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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.
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.
Simultaneous Proximinality Of Vector Valued Function Spaces, Mona Khandaqji, Fadi Awawdeh, Jamila Jawdat
Simultaneous Proximinality Of Vector Valued Function Spaces, Mona Khandaqji, Fadi Awawdeh, Jamila Jawdat
Turkish Journal of Mathematics
A characterization of best simultaneous approximation of Köthe spaces of vector-valued functions is given. This characterization is a generalization of some analogous theorems for Orlicz Bochner spaces.
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.
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.
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.
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.
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 …
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.
Best Constants In Second-Order Sobolev Inequalities On Compact Riemannian Manifolds In The Presence Of Symmetries, Mohammed Ali
Best Constants In Second-Order Sobolev Inequalities On Compact Riemannian Manifolds In The Presence Of Symmetries, Mohammed Ali
Turkish Journal of Mathematics
Let (M,g) be a smooth compact 3\leq n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.
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.
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.
Pointwise Slant Submanifolds In Almost Hermitian Manifolds, Bang-Yen Chen, Oscar J. Garay
Pointwise Slant Submanifolds In Almost Hermitian Manifolds, Bang-Yen Chen, Oscar J. Garay
Turkish Journal of Mathematics
An interesting class of submanifolds of almost Hermitian manifolds (\tilde M,\tilde g,J) is the class of slant submanifolds. Slant submanifolds were introduced by the first author in [6] as submanifolds M of (\tilde M,\tilde g,J) such that, for any nonzero vector X \in T_pM, p \in M, the angle \theta(X) between JX and the tangent space T_pM is independent of the choice of p\in M and X \in T_pM. The first results on slant submanifolds were summarized in the book [7]. Since then slant submanifolds have been studied by many geometers. Many nice results on slant submanifolds have been obtained …
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.
On Some New Inequalities For Convex Functions, Mevlüt Tunç
On Some New Inequalities For Convex Functions, Mevlüt Tunç
Turkish Journal of Mathematics
In the present paper we establish some new integral inequalities analogous to the well known Hadamard's inequality by using a fairly elementary analysis.
On \Alpha-Skew Mccoy Modules, Jian Cui, Jianlong Chen
On \Alpha-Skew Mccoy Modules, Jian Cui, Jianlong Chen
Turkish Journal of Mathematics
Let \alpha be a ring endomorphism. Extending the notions of McCoy modules and \alpha-skew McCoy rings, we introduce the notion of \alpha-skew McCoy modules, which can also be regarded as a generalization of \alpha-skew Armendariz modules. A number of illustrative examples are given. Various properties of these modules are developed, and equivalent conditions for \alpha-skew McCoy modules are established. Furthermore, we study the relationship between a module and its polynomial module.
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.
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.
On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang
On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang
Turkish Journal of Mathematics
In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')^n and g + a(g')^n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.
Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu
Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu
Turkish Journal of Mathematics
We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B\rangle of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided.
Extended Cross Product In A 3-Dimensional Almost Contact Metric Manifold With Applications To Curve Theory, Çeti̇n Camci
Extended Cross Product In A 3-Dimensional Almost Contact Metric Manifold With Applications To Curve Theory, Çeti̇n Camci
Turkish Journal of Mathematics
In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.
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.
Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen
Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen
Turkish Journal of Mathematics
Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference \Delta^nf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.
On F_S-Supplemented Primary Subgroups Of Finite Groups, Lujin Zhu, Long Miao
On F_S-Supplemented Primary Subgroups Of Finite Groups, Lujin Zhu, Long Miao
Turkish Journal of Mathematics
Let G be a finite group and F a formation of finite groups. A subgroup H of G is called F_s-supplemented in G if there exists a subnormal subgroup T of G such that G = HT and (H \cap T)H_G/H_G is contained in the F-hypercenter Z^F_{\infty}(G/H_G) of G/H_G. In this paper, we study the structure of finite groups by using F_s-supplemented subgroups.
On The Order Of Weighted Approximation By Positive Linear Operators, Tüli̇n Coşkun
On The Order Of Weighted Approximation By Positive Linear Operators, Tüli̇n Coşkun
Turkish Journal of Mathematics
An estimation of approximation of continuous functions by positive linear operators in weighted norm using the weighted modulus of continuity is established. Application of the main result to the known Gadjiyev-Ibragimov operators is given.
C^*-Convexity And C^*-Faces In *-Rings, Ali Ebrahimi Meymand, Gholam Hossein Esslamzadeh
C^*-Convexity And C^*-Faces In *-Rings, Ali Ebrahimi Meymand, Gholam Hossein Esslamzadeh
Turkish Journal of Mathematics
Existence of rich algebraic, geometric and topological structures on self-adjoint operator algebras raises the general question that, for a particular theorem which of these structures have made the result work. The present paper is an effort toward the answer of this question, by investigating the role of algebraic structure in the subject of C^*-convexity. In this paper, we extend the notions of C^*-convexity, C^*-extreme point and C^*-face to *-rings and we study some of their properties. We introduce the notion of C^*-convex map on C^*-convex subsets of a *-ring. Moreover we identify optimal points of some unital *-homomorphisms on some …