A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...

Generalized Haar wavelets were introduced in connection with the problem of detecting specific periodic components in noisy signals. John Benedetto and I showed that the non–normalized continuous wavelet transform of a periodic function taken with respect to a generalized Haar wavelet is periodic in time as well as in scale, and that generalized Haar wavelets are the only bounded functions with...

We study global reflection symmetries of almost periodic functions. In the non-limit periodic case, we establish an upper bound on the Haar measure of the set of those elements in the hull which are almost symmetric about the origin. As an application of this result we prove that in the nonlimit periodic case, the criterion of Jitomirskaya and Simon ensuring absence of eigenvalues for almost pe...

In this note a method of designing optimal vibration control based on Haar functions to control of bounce and pitch vibrations in engine-body