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1
TitleLeft Ideals and Pair of Generalized Derivations in Semiprime Rings
Vol.40(4) (2016) page: 461-465
Author(s): A. Ali and S. Khan  
Abstract:

Let R be an n!-torsion free semiprime ring, and let F,G :R→ R be two generalized derivations of R. In this paper we will show that if the mapping F2+G is n-commuting (or n-skew-commuting ) on a nonzero left ideal λ of R, then either R contains a nonzero central ideal or λd(Z) ⊆ Z, where d is the derivation associated with F.


Keywords: Semiprime rings; Left ideals; Generalized derivations.
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2
TitleBest Proximity Points for ??-contractions and Weak ??-contractions
Vol.40(4) (2016) page: 467-477
Author(s): D. Dey, P. Dan and M. Saha  
Abstract:

In the present paper, we study the best proximity points for a class of φ-contraction and weak φ-contraction mappings. The results achieved in this paper generalize in the light of improvement and unification of the results due to Caballero et al. [11], Mongkolkeha et al. [18] and others.


Keywords: Best proximity point; Proximal contraction; Metric space; ??-contraction; Weak ??-contractions.
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3
TitleA Note on the Topological Centers of Module Actions
Vol.40(4) (2016) page: 479-497
Author(s): K. Haghnejad Azar and A. Bodaghi   
Abstract:

In this paper, we extend some propositions of Banach algebras into module actions and establish the relationships between topological centers of module actions. We introduce some new concepts as Lw*w-property and Rw*w-property for Banach modules and we obtain some conclusions in the topological center of module actions and Arens regularity of Banach algebras.


Keywords: Arens regularity; Bilinear mappings; Factorization; Module action; Second dual; Topological center.
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4
TitleConstruction of Random Error Correcting and P-burst Error Detecting LPA Codes
Vol.40(4) (2016) page: 499-510
Author(s): S. Jain  
Abstract:

Linear partition Arihant (LPA) codes [3] have been introduced by the author as a generalization of error block codes [1] and a study of error correcting/detecting capabilities of these code was made with respect to the random block errors [3]. Also, the concept of P-bursts in block coding has been formulated by the author to study clustered block errors that occur during the process of communication [5]. In this paper, we take up the problem of simultaneous random error correction with P-burst error detection in LPA codes and obtain a bound on the number of parity check digits required for the same.


Keywords: LPA codes; LPA distance; P-bursts.
Size:132KB   download
 
5
TitleHom-Hopf Algebras Arising From (Co)-Braided Hom-Hopf Algebras
Vol.40(4) (2016) page: 511-527
Author(s): L. Jia and X. Chen   
Abstract:

Hom-structures (Lie algbras, bialgebras, Hopf modules) have been payed more and more attention recently. In this paper, we first introduce the notions of Hom-skew pairings, Hom-comodule coalgebras and Hom-module coalgebras. Then we give the examples arising from (co)braided Hom-Hopf algebras. Next we give the sufficient and necessary conditions for it to be a Hom-Hopf agebra and discuss the dual case.


Keywords: Hom-Hopf algebra; Hom-skew pairing; Hom-generalized Smash product.
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6
TitleRandom Fixed Point of Ciric Type Contractive Operator
Vol.40(4) (2016) page: 529-544
Author(s): A.K. Laha and M. Saha  
Abstract:

In the present paper, random fixed point of \′Ciri\′c type contractive operator in a complete probability measure space has been investigated. The results obtained in this paper are stochastic generalization of important deterministic results in the literature. Finally, an application has been shown to ensure the existence of random solution of a non-linear stochastic integral equation of the Hammerstein type.


Keywords: Random fixed point; \??Ciri\??c operator; Random solution; Random integral equation.
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7
TitleSchauder Bases in Dirac Kernels
Vol.40(4) (2016) page: 545-569
Author(s): S.V. Ludkovsky   
Abstract:

Dirac kernels are investigated on compact domains relative to the supremum norm and Hardy's norm with the parameter 1 < p < ∞ as well. An existence of Schauder bases over the real field in them is proved. Procedures for construction of such bases are outlined.


