scholarly journals ε-Positional Strategies in the Theory of Differential Pursuit Games and the Invariance of a Constant Multivalued Mapping in the Heat Conductivity Problem

2019 ◽  
Vol 65 (1) ◽  
pp. 124-136
Author(s):  
M Tukhtasinov ◽  
Kh Ya Mustapokulov
Keyword(s):  
Heat Conductivity ◽  
Multivalued Mapping ◽  
Conductivity Equation ◽  
Pursuit Games ◽  
Terminal Set ◽  
Distributed Parameters ◽  
Heat Conductivity Equation ◽  
Differential Pursuit ◽  
The Right ◽  
Additive Control

In this paper, we consider two problems. In the first problem, we prove that if the assumption from the paper [1] and one additional condition on the parameters of the game hold, then the pursuit can be finished in any neighborhood of the terminal set. To complete the game, an ε-positional pursuit strategy is constructed.In the second problem, we study the invariance of a given multivalued mapping with respect to the system with distributed parameters. The system is described by the heat conductivity equation containing additive control terms on the right-hand side.

scholarly journals On an Invariant Set in the Heat Conductivity Problem with Time Lag

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
M. Tukhtasinov ◽  
G. I. Ibragimov ◽  
N. O. Mamadaliev
Keyword(s):  
Heat Conductivity ◽  
Multivalued Mapping ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Conductivity Equation ◽  
Strong Invariance ◽  
Heat Conductivity Equation ◽  
Conductivity Problem

The problems of weak and strong invariance of a constant multivalued mapping with respect to the heat conductivity equation with time lag are studied. Sufficient conditions of weak and strong invariance of a given multivalued mapping are obtained.

scholarly journals EFFECT OF FREE ELECTRONS IN STEEL ON ITS QUENCHING PROCESS IN WATER AND WATER SALT SOLUTIONS

2018 ◽  
Vol 1 ◽  
pp. 39-46 ◽  
Author(s):  
Nikolai Kobasko
Keyword(s):  
Heat Conductivity ◽  
Nucleate Boiling ◽  
Conductivity Equation ◽  
Free Electrons ◽  
Heat Conductivity Equation ◽  
Quenching Process ◽  
Water Salt ◽  
Electrical Layer ◽  
The Common ◽  
Common Nature

In the paper some phenomena of physics taking place during quenching steel in liquid media is widely discussed. It is shown that a double electrical layer is responsible for unknown impulse like effect constantly observed during quenching probes in electrolytes. It can be used for transient nucleate boiling process evaluation that is a basis for designing intensive quenching technology known as IQ-2 process. Early published phenomena of physics such as a poker effect, two stage cooling, and optimal concentration of electrolytes have the common nature – free electrons in metal. The observed phenomena of physics can be governed by hyperbolic heat conductivity equation with the appropriate initial and boundary conditions instead of parabolic heat conductivity widely used equation. At present time, fortunately, mathematicians started seriously investigations in this area by solving hyperbolic heat conductivity equations which can release in the future more new unknown phenomena to be widely used in the practice.

Sign in / Sign up

Export Citation Format

Share Document