This paper is concerned with the solvability of implicit time-stepping methods for simulating the dynamics of multi-body systems. The standard approach is to select a time-step based on desired level of accuracy and computational efficiency of integration. Implicit methods impose an additional but often overlooked requirement that the resulting nonlinear root-finding problem is solvable and has...

We study the notion of solvability in the resource calculus, an extension of the λ-calculus modelling resource consumption. Since this calculus is non-deterministic, two different notions of solvability arise, one optimistic (angelical, may) and one pessimistic (demoniac, must). We give a syntactical, operational and logical characterization for the may-solvability and only a partial characteri...

We study the solvability of sparse blind separation of n non-negative sources from m linear mixtures in the under-determined regime m < n. The geometric properties of the mixture matrix and the sparseness structure of the source matrix are closely related to the identification of the mixing matrix. We first illustrate and establish necessary and sufficient conditions for the unique separation f...

This work is devoted to the question of uniqueness and solvability for the linear problem of ship waves, describing the forward motion of rigid totally submerged bodies in an unbounded fluid with a free surface. We discuss the statement of the problem with some attention paid to the conditions at infinity. For the problem we derive Green’s identity and boundary Fredholm integral equations on th...

A direct and inverse scattering theory on the full line is developed for a class of firstorder selfadjoint 2n • 2n systems of differential equations with integrable potential matrices. Various properties of the corresponding scattering matrices including unitarity and canonical Wiener-Hopf factorization are established. The Marchenko integral equations are derived and their unique solvability i...

This paper investigates whether the assumption of unique identifiers is essential for wait-free distributed computing using shared objects of various types. Algorithms where all processes are programmed identically and do not use unique identifiers are called anonymous. A variety of results are given about the anonymous solvability of two key problems, consensus and naming, in systems of variou...

We study the inverse problem of recovering source function in a degenerate parabolic equation with many spatial variables. An additional integral observation condition is imposed. find sufficient conditions for unique solvability cases where unknown looked space L2(0, T) or L∞(0, T). The results obtained are based on preliminary corresponding direct which independent interest.

in this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. with this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. n(g) and s(g) are the set of all nilpotency classes and the set of all solvability classes for the group g with respect to different automorphi...

We consider the averaging principle for stochastic reaction–diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical ...