سال:1392 | دوره: | شماره: |تعداد مقالات:10

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly differential hyperringR and for any strongly differential hyperideal Iof R, the factor hyperring R/I is a strongly differential hyperring.Further we prove that a map d: R ®R is a derivation of a hyperring R if and only if the induced map jd is a homomorphism.

In this paper, for any ideal I of BCH-algebra X, we introduce the concept of ÖI and show that it is an ideal of X, when I is a closed ideal. Then we verify some useful properties of it and prove that it is the union of all k−nil ideals of I. Moreover, if I is a closed ideal of X, then ÖI is a closed translation ideal and so we can construct a quotient BCH-algebra. We prove this quotient BCH-algebra is a P-semisimple BCI-algebra and so it is an abelian group. Finally, we use the concept of radical in order to construct the second and the third isomorphism theorems.

Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel sub fusion sequences and sub fusion frames and we investigate the relationship between their operations. Also, the definition of the orthogonal complement of sub fusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these notions are shown.

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation Snk=2 Ski1=2 Sk+1i2=i1+1 · Sn in-k+1=in-k+1 ¦ (Sni=1, i ¹i1, ···, in-k+1 ci -Sn-k+1r=1 cir) + ¦ (Sni=1 ci) -2n-1 ¦ (c1)=0, where n is an integer greater than 1.

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications.In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for solving Fredholm integral equations.

In this paper we are concerned with cuts in models of Samuel Buss’ theories of bounded arithmetic, i.e. theories like Si2 and Ti2. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of pcuts and small cuts. In particular, we prove some overspill and underspill properties for them.

A concept of ideal extensions in ternary semigroups is introduced and throughly investigated. The connection between an ideal ex-tensions and semilattice congruences in ternary semigroups is considered.

In this paper, we introduce the notions of (ʘ,⊕) -derivations and (ϴ,ʘ) -derivations for MV -algebras and discuss some related results.We study the connection between these derivations on an MV -algebra Aand the derivations on its boolean center. We characterize the isotone (ʘ,⊕) -derivations and prove that (ϴ,ʘ) -derivations are isotone. Finally we determine the relationship between (ʘ,⊕) -derivation and (ϴ,ʘ) -derivation for MV -algebras.

In this paper we present a new method to find simple or multiple roots of functions in a finite interval. In this method using bisection method we can find an interval such that this function is one to one on it, thus we can transform problem of finding roots in this interval into an ordinary differential equation with boundary conditions.By solving this equation using collocation method we can find a root for given function in the special interval. We also present convergence analysis of the new method. Finally some examples are given to show efficiency of the presented method.

The diameter of a connected graph G, denoted by diam (G), is the maximum distance between any pair of vertices of G. Let L (G) be the line graph of G. We establish necessary and sufficient conditions under which for a given integer k³2, diam (L(G))£k.