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New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi
New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi
Turkish Journal of Mathematics
We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylindrical helices. One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are straight forward and classical. However, there have been no papers …
Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci
Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci
Turkish Journal of Mathematics
This article introduces the concept of a \tau-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor \tau, we say that a module M is \tau-supplemented when for every submodule N of M there exists a direct summand K of M such that K\leq N and N/K is \tau-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of \tau-supplemented modules under certain conditions on modules. The question of which direct sum of \tau-supplemented R-modules are \tau-supplemented is treated here.
Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith
Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith
Turkish Journal of Mathematics
Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For example, if G is torsion-free and locally soluble-by-finite then either G has finite 0-rank or G is nilpotent. Several results are obtained on soluble (respectively, locally soluble-by-finite) groups satisfying the stated hypothesis on subgroups.
On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş
On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş
Turkish Journal of Mathematics
In this paper, we present some results concerning two generalized derivations on a semiprime ring. These results are a generalization of results of M. Bre\u{s}ar and J. Vukman in [2], which are related to a theorem of E. Posner for the product of derivations on a prime ring.
On Near-Rings With Two-Sided \Alpha-Derivations, Nurcan Argaç
On Near-Rings With Two-Sided \Alpha-Derivations, Nurcan Argaç
Turkish Journal of Mathematics
In this paper, we introduce the notion of two-sided \alpha-derivation of a near-ring and give some generalizations of [1]. Let N be a near ring. An additive mapping f: N\rightarrow N is called an { \it (\alpha, \beta)-derivation } if there exist functions \alpha,\beta : N\rightarrow N such that f(xy)=f(x)\alpha(y)+\beta (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is called a two-sided \alpha-derivation if d is an (\alpha,1)-derivation as well as a (1,\alpha)-derivation. The purpose of this paper is to prove the following two assertions: (i) Let N be a semiprime near-ring, I be a subset of N …
Ideal Theory In Topological Algebras, A. Najmi
Ideal Theory In Topological Algebras, A. Najmi
Turkish Journal of Mathematics
Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.
On Simultaneous Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali J. Mohammad
On Simultaneous Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali J. Mohammad
Turkish Journal of Mathematics
In [1] we introduced a new sequence of linear positive operators M_{n} to approximate unbounded continuous functions of exponential growth on [0,\infty). As this sequence is saturated with O(n^{-1}), to accelerate the rate of convergence we applied the technique of linear combination introduced by May [3] and Rathore et al. [4] to these operators. The object of the present paper is to study the phenomena of simultaneous approximation (approximation of derivatives of functions by the corresponding order derivatives of operators) by the linear combination M_{n} ( . , k, x) of M_{n}. First, we establish a Voronovskaja-type asymptotic formula and …
Coisotropic Submanifolds Of A Semi-Riemannian Manifold, Erol Kiliç, Bayram Şahi̇n, H. B. Karadağ, R. Güneş
Coisotropic Submanifolds Of A Semi-Riemannian Manifold, Erol Kiliç, Bayram Şahi̇n, H. B. Karadağ, R. Güneş
Turkish Journal of Mathematics
In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on Ricci tensor of a coisotropic submanifold to be symmetric. Finally, we present some new theorems and results about totally umbilical coisotropic submanifolds of a semi-Riemannian manifold
F-Invariant Submanifolds Of Kaehlerian Product Manifold, Mehmet Atçeken
F-Invariant Submanifolds Of Kaehlerian Product Manifold, Mehmet Atçeken
Turkish Journal of Mathematics
In this paper, the geometry of F-invariant submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic submanifold and locally decomposable Riemannian product manifold.
A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen
A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen
Turkish Journal of Mathematics
The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, then G is nilpotent.
On Local Hörmander-Beurling Spaces, Jairo Villegas
On Local Hörmander-Beurling Spaces, Jairo Villegas
Turkish Journal of Mathematics
In this paper we aim to extend a result of Hörmander's, that \mathcal{B}_{p,k}^{loc}(\Omega)\subset\mathcal{C}^m(\Omega) if \frac{(1+\left \cdot\right )^m}{k}\in L_{p^\prime}, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space \bigcap_{j=1}^\infty\mathcal{B}_{p_j,k_j}^{loc} (\Omega, E) (1\leq p_j\leq\infty, k_j=e^{j\omega}, j=1,2,\dots) is topologically isomorphic to \mathcal{E}_\omega(\Omega, E ). Moreover, it is well known that the union of Sobolev spaces \mathcal{H}_{s}^{loc}(\Omega) (=\mathcal{B}_{2,(1+ \cdot ^2)^{s/2}}^{loc}(\Omega)) coincides with the space \mathcal{D}^{\prime\,F}(\Omega) of finite order distributions on \Omega. We show that this is also verified in the context of vector valued Beurling ultradistributions.
On A Certain Class Of Bessel Integrals, Ali A. Al-Jarrah, A. Al-Momani
On A Certain Class Of Bessel Integrals, Ali A. Al-Jarrah, A. Al-Momani
Turkish Journal of Mathematics
There are many old results of integrals involving Bessel functions, currently available in handbooks, but we found no recourse in the well-known references to how they were established. In this paper, we attempt to have a clear way of proving some of these results. In fact, we consider a certain class of Bessel integrals where we prove that such integrals vanish under certain conditions. To this end some theorems regarding this class of integrals with their proofs are put forward. A computer algorithm is provided to implement some of our results. The result in this paper extend the work in …
A Note On Groups With All Subgroups Subnormal, Ahmet Arikan, Tahi̇re Özen
A Note On Groups With All Subgroups Subnormal, Ahmet Arikan, Tahi̇re Özen
Turkish Journal of Mathematics
We prove that if G is a periodic group with all subgroups subnormal, and if for every x, y \in G, ^{G} is an FC-group, then G is nilpotent.
