Eigenvalues and eigenvectors assignment for neutral type systems

Abstract

International audienceFor a class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors. The result is used for the analysis of the critical number of solvability of a vector moment problem

Spectral Assignment for Neutral-Type Systems and Moment Problems

“…The present paper is a detailed version of the short note published in Comptes Rendus Mathematiques [7].…”

“…The elements of matrices A 2 (·) and A 3 (·) take values in L 2 (−1, 0). The neutral-type term A −1ż (t − 1) consists of a simple delay, while the others include multiple discrete and distributed delays.As shown in [3,18,19], this system can be rewritten in the operator form (1.2)ẋ(t) = Ax(t), x(t) = y(t) z t (·) , * Some results developed here were announced in a short note published by Comptes Rendus Mathématique [24]. …”

“…we consider an arbitrary set of distinct complex numbers {λ This theorem was announced in Comptes Rendus Mathematique [24].…”

On Asymptotic Estimation of a Discrete Type $$C_0$$ C 0 -Semigroups on Dense Sets: Application to Neutral Type Systems

“…, 0 , are different and simple, the corresponding eigenvalues of A, say {λ k } k∈Z (and A + BF), are also simple and are in some disjoint circles of summable with square radii r k . It was proven (see [14,Theorem 8] and [18,19]) that in such a case for any choice of complex sequence {λ k } k∈Z in the same circles, there exists feedback F of the form (27) such that the numbersλ k will be eigenvalues of A + BF. In other words, the eigenvalues of A can be moved by the feedback to any point of corresponding circles.…”

Use of liquid digestate of biogas production to fertilize winter wheat

“…Унаслідок біохімічних перетворень зі збродженого субстрату утворюється біогаз і переброджена органічна маса. Склад органічних продуктів, отриманих на виході з біогазових установок, залежить від біохімічного складу вихідного гною та іншої сировини, яка завантажується в метантенк [19]. Так, з 1 т вихідного продукту утворюється дигестату, кг: силосу кукурудзи -780, курячого посліду -890, жому -910, гною ВРХ -920, гноївки свиней -990.…”