Iranian Journal of Mathematical Sciences and Informatics
Year:2013 | Volume:8 | Issue:2|Papers Count:12

It is the purpose of the present paper to outline an introduction in theory of embeddings in the 2-osculator bundle. First, we recall the notion of 2-osculator bundle ([9], [2], [4]) and the notion of submani-folds in the 2-osculator bundle ([9]). A moving frame is constructed. The induced connections and the relative covariant derivation are discussed in the fourth and fifth section ([15], [16]). The Ricci identities for the deflection tensors are presented in the seventh section.

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs Yn are equal to 7/4 for any n³5, and we will gave a partial answer to a question of Csirmaz [10]. We will also study the information ratio of two other families Cm×Cn and Pm×Cn and obtain the exact value of information ratio of these graphs.

In this paper, the generalized a-centroidal mean and its dual form in 2 variables are introduced. Also, we will study some properties and prove their monotonicity. Further, shown that various means are particular cases of generalized a-centroidal mean.

A graph G is called P4-free, if G does not contain an induced subgraph P4. The domination polynomial of a graph G of order n is the polynomial D (G, x)=Sni=1d (G, i) xi, where d (G, i) is the number of dominating sets of G of size i. Every root of D (G, x) is called a domination root of G. In this paper we state and prove formula for the domination polynomial of non P4-free graphs. Also, we pose a conjecture about domination roots of these kind of graphs.

This paper studies the algebraic structure of transposition hypergroups with idempotent identity. Their subhypergroups and their properties are examined. Right, left and double cosets are defined through symmetric subhypergroups and their properties are studied. Further-more, this paper examines the homomorphisms, the behaviour of attractive and non-attractive elements through them, as well as the relation of their kernels and images to symmetric subhypergroups.

In this paper we introduce the concept of generalized weakly contractiveness for a pair of multivalued mappings in a metric space. We then prove the existence of a common fixed point for such mappings in a complete metric space. Our result generalizes the corresponding results for single valued mappings proved by Zhang and Song [14], as well as those proved by D. Doric [4].

In this paper, we present an example in which the sum of two maximal abstract monotone operators is maximal. Also, we shall show that the necessary condition for Rockafellar's surjectivity which was obtained in ([19], Theorem 4.3) can be sufficient.

In this article we generalize the notion of complete parts, by introducing a weaker condition in definition. Using this generalization we define and analyse a new class of semihypergroups, which are called weak complete semihypergroups. Complete parts were introduced about 40 years ago by M. Koskas and they represent a basic notion of hyperstucture theory, utilized in constructing an important class of subhypergroups of a hypergroup and also they are used to define complete hypergroups.

In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations x2±kxy-y2±x=0, where k is a positive integer, and describe the structure of solutions.

In this paper, we introduce the notion of a frame in a 2-inner product space and give some characterizations. These frames can be considered as a usual frame in a Hilbert space, so they share many useful properties with frames.

Let c0 be the real vector space of all real sequences which converge to zero. For every x, yÎc0, it is said that y is block diagonal majorized by x (written y<b x) if there exists a block diagonal row stochastic matrix R such that y=Rx. In this paper we find the possible structure of linear functions T: c0®c0 preserving <b.