(1) ∂tu = a∆u− f0(u, t) + g0(x, t), u|∂Ω = 0 (or ∂u/∂ν|∂Ω = 0) where u = u(x, t) = (u, . . . , u ), x ∈ Ω b R, t ≥ 0, f0(v, s) = (f 0 , . . . , f 0 ), (v, s) ∈ R × R+, g0(x, s) = (g 0 , . . . , g 0 ), x ∈ Ω, s ≥ 0. We assume that the matrix a and the functions f0, g0 satisfy some general conditions (see Section 2). These conditions provide the existence of a solution u of the Cauchy problem for...

SparseM provides some basic R functionality for linear algebra with sparse matrices. Use of the package is illustrated by a family of linear model fitting functions that implement least squares methods for problems with sparse design matrices. Significant performance improvements in memory utilization and computational speed are possible for applications involving large sparse matrices.

Abstract The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, – where the standard definitions are shown to be deficient, – is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differ...

Given a simple Lie algebra g, we consider the orbits in g * which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of R-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pe...

A graph G = (V, E) is said to admit a system of μ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices u, v of G a spanning tree T ∈ T (G) exists such that the distance in T between u and v is at most r plus their distance in G. In this paper, we examine the problem of finding “small” systems of collective additive tree r...

For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The twoparameter family is closely related to two two-...

Resonance theory deals with the description of the nucleon-nucleus interaction and aims at the prediction of the experimental structure of cross sections. Resonance theory is basically an interaction model which treats the nucleus as a black box, whereas nuclear models are concerned with the description of the nuclear properties based on models of the nuclear forces (nuclear potential). Any the...

We present an integral formula for the universal R -matrix of quantum affine algebra Uq(ĝ) with ’Drinfeld comultiplication’. We show that the properties of the universal R -matrix follow from the factorization properties of the cycles in proper configuration spaces. For general g we conjecture that such cycles exist and unique. For Uq(ŝl2) we describe precisely the cycles and present a new simp...