The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert spa...The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.展开更多
Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a sy...Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.展开更多
The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with sma...The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.展开更多
FOR Lovering Stchizya, a 37-yearoold Zambian journalist working with the Zambia News and Infor- mation Services, a one-year master＇s program in China has brought fresh enthusiasm for his chosen profession. ＂The mos...FOR Lovering Stchizya, a 37-yearoold Zambian journalist working with the Zambia News and Infor- mation Services, a one-year master＇s program in China has brought fresh enthusiasm for his chosen profession. ＂The most interesting thing I＇ve learned in China is how the media can contribute to the solution of social dilemmas in society, using the constructive journalism approach,＂ he told ChinAfrica, adding that constructive journalism is a new concept he learned here.展开更多
This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
文摘The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.
文摘Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.
基金Project supported by National Natural Science Foundation of China.
文摘The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.
文摘FOR Lovering Stchizya, a 37-yearoold Zambian journalist working with the Zambia News and Infor- mation Services, a one-year master＇s program in China has brought fresh enthusiasm for his chosen profession. ＂The most interesting thing I＇ve learned in China is how the media can contribute to the solution of social dilemmas in society, using the constructive journalism approach,＂ he told ChinAfrica, adding that constructive journalism is a new concept he learned here.
文摘This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
