Ladislav Adamec

On kinetics of reactions in HV circuit breakers after current zero

An analysis of six different definitions of the rate of reaction is made and it is shown that some of the definitions are not consistent with the mass action law. Kinetic equations are derived whose solution is the time dependence of the composition of an arbitrary closed gaseous system in an ideal state for a given time dependence of temperature on the assumption that either the time dependence of pressure in or the time dependence of the volume of is given. Results are given of the computation of composition of a system of SF6 dissociation and ionization products at a temperature drop from 12 000 K to room temperature and a comparison is made of the time-dependent composition with equilibrium composition for pressures of 0.1, 0.5, 1 and 2 MPa.

A note on continuous dependence of solutions of dynamic equations on time scales

We give a precise formulation and a proof as constructive as possible of the widely accepted claim that solutions of a dynamic equation depend continuously on the base time scale. Our approach to this problem is via Euler polygons which opens possibilities for development of numerical analysis of dynamic equations on time scales.

A Remark on Matrix Equation x^{ \Delta } = A(t)x on Small Time Scales

In this paper, we study the structure of a principal fundamental matrix of a linear time-dependent equation on a time scale 𝕋. We derive an explicit formula for which, if 𝕋 is in a sense small, allows to replace by a restriction of a principal fundamental matrix of an ordinary differential equation

Comments on the computation of the composition of quenching media in HV circuit breakers after current zero

General equations are derived whose solution gives the dependence of species concentrations of a closed gaseous system on time for a given dependence of temperature on time, on the assumption that either the dependence of pressure in on time or the dependence of volume of system on time is given. Some results from solving a previously proposed model are given for the case when is created by the products of dissociation and ionization and the temperature decreases exponentially from 10 000 K to 2500 K. Special attention is devoted to the relation between time-dependent composition and equilibrium composition.

A theorem of Ważewski and dynamic equations on time scales

An important and well known extension of the direct method of Lyapunov functions is a simple topological principle, in the geometrical theory of ordinary differential equations known as Ważewskis principle. It is much less known that there is an old variant of this principle for difference equations stated by Coffman. In this paper, we combine both methods to a method usable for dynamic systems on time scales and discuss some first results.

Oscillation Conditions for a Third-Order Linear Equation.

Consider the equation (1.1) u+p(t)u=0 were p is a locally integrable function. A solution of Eq. is defined as a function u locally absolutely continuous together with its first-and second-order derivatives and satisfying the equation almost everywhere. A nontrivial solution of Eq.(1.1)is said to be oscillating if it has infini tely many zeros and nonoscillating otherwise. Equation (1.1) is oscillating if it has at least one oscillating solution and nonoscillating otherwise. In the present paper, we prove integral oscillation criteria for Eq. (1.1), we assume that p is of constant sign.

On asymptotic properties of a strongly nonlinear differential equation

AbstractThe paper describes asymptotic properties of a strongly nonlinear system

A ROUTE TO ROUTH — THE CLASSICAL SETTING

\dot x = f(t,x),{\text{ }}(t,x) \in \mathbb{R} \times \mathbb{R}^n