‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

the aim of this paper is a) if σak2 < ∞ then σak rk(x) is in bmo that{rk(x)} is rademacher system. b) p1k=1 ak!nk (x) 2 bmo; 2k  nk < 2k+1that f!n(x)g is walsh system. c) if jakj < 1k then p1k=1 ak!k(x) 2 bmo.

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

The classical Haar wavelet system of L2(R) is commonly considered to be very local in space. We introduce and study in this paper piecewise-constant framelets (PCF) that include the Haar system as a special case. We show that any bi-framelet pair consisting of PCFs provides the same Besov space characterizations as the Haar system. In particular, it has Jackson-type performance sJ = 1 and Berns...

We present a system for object detection applied to street detection in satellite images. Our system is based on asymmetric Haar features. Asymmetric Haar features provide a rich feature space, which allows to build classifiers that are accurate and much simpler than those obtained with other features. The extremely large parameter space of potential features is explored using a genetic algorit...

This paper deals with Szegö type limits for multiplication operators on L(R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class o...

In this paper, Haar wavelet based identification of a continuous-time linear time-varying (LTV) system is proposed. For that purpose, input and output data are analyzed to derive an algebraic equation, leading to estimation of Haar wavelet coefficients for the impulse response. Finally, it is demonstrated that an LTV system can be effectively identified by solving the algebraic equation and by ...