using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

The key polynomials, defined by Lascoux–Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free polynomials. proof uses two combinatorial models first is due to Kohnert. second in terms Searles’ rule quasi-key polynomials Assaf–Searles. Our argument proves a sufficient condition polynomial be multiplicity-free.

Large sets of combinatorial designs has always been a fascinating topic in design theory. These form partition the whole space into with same parameters. In particular, large set block designs, whose blocks are size k taken from an n-set, is all k-subsets n-set disjoint copies defined on and The current most intriguing question this direction whether Steiner quadruple systems exist to provide e...

Let (R,m) be a d-dimensional Noetherian local ring and E a finitely generated R-submodule of a free module R. In this work we introduce a Buchsbaum-Rim multiplicity sequence ck(E), k = 0, . . . , d + p − 1 for E that generalize the Buchsbaum-Rim multiplicity defined when E has finite colength in R as well as the Achilles-Manaresi multiplicity sequence that applies when E ⊆ R is an ideal. Our ma...

The multiplicity of a zero of a (univariate, polynomial) spline is defined in terms of its B-spline coefficients, thus making certain bounds trivial while, at the same time, adhering to the principle that the multiplicity of a zero indicates the number of simple zeros nearby achievable by a nearby element from the same class. In particular, the multiplicity depends on the class to which the fun...