We give a new generalization of the spt-function of G.E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F.G. Garvan, to jsptk(n), thus providing a two-fold generalization of spt(n), and give its combinatorial interpretation.

A modification of the Balanced Stoc1insiti.c Truncation method fqr relative error model reduction is introduced. The method is based on replac~ng the truncat~on step w ~ t h a generalized s~iigular pertmbat~on approxlmatlon. The new method is shown to satisfy an infinity norm bound on the relative error between the full order and the reduced order models. The discrete time balaiiced stochastic ...

In this communication, we consider and study a generalized two parameters entropy of order statistics and derive bounds for it. The generalized residual entropy using order statistics has also been discussed.

We prove upper and lower bounds for the leading coefficient of Kolchin dimension polynomial systems partial linear differential equations in case codimension two, quadratic with respect to orders system. A notion typical plays an important role algebra, some its estimations were proved by J. Ritt E. Kolchin; they also advanced several conjectures that later refuted. Our bound generalizes analog...

We give a complete solution to the Borel–Ritt problem in non-uniform spaces $${\mathscr {A}}^-_{(M)}(S)$$ of ultraholomorphic functions Beurling type, where S is an unbounded sector Riemann surface logarithm and M strongly regular weight sequence. Namely, we characterize surjectivity existence continuous linear right inverse asymptotic Borel map on terms aperture sequence M. Our work improves p...

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...