Algorithm of Hardy Function Interpolation and its Visualization in the Formation of the Virtual Battlefield Terrain

this thesis puts forward the idea of using the searching method to retrieve two kinds of data points of the circle and the square to generate DEM data of the collected discrete points by means of using C# language and OpenGL DLL, thus realizing the visualization of the three-dimensional virtual terrain from contours on the two-dimensional surface. This thesis makes a comparison and analysis of the visualization effect which indicates that this algorithm is quick and effective. This research has a certain reference value for the formation of the virtual battlefield terrain.

THE EFFECTIVENESS OF THE LEARNING ALGORITHM OF RADIAL BASIS NETWORKS WITH RELATION TO THE TRANSFER FUNCTIONS APPLIED ON THE EXAMPLE OF MAPPING OF THE LIE LAND OF ZIELONA GORA CITY

The article presents problems connected to the use of radial basis networks for the approximation of the ground surface. The main goal of this paper is to research into the precision of topographic profile representation with relation to the transfer functions applied. The paper contains a description of the structure of a radial basis network and a description of networks learning by means of the hybrid method with the use of the notion of the Green matrix pseudoinverse. Special attention was given to the problem of a choice of transfer functions: the Gauss function, the exponential function, the Hardy function, the spliced function of the third and fourth degree as well as bicentral functions with an independent slope and rotation. the result of this article is an example of the operation of a network with relation the transfer functions under discussion.

Unique continuation properties of the nonlinear Schrödinger equation

Consider the unique continuation problem for the nonlinear Schrödinger (NLS) equationBy using the inverse scattering transform and some results from the Hardy function theory, we prove that if u ∈ C(R; H1(R)) is a solution of the NLS equation, then it cannot have compact support at two different moments unless it vanishes identically. In addition, it is shown under certain conditions that if u is a solution of the NLS equation, then u vanishes identically if it vanishes on two horizontal half lines in the x–t space. This implies that the solution u must vanish everywhere if it vanishes in an open subset in the x–t space.