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1
TitleCharacterization of the Linear Groups PSL(2, p)
Vol.38(4) (2014) page: 471-478
Author(s): A.K. Asboei and S.S.S. Amiri  
Abstract:

Let G be a finite group and πe(G) be the set of element orders of G . Let k ∈ πe(G) and mk be the number of elements of order k in G. Set nse(G):={ mk | k ∈ πe(G)}. In this paper, it is proved if G is a group with the following properties, then G ≅ PSL(2, p).

    1) p is the prime divisor of order G but p2 not divide order of G.
    2) nse(G)=nse(PSL(2, p)).

 


Keywords: Element order; Set of the numbers of elements of the same order; Linear group.
Size:132KB   download
 
2
TitleA Note on the Factorisation of (m, r)-Potent Elements in Tn
Vol.38(4) (2014) page: 479-485
Author(s): S. Atl han  
Abstract:

In [1], for an element α of a finite full transformation semigroup of index m and period r, the authors obtained a unique factorisation α = θγ such that Shift(θ)∩Shift(γ)=∅, where θ is a permutation of order r and γ is an m-potent element. The main aim of this article is to examine whether the condition Shift(θ)∩Shift(γ)=∅ in [1, Theorem 4] can be removed or not in the case n=m+r.


Keywords: Tn; m-potent; Fix; Shift; Def.
Size:123KB   download
 
3
TitleSome Results on Convexity of Integral Operators
Vol.38(4) (2014) page: 487-491
Author(s): D. Bansal and B.A. Frasin  
Abstract:

In the present paper, we obtain some closed properties for integral operator Iδiγi for functions belonging to class of convex functions and also for a class of α-convex functions of order β. Several corollaries and consequences of the main results are also considered. 


Keywords: Analytic and univalent functions; Starlike and convex functions; Integral operators.
Size:98KB   download
 
4
TitleAnnihilating Conditions and Central Values of Generalized Derivations on Lie Ideals
Vol.38(4) (2014) page: 493-500
Author(s): V. De Filippis and B. Dhara  
Abstract:

Let R be a prime ring, U the Utumi quotient ring of R, C the extended centroid of R (C=Z(U)), L a noncommutative Lie ideal of R, H a nonzero generalized derivation of R and s( ≥ 0), t( ≥ 0) fixed integers. Suppose that there exists 0 ≠ a ∈ R such that ausH(u)ut ∈ C for all u ∈ L, then one of the following holds:

    (1) s=0, there exists p ∈ U such that H(x)=px for all x ∈ R with ap=0;
    (2) R satisfies s4.

Keywords: Prime rings; Differential identities; Generalized derivations.
Size:114KB   download
 
5
TitleInclusion Properties Regarding the Meromorphic Structure of Srivastava-Attiya Operator
Vol.38(4) (2014) page: 501-512
Author(s): R.M. El-Ashwah  
Abstract:

Let ∑ denote the class of analytic functions in the punctured unit disc U={ z ∈ \mathbbC:0 < | z| < 1} . In this paper, we introduce several new subclasses of meromorphic functions defined by means of the linear operator F ds(a,c;z)(s ∈ \mathbbC;a ∈ \mathbbC;c,d ∈ \mathbbC\\mathbbZ0).  Inclusion properties of these classes and some applications involving integral operator are also considered. 


Keywords: Meromorphic functions; Hurwitz-Lerech Zeta function; Convolution.
Size:138KB   download
 
6
TitleThe Generalization of the Formula V(G)=E(G)+1 for Simplicial Trees
Vol.38(4) (2014) page: 513-525
Author(s): F. Khosh-Ahang, Z. Barati and N. Hoseini  
Abstract:

In this note, firstly we introduce roses and double simplicial roses as a special class of simplicial complexes, which have close relation with simplicial trees. Then, we used them to generalize the well-known equation V(G)=E(G)+1 (for a tree graph G) to simplicial trees.


Keywords: Connection; Rose; Simplicial complex; Tree.
Size:147KB   download
 
7
TitleWeakly Armendariz Rings Relative to Skew Polynomial Rings
Vol.38(4) (2014) page: 527-533
Author(s): L. Liang and C.H. Yang  
Abstract:

For a ring endomorphism α, we introduce the notion of α-skew weakly Armendariz rings that extends the notions of α-skew Armendariz rings and weakly Armendariz rings. Some properties and extensions of α-skew weakly Armendariz rings are studied. As consequences, several known results are extended to more general classes of rings.


Keywords: Semicommutative rings; Armendariz rings; ??-skew Armendariz rings; ??-skew weakly Armendariz rings.
Size:118KB   download
 
8
TitleThe Endotype of (n−3)-Regular Graphs of Order n
Vol.38(4) (2014) page: 535-541
Author(s): N. Pipattanajinda  
Abstract:

Let G be a graph, the endotype of G is between 0 and 31. In this paper, we will show that the endotype of an (n−3)-regular graph of order n is division by 4.


