Numerous techniques have been proposed for shape representation, including landmarks [1], medial representation [2], spherical harmonics (SPHARM) [3], weighted SPHARM [4], and spherical wavelets (SW) [5]. Among them, both weighted SPHARM and SW have been used for local shape representation of biological structures. Questions we address in this paper are what is the relationship between them, ho...

“If there is technological advance without social advance, there is, almost automatically, an increase in human misery, . . . ”

We give wavelet description for nonlinear optimal dynamics (energy minimization in high power electromechanical system). We consider two cases of our general construction. In a particular case we have the solution as a series on shifted Legendre polynomials, which is parametrized by the solution of reduced algebraical system of equations. In the general case we have the solution as a multireso-...

We give the explicit time description of optimal dynamics for nonlinear diierential systems of equations (energy minimization in high power electromechanical system). We consider two cases of our general construction. In a particular case we have the solution as a series on shifted Legendre polynomials, which is parametrized by the solution of reduced algebraical system of equations. In the gen...

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...