We introduce a family of first-order multi-dimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations “stabilized inverse diffusion eq...

Incremental stability analysis for time-delay systems has attracted more and attention its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches the criteria exponential incremental with continuous or discontinuous right-hand sides. Firstly, sufficient conditions sides are studied, several corollaries specific case...

In this paper, we consider using Galerkin projection methods for solving multiple linear systems A (i) x (i) = b (i) , for 1 i s, where the coeecient matrices A (i) and the right-hand sides b (i) are diierent in general. In particular, we focus on the seed projection method which generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed ...

The notion of call-by-need evaluation has turned out to be very fruitful when applied to dialects of the i-calculus (Henderson and Morris, 1976, in “Proc. 3rd ACM Symp. on the Principles of Programming Languages, Atlanta; Kahn and Mac Queen, 1977, in “IFIP 77,” North-Holland, Amsterdam; Turner, 1979, Software Practice and Experience, Vol. 9; Vuillemin, 1974, J. Cornput. System3 .Sci. 9, 332-354...

It is now a good time to go back to the MZV story. where F (a, b; c; z) denotes the hypergeometric function and i = √ −1. Proof. Routine verification (with a help of Lemma 4.1 for the left-hand side) shows that the both sides of the required equality are annihilated by action of the differential operator (1 − z) d dz 2 z d dz 2 − t 4 ; in addition, the first terms in z-expansions of the both si...