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-...

In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for appr...

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 present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

We show that with small modifications in diverse expressions for the shifted Legendre polynomials, we can obtain the corresponding relations for Daubechies polynomials.