This paper is concerned with solvability and solution stability of parametric generalized equations governed by set-valued mappings. By a degree-theoretic approach for multifunctions, some new results on lower semicontinuity of the solution map to a parametric generalized equation are established.

Consider linear systems whose matrix and right-hand side vector depend affine-linearly on parameters varying within prescribed bounds We present some sufficient conditions under which the interval hull (or some bounds) of the solution set of a parametrised interval linear system coincides with the interval hull (or bounds) of the non-parametric interval linear system corresponding to the parame...

Consider linear systems whose matrix and right-hand side vector depend affine-linearly on parameters varying within prescribed bounds We present some sufficient conditions under which the interval hull (or some bounds) of the solution set of a parametrised interval linear system coincides with the interval hull (or bounds) of the non-parametric interval linear system corresponding to the parame...

An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.

This paper describes an eecient and numerically stable modiication of the QR decomposition for solving a parametric set of linear least squares problems with a parametric matrix A+B for several values of the parameter. The method is demonstrated on a typical application.

Consider linear systems involving affine-linear dependencies on interval parameters. Presented is a free C-XSC software implementing a generalized parametric fixed-point iteration method for verified enclosure of the parametric solution set. Some specific features of the corresponding algorithm concerning sharp enclosure of the contracting matrix and inner approximation of the solution enclosur...

In this paper, we merge the parametric structure of neural networks into a segmental semi-Markov model to set up a Bayesian framework for protein structure prediction. The parametric model, which can also be regarded as an extension of a sigmoid belief network, captures the underlying dependency in residue sequences. The results of numerical experiments indicate the usefulness of this approach.

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of n linear differential polynomial parametric equations in n− 1 differential parameters. We give necessary conditions to ensure properness of the system of differential polynom...

Consider a linear system A(p) · x = b(p), where the elements of the matrix and the right-hand side vector depend linearly on a m-tuple of parameters p = (p1, . . . , pm), the exact values of which are unknown but bounded within given intervals. Apart from quantifier elimination, the only known general way of describing the solution set {x ∈ Rn | ∃p ∈ [p],A(p)x = b(p)} is a lengthy and non-uniqu...