the maximal operator \overset{\sim}{\sigma}^{\ast}f:=\underset{n \in P} \sup\frac{ \sigma _nf }{\log^2 (n+1)} is bounded from the Hardy space H_{1/2} to the space L_{1/2}, where \sigma _nf are Fejér means of bounded Vilenkin-Fourier series.


A Note On Chaos In Product Maps, Risong Li, Xiaoliang Zhou Jan 2013

A Note On Chaos In Product Maps, Risong Li, Xiaoliang Zhou

Turkish Journal of Mathematics

In this paper, we mainly discuss how chaos conditions on semi-flows carry over to their products. We show that if two semi-flows (or even one of them) are sensitive, so does their product. On the other side, the product of two topologically transitive semi-flows need not be topologically transitive. We then provide several sufficient conditions under which the product of two chaotic semi-flows is chaotic in the sense of Devaney. Also, stronger forms of sensitivity and transitivity for product systems are studied. In particular, we introduce the notion of ergodic sensitivity and prove that for any given two (not-necessarily continuous) …


Strongly Gorenstein Flat And Gorenstein Fp-Injective Modules, Chunhua Yang Jan 2013

Strongly Gorenstein Flat And Gorenstein Fp-Injective Modules, Chunhua Yang

Turkish Journal of Mathematics

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfd_RM=Gpd_RM, and hence SGfd_RM< \infty if and only if Gfd_RM


Existence And Multiplicity Of Positive Solutions For A Class Of Nonlinear Elliptic Problems, Asadollah Aghajani, Jamile Shamshiri, Frajollah Mohammadi Yaghoobi Jan 2013

Existence And Multiplicity Of Positive Solutions For A Class Of Nonlinear Elliptic Problems, Asadollah Aghajani, Jamile Shamshiri, Frajollah Mohammadi Yaghoobi

Turkish Journal of Mathematics

We study the existence and multiplicity of nonnegative solutions for the nonlinear elliptic problem, -\Delta u+v(x)u=a(x)u^p+\lambda f(x,u) for x\in\Omega and u=0 on \partial\Omega, where \Omega is a bounded region in R^N, N>2, 1


Finitistic Dimension Conjectures For Representations Of Quivers, Sergio Estrada, Salahatti̇n Özdemi̇r Jan 2013

Finitistic Dimension Conjectures For Representations Of Quivers, Sergio Estrada, Salahatti̇n Özdemi̇r

Turkish Journal of Mathematics

Let R be a ring and Q be a quiver. We prove the first Finitistic Dimension Conjecture to be true for RQ, the path ring of Q over R, provided that R satisfies the conjecture. In fact, we prove that if the little and the big finitistic dimensions of R coincide and equal n


Sasakian Finsler Manifolds, Ayşe Funda Yaliniz, Nesri̇n Çalişkan Jan 2013

Sasakian Finsler Manifolds, Ayşe Funda Yaliniz, Nesri̇n Çalişkan

Turkish Journal of Mathematics

In this study, almost contact Finsler structures on vector bundle are defined and the condition of normality in terms of the Nijenhuis torsion N_{\phi} of almost contact Finsler structure is obtained. It is shown that for a K-contact structure on Finsler manifold \nabla_X \xi =-\frac{1}{2} \phi X and the flag curvature for plane sections containing \xi are equal to \frac{1}{4}. By using the Sasakian Finsler structure, the curvatures of a Finsler connection \nabla on V are obtained. We prove that a locally symmetric Finsler manifold with K-contact Finsler structure has a constant curvature \frac{1}{4}. Also, the Ricci curvature on Finsler …


Products Of Conjugacy Classes And Products Of Irreducible Characters In Finite Groups, Mohammad Reza Darafsheh, Sajjad Mahmood Robati Jan 2013

Products Of Conjugacy Classes And Products Of Irreducible Characters In Finite Groups, Mohammad Reza Darafsheh, Sajjad Mahmood Robati

Turkish Journal of Mathematics

Let G be a finite group. If A and B are two conjugacy classes in G, then AB is a union of conjugacy classes in G and \eta(AB) denotes the number of distinct conjugacy classes of G contained in AB. If \chi and \psi are two complex irreducible characters of G, then \chi\psi is a character of G and again we let \eta(\chi\psi) be the number of irreducible characters of G appearing as constituents of \chi\psi. In this paper our aim is to study the product of conjugacy classes in a finite group and obtain an upper bound for \eta …


On Modules Which Satisfy The Radical Formula, Bülent Saraç, Yücel Tiraş Jan 2013

On Modules Which Satisfy The Radical Formula, Bülent Saraç, Yücel Tiraş

Turkish Journal of Mathematics

In this paper, the authors prove that every representable module over a commutative ring with identity satisfies the radical formula. With this result, they extend the class of modules satisfying the radical formula from that of Artinian modules to a larger one. They conclude their work by giving a description of the radical of a submodule of a representable module.