Uniqueness Of Primary Decompositions, Patrick F. Smith
Uniqueness Of Primary Decompositions, Patrick F. Smith
Turkish Journal of Mathematics
Uniqueness properties of primary decompositions in modules over non-commutative rings are presented.
Professor Masatoshi Gündüz Ikeda: A Life Devoted To Mathematics, Cemal Koç
Professor Masatoshi Gündüz Ikeda: A Life Devoted To Mathematics, Cemal Koç
Turkish Journal of Mathematics
No abstract provided.
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
Turkish Journal of Mathematics
In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.
On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n
On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n
Turkish Journal of Mathematics
Hecke groups H(\lambda _q) have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group H(\lambda_3), the modular group PSL(2, \Bbb{Z} ) , has especially been of great interest in many fields of mathematics, for example number theory, automorphic function theory and group theory. In this paper we consider the extended Hecke groups \overline{H}(\lambda _q) which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in \overline{H}(\lambda _q). Using this we give some results about the normal subgroups and Fuchsian subgroups of \overline{H}(\lambda _q).
Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen
Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen
Turkish Journal of Mathematics
In this paper, we presented a brief review of crossed modules [7], cat^1-groups [6], pullback crossed modules [4], pullback cat^1-group [1], profinite crossed modules [5], cat^1-profinite groups [5], pullback profinite crossed modules [5], pullback cat^1-profinite groups [3]. We defined the pushout cat^1-profinite groups and gave the left adjoint constructions.
Shape Operator A_H For Slant Submanifolds In Generalized Complex Space Forms, Adela Mihai
Shape Operator A_H For Slant Submanifolds In Generalized Complex Space Forms, Adela Mihai
Turkish Journal of Mathematics
In this article, we establish an inequality between the sectional curvature function K and the shape operator A_H at the mean curvature vector for slant submanifolds in generalized complex space forms. Also a sharp relationship between the k-Ricci curvature and the shape operator A_H is proved.
Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah
Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah
Turkish Journal of Mathematics
In this paper, we study certain classes of oscillatory singular integral operators with kernels in Llog L(S^{n-1}) which is known to be the most desirable size condition for the L^{p} boundedness to hold. We prove that such operators are bounded on L^{p}. Our results extend and improve previously known results. Variations of our approach in this paper can be applied to handle more general oscillatory singular integral operators. This concludes by indicating a variety of results that can be obtained.
On General Fibonacci Sequences In Groups, Engi̇n Özkan
On General Fibonacci Sequences In Groups, Engi̇n Özkan
Turkish Journal of Mathematics
In this paper, we have constituted 3-step general Fibonacci sequences in a nilpotent group with exponent p (p is a prime number) and nilpotency class 4 and given formulas to find the \alpha term of the sequence.
Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem
Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem
Turkish Journal of Mathematics
We establish the L^p boundedness of singular integrals on product domains with rough kernels in L(log L)^2 and are supported by subvarieties.
Some Asymptotic Results For The Semi-Markovian Random Walk With A Special Barrier, Tahi̇r Khani̇yev
Some Asymptotic Results For The Semi-Markovian Random Walk With A Special Barrier, Tahi̇r Khani̇yev
Turkish Journal of Mathematics
In this study, the semi-Markovian random walk with a special barrier (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. Moreover, the characteristic function of ergodic distribution of X(t) is given by using a joint distribution of random variables N and Y_{N} and some exact formulas for the first and second moments of ergodic distribution of the process X(t) are obtained. Based on these results, the asymptotic behaviours of expectation and variance of this process are investigated as S-s \to \infty . It is finally proved that the ergodic distribution of the process is …
Boundary Points Of Self-Affine Sets In R, İbrahi̇m Kirat
Boundary Points Of Self-Affine Sets In R, İbrahi̇m Kirat
Turkish Journal of Mathematics
Let A be an n \times n expanding matrix with integer entries and D = \{0, d_1, ... , d_{N-1} \} \subseteq {\Bbb{Z}}^n be a set of N distinct vectors, called an N-digit set. The unique non-empty compact set T = T(A,D) satisfying AT = T + D is called a self-affine set. If T has positive Lebesgue measure, it is called a self-affine region. In general, it is not clear how to determine a point to be on the boundary of a self-affine region. In this note, we consider one-dimensional self-affine regions T and present a simple approach to …
On Lightlike Hypersurfaces Of A Semi-Riemannian Space Form, Rifat Güneş, Bayram Şahi̇n, Erol Kiliç
On Lightlike Hypersurfaces Of A Semi-Riemannian Space Form, Rifat Güneş, Bayram Şahi̇n, Erol Kiliç
Turkish Journal of Mathematics
In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric. Also, we show that a lightlike Hypersurface of IR_{4q}^{4m}(m,q > 1) is totally geodesic under some restrictions. Finally, we give some results on Ricci curvature of a lightlike hypersurface to be symmetric.