Summary: The article offers an approach to establishment of conditions of existence and uniqueness of solution of the boundary value problem for the linear integro-differential equation with a parameter, as well as represents the method of reducing the given problem to the equivalent integral equation.
The article is of theoretical nature. The results obtained may be used for treatment of specific applied problems. Theoretical computations are illustrated with specific example.
Keywords: boundary-value problem, integro-differential equation, uniqueness of a solution, integral equation.
Anotation: This paper describes N.N.Boholyubov fundamental contribution to the development of statistical mechanics on the example of the principle of correlation weakening.
Keywords: Bogolyubov, correlation, principle of weakening correlation, quasiaverage.
Summary: Offered the elementary static geometric model of nucleus from nuclons with 4 bonds describes the method of nucleus formation and shape-generating clusters, explain main features of fission mass-spectrums, allows to show out discrete of nucleus binding energy formula. Two ways of mass number increase are educed - concentric and linear chainlets of clusters. The Form Distinction of nucleus with a equal nuclon depot looks in a model as the isomeria reason. A possible analogy is indicated between the forms of nucleus and accessible to the supervision by the clusters of amorphous silicon.
The Key Words: nucleus form, tetrahedron, clusters, binding energy.