Weakly Normal Rings,
2012
TÜBİTAK
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 …
A Homotopy For A Complex Of Free Lie Algebras,
2012
TÜBİTAK
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
On Cosets In Coxeter Groups,
2012
TÜBİTAK
On Cosets In Coxeter Groups, Sarah B. Hart, Peter J. Rowley
Turkish Journal of Mathematics
In this paper the notion of Coxeter length for a subset of a Coxeter group, as introduced in [9], is investigated for various subsets of a Coxeter group. Mostly cosets of various subgroups are examined as well as the associated idea of X-posets, which is a vast generalization of the Bruhat order.
On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids,
2012
TÜBİTAK
On The Automorphisms Of Direct Product Of Monogenic Semigroups And Monoids, Karim Ahmadidelir, Hossein Doostie
Turkish Journal of Mathematics
This paper investigates the automorphism group of monogenic [4] semigroups (or monoids) to find its relationship with the automorphism group of cyclic groups. Then, by considering a presentation related to the direct product of monogenic semigroups, verify the relationship between the automorphism group of These and the automorphism group of the group presented by the same presentation. This study gives us some [4]explicit formulas for computing the order of automorphism groups of these algebraic structures.
Best Simultaneous Approximation In Function And Operator Spaces,
2012
TÜBİTAK
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 …
Banach Limit And Some New Spaces Of Double Sequences,
2012
TÜBİTAK
Banach Limit And Some New Spaces Of Double Sequences, Mohammad Mursaleen, Syed Abdul Mohiuddine
Turkish Journal of Mathematics
In this paper, we define and study the Banach limit for double sequences and introduce some new spaces related to the concept of almost and strong almost convergence for double sequences. We characterize these spaces through some sublinear functionals and we also establish some inclusion relations.
Approximate Groups Iii: The Unitary Case,
2012
TÜBİTAK
Approximate Groups Iii: The Unitary Case, Emmanuel Breuillard, Ben Green
Turkish Journal of Mathematics
By adapting the classical proof of Jordan's theorem on finite subgroups of linear groups, we show that every approximate subgroup of the unitary group U_n(C) is almost abelian.
An Oscillation Theorem For Second-Order Nonlinear Differential Equations Of Euler Type,
2012
TÜBİTAK
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.
On Injective And Subdirectly Irreducible S-Acts Over Left Zero Semigroups,
2012
TÜBİTAK
On Injective And Subdirectly Irreducible S-Acts Over Left Zero Semigroups, Gholamreza Moghaddasi
Turkish Journal of Mathematics
The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups. Also we compute the number of such acts and specify cogenerators acts over left zero semigroups. To do these we first take another look at the description of injective hulls of the separated S-acts over left zero semigroups.
Uc Modules With Respect To A Torsion Theory,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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,
2012
TÜBİTAK
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.