Generalized Sobolev-Shubin Spaces, Boundedness And Schatten Class Properties Of Toeplitz Operators, Ayşe Sandikçi, Ahmet Turan Gürkanli Jan 2013

Generalized Sobolev-Shubin Spaces, Boundedness And Schatten Class Properties Of Toeplitz Operators, Ayşe Sandikçi, Ahmet Turan Gürkanli

Turkish Journal of Mathematics

Let w and \omega be two weight functions on R^{2d} and 1 \leq p,q \leq \infty. Also let M(p,q,\omega) (R^d) denote the subspace of tempered distributions S' (R^d) consisting of f \in S' (R^d) such that the Gabor transform V_g f of f is in the weighted Lorentz space L(p,q,\omega d\mu) (R^{2d}) . In the present paper we define a space Q_{g,w}^{M(p,q,\omega) (R^d) as counter image of M(p,q,\omega) (R^d) under Toeplitz operator with symbol w. We show that Q_{g,w}^{M(p,q,\omega)}(R^d) is a generalization of usual Sobolev-Shubin space Q_s (R^d). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.


A Scheme Over Prime Spectrum Of Modules, Ahmad Abbasi, Dawood Hassanzadeh Lelekami Jan 2013

A Scheme Over Prime Spectrum Of Modules, Ahmad Abbasi, Dawood Hassanzadeh Lelekami

Turkish Journal of Mathematics

Let R be a commutative ring with nonzero identity and let M be an R-module with X=Spec(M). It is introduced a scheme O_X on the prime spectrum of M and some of its properties have been investigated.


Global And Finitistic Dimension Of Hopf-Galois Extensions, Ling Liu, Qiaoling Guo Jan 2013

Global And Finitistic Dimension Of Hopf-Galois Extensions, Ling Liu, Qiaoling Guo

Turkish Journal of Mathematics

Let H be a Hopf algebra over a field k and A/B a right H-Galois extension. Then in this note a spectral sequence for Ext will be constructed which yields the estimate for global dimension of A in terms of the corresponding data for H and B. As an application, we obtain the Maschke-type theorems for crossed products and twisted smash products. Finally, the relationship of finitistic dimensions between A and B will be given, if H is semisimple.


Some Properties On The Baer-Invariant Of A Pair Of Groups And V_G-Marginal Series, Mohammad Reza Rismanchian, Mehdi Araskhan Jan 2013

Some Properties On The Baer-Invariant Of A Pair Of Groups And V_G-Marginal Series, Mohammad Reza Rismanchian, Mehdi Araskhan

Turkish Journal of Mathematics

The aim of this paper is to present some properties of the Baer-invariant of a pair of groups with respect to a given variety of groups V. We derive some equalities and inequalities of the Baer-invariant of a pair of finite groups, as long as V is considered to be a Schur-Baer variety. Moreover, we present a relative version of the concept of lower marginal series and give some isomorphisms among V_G-marginal factor groups. Also, we conclude a generalized version of the Stallings' theorem.


New Trace Formula For The Matrix Sturm-Liouville Equation With Eigenparameter Dependent Boundary Conditions, Chuan Fu Yang Jan 2013

New Trace Formula For The Matrix Sturm-Liouville Equation With Eigenparameter Dependent Boundary Conditions, Chuan Fu Yang

Turkish Journal of Mathematics

A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained.


Contact 3-Structure Qr-Warped Product Submanifold In Sasakian Space Form, Esmaiel Abedi, Ghorbanali Haghighatdoost, Mohammad Ilmakchi, Zahra Nazari Jan 2013

Contact 3-Structure Qr-Warped Product Submanifold In Sasakian Space Form, Esmaiel Abedi, Ghorbanali Haghighatdoost, Mohammad Ilmakchi, Zahra Nazari

Turkish Journal of Mathematics

In the present paper we obtain sharp estimates for the squared norm of the second fundamental form in terms of the mapping function for contact 3-structure CR-warped products isometrically immersed in Sasakian space form.


On Nash\'S 4-Sphere And Property 2r, Motoo Tange Jan 2013

On Nash\'S 4-Sphere And Property 2r, Motoo Tange

Turkish Journal of Mathematics

D. Nash defined a family of homotopy 4-spheres in [11]. Proving that his manifolds S_{m,n,m',n'} are all real S^4, we show that they have handle decomposition with no 1-handles, two 2-handles and two 3-handles. The handle structures give new potential counterexamples to the Property 2R conjecture.


Finite Rings And Wilson's Theorem, Yasuyuki Hirano, Manabu Matsuoka Jan 2013

Finite Rings And Wilson's Theorem, Yasuyuki Hirano, Manabu Matsuoka

Turkish Journal of Mathematics

In this paper we consider the product of all elements in the group of units in a finite ring and we generalize Wilson's theorem to finite rings. As an application, we study some generalizations of Wilson's theorem on residually finite Dedekind domains. And we also give some examples for such rings. Moreover we study some generalizations of Wilson's theorem on rings of matrices over a finite commutative ring.


