Theory of Approximation and Applications
Volume:12 Issue: 1, Winter and Spring 2018

Let R be a commutative ring and G(R) be a graph with vertices as proper and non-trivial ideals of R. Two distinct vertices I and J are said to be adjacent if and only if I J = R. In this paper we study a graph constructed from a subgraph G(R)\Δ(R) of G(R) which consists of all ideals I of R such that I Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper we study about the relation between the number of maximal ideal of R and the number of partite of graph G(R)\4(R). Also we study on the structure of ring R by some properties of vertices of subgraph G(R)\4(R). In another section, it is shown that under some conditions on the G(R), the ring R is Noetherian or Artinian. Finally we characterize clean rings and then study on diameter of this constructed graph.

In this paper, we use an input oriented chance-constrained DEA model with random inputs and outputs. A super-eciency model with chance constraints is used for ranking. However, for convenience in calculations a non-linear deterministic equivalent model is obtained to solve the models. The non-linear model is converted into a model with quadratic constraints to solve the nonlinear deterministic model. Finally, data related to twenty-eight maintenance groups of Iranian Aluminum Company (IRALCO) is used to demonstrate the applicability of the used Models in this paper.

The goal of this paper is to calculate of order reduction of the KdV type equation and the non-isospectral KdV type equation using the μ-symmetry method.
Moreover we obtain μ-conservation law of the non-isospectral KdV type equation using the variational problem method.

The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.
Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value index and ambiguity index for GIVIFNs are de ned. Finally, we develop a value and ambiguity-based ranking method.

In this paper, a numerical solution of time fractional advection-dispersion equations are presented. The new implicit nite di erence methods for solving these equations are studied. We examine practical numerical methods to solve a class of initial-boundary value fractional partial di erential equations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergence of the method are examined and the local truncation error is O(Δt h). This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. The results are justi ed by some numerical implementations. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.

The fuzzy linear second order equations with fuzzy initial values are investigated in this paper. The analytic general solution solutions of them using a rst solution is founded. The parametric form of fuzzy numbers is applied to solve the second order equations. General solutions for fuzzy linear second order equations with fuzzy initial values are investigated and formulated in four cases. A example is solved to illustrate method better and solutions are searched in four cases under Hakuhara derivation. Finally the solutions of example are shown in gures for four cases.