Keywords: Schauder basis; Real Banach space; Dirac kernel.
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8
TitlePersistence Property for Associated Primes of a Family of Ideals
Vol.40(4) (2016) page: 571-575
Author(s): M. Nasernejad  
Abstract:

Let R be a commutative Noetherian ring. For a family of ideals Φ of R with relation ≤ on Φ such that (Φ, ≤ ) is a partially ordered set, we say that (Φ, ≤ ) satisfies the persistence property for associated primes if, for all \mathfrakb ∈ Φ, the set (∪\mathfraka ∈ ΦAssR(R/\mathfraka))∩V(\mathfrakb) is finite and for \mathfraka,\mathfrakb ∈ Φ with \mathfraka ≤ \mathfrakb, we have that AssR(R/\mathfraka) ⊆ AssR(R/\mathfrakb). In this note by using the concepts of regular sequences and u.s.d-sequences, we provide two families of ideals of R with the persistence property.


Keywords: Associated prime ideals; d-sequence; u.s.d-sequence.
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9
TitleA Sharp Generalization of Schwarz and Carath??odory Inequality on the Boundary
Vol.40(4) (2016) page: 577-584
Author(s): B.N. Ornek  
Abstract:

In this paper, a boundary version of the Generalization of Schwarz and Carathéodory inequality are investigated. New inequalities of the Carathéodory's and Schwarz inequality at boundary are obtained by taking into account zeros of f(z) function which are different from zero. Also, we obtain sharp lower bounds on the angular derivative f(z0) at the point z0 where | z0| = |f(z0)| = 1.


Keywords: Schwarz lemma on the boundary; Carath??odory inequality; Holomorphic function.
Size:117KB   download
 
10
TitleSome Dirichlet Series and Means of Their Coefficients
Vol.40(4) (2016) page: 585-591
Author(s): G. Sudhaamsh Mohan Reddy, S. Srinivas Rau and B. Uma  
Abstract:

We derive explicit formulas for Dirichlet series which do not appear in the Catalog [3]. We calculate the mean of the Dirichlet coefficients by Tauberian and Abelian theorems.


Keywords: Dirichlet series; Mean of Dirichlet Coefficients; Wiener-Ikehara Theorem.
Size:112KB   download
 
11
TitleOperator Space Structures on Banach Spaces
Vol.40(4) (2016) page: 593-602
Author(s): P. Vinod Kumar and M.S. Balasubramani  
Abstract:

If X is a Banach space, then any linear isometry from X to B(H), for some Hilbert space H endows an operator space structure on X. Among these operator space structures admissible on X, two are of special importance, namely, the minimal operator space structure Min(X) and the maximal operator space structure Max(X). In this note, we present a characterization of these spaces up to complete isomorphism. We derive some conditions for a completely bounded linear bijection to become a complete isomorphism. Also, we introduce the notion of complete equivalence of operator space structures on a Banach space.


Keywords: Operator spaces; Completely bounded mappings; Complete isomorphisms; Completely equivalent operator space structures; Minimal and maximal operator spaces.
Size:130KB   download
 
12
TitleOn the Hyperstructure Theory
Vol.40(4) (2016) page: 603-620
Author(s): T. Vougiouklis  
Abstract:

Hv-structures are hyperstructures where the equality is replaced by the non-empty intersection. This class of the hyperstructures is very large so one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory.

In this paper I present some results, problems and applications on Hv-structures on which I worked and I follow the same process which I follow in my research. I mainly focus on the representation theory of Hv-groups by Hv-matrices. On the way to reach this target one needs Hv-groups, Hv-rings, Hv-matrices, Hv-vector spaces and many other structures.

 


Keywords: Hyperstructure; Hv-structure; Hope.
Size:189KB   download
 
12 Records!

 


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