Journal of Mathematical Extension
Volume:3 Issue: 2, Spring 2009

In this paper the definition and some properties of semigroupoids are considered. Representations, tight representations, and universal representations of a cancellative semigroupoid are discussed. Also, the C ∗ -algebra of a semigroupoid is introduced and it is shown that source elements transfer to zero by tight representations.

In this paper, we introduce a three–parameter generalization of the Lindley distribution. This includes as special cases the exponential and gamma distributions. The distribution exhibits decreasing, increasing and bathtub hazard rate depending on its parameters. We study various properties of the new distribution and provide numerical examples to show the flexibility of the model. We also derive a bivariate version of the proposed distribution.

We give sufficient conditions on a domain Ω so that the associated canonical model is reflexive. Also, we discuss a class of shifts that are reflexive, and the operator Mz of multiplication by z on a Banach space of functions analytic on a domain is shown to be reflexive whenever Mz is polynomially bounded.

To test whether a set of data has a specific distribution or not, we can use the goodness of fit test. This test can be done by one of Pearson X 2 -statistic or the likelihood ratio statistic G 2 , which are asymptotically equal, and also by using the Kolmogorov-Smirnov statistic in continuous distributions. In this paper, we introduce a new test statistic for goodness of fit test which is based on entropy distance, and which can be applied for large sample sizes. We compare this new statistic with the classical test statistics X 2 , G 2 , and Tn by some simulation studies. We conclude that the new statistic is more sensitive than the usual statistics to the rejection of distributions which are almost closed to the desired distribution. Also for testing independence, a new test statistic based on mutual information is introduced.

In this paper, He’s variational iteration method (VIM) is used to obtain the exact solution of the Equation Governing the Unsteady Flow of a Polytropic Gas. This method is based on Lagrange multiplier for identification of optimal value of parameter in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the Adomian polynomials. The results reveal that He’s variational iteration method is very effective for these types of equations.

In this paper we study some sufficient conditions for commutativity of a ring according to Jacobsons’idea. Jacobson proved that if R is a ring satisfying x n = x (n > 1) for each x ∈ R, then R is commutative. In this paper, we show that R is commutative if for every x, y ∈ R there exists a positive integer n = n(x, y) such that (x[x, y])n = x[x, y].

In this article, the Homotopy Perturbation Method (HPM) is employed to approximate solutions of a modified Lotka - Volterra equation. HPM has been introduced by He to solve approximately linear or nonlinear differential equations. Approximate polynomials have also been constructed to find approximate solutions of a modified Lotka - Volterra system. Numerical comparisons are made between HPM and maple numerical results.

Let Xi1, · · · , Xini be a random sample from a gamma distribution with known shape parameter νi > 0 and unknown scale parameter βi > 0, i = 1, 2, satisfying 0 < β1 6 β2. We consider the class of mixed estimators for estimation of β1 and β2 under reflected gamma loss function. It has been shown that the minimum risk equivariant estimator of βi, i = 1, 2, which is admissible when no information on the ordering of parameters are given, is inadmissible and dominated by a class of mixed estimators when it is known that the parameters are ordered. Also, the inadmissible estimators in the class of mixed estimators are derived. Finally the results are extended to some subclass of exponential family.

Join-irreducible elements in a lattice have an important role. They act like blocks of a lattice. In DCC lattices each element of the lattice has a unique finite representation as a join of join-irreducible elements. In this paper, we seek lattices which contains elements that can be represented as an infinite supremum of join-irreducible elements. One of these lattices is the lattice of sequences. Finally, we give a new characterization for such lattices.

First kind integral equations can be solved numerically with several methods. In this paper we describe a recursive method for solving Volterra integral equation that don’t need to solve system of algebraic equation. This method offers several advantages in reducing computational burden. Finally by comparison of numerical results, simplicity and efficiency of this method will be shown.