Journal of Mathematical Extension
Volume:7 Issue: 2, Spring 2013

Decomposer functional equations were introduced by the author and have been completely solved on arbitrary groups. Their solutions are as decomposer functions and play important role regarding to decomposition (factorization) of groups by their two subsets. In this paper, we introduce an important class of strong decomposer functions, namely parter (or cyclic decomposer) functions. As some important applications of this topic, we characterize all periodic , coperiodic functions in arbitrary groups and give general solution of their functional equations:f(bx) = f(x) , f(xb) = f(x), f(bx) = bf(x) and f(xb) = f(x)b. Moreover, we characterize all parter functions in arbitrary groups and completely solve the decomposer equation with the condition which its -range is a cyclic subgroup of G. Finally, we give some functional characterization for related projections and b-parts functions and also, we introduce some uniqueness conditions for b-parts of real numbers.

A new and effective direct method to determine the numerical solution of linear and nonlinear differential-algebraic equations (DAEs) is proposed. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are presented. A general procedure for forming these matrices is given. These matrices play an important role in modelling of problems. By using these operational matrices together, a differentialalgebraic equation can be transformed to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

The appropriate choice of input-output weights is necessary to have a successful DEA model. Generally, if the number of DMUs i.e., n, is less than number of inputs and outputs i.e., m+s, then many of DMUs are introduced as efficient then the discrimination between DMUs is not possible. Besides, DEA models are free to choose the best weights. For resolving the problems that are resulted from freedom of weights, some constraints are set on the input-output weights. Symmetric weight constraints are a kind of weight constrains. In this paper, we represent a new model based on a multi-criterion data envelopment analysis (MCDEA) are developed to moderate the homogeneity of weights distribution by using symmetric weight constrains. Consequently, we show that the improvement of the dispersal of unrealistic input-output weights and the increasing discrimination power for our suggested models. Finally, as an application of the new model, we use this model to evaluate and ranking guilan selected hospitals.

In this paper we shall first introduce the Pascal-like triangle, using a generalization of the recurrence relation for arrays of Pascal triangle. Then we define the Pascal-like functional and Fermat-like matrices and investigate their algebraic properties. Finally, we obtain some binomial identities, using these matrices.

The asymptotic distribution for the ratio of sample variances in two independent populations is established. The presented method can be used to derive the asymptotic confidence interval and hypothesis testing for the ratio of population variances. The performance of the new interval is comparable with similar confidence intervals in the large sample cases. Then the simulation study is provided to compare our confidence interval with F-statistic method. The proposed confidence set has a good coverage probability witha shorter length.

Let R be a commutative ring with identity and R[[x]] be the ring of formal power series with coefficients in R. In this article we consider sufficient conditions in order that P[[x]] is a minimal prime ideal of R[[x]] for every minimal prime ideal P of R and also every minimal prime ideal of R[[x]] has the form P[[x]] for some minimal prime ideal P of R. We show that a reduced ring R is a Noetherian ring if and only if every ideal of R[[x]] is nicely-contractible (we call an ideal I of R[[x]] a nicely-contractible ideal if (I \ R)[[x]] I). We will trivially see that an ideal I of R[[x]] is a z-ideal if and only if we have I = (I, x) in which I is a z-ideal of R and also we show that whenever every minimal prime ideal of R[[x]] is nicely-contractible, then I[[x]] is a z-ideal of R[[x]] if and only if I is an @0-z-ideal.

For a separable Banach space X, let L denotes the algebra of bounded operators on X endowed with the strong operator topology. In this note we provide a sufficient condition,in terms of open set in the strong operator topology, for a bounded linear mapping acting on L to be supercyclic with this topology. The main result has some useful consequences and make easy the proof of some related results.