JOURNAL OF MATHEMATICAL EXTENSION
Year:2006 | Volume:1 | Issue:1|Papers Count:8

The usual kurtosis measure, forth central moment divided by second central moment, does not measure only peaked ness of distribution with respect to normal distribution. But it measures both peaked ness and tail weight of distributions. In this paper we consider some disadvantages of the kurtosis measure. It can be misleading as a measure of departure from normality. This measure does not work well for some families, for example Ali's scale contaminated normal distribution. It is infinite for heavy tail distribution. In other words it is so sensitive to extreme values. We introduce a modified of kurtosis which is robust against the extreme values. We name the kurtosis measure by bqp (F). Properties of the introduced measure are as the same as usual kurtosis measure. By using this measure and Van Zwet’s ordering we can sort distributions based on heaviness or peaked ness separately. Finally by Monte Carlo simulation we find the critical values at some levels for the measure.

In this article we consider P (X>Y) for two in dependent random variables X~B (n+m, p1) and Y~B (n, p2).This is a useful measure in biomedical studies and engineering reliability. The calculation of this probability is discussed by using a combinatorial identity and the approximate value of that is given when n is large. Finally some special cases are discussed.

In this paper we investigate the cyclicity of the multiplication operator Mz acting on the weighted Hardy spaces of formal Laurent series.

In this article, we find the set of all limit points of sequences of polynomials with real coefficients, in cos n, n=1, 2, 3, ···with degree less than or equal to three. Also, when the degree is four, the mentioned set is found in some special cases.

In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces.

In this paper by using a nice criterion, we show that the perturbation of identity operators by some multiples of the standard backward shift is hypercyclic. This gives a new proof for Salas Theorem in ( [10 ], Theorem 3.3).

Let {b (n)} ¥n=0 be a sequence of positive numbers and 1<p<¥. We consider the weighted Hardy space Hp (b). We investigate the relation between the generating function and the functional of pointe valuations. Also, under a sufficient condition we determine the structure of all non-zero multiplicative linear functionals on Hp (b).

In this paper we will consider the crossed product C (T) × a Z, where T is the unit circle, a (n) = an is a rotation through the angle -2 pnq for n  Î Z, and q is a fixed irrational number. We will apply some results about patial actions to represent this crossed product as a C*-subalgebra of B (L2 (T)). Also, by a different method form the proof of Davidson, we show that this crossed product is isomorphic to the irrational rotation algebra.