in this study a numerical method is developed to solve the hammerstein integral equations. to this end the kernel has been approximated using the leastsquares approximation schemes based on legender-bernstein basis. the legender polynomials are orthogonal and these properties improve the accuracy of the approximations. also the nonlinear unknown function has been approximated by using the berns...

In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...

This paper presents a method for solving the problem of global illumination for general environments, using projection of the radiance function on a set of orthonormal basis functions. Wavelet scaling functions form this basis set. The highlights of the paper are : it (i) points out the di culty associated with the straightforward projection of the integral operator associated with the radiance...

‎let $g_{i} $ be a subgroup of $ s_{m_{i}}‎ ,‎ 1 leq i leq k$‎. ‎suppose $chi_{i}$ is an irreducible complex character of $g_{i}$‎. ‎we consider $ g_{1}times cdots times g_{k} $ as subgroup of $ s_{m} $‎, ‎where $ m=m_{1}+cdots‎ +‎m_{k} $‎. ‎in this paper‎, ‎we give a formula for the dimension of $h_{d}(g_{1}times cdots times g_{k}‎, ‎chi_{1}timescdots times chi_{k})$ and investigate the existe...