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Quasi-Dual Modules, M. Tamer Koşan Jan 2006

Quasi-Dual Modules, M. Tamer Koşan

Turkish Journal of Mathematics

Let R be a ring, M be a right R-module and S = End_R(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of r_M(X) where X \subseteq S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m \in M, r_M \ell_S(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(_SM) \subseteq Rad (M_R).


On Uniform Hermitian P-Normed Algebras, A. El-Kinani Jan 2006

On Uniform Hermitian P-Normed Algebras, A. El-Kinani

Turkish Journal of Mathematics

We show that the completion of a uniform hermitian p-normed algebra is a commutative C^*-algebra.


A Survey On The Distribution Of B-Free Numbers, Emre Alkan, Alexandru Zaharescu Jan 2006

A Survey On The Distribution Of B-Free Numbers, Emre Alkan, Alexandru Zaharescu

Turkish Journal of Mathematics

In this paper we present a survey of recent progress on the distribution of B-free numbers in short intervals and some of its applications.


Existence Of Linear-Quadratic Regulator For Degenerate Diffusions, Md. Azizul Baten Jan 2006

Existence Of Linear-Quadratic Regulator For Degenerate Diffusions, Md. Azizul Baten

Turkish Journal of Mathematics

This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation.


Diagonal Lift In The Tangent Bundle Of Order Two And Its Applications, Fouzi Hathout, H. M. Dida Jan 2006

Diagonal Lift In The Tangent Bundle Of Order Two And Its Applications, Fouzi Hathout, H. M. Dida

Turkish Journal of Mathematics

In this paper we define a diagonal lift ^{D}g of Riemannian metric g of manifold M_n to the tangent bundle of order two denoted by T^{2}M_n of M_n, we associate to ^{D}g its Levi-civita connection of T^2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.


Remarks About Some Weierstrass Type Results, Mihai Turinici Jan 2006

Remarks About Some Weierstrass Type Results, Mihai Turinici

Turkish Journal of Mathematics

The Weierstrass type results of Gajek and Zagrodny [7] are not in general retainable in the precise context. Our first aim in this exposition is to show that a completion of the imposed conditions may be offered so that these results be true. As a second aim, alternate proofs of the statements in question are performed, via ordering principles comparable with the one in Brezis and Browder [3].


A Fractal Example Of A Continuous Monotone Function With Vanishing Derivatives On A Dense Set And Infinite Derivatives On Another Dense Set, Bünyami̇n Demi̇r, Vakif Dzhafarov, Şahi̇n Koçak, Mehmet Üreyen Jan 2006

A Fractal Example Of A Continuous Monotone Function With Vanishing Derivatives On A Dense Set And Infinite Derivatives On Another Dense Set, Bünyami̇n Demi̇r, Vakif Dzhafarov, Şahi̇n Koçak, Mehmet Üreyen

Turkish Journal of Mathematics

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on another dense set. Although such examples could be constructed by classical means of probability and measure theory, this one is more elementary and emerges naturally as a byproduct of some new fractal constructions.


Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal Jan 2006

Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal

Turkish Journal of Mathematics

We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.


Quasi Separation Axioms, Mohammad S. Sarsak Jan 2006

Quasi Separation Axioms, Mohammad S. Sarsak

Turkish Journal of Mathematics

In [5], Maheshwari et al. introduced and studied some new separation axioms, namely, quasi semi T_i axioms where i \in {0, 1, 2}, the quasi semi T_{1/2} axiom was then introduced and investigated by Gyu-Ihn et al. in [2]. In the present paper we introduce and study quasi T_i axioms, i \in {0, 1 / 2, 1, 2} as a special variety of quasi semi T_i axioms, the class of quasi T_{1/2} (respectively, quasi T_1) bitopological spaces is placed between quasi T_0 (respectively, quasi T_{1/2}) bitopological spaces and quasi T_1 (respectively, quasi T_2) bitopological spaces. Among several counter examples we …


P-Elastica In The 3-Dimensional Lorentzian Space Forms, Nevi̇n Gürbüz Jan 2006

P-Elastica In The 3-Dimensional Lorentzian Space Forms, Nevi̇n Gürbüz

Turkish Journal of Mathematics

R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature [1]. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms


Inequality For Ricci Curvature Of Slant Submanifolds In Cosymplectic Space Forms, Dae Won Yoon Jan 2006

Inequality For Ricci Curvature Of Slant Submanifolds In Cosymplectic Space Forms, Dae Won Yoon

Turkish Journal of Mathematics

In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifold in a cosymplectic space form of constant \varphi-sectional curvature with arbitrary codimension.