Keywords: Endomorphism type; (n−3)-regular graph of order n; Join.
Size:114KB   download
 
9
TitleNear Relatives of Homogeneous Maps
Vol.38(4) (2014) page: 543-554
Author(s): I. Ramabhadra Sarma, J. Madhusudana Rao, T.V.N. Prasanna and A.V. Ramakrishna  
Abstract:

We extend the notion of semilinearity introduced by K.D. Magill, Jr. on \mathbbRn to a real linear space X and present some properties of these functions. We also study some properties of the near algebra Xλ where X is a linear space on which the multiplication is induced by a semilinear map λ:X→ \mathbbR. 


Keywords: Homogeneous and positively homogeneous functions; Semilinear map; Semilinear transformation; Near algebras.
Size:137KB   download
 
10
TitleTopological Characterization of Dually B-Normal Almost Distributive Lattices
Vol.38(4) (2014) page: 555-562
Author(s): G.C. Rao, N. Rafi and R.K. Bandaru  
Abstract:

We introduce the concept of dually B−normal ADL, where B is the Birkhoff centre of the ADL and derived that an ADL R in which every dual dense element is a zero element is dually B−normal if and only if the space MaxR of all maximal ideals of an ADL R with the hull-kernel topology is a Boolean space. 


Keywords: Almost distributive lattice (ADL); Birkhoff centre; Prime ideal; Maximal ideal; Dual dense element; Dually B−normal ADL; Boolean space.
Size:117KB   download
 
11
TitleGeneralized Derivations Acting as Lie Homomorphisms on Polynomials in Prime Rings
Vol.38(4) (2014) page: 563-572
Author(s): G. Scudo  
Abstract:

Let R be a non-commutative prime ring of characteristic different from 2, with center Z(R) and extrended centroid C and let F be a non-zero generalized derivation of R. Denote by f(R)={f(r1,…,rn): r1,…,rn ∈ R}, the set of all the evaluations of a non-central polynomial f(x1,…,xn) over C. If F acts as a Lie homomorphism on f(R) then F is the identity map. 


Keywords: Prime rings; Differential identities; Generalized derivations.
Size:117KB   download
 
12
TitleSome Limit Theorems for Arbitrary Random Fields With Respect to Geometric Distributions Indexed by a Homogeneous Tree
Vol.38(4) (2014) page: 573-587
Author(s): K.K. Wang and D.C. Zong  
Abstract:

In this paper, we establish a class of strong limit theorem for the arbitrary random field with respect to the product geometric distributions indexed by the homogeneous tree by constructing the consistent distribution functions and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the entropy density and the random field which obeys geometric distributions indexed by the homogeneous tree are studied. 


Keywords: The homogeneous tree; Random field; The geometric distribution; Nonnegative martingale; Strong limit theorem.
Size:153KB   download
 
13
TitleSome Normal Criteria of Meromorphic Functions Concerning Shared Analytic Function
Vol.38(4) (2014) page: 589-602
Author(s): Q. Wang, W. Chen and H.G. Tian  
Abstract:

In this paper, we study the normality of meromorphic functions shared an analytic function. We obtain: Let k be a positive integer and m be an even number. Suppose that ψ(z)\noindentt ≡ 0 is a holomorphic function with zeros of multiplicity m. Let F be a family of meromorphic functions in a domain D. If for each f ∈ F, all zeros of f have multiplicity at least k+m+1 and all of poles of f are of multipicity at least m+1. If ff(k) and gg(k) share ψ(z) in D for every pair of functions f, g ∈ F, then F is normal in D. This improves and generalizes the related previous results ([29 ,14]). 


Keywords: Meromorphic function; Shared value; Normal criterion.
Size:168KB   download
 
14
TitleHermite Matrix based Polynomials of two Variables and Lie Algebraic Techniques
Vol.38(4) (2014) page: 603-618
Author(s): G. Yasmin and S. Khan  
Abstract:

In this paper, the generalized 2-variable Hermite generalized Hermite matrix polynomials (G2VHGHMP) denoted by HHn,mλ(x,y;A) are introduced by means of generating function and series definition. In order to use the representation theory of the harmonic oscillator Lie algebra G(0,1), we consider the particular case of G2VHGHMP HHn,mλ(x,y;A) by taking m=2. Further, denoting the resultant 2-variable Hermite generalized Hermite matrix polynomials (2VHGHMP) by HHnλ(x,y;A) and framing them within the context of representation ↑0,1 of G(0,1), certain results are derived. The generating relations for some related matrix polynomials are also obtained as applications.


Keywords: Generalized 2-variable Hermite generalized Hermite matrix polynomials; 2-variable Hermite generalized Hermite matrix polynomials; Lie group; Lie algebra; Representation theory; Generating relations.
Size:171KB   download
 
14 Records!

 


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