Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz Чехословацкий математический журнал т. 11 (86) 1961, Прага LES COMPLEXES OSCULATEURS DES CONGRUENCES DE DROITES VLADIMIR HORÀK, Brno (Reçu le 10 mai 1960) L'auteur étudie dans l'espace projectif à cinq dimensions de Klein les variétés (Q) qui sont les images secondaires des complexes linéaires osculateurs des droites des congruences non-paraboliques, c.-à-d. des congruences W et des congruences qui possèdent une surface focale développable et une courbe directrice non rectiligne. Moyennant des variétés (Q), l'auteur décrit quelquesuns des types remarquables des congruences W et déduit leurs nouvelles propriétés.
This paper presents an extension of the non-field analytical method—known as the method of Kulish—to solving heat transfer problems in domains with a moving boundary. This is an important type of problems with various applications in different areas of science. Among these are heat transfer due to chemical reactions, ignition and explosions, combustion, and many others. The general form of the non-field solution has been obtained for the case of an arbitrarily moving boundary. After that some particular cases of the solution are considered. Among them are such cases as the boundary speed changing linearly, parabolically, exponentially, and polynomially. Whenever possible, the solutions thus obtained have been compared with known solutions. The final part of the paper is devoted to determination of the front propagation law in Stefan-type problems at large times. Asymptotic solutions have been found for several important cases of the front propagation.
The paper is focused on developing a mathematical model capable to describe thermodynamic processes connected with the vacuum technique. The model is based on the laws of energy and mass conservation, the air state behavior, and the principles of airflow, including the critical flow. The problem has been solved numerically by MATLAB. The results of the solution include the pressure evolution for a given pumping speed and the volume to be evacuated. Solutions are obtained for cases of airflow to the vacuum chamber through an inlet opening for three various diameters. The solutions are validated by comparing with experimental data. The presented model agrees with the experiment quite well. One very useful application is the determination of the relation between the diameter of the inlet opening and the pumping speed of the vacuum pump at the pressure steady state condition. This is an important knowledge for a simple and reliable quantitative pressure control in vacuum systems.
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