Existence Of Periodic Solutions For Second Order Rayleigh Equations With Piecewise Constant Argument, Gen-Qiang Wang, Sui Sun Cheng Jan 2006

Existence Of Periodic Solutions For Second Order Rayleigh Equations With Piecewise Constant Argument, Gen-Qiang Wang, Sui Sun Cheng

Turkish Journal of Mathematics

Based on a continuation theorem of Mawhin, periodic solutions are found for the second-order Rayleigh equation with piecewise constant argument.


A Connected Sum Of Knots And Fintushel-Stern Knot Surgery On 4-Manifolds, Manabu Akaho Jan 2006

A Connected Sum Of Knots And Fintushel-Stern Knot Surgery On 4-Manifolds, Manabu Akaho

Turkish Journal of Mathematics

We give some new examples of smooth 4-manifolds which are diffeomorphic although they are obtained by Fintushel-Stern knot surgeries on a smooth 4-manifold with different knots; the first such examples are given by Akbulut [1]. In the proof we essentially use the monodromy of a cusp.


On Irregular Semi Strong P-Adic U Numbers, Hülya Duru Jan 2006

On Irregular Semi Strong P-Adic U Numbers, Hülya Duru

Turkish Journal of Mathematics

The concept of the ``relation of comparability'' was introduced by Maillet in [7], who showed that if \alpha,\beta are comparable Liouville numbers then each of the numbers \alpha +\beta, \alpha -\beta, \alpha \beta and \alpha /\beta is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and to \alpha and \beta. Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, …


On Finitary Permutation Groups, Ali̇ Osman Asar Jan 2006

On Finitary Permutation Groups, Ali̇ Osman Asar

Turkish Journal of Mathematics

In this work we give some sufficient conditions under which the structure of a transitive group of finitary permutations on an infinite set can be determined from the structure of a point stabilizer. Also, we give some sufficient conditions for the existence of a proper subgroup having an infinite orbit in a totally imprimitive p-group of finitary permutations. These results, with the help of some known results, give sufficient conditions for the nonexistence of a perfect locally finite minimal non FC - (p-group).


On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain Jan 2006

On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain

Turkish Journal of Mathematics

In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.


On The Power Subgroups Of The Extended Modular Group \Overline{\Gamma} (Corrigendum - Turk. J. Math. 28,143-151, 2004), Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu Jan 2006

On The Power Subgroups Of The Extended Modular Group \Overline{\Gamma} (Corrigendum - Turk. J. Math. 28,143-151, 2004), Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu

Turkish Journal of Mathematics

No abstract provided.


Finite Groups All Of Whose Abelian Subgroups Of Equal Order Are Conjugate, Sezgi̇n Sezer, Robert W. Van Der Waall Jan 2006

Finite Groups All Of Whose Abelian Subgroups Of Equal Order Are Conjugate, Sezgi̇n Sezer, Robert W. Van Der Waall

Turkish Journal of Mathematics

In this paper we classify the finite groups whose abelian subgroups of equal order (B^*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B^*-groups, provided in the course of the paper.


On Certain Modified Meyer-König And Zeller Operators, Lucyna Rempulska, Karolina Tomczak Jan 2006

On Certain Modified Meyer-König And Zeller Operators, Lucyna Rempulska, Karolina Tomczak

Turkish Journal of Mathematics

We introduce certain modified Meyer-König and Zeller operators and we study their approximation properties. The similar results for modified Bernstein polynomials were given in [6].


On Lifts Of Paracomplex Structures, Mehmet Tekkoyun Jan 2006

On Lifts Of Paracomplex Structures, Mehmet Tekkoyun

Turkish Journal of Mathematics

In this paper, we obtain vertical, complete and horizontal lifts of paracomplex geometric structures on paracomplex manifolds to its tangent bundle. Also, we obtain integrability on paracomplex tangent bundle.


Decompositions Of Continuity, Talal Al-Hawary, Ahmad Al-Omari Jan 2006

Decompositions Of Continuity, Talal Al-Hawary, Ahmad Al-Omari

Turkish Journal of Mathematics

In 2004, Al-Hawary and Al-Omari introduced and explored the class of \omega^o-open sets which is strictly stronger than the class of \omega-open sets and weaker than that of open sets. In this paper, we introduce what we call \omega^o-continuity and \omega_X^o-continuity and we give several characterizations and two decompositions of \omega ^o-continuity. Finally, new decompositions of continuity are provided.


Connectedness In Isotonic Spaces, Eissa D. Habil, Khalid A. Elzenati Jan 2006

Connectedness In Isotonic Spaces, Eissa D. Habil, Khalid A. Elzenati

Turkish Journal of Mathematics

An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X. Many properties which hold in topological spaces hold in isotonic spaces as well. The notion of connectedness that is familiar from topological spaces generalizes to isotonic spaces. We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.


