Тhe multidimensional analog of the frequencies polygon method with the absorption estimators for global approximation of the solution of integral equation of the second kind is considered. The upper boundary of the error is constructed and the conditionally optimal values of the parameters are obtained on base of C-approach. The results of test calculations for a model integral equation are presented 

Это --- слегка расширенный текст доклада, прочитанного на конференции по математической гидродинамике в университете г. Халл, Англия, 10 апреля 2001 г. Доклад был также повторен в Институте Ньютона, Кембридж, 23 апреля 2001 г. Название доклада предложил В.А.Владимиров, пригласив меня выступить на конференции в Халле. "Почему 11?" --- спросил я его. "Да так, --- ответил он. --- У Гильберта было 20 проблем, у Смейла --- 19, но это же по всей математике. Ну, если Вам не нравится, можно заменить название." Но мне число 11 понравилось. Оно встречается не так часто, как, скажем, 12 или 7, и вспомнилось, что разные и притом любимые мною авторы упоминают его, говоря о сражениях и атаках (на докладе мне еще напомнили, что в футбольной команде 11 игроков. А недавно я прочитал в статье А.Казанцева, в журнале "Шахматное обозрение", 2, 2001, что "11 --- по исследованиям создателя альфаметрики В.И.Авинского --- модуль Вселенной, причастный ко всем размерам и микро-, и макромиров"). Так что это боевое число, пусть оно остается в заголовке, хотя не следует его принимать слишком всерьез ...  

Low frequency free vibrations and buckling under action external pressure for non-streight cirkle conical shell are considered. The results of zero-approximation for frequency and buckling parameters for the different kinds of non-streight conical shells are presented. At the end of every chapter the deformed shapes for the vibrations and the buckling of the shells are illustrated 

The question of the solvability of the rod force bending problem by the method, suggested by Sen-Venan is considered. This question is reduced to the solving of some linear algebraic system of equations. The unequality of the determinant of the system to the zero is proved 

The analysis of a boundary value problem concerned with the Reynolds equation of gas bearing theory is carried out. The existence and uniqueness of the solution of this problem is proved. Some estimations for the solution are obtained. The numerical algorithm is constructed and its convergence is proved 

Ultimate breaking loads obtained with the framework of classical fracture criterion and structural-temporary fracture criterion is carried out. Is shown, that the classical criterion gives an visible divergence with experiment, while the analysis of the experimental data on the basis of the theory of incubation time the exact results gives. The dynamics viscosity values for specimens with macrocracs are estimated. Is shown, that the dynamic viscosity is not a constant and depends on the initial conditions of loading 

Special features of fracture under impact loading are cosidered. A micromechanical nucleation and growth model is described and analyzed. The incubation time of fracture is described like a stress relaxation time. A solution of the one-dimensional problem of scabbing is obtained. A curve of strength-time dependence for aluminum and pmma is built by structure-time criterion of strength. A good correspondence between calculation solution and experimental data is marked. The incubation time is interpreted like time of microfracture relaxation 

The transversal flow of a plate in the supersonic flow of rarefied gas is considered. The flow is researched on the basis of a numerical solution of a kinetic equation by a method of finite differences.s.The flow about of a heat-insulated plate up to a Mach number 21.90 and the flow about a cold plate up to a Mach number 10.95 is investigated. The area of rarefaction behind a plate is founded. The drag coefficient of a heat-insulated plate is calculated 

The problem of physical realizability of a state of a cantilever bar corresponding with the solution of the variational problem is considered. The criterion of continuity of relation between the solution of the problem and and parameters of the considered functional is obtained 

The fast algorithm for the calculation of sliding Fourier spectrum segment is elaborated. Efficiency evaluation is done