Dissipative Operators in a Hilbert Space With an Indefinite Metric

Abstract

The article describes a small and portable apparatus designed to measure the dynamic stiffness of roads and soils under sinusoidal loading, at frequencies between 5 and lo00 Hz. An electromagnetic vibrator applies forces of up to rf: 14 lb (about its dead weight of 45 lb) to the road surface, the force itself and the resulting displacement of the road surface being measured by means of electrical transducers feeding a phase-sensitive voltmeter. Values of the elastic stiffness of the construction and values of the damping are obtained. Check tests of the behaviour of the apparatus are described, and some typical results on various types of road pavement are given.

Operator identities corresponding to inverse problems for Dirac systems

“…that is, the operator A * is S ε -dissipative. Next, we will use several statements from [5], where earlier results (results on operators in the space Π κ from [21,22] ) are developed for the case that we are interested in. Because of [5, statement 9 • ] we see that A * ker S ε ⊆ ker S ε .…”

On a Linear Problem Connected with Equilibrium Figures of a Uniformly Rotating Viscous Liquid

“…To prove the estimate (1.7), one can use the method of "generalized energy" suggested by Padula [7][8][9]. The proof of Theorem 1.2 is based on the theorem about the invariant spaces of dissipative operators [10,11] applied to the spectral problem…”

“…By the Krein-Langer-Azizov theorem [10,11], −iA has a k-dimensional invariant subspace H k such that (J U,U) 0 ∀U ∈ H k and the spectrum of −iA…”

Dimerization of Propene in Ionic Liquids Using Nickel-Containing Catalytic Ditiosystems

“…В ИНХП Национальной Академии Наук Азербайджана нами ранее было создано семейство новых высокоактивных каталитических дитиосистем на основе органических дитиопроизводных (дитиофосфатов, дитиокарбаматов и ксантогенатов) никеля и кобальта и алюминийорганических соединений (AOC) для (со)димеризации, олигомеризации и полимеризации олефинов и диенов [10][11][12][13][14][15]. При растворении в алифатических, хлорированных или ароматических углеводородах никельсодержащие каталитические дитиосистемы оказались эффективными катализаторами димеризации пропилена с производительностью 25 кг димера / г Ni•час [10].…”