Volume 16, Issue 6

Abstract - The problem of thin-wire antenna radiation under pulse excitation reduces to the solution of a hypersingular integral equation of the first kind on a segment, with the Dirac d-function in its right-hand side. We propose and justify the numerical method of the type of the discrete vortex pair method. We compare the numerical solution for a half-wave rectilinear cylindrical dipole with the well-known solution resulting from other considerations. We study problems of the unique existence of the solution to the corresponding characteristic hypersingular integral equation. For this purpose the equation is regarded as a pseudodifferential operator in some weight Sobolev spaces.

- We consider dynamic random- structure systems. We construct a statistical simulation algorithm based on the numerical solution of stochastic differential equations (SDEs) for the probabilistic analysis of two types of random- structure systems and give the results of numerical experiments.

Abstract - In this work we consider the problem of calculating the probability that a random process fails to reach the boundary in a definite time. We justify the application of the splitting method and the principle of importance sampling for calculation optimization. We give the results of numerical calculations which confirm the validity of theoretical conclusions

- A brief critical survey of the main achievements in ocean modelling, which is based essentially on the author’s 50-year experience, is presented. Several conclusions are made: (1) the rot t is not the main part of external mechanical driving. The wind stress also acts in the form of divt and even just as constant t; (2) the b-effect is not the main factor in westward intensification. There are other coastal intensifications, upwellings-downwellings; (3) the baroclinicity of ‘open ocean’ zonal currents, bottom topography, and the JEBAR play an important role in those processes.

Abstract - We establish the uniform convergence of a difference solution to the Dirichlet problem for the Laplace equation on a rectangular parallelepiped, which is of the second order with respect to a grid step. The given boundary conditions are supposed to have the second derivatives on the parallelepiped faces, which satisfy the H¨older condition. We give no compatibility conditions for boundary values on edges except for a continuity condition. Thus, the discontinuities of the second derivatives of the sought solution on edges are admissible. Wasov [11] and the author [7] obtained the analogous result on a rectangle for the two-dimensional case. The Wasov method cannot be used for the three-dimensional case. By contrast, the method [7] with essential additions is used.