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Full-Text Articles in Physical Sciences and Mathematics
Generalization Of Some Properties Of Banach Algebras To Fundamental Locally Multiplicative Topological Algebras, Ali Zohri, Ali Jabbari
Generalization Of Some Properties Of Banach Algebras To Fundamental Locally Multiplicative Topological Algebras, Ali Zohri, Ali Jabbari
Turkish Journal of Mathematics
In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by FLM). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.
Hypercyclic Tuples Of The Adjoint Of The Weighted Composition Operators, Rahmat Soltani, Bahram Khani Robati, Karim Hedayatian
Hypercyclic Tuples Of The Adjoint Of The Weighted Composition Operators, Rahmat Soltani, Bahram Khani Robati, Karim Hedayatian
Turkish Journal of Mathematics
An n-tuple of commuting operators, (T_1,T_2,...,T_n) on a Hilbert space \cal H is said to be hypercyclic, if there exists a vector x \in \cal H such that the set {T_1^{k_1} T_2^{k_2}... T_n^{k_n}x : k_i \geq 0, i=1,2,...n} is dense in \cal H. In this paper, we give sufficient conditions under which the adjoint of an n-tuple of a weighted composition operator on a Hilbert space of analytic functions is hypercyclic.
Generalized Berwald Metrics, Esmaeil Peyghan, Akbar Tayebi
Generalized Berwald Metrics, Esmaeil Peyghan, Akbar Tayebi
Turkish Journal of Mathematics
In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric. Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.
Bruhat-Chevalley Order On The Rook Monoid, Mahi̇r Bi̇len Can, Lex E. Renner
Bruhat-Chevalley Order On The Rook Monoid, Mahi̇r Bi̇len Can, Lex E. Renner
Turkish Journal of Mathematics
The rook monoid R_n is the finite monoid whose elements are the 0-1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of R_n is isomorphic to the symmetric group S_n. The natural extension to R_n of the Bruhat-Chevalley ordering on the symmetric group is defined in [1]. In this paper, we find an efficient, combinatorial description of the Bruhat-Chevalley ordering on R_n. We also give a useful, combinatorial formula for the length function on R_n.
Lower Bounds For The Maximum Genus Of 4-Regular Graphs, Ding Zhou, Rongxia Hao, Weili He
Lower Bounds For The Maximum Genus Of 4-Regular Graphs, Ding Zhou, Rongxia Hao, Weili He
Turkish Journal of Mathematics
This paper investigates the maximum genus and upper embeddability of connected 4-regular graphs. We obtain lower bounds on the maximum genus of connected 4-regular simple graphs and connected 4-regular graphs without loops in terms of the Betti number. The definition of the Betti number is referred to [Gross and Tucker, Topological Graph Theory, New York, 1987]. Furthermore, we give examples that show that these lower bounds are tight.
Multiplication Modules With Krull Dimension, Mahmood Behboodi, Maryam Molakarimi
Multiplication Modules With Krull Dimension, Mahmood Behboodi, Maryam Molakarimi
Turkish Journal of Mathematics
In ring theory, it is shown that a commutative ring R with Krull dimension has classical Krull dimension and satisfies k.dim(R)=cl.k.dim(R). Moreover, R has only a finite number of distinct minimal prime ideals and some finite product of the minimal primes is zero (see Gordon and Robson [9, Theorem 8.12, Corollary 8.14, and Proposition 7.3]). In this paper, we give a generalization of these facts for multiplication modules over commutative rings. Actually, among other results, we prove that if M is a multiplication R-module with Krull dimension, then: (i) M is finitely generated, (ii) R has finitely many minimal prime …
Essential Normality For Certain Weighted Composition Operators On The Hardy Space H^2, Mahsa Fatehi, Bahram Khani Robati
Essential Normality For Certain Weighted Composition Operators On The Hardy Space H^2, Mahsa Fatehi, Bahram Khani Robati
Turkish Journal of Mathematics
We characterize the essentially normal weighted composition operators C_{\psi,\varphi} on the Hardy space H^2, whenever \varphi is a linear-fractional transformation and \psi \in A(D). Also we investigate the essential normality problem for some other weighted composition operators on H^2.
On Similarity Of Powers Of Shift Operators, Masoumeh Faghih Ahmadi, Karim Hedayatian
On Similarity Of Powers Of Shift Operators, Masoumeh Faghih Ahmadi, Karim Hedayatian
Turkish Journal of Mathematics
Let M_z and B denote, respectively, the multiplication operator and the backward shift operator on a weighted Hardy space. We present sufficient conditions so that M_{z^n} is similar to \bigoplus_1^nM_z, and B^n is similar to \bigoplus_1^nB. The first part generalizes a result obtained by Yucheng Li.
