The aim of this paper is to introduce the concept of convergence of a sequence on hypernormed spaces and establish a few basic properties of convergent sequences and Cauchy sequences on hypernormed spaces. Also we have established a necessary and sufficient condition for a Cauchy sequence to be convergent sequence in this spaces. In fact, also it has been shown that limit of a convergent sequen...

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

We draw here on the relation between the Cauchy and hyperbolic secant distributions to prove that the MLE of the scale parameter of Cauchy distribution is log-normally distributed and to study the properties of a Hodges-Lehmann type estimator for the scale parameter. This scale estimator is slightly biased but performs well even on small samples regardless of the location parameter. The asympto...

We present an affirmative answer to Stanley’s zrank conjecture, namely, the zrank and the rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs are determined by the number of zero entries. We also give a characterization of the rank in terms of the Giambelli-type matrices of the corresponding skew Schur func...

Motivated by some results about reverses of the Jensen inequality for positive measure, in this paper we give generalizations those real Stieltjes measure dλ which is not necessarily using several Green functions. Utilizing these define new mean value theorems Lagrange and Cauchy types, derive Cauchy-type means.

This paper contains a theoretical formulation of multiple interface cracks in two bonded dissimilar half planes subjected to in-plane traction. The distributed dislocation technique is used to construct integral equations for a dissimilar mediums weakened by several interface cracks. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obta...

Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏ (i,j)∈η(1 − xiyj) −1, where the product is over all cell-coordinates (i, j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest s...