Journal of Mahani Mathematical Research
Volume:2 Issue: 1, Summer 2013

In a previous work, we introduced particular fuzzy numbers and discussed some of their properties. In this paper we use the comparison method introduced by Dorohonceanu and Marin[5] to compare between these fuzzy numbers.

A novel and e ective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-di erential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our new method is based on this matrix and the vector forms for representation of Haar wavelets. In addition, an error and convergence analysis of the Haar- approximation is discussed. Since this approach does not need any integration, all calculations would be easily implemented, and it has several advantages in reducing the computational burden. Some examples are included to demonstrate the validity and applicability of the technique.

One-way analysis of covariance is a popular and common statistical method, wherein the equality of the means of several random variables which have a linear relationship with a random mathematical variable, is tested. In this study, a method is presented to improve the one-way analysis of covari- ance when there is an uncertainty in accepting the statistical hypotheses. The method deals with a fuzzy test statistic which is produced by a set of con dence intervals. Finally an example is provided for illustration.

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) module generalized derivations and generalized first cohomology groups, we present several results concerning the relations between module generalized derivations from $A_i$ into the dual space $A^*_i$ (for $i=1,2$) and such derivations from the triangular Banach algebra of the form $mathcal{T}: =left(begin{array}{lc} A_1 &X 0 & A_2end{array}right)$ into the associated triangular $mathcal{T}$- bimodule $mathcal{T}^*$ of the form $mathcal{T}^*:=left(begin{array}{lc} A_1^* &X^* 0 & A_2^*end{array}right)$. In particular, we show that the so-called generalized first cohomology group from $mathcal{T}$ to $mathcal{T}^*$ is isomorphic to the directed sum of the generalized first cohomology group from $A_1$ to $A^*_1$ and the generalized first cohomology group from $A_2$ to $A_2^*$.

Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, there exists an order preserving transformation with entropy $r$.

In this paper, modi cation of the optimal homotopy asymptotic method (MOHAM) is applied upon singular initial value Lane-Emden type equations and results are compared with the available exact solutions. The modi ed algorithm give the exact solution for di erential equations by using one iteration only.