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Geodesics In A Tensor Bundle, Abdullah Kopuzlu, Ari̇f A. Salimov
Geodesics In A Tensor Bundle, Abdullah Kopuzlu, Ari̇f A. Salimov
Turkish Journal of Mathematics
The main purpose of the present paper is to study geodesics in a tensor bundle T^{p}_q(M_n) with respect to the horizontal lift ^H\nabla of an affine connection \nabla .
A Stone's Representation Theorem And Some Applications, Eissa D. Habil
A Stone's Representation Theorem And Some Applications, Eissa D. Habil
Turkish Journal of Mathematics
In this paper, we prove the following form of Stone's representation theorem: Let \sum be a \sigma-algebra of subsets of a set X. Then there exists a totally disconnected compact Hausdorff space {\cal K} for which (\sum, \cup, \cap) and ({\cal C}({\cal K}), \cup ,\cap), where {\cal C}({\cal K}) denotes the set of all clopen subsets of {\cal K}, are isomorphic as Boolean algebras. Furthermore, by defining appropriate joins and meets of countable families in {\cal C}({\cal K}), we show that such an isomorphism preserves \sigma-completeness. Then, as a consequence of this result, we obtain the result that if ba(X,\sum) …
Univalent Harmonic Mappings Onto Half Planes, Meti̇n Öztürk
Univalent Harmonic Mappings Onto Half Planes, Meti̇n Öztürk
Turkish Journal of Mathematics
We consider the class S_H(D,\Omega ) of complex functions f which are univalent, harmonic, sense preserving on a simple connected domain D\neq {\Bbb C} \ containing the origin, satisfy f(0)=a_0, f_{\bar z}(0)=0a,\ a\in {\Bbb R}\}. In particularly, we describe the closure \overline{S_H(D,\Omega )} of S_H(D,\Omega ) and characterize its extreme points, as well as sharp estimates for coefficients and distortion theorems.
Criteria Of Le Page Type In Involutive Banach Algebras, Abdellah El Kinani, Mohamed Oudadess
Criteria Of Le Page Type In Involutive Banach Algebras, Abdellah El Kinani, Mohamed Oudadess
Turkish Journal of Mathematics
The Le Page inequality in Banach algebras is \parallel xy \parallel\leq\alpha\parallel yx\parallel. We consider inequalities where a linear involution appears and has consequences on the involution itself and commutativity results.^1
Segal Algebra As An Ideal In Its Second Dual Space, Heybet S. Mustafayev
Segal Algebra As An Ideal In Its Second Dual Space, Heybet S. Mustafayev
Turkish Journal of Mathematics
For a locally compact group G, let S(G) be a symmetric Segal algebra. We prove that S(G) is an ideal in its second dual space if and only if G is compact, where the second dual is equipped with an Arens multiplication.
Some Results On Space-Like Line Congruences And Their Space-Like Parameter Ruled Surface, E. Özyilmaz
Some Results On Space-Like Line Congruences And Their Space-Like Parameter Ruled Surface, E. Özyilmaz
Turkish Journal of Mathematics
Using dual vectors, space-like ruled surfaces was introduced in [2]. In this paper, we define space-like line congruence and their space-like parameter ruled surfaces {\mathbf R_{11}(t)} and {\mathbf R_{21}(t)} of R_1^3. Then, by choosing space-like parameter ruled surfaces as space-like principle ruled surfaces, we obtain some relations among the magnitudes of space-like ruled surfaces {\mathbf R_1(t)}, {\mathbf R_{11}(t)}.
Cycloidal Normal Subgroups Of Hecke Groups Of Finite Index, İsmai̇l Naci̇ Cangül, Osman Bi̇zi̇m
Cycloidal Normal Subgroups Of Hecke Groups Of Finite Index, İsmai̇l Naci̇ Cangül, Osman Bi̇zi̇m
Turkish Journal of Mathematics
Cycloidal normal subgroups, that is, subgroups with only one cusp, of finite index of Hecke groups, which have been introduced by E. Hecke, and can be thought of as some kind of generalisation of the well-known modular group, are studied. It is shown that they correspond to cyclic quotients of Hecke groups and therefore have non-compact associated Riemann surfaces with a cusp. Finally, their total number have been formulated.
Augmented Noetherian Graded Modules, Mashhoor Refai̇
Augmented Noetherian Graded Modules, Mashhoor Refai̇
Turkish Journal of Mathematics
Let $G$ be a multiplicative group with identity $e$, and let $R$ be an associative $G$-graded ring with unity 1. In this paper we study the augmented graded Noetherian modules and try to give some relationships between the Noetherian modules in the category $R-Agr$ and the Noetherian modules in the category $R_e-gr$.