An Identity Between The M-Spotty Weight Enumerators Of A Linear Code And Its Dual, İrfan Şi̇ap
An Identity Between The M-Spotty Weight Enumerators Of A Linear Code And Its Dual, İrfan Şi̇ap
Turkish Journal of Mathematics
The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. Here, we introduce the m-spotty weights and m-spotty weight enumerator of linear codes over the ring F_2+uF_2 and prove a MacWilliams type identity.
Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski
Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski
Turkish Journal of Mathematics
Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.
Invariants Of Symmetric Algebras Associated To Graphs, Maurizio Imbesi, Monica La Barbiera
Invariants Of Symmetric Algebras Associated To Graphs, Maurizio Imbesi, Monica La Barbiera
Turkish Journal of Mathematics
In this work we deal with the symmetric algebra of monomial ideals that arise from graphs, the edge ideals. The notion of s-sequence is explored for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.
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 …
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 …
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 …
Invariant Parametrizations And Complete Systems Of Global Invariants Of Curves In The Pseudo-Euclidean Geometry, Ömer Pekşen, Djavvat Khadjiev, İdri̇s Ören
Invariant Parametrizations And Complete Systems Of Global Invariants Of Curves In The Pseudo-Euclidean Geometry, Ömer Pekşen, Djavvat Khadjiev, İdri̇s Ören
Turkish Journal of Mathematics
Let M(n, p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E^n_p of index p generated by all pseudo-orthogonal transformations and parallel translations of E^n_p. Definitions of a pseudo-Euclidean type of a curve, an invariant parametrization of a curve and an M(n, p)-equivalence of curves are introduced. All possible invariant parametrizations of a curve with a fixed pseudo-Euclidean type are described. The problem of the M(n, p)-equivalence of curves is reduced to that of paths. Global conditions of the M(n, p)-equivalence of curves are given in terms of the pseudo-Euclidean type of a curve and the system …
Oscillation Of Third-Order Nonlinear Delay Difference Equations, Mustafa Fahri̇ Aktaş, Aydin Ti̇ryaki̇, Ağacik Zafer
Oscillation Of Third-Order Nonlinear Delay Difference Equations, Mustafa Fahri̇ Aktaş, Aydin Ti̇ryaki̇, Ağacik Zafer
Turkish Journal of Mathematics
Third-order nonlinear difference equations of the form \Delta (c_n\Delta (d_n\Delta x_n))+p_n\Delta x_{n+1}+q_nf(x_{n-\sigma})=0, n\geq n_{0} are considered. Here, {c_n}, {d_n}, {p_n}, and {q_n} are sequences of positive real numbers for n_0 \in N, f is a continuous function such that f(u) /u\geq K > 0 for u \neq 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.
On The Biharmonic Vector Fields, Mustapha Djaa, Hichem Elhendi, Seddik Ouakkas
On The Biharmonic Vector Fields, Mustapha Djaa, Hichem Elhendi, Seddik Ouakkas
Turkish Journal of Mathematics
The problem studied in this paper is related to the biharmonicity of a vector field from a Riemannian manifold (M,g) to its tangent bundle TM equipped with the Sasaki metric g^s. We show that a vector field on a compact manifold is biharmonic if and only if is harmonic. We also investigate the biharmonicity of vector field of M, as a map from (M,g) to (TM,g^s).
Structure Theory Of Central Simple Z_D-Graded Algebras, Cemal Koç, Yosum Kurtulmaz
Structure Theory Of Central Simple Z_D-Graded Algebras, Cemal Koç, Yosum Kurtulmaz
Turkish Journal of Mathematics
This paper investigates the structure theory of Z_d-central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of Z_d-central simple graded algebras.
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
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.
Hilbert Functions And Betti Numbers Of Reverse Lexicographic Ideals In The Exterior Algebra, Marilena Crupi, Carmela Ferro'
Hilbert Functions And Betti Numbers Of Reverse Lexicographic Ideals In The Exterior Algebra, Marilena Crupi, Carmela Ferro'
Turkish Journal of Mathematics
Let K be a field, V a K-vector space with basis e_1,...,e_n and let E be the exterior algebra of V. We study the class of reverse lexicographic ideals in E. We analyze the behaviour of their Hilbert functions and Betti numbers.
