At Exchange Process in Rotary Regenerative Air Pre–Heater

A simplified mathematical model of a rotary regenerative air pre–heater (RRAP) is suggested and studied based on the averaged dynamics of the heat exchange process between nozzles and a heat carrier (i.e. air or gas–smoke mixture). Averaging in both spatial coordinates and time gives a linear discrete system that allows deriving explicit formulas for determining the characteristics of the air heater and establishing some properties such as periodicity, stability, ergodicity and others.This work was supported by Committee for Coordination Science and Technology Development Under Cabinet of Ministers of Uzbekistan (projectno F4–FA–F014).Authors express their gratitude to G.I.I bragimov for useful discussion and help

SIMPLIFIED MODEL OF THE HEAT EXCHANGE PROCESS IN ROTARY REGENERATIVE AIR PRE–HEATER

A simplified mathematical model of a rotary regenerative air pre–heater (RRAP) is suggested and studied based on the averaged dynamics of the heat exchange process between nozzles and a heat carrier (i.e. air or gas–smoke mixture). Averaging in both spatial coordinates and time gives a linear discrete system that allows deriving explicit formulas for determining the characteristics of the air heater and establishing some properties such as periodicity, stability, ergodicity and others.A simplified mathematical model of a rotary regenerative air pre-heater (RRAP) is suggested and studied based on the averaged dynamics of the heat exchange process between nozzles and a heat carrier (i.e. air or gas-smoke mixture). Averaging in both spatial coordinates and time gives a linear discrete system that allows deriving explicit formulas for determining the characteristics of the air heater and establishing some properties such as periodicity, stability, ergodicity and others

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD

The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous'ko, a method of  grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form

The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

Solution of a linear pursuit-evasion game with integral constraints.

A linear two player zero-sum pursuit-evasion differential game is considered. The control functions of players are subject to integral constraints. In the game, the first player, the Pursuer, tries to force the state of the system towards the origin, while the aim of the second player, the Evader, is the opposite. We construct the optimal strategies of the players when the control resource of the Pursuer is greater than that of the Evader. The case where the control resources of the Pursuer are less than or equal to that of the Evader is studied to prove the main theorem. For this case a new method for solving of the evasion problem is proposed. We assume that the instantaneous control employed by the Evader is known to the Pursuer. For construction, the strategy of the Evader information about the state of the system and the control resources of the players is used

The Birman-Schwinger principle in von Neumann algebras of finite type

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the algebra in terms of the relative index

Fixed duration pursuit-evasion differential game with integral constraints

We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize it. Optimal strategies of the players are constructed, and the value of the game is found. It should be noted that energy resource of any pursuer may be less than that of the evader