JOURNAL OF MATHEMATICAL EXTENSION
Year:2009 | Volume:4 | Issue:1 (S.N. 7)|Papers Count:10

Let G be a group and Aut (G) be the group of auto-morphisms of G. Then [g, a, b] = (g-1ga)-1 (g-1ga)b is the autocommutator of the element g Î G and a, b Î Aut (G) of weight 3. Also, we define K2 (G) =< [g, a, b]: g Î G, a, b Î Aut (G) > to be the third term of the lower autocentral series of subgroups of G. In this paper, it is shown that every finite abelian group is isomorphic to the third term of the autocentral series of some finite abelian group.

We will relate the degree of rational approximation of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak* limit of the normalized pole-counting measures.

We show that the tensor product of two operator- valued frames for two Hilbert C*-modules is an operator-valued frame for the tensor product of these Hilbert C*-modules.

The symmetric hit problem was introduced for the first time by the author in his thesis ([5]). The aim of this paper is to solve an important open problem posed in ([7]), in an special case, which is one of the fundamental results in the studies of the symmetric hit problem.

In this paper, some concepts of negative dependence for bivariate distributions, especially hazard and local negative de-pendence (HND, LND) are studied. The Clayton-Oakes,  j and  g measures of association and relationship of HND with these mea-sures are obtained. In addition, various examples illustrate the usefulness of these notions in some family of distributions.

In this paper, we will consider third order linear differential equationy’’’+ay’’+by’+gy+ f (t, y) = e (t)where a, b, g are constant coefficients, f (t, y) is continuous, e (t) is discontinuous, and f and e are periodic functions with respect to t of period w. We will introduce sufficient conditions under which the above equation have at least one non-trivial periodic solution of period w. We will see that under the so called conditions, all the solutions of the equation will be bounded. It must be mentioned that e in this equation is called "controller" in the en-gineering problems and it was always considered to be continuous to ensure us that periodic solution exists. In this paper, we will show the existence of periodic solution without supposing that e to be continuous.

This paper is a continuation of our recent paper enti- tled limit summability of real functions ([2]). In this work weak, semi, absolutely and uniformly limit summability will be given.Also, we generalize and extend some results of [2].

This paper is concerned with admissible and minimax estimation of scale parameter q of a gamma distribution under the entropy loss function, when it is known that q ³a for some known a>0. An admissible minimax estimator of q, which is the pointwise limit of a sequence of Bayes estimators, is derived. Also, the admissible estimators and the only minimax estimator of µ in the class of truncated linear estimators are obtained. Finally, the results are extended to a subclass of scale parameter exponential family and the family of transformed chi-square distributions.

The concept of Hyers-Ulam-Rassias stability has been originated from a stability theorem due to Th. M. Rassias. Re-cently, the Hyers-Ulam-Rassias stability of the functional Equationf (x+2y)+f (x-2y) = 2f (x)-f (2x)+ 4{ f (x+y) +f (x-y) },has been proved in the case of Banach spaces. In this paper, we will find out the generalized Hyers-Ulam-Rassias stability problem of the above functional equation in random normed spaces.

Data envelopment analysis is a technique for measuring the relative efficiency of a set of decision making units with crisp data, but in this paper we explain a new method for evaluating of decision making units with fuzzy data.At first, we introduce fuzzy data envelopment analysis models with parameters as trapezoidal membership function. Then we extend this method for solving models with general parameters.