Uc Modules With Respect To A Torsion Theory, Seçi̇l Çeken, Mustafa Alkan
Uc Modules With Respect To A Torsion Theory, Seçi̇l Çeken, Mustafa Alkan
Turkish Journal of Mathematics
In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of \tau-closed submodule which was studied in [2]. We compare UC and \tau-UC modules and examine the relationships between them. We also give some examples of \tau-UC and UC modules and submodules which have a unique \tau-closure and unique closure.
Contact Cr-Warped Product Submanifolds In Generalized Sasakian Space Forms, Si̇bel Sular, Ci̇han Özgür
Contact Cr-Warped Product Submanifolds In Generalized Sasakian Space Forms, Si̇bel Sular, Ci̇han Özgür
Turkish Journal of Mathematics
We consider a contact CR-warped product submanifold M=M_{\top} \times_fM_{\bot} of a trans-Sasakian generalized Sasakian space form \widetilde{M} (f_1,f_2,f_3). We show that M is a contact CR-product under certain conditions.
Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi
Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi
Turkish Journal of Mathematics
Let R be a commutative Noetherian ring, M a finitely generated R-module, and N a minimax R-module. It is shown that if a is an ideal of R, such that cd(a)=1, where cd is the cohomological dimension of a in R, then H_a^j(M, N) and Ext_R^i(M,H_a^j(N)) are a-cominimax for all i,j. Furthermore, if t is a non-negative integer such that H_a^j(M, N) is a-minimax for all j
Extensions And S-Comparability Of Exchange Rings, Chaoling Huang
Extensions And S-Comparability Of Exchange Rings, Chaoling Huang
Turkish Journal of Mathematics
Let S be a ring extension of R. In this note, for any positive integer s we study s-comparability related to ring extensions. We show that if S is an excellent extension of R, R and S are exchange rings, and R has the n-unperforation property. R satisfies s-comparability if and we only if so does S, and we prove that for a 2-sided ideal J of S, and an exchange subring R of the exchange ring S, which contains J as a direct summand, then R satisfies s-comparability if and only if so does R/J.
P-Rank And P-Groups In Algebraic Groups, Adrien Deloro
P-Rank And P-Groups In Algebraic Groups, Adrien Deloro
Turkish Journal of Mathematics
A few remarks on the measures of the p-rank of a group equipped with a dimension, including the refutation of a result of Burdges and Cherlin.
Flat Surfaces In The Minkowski Space E^3_1 With Pointwise 1-Type Gauss Map, Uğur Dursun, Emel Coşkun
Flat Surfaces In The Minkowski Space E^3_1 With Pointwise 1-Type Gauss Map, Uğur Dursun, Emel Coşkun
Turkish Journal of Mathematics
In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space E^3_1 with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in E^3_1 are the only cones in E^3_1 with pointwise 1-type Gauss map of the second kind. We conclude that there is no tangent developable surface fully lying in E^3_1 with pointwise 1-type Gauss map of the second kind.
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
Turkish Journal of Mathematics
Let (H,) be a real Hilbert space and let K be a compact and connected subset of H. We show that every continuous mapping T:K \rightarrow K satisfying a mild condition has a fixed point.
Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu
Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu
Turkish Journal of Mathematics
Let R be a commutative ring and C be a semidualizing R-module. For a given class of R-modules Q, we define a class Q_C by M \in Q_C \Leftrightarrow Hom_R(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then Q_C^{\bot} is special preenveloping. As corollaries, we can show that p_C^{n \bot} and f_C^{n \bot} are both special preenveloping. Finally, we show that I_C^n is covering, I_C^{n \bot} is enveloping and special preenveloping provided R is Noetherian.
Combinatorial Results For Order-Preserving And Order-Decreasing Transformations, Gonca Ayik, Hayrullah Ayik, Meti̇n Koç
Combinatorial Results For Order-Preserving And Order-Decreasing Transformations, Gonca Ayik, Hayrullah Ayik, Meti̇n Koç
Turkish Journal of Mathematics
Let O_n and C_n be the semigroup of all order-preserving transformations and of all order-preserving and order-decreasing transformations on the finite set X_n={1,2,\ldots ,n}, respectively. Let \fix (\alpha )={x\in X_n:x\alpha =x} for any transformation \alpha. In this paper, for any Y\subseteq X_n, we find the cardinalities of the sets O_{n,Y}={\alpha\in O_n:\fix (\alpha)=Y} and C_{n,Y}={\alpha\in C_n: \fix (\alpha )=Y}. Moreover, we find the numbers of transformations of O_n and C_n with r fixed points.