Journal of Hyperstructures
Volume:3 Issue: 1, Winter and Spring 2014

Let $R$ be a commutative ring, $I$ be a 2-absorbing ideal of $R$ and let $I=Q_1\cap\cdots\cap Q_n \ \ (n\geq 2)\ \ \text{with} \ \ \sqrt Q_{i}=P_i \ \ \text{for}\ \ i=1,\cdots, n$ be a minimal primary decomposition of $I$. Let $\Gamma_E(R/I)$ denote the graph of equivalence classes of zero divisors of $R/I$. It is shown that $Q_1\cap\cdots\cap Q_{n-1}, Q_1\cap\cdots\cap Q_{n-2},\cdots, Q_1, P_1, P_2 \cdots, P_n$ are all vertexes of $\Gamma_E(R/I)$ and also the degrees of all vertexes are determined.

In this paper by considering the notion of BCK-module, we have introduced pure BCK- submodules and we have proved some results by it. As a result we have shown that if X is a BCK- algebra, M is a cyclic BCK-module and N a prime BCK- submodule of M, then N is a pure BCK-submodule of M.

In this paper, we introduce the notions of semi prime ideals, 2-potent prime ideals,weakly prime ideals and weakly primary ideals in a Boolean like semi ring of fractions. Further, we obtain various properties concerning the notions.

In this paper, the residuated graph of residuated lat- tices will be studied. To do so, the notion of zero divisors of a nonempty subset of a residuated lattice is rst introduced and some related properties are investigated. By means of the set of all zero- divisors of an element of a residuated lattice L, residuated graph 􀀀(L) is dened and several examples are given. This graph is con- nected and also some necessary conditions for the residuated graph to be a star graph are found. Finally, the relation between a resid- uated lattice L and the residuated graph 􀀀(L) are studied.

In this paper, the parametric quintic spline method is used for finding the solution of variational problems associated in engineering and physics. The present approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

In this paper, a numerical scheme was developed based on mollification method and space marching scheme for solving an inverse heat conduction problem. The proposed inverse problem contains the estimation of two unknown functions at the boundaries named proportional factors. The temperature and heat flux measurements in an interior point are considered as overspecified data with the presence of noise. Convergence and stability of the solution for the proposed method are analyzed. To support the numerical achievements, some numerical examples are considered and discussed.

In this paper, the Modied two-dimensional block-pulse functions (M2D-BFs) are used as a new set of basis functions for expanding two-dimensional functions. The main properties of M2D-BFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimensional Volterra integral equations of the rst kind. Some theorems are included to show convergence and advantage of the method. Finally, numerical example is presented to show the efciency and accuracy of the method.