On Theta Pair For A Proper Subalgebra, Ali Reza Salemkar, Sara Chehrazi, Hamid Mohammadzadeh Jan 2013

On Theta Pair For A Proper Subalgebra, Ali Reza Salemkar, Sara Chehrazi, Hamid Mohammadzadeh

Turkish Journal of Mathematics

For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a \theta-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and for each proper subalgebra C/B of A/B which is an ideal of L/B, we have L\neq C+K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.


C.P. Modules And Their Applications, Qiongling Liu, Jianlong Chen Jan 2013

C.P. Modules And Their Applications, Qiongling Liu, Jianlong Chen

Turkish Journal of Mathematics

Let R be a ring. A left R-module M is called a c.p. module if every cyclic submodule of M is projective. This notion is a generalization of left p.p. rings in the general module theoretic setting. The aim of this article is to investigate these modules. Some characterizations and properties are given. As applications, the connections among Baer rings, p.p. rings and von Neumann regular rings are studied.


Integral Polytopes And Polynomial Factorization, Fati̇h Koyuncu Jan 2013

Integral Polytopes And Polynomial Factorization, Fati̇h Koyuncu

Turkish Journal of Mathematics

For any field F, there is a relation between the factorization of a polynomial f \in F[x_1,...,x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x_1,...,x_n] where R is any ring containing some elements which are not zero-divisors. Moreover, we have constructed some new families of integrally indecomposable polytopes in \mb giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.


A Nonlocal Parabolic Problem In An Annulus For The Heaviside Function In Ohmic Heating, Fei Liang, Hongjun Gao, Charles Bu Jan 2013

A Nonlocal Parabolic Problem In An Annulus For The Heaviside Function In Ohmic Heating, Fei Liang, Hongjun Gao, Charles Bu

Turkish Journal of Mathematics

In this paper, we consider the nonlocal parabolic equation u_t=\Delta u+\frac{\lambda H(1-u)}{\big(\int_{A_{\rho, R}} H(1-u)dx\big)^2}, x\in A_{\rho, R} \subset R^2, t>0, with a homogeneous Dirichlet boundary condition, where \lambda is a positive parameter, H is the Heaviside function and A_{\rho, R} is an annulus. It is shown for the radial symmetric case that: there exist two critical values \lambda_* and \lambda^*, so that for 0


Approximation By Iterates Of Beta Operators, Purshottam Narain Agrawal, Karunesh Kumar Singh, Vikas Kumar Mishra Jan 2013

Approximation By Iterates Of Beta Operators, Purshottam Narain Agrawal, Karunesh Kumar Singh, Vikas Kumar Mishra

Turkish Journal of Mathematics

In this paper, we study the degree of approximation by an iterative combination T_{n,k} of the beta operators introduced by Upreti [8].


On Characterization And Stability Of Alternate Dual Of G-Frames, Ali Akbar Arefijamaal, Soheila Ghasemi Jan 2013

On Characterization And Stability Of Alternate Dual Of G-Frames, Ali Akbar Arefijamaal, Soheila Ghasemi

Turkish Journal of Mathematics

One of the essential applications of frames is that they lead to expansions of vectors in the underlying Hilbert space in terms of the frame elements. In this decomposition, dual frames have a key role. G-frames, introduced by Sun, cover many other recent generalizations of frames. In this paper, we give some characterizations of dual g-frames. Moreover, we prove that if two g-frames are close to each other, then we can find duals of them which are close to each other.


Scalar Curvature And Symmetry Properties Of Lightlike Submanifolds}, Cyriaque Atindogbe, Oscar Lungiambudila, Joel Tossa Jan 2013

Scalar Curvature And Symmetry Properties Of Lightlike Submanifolds}, Cyriaque Atindogbe, Oscar Lungiambudila, Joel Tossa

Turkish Journal of Mathematics

In this paper, the induced Ricci tensor and the extrinsic scalar curvature on lightlike submanifolds are obtained. This scalar quantity extend the result given by C. Atindogbe in [1]. An example of extrinsic scalar curvature on one class of 2-degenerate manifolds is provided. We investigate lightlike submanifolds which are locally symmetric, semi-symmetric, Ricci semi-symmetric in indefinite spaces form. In the coisotropic case, we show that, under some conditions, these lightlike submanifolds are totally geodesic.


Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n Jan 2013

Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we first define the concept of paracontact semi-Riemannian submersions between almost paracontact metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost paracontact structure of the total manifold. The study is focused on fundamental properties and the transference of structures defined on the total manifold. Moreover, we obtain various properties of the O'Neill's tensors for such submersions and find the integrability of the horizontal distribution. We also find necessary and sufficient conditions for a paracontact semi-Riemannian submersion to be totally geodesic. Finally, …