Journal of Hyperstructures
Volume:2 Issue: 1, Winter and Spring 2013

In this paper, we study some properties of special weak free (semi)hypergroups and we generalize the Nielsen-Schreier theorem for the class of special weak free hypergroups.

We introduce the notion of fuzzy small right ideal,fuzzy small right prime ideal and fuzzy maximal small right ideal in a ring.We have obtained necessary and sucient condition for a fuzzy small right ideal to be fuzzy small prime right ideal.We have also shown that fuzzy Jacobson radical is the sum of fuzzy small right ideals.

In this paper we discuss some basic properties of rough soft sets and hence we introduce the notion of rough soft group. Basic properties of rough soft group are presented and supported by some illustrative examples.

In this paper we shall develop a structure theory for multiplicatively ideal in rings. We introduce the notion multiplication ideal in Gamma-rings and we obtain some equivalent conditions for multiplication ideal in Gamma-rings.

In this paper we study a discrete time version of Bolza type problems in optimization in infinite dimensional. The functionals are assumed to be merely lower semi continuous. We obtain optimality conditions which are always necessary and which are also sufficient in the convex case whenever the given problem satisfies a qualification condition

Integral equations play major roles in di®erent ¯elds of science and engineering, therefore a new method for ¯nding a solution of the Fred- holm integral equation is presented. So we have applied a structure of hybrid neural networks (NNs). The proposed neural net can get a real input vector and calculates its corresponding output vector. Next a learning algorithm based on the gradient descent method has been de- ¯ned for adjusting the connection weights. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generaliza- tion and high accuracy. The proposed method is illustrated by several examples with computer simulations.

This paper presents a computational technique for the solution of the nonlinear Fredholm Hammerstein integral and integro-differential equations. A hybrid of block-pulse functions and the second kind Chebyshev polynomials (hereafter called as HBC) is used to approximate the nonlinear Fredholm-Hammerstein integral and integro differential equations. The main properties of HBC are presented. Also, the operational matrix of integration together with the Newton-Cotes nodes are applied to reduce the computation of the nonlinear Fredholm Hammerstein integral and integro-differential equations into some algebraic equations. The efficiency and accuracy of the proposed method have shown by three numerical examples.