O matematice v mobilu
Some estimates for the oscillation of the deformation gradient
As a measure of deformation we can take the difference , where is the deformation gradient of the mapping and is the deformation gradient of the mapping , which represents some proper rigid motion. In this article, the norm is estimated by means of the scalar measure of nonlinear strain. First, the estimates are given for a deformation satisfying the condition . Then we deduce the estimate in the case that is a bi-Lipschitzian deformation and .
Reproducing kernel particle method and its modification
Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications...
Integral transforms -- the base of recent technologies
In this article, the attention is paid to Fourier, wavelet and Radon transforms. A short description of them is given. Their application in signal processing especially for repairing sound and reconstructing image is outlined together with several simple examples.
Realization of Dirichlet conditions in RKPM
Shape functions and wavelets - tools of numerical approximation
Solution of a boundary value problem is often realized as the application of the Galerkin method to the weak formulation of given problem. It is possible to generate a trial space by means of splines or by means of functions that are not polynomial and have compact support. We restrict our attention only to RKP shape functions and compactly supported wavelets. Common features and comparison of approximation properties of these functions will be studied in the contribution.
Wavelets and prediction in time series
Wavelets (see [2, 3, 4]) are a recent mathematical tool that is applied in signal processing, numerical mathematics and statistics. The wavelet transform allows to follow data in the frequency as well as time domain, to compute efficiently the wavelet coefficients using fast algorithm, to separate approximations from details. Due to these properties, the wavelet transform is suitable for analyzing and forecasting in time series. In this paper, Box-Jenkins models (see [1, 5]) combined with wavelets...
Numerical solution of boundary value problems by means of B-splines
Why are the meshless methods used?
Bézier curves and their applications
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