The Restriction And The Continuity Properties Of Potentials Depending On \Lambda-Distance, M. Zeki̇ Sarikaya, Hüseyi̇n Yildirim Jan 2006

The Restriction And The Continuity Properties Of Potentials Depending On \Lambda-Distance, M. Zeki̇ Sarikaya, Hüseyi̇n Yildirim

Turkish Journal of Mathematics

In this study we establish theorems on the restriction and continuity of the generalized Riesz potentials with the non-isotropic kernels depending on \lambda-distance.


On Reduced And Semicommutative Modules, Muhi̇tti̇n Başer, Nazim Agayev Jan 2006

On Reduced And Semicommutative Modules, Muhi̇tti̇n Başer, Nazim Agayev

Turkish Journal of Mathematics

In this paper, various results of reduced and semicommutative rings are extended to reduced and semicommutative modules. In particular, we show: (1) For a principally quasi-Baer module, M_R is semicommutative if and only if M_R is reduced. (2) If M_R is a p.p.-module then M_R is nonsingular.


Two-Weight Norm Inequalities For Some Anisotropic Sublinear Operators, Yusuf Zeren, V. S. Guliyev Jan 2006

Two-Weight Norm Inequalities For Some Anisotropic Sublinear Operators, Yusuf Zeren, V. S. Guliyev

Turkish Journal of Mathematics

In this paper, we establish several general theorems for the boundedness of the anisotropic sublinear operators on a weighted Lebesgue space. Conditions of these theorems are satisfied by many important operators in analysis. We also give some applications the boundedness of the parabolic singular integral operators, and the maximal operators associated with them from one weighted Lebesgue space to another one. Using this results, we prove weighted embedding theorems for the anisotropic Sobolev spaces W_{\omega_0,\omega_1,...,\omega_n}^{l_1,...,l_n}(\Rn).


On Graded Weakly Prime Ideals, Shahabaddin Ebrahimi Atani Jan 2006

On Graded Weakly Prime Ideals, Shahabaddin Ebrahimi Atani

Turkish Journal of Mathematics

Let G be an arbitrary group with identity e, and let R be a G-graded commutative ring. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in [1]. Here we study the graded weakly prime ideals of a G-graded commutative ring. A number of results concerning graded weakly prime ideals are given. For example, we give some characterizations of graded weakly prime ideals and their homogeneous components.


Some Random Fixed Point Theorems For Non-Self Nonexpansive Random Operators, Poom Kumam, Somyot Plubtieng Jan 2006

Some Random Fixed Point Theorems For Non-Self Nonexpansive Random Operators, Poom Kumam, Somyot Plubtieng

Turkish Journal of Mathematics

Let (\Omega, \Sigma) be a measurable space, with \sum a sigma-algebra of subsets of \Omega, and let E be a nonempty bounded closed convex and separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1. We prove that a multivalued nonexpansive, non-self operator T: \Omega \times E \rightarrow KC(X) satisfying an inwardness condition and itself being a 1-\chi-contractive nonexpansive mapping has a random fixed point. We also prove that a multivalued nonexpansive, non-self operator T:\Omega\times E\rightarrow KC(X) with a uniformly convex X satisfying an inwardness condition has a random fixed point.


Note On Generalized Jordan Derivations Associate With Hochschild 2-Cocycles Of Rings, Atsushi Nakajima Jan 2006

Note On Generalized Jordan Derivations Associate With Hochschild 2-Cocycles Of Rings, Atsushi Nakajima

Turkish Journal of Mathematics

We introduce a new type of generalized derivations associate with Hochschild 2-cocycles and prove that every generalized Jordan derivation of this type is a generalized derivation under certain conditions. This result contains the results of I. N. Herstein [6, Theorem 3.1] and M. Ashraf and N-U. Rehman [1, Theorem].


Weighted Norm Inequalities For A Class Of Rough Maximal Operators, Hussain Al-Qassem Jan 2006

Weighted Norm Inequalities For A Class Of Rough Maximal Operators, Hussain Al-Qassem

Turkish Journal of Mathematics

We consider maximal singular integral operators arising from rough kernels satisfying an H^1-type condition on the unit (n-1)-sphere and prove weighted L^p estimates for certain radial weights. We also prove weighted L^p estimates with A_p-weights where in this case the H^1 -type condition is replaced by an L^q-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.


Local Fourier Bases And Modulation Spaces, Salti Samarah, Rania Salman Jan 2006

Local Fourier Bases And Modulation Spaces, Salti Samarah, Rania Salman

Turkish Journal of Mathematics

It is shown that local Fourier bases are unconditional bases for modulation spaces. We prove first a version of the Schur test for double sequence with mixed norm and then use it to show boundedness of the analysis operator on the modulation space M_{p,q}^w