Generalized Solutions Of A Class Of Linear And Quasi-Linear Degenerated Hyperbolic Equations, Rossitza Semerdjieva
Generalized Solutions Of A Class Of Linear And Quasi-Linear Degenerated Hyperbolic Equations, Rossitza Semerdjieva
Turkish Journal of Mathematics
The equation $L(u):=k(y)u_{xx}-\partial_y(\ell(y)u_y)+r(x,y)u=f(x,y,u),$ where $k(y)>0, \ell(y)>0$ for $y>0,k(0)=\ell(0)=0$ and $lim_{y\rightarrow 0}k(y)/\ell(y)$ exists, is strictly hyperbolic for $y>0$ and its order degenerates on the line $y=0$. We consider the boundary value problem $Lu=f(x,y,u)$ in $G, u\mid_{AC}=0$, where $G$ is a simply connected domain in $R^2$ with piecewise smooth boundary $\partial G=AB\cup AC\cup BC; AB=\{(x,0): 0\leq x\leq 1\}, AC : x=F(y) =\int_0^y(k(t)/\ell (t))^{1/2}dt$ and $BC: x=1-F(y)$ are characteristic curves. The existence and uniqueness of a generalized solution to this problem are proved in the linear case (where $f=f(x,y));$ the nonlinear case is treated by using the Schauder Fixed …
The Isometries Of The Bochner Space L^P(\Mu,H), Bahatti̇n Cengi̇z
The Isometries Of The Bochner Space L^P(\Mu,H), Bahatti̇n Cengi̇z
Turkish Journal of Mathematics
In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(\mu, H)$, for a $\sigma$-finite measure $\mu$ and an arbitrary Hilbert space $H$, in terms of regular set isomorphisms of the $\sigma$-algebra involved and strongly measurable families of surjective isometries of $H$, is extended to arbitrary measures.
Structure Of M-Dimensional Implicitly Defined Surfaces In N-Dimensional Euclidean Space E_N, Alla Borisovna Kotlyar
Structure Of M-Dimensional Implicitly Defined Surfaces In N-Dimensional Euclidean Space E_N, Alla Borisovna Kotlyar
Turkish Journal of Mathematics
We consider the structure of the surface in the given point, if we vary all its normals in this point.
Modular Symmetry Classes Of Tensors, M. Shahryari, M. A. Shahabi
Modular Symmetry Classes Of Tensors, M. Shahryari, M. A. Shahabi
Turkish Journal of Mathematics
We introduce the notion of modular symmetry classes of tensors and give a necessary and sufficient condition for a modular symmetry class of tensors associated with the full symmetric group to be non-zero. Then we use modular symmetry classes of tensors to study the polynomial representations of $GL(V)$, where $V$ is a vector space over a field of characterisitic $p$. At the end we introduce a non-degenerate bilinear form on a modular symmetry class. Some problems are also given.
Two Lemmas On Formal Power Series, Kazim İlhan İkeda, Masatoshi İkeda
Two Lemmas On Formal Power Series, Kazim İlhan İkeda, Masatoshi İkeda
Turkish Journal of Mathematics
Let $L$ be a local field and $\tilde{L}$ the completion of the maximal unramified extension of $L$. In this short note, we prove \noindent (I) the sequences \noindent (1$^{\prime\prime}$) $0\rightarrow {\cal O}_L$[[$X_1,\ldots,X_n$]]$\rightarrow{\cal O}_{\tilde{L}}$[[$X_1,\ldots,X_n$]] $\stackrel{\phi_L-1}{\ra}{\cal O}_{\tilde{L}}$[[$X_1,\ldots,X_n$]]$\rightarrow 0$ \noindent and \noindent (2$^{\prime\prime}$) $1\rightarrow {\cal O}_L$[[$X_1,\ldots,X_n$]]$^x\rightarrow{\cal O}_{\tilde{L}}$[[$X_1,\ldots,X_n$]] $^x\stackrel{\phi_L-1}{\ra}{\cal O}_{\tilde{L}}$[[$X_1,\ldots,X_n$]]$\rightarrow 1$ \noindent are exact, where $\theta_L$ is the Frobenius automorphism over $L$ applied on the coefficients of ${\cal O}_{\tilde{L}}$[[$X_1,\ldots, X_n$]], and $\theta_L-1$ respectively denotes the mapping $\alpha\mapsto\alpha^{\theta L}-\alpha$ for \noindent (1$^{\prime\prime}$) and $\epsilon\mapsto\frac{\epsilon^{\phi}L}{\epsilon}$ for (2$^{\prime\prime}$); \noindent (II) ${\cal C}^{\circ}(\tilde{L},h)$ being the group the Coleman power series of degree 0, the sequence $$ 1\rightarrow {\cal …
A Class Of Banach Algebras Whose Duals Have The Schur Property, H. Mustafayev, A. Ülger
A Class Of Banach Algebras Whose Duals Have The Schur Property, H. Mustafayev, A. Ülger
Turkish Journal of Mathematics
Call a commutative Banach algebra $A$ a $\gamma$-algebra if it contains a bounded group $\Gamma$ such that $\overline{aco(\Gamma)}$ contains a multiple of the unit ball of $A$. In this paper, first by exhibiting several concrete examples, we show that the class of $\gamma$-algebras is quite rich. Then, for a $\gamma$-algebra $A$, we prove that $A^{\star}$ has the Schur property iff the Gelfand spectrum $\sum$ of $A$ is scattered iff $A^{\star}=ap(A)$ iff $A^{\star}=\overline{Span(\sum)}$.
Masatoshi Gündüz İkeda, Mehpare Bi̇lhan
Masatoshi Gündüz İkeda, Mehpare Bi̇lhan
Turkish Journal of Mathematics
No abstract provided.
The Weight Equations For Binary Linear Codes, Ersan Akyildiz, İsmai̇l Ş. Güloğlu, Masatoshi Ikeda
The Weight Equations For Binary Linear Codes, Ersan Akyildiz, İsmai̇l Ş. Güloğlu, Masatoshi Ikeda
Turkish Journal of Mathematics
The system of weight equations for a binary $(n, m)$-code with respect to its ordered basis is introduced. It connects certain quantities (characteristics) related to the basis with the weights of non-zero words in the code. It is shown that the portion involving the variables does not depend neither on the code nor on the basis. Explicit forms of the matrix of coefficients in the system and its inverse matrix are computed.
A Survey On Drinfeld Modular Forms, Ernst-Ulrich Gekeler
A Survey On Drinfeld Modular Forms, Ernst-Ulrich Gekeler
Turkish Journal of Mathematics
No abstract provided.
On The Artin Conductor F_{Artin}(\Chi) Of A Character \Chi Of Gal (E/K) I: Basic Definitions, Kazim İlhan İkeda
On The Artin Conductor F_{Artin}(\Chi) Of A Character \Chi Of Gal (E/K) I: Basic Definitions, Kazim İlhan İkeda
Turkish Journal of Mathematics
Let $K$ be a local field with finite residue class field and $E$ a finite Galois extension over $K$. In this paper, we study the Artin conductor $\frak f_{\rm Artin}(\chi_\rho)$ of a character $\chi_\rho$ associated to a representation $\rho:\mbox{Gal}(E/K)\rightarrow GL(V)$ of $\mbox{Gal}(E/K)$ with metabelian kernel $\mbox{ker}(\rho)$. In order to do so, we first review the Artin character $a_{\mbox{Gal}(E/K)}$ of $\mbox{Gal}(E/K)$ and review the metabelian local class field theory. We finally propose the definition of the conductor $\frak f(E/K)$ of a metabelian extension $E/K$ in the sense of Koch-de Shalit local class field theory, and compute $\frak f_{\rm Artin}(\chi_\rho)$ under a …
The Projectivity Of The Fundamental Group Of An Affine Line, Moshe Jarden
The Projectivity Of The Fundamental Group Of An Affine Line, Moshe Jarden
Turkish Journal of Mathematics
No abstract provided.
On The Asymptotic Behavior Of Heegner Points, Jan Nekovar, Norbert Schappacher
On The Asymptotic Behavior Of Heegner Points, Jan Nekovar, Norbert Schappacher
Turkish Journal of Mathematics
We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modular Jacobian variety $J_0(N)$) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.
Shafarevich-Tate Set For Y^4 = X^4 _ L^2, Takashi Ono
Shafarevich-Tate Set For Y^4 = X^4 _ L^2, Takashi Ono
Turkish Journal of Mathematics
No abstract provided.
On Generalized Shioda - Inose Structures, H. Önsi̇per, Si̇nan Sertöz
On Generalized Shioda - Inose Structures, H. Önsi̇per, Si̇nan Sertöz
Turkish Journal of Mathematics
No abstract provided.
Weak Localization In Disordered Two-Dimensional Crystals With Half-Filled Band, E.P. Nakhmedov, T. Kaya
Weak Localization In Disordered Two-Dimensional Crystals With Half-Filled Band, E.P. Nakhmedov, T. Kaya
Turkish Journal of Physics
Effect of subtitutional impurities on electron localization in two dimensional (2D) lattice near the middle of the band is studied. Calculation of density of the electronic states, \rho (\varepsilon ), increases logaritmically in the middle of the band. This singularity in the density of states of noninteracting electron gas on lattice gives rise to anomalous dependencies of thermodynamic quantities on the temperature. The quantum correction to the conductivity of a nonintreracting electron gas due to Umklapp electron--impurity scattering is calculated. This correction to the conductivity is shown to compete with that from the localization corrrection for a Normal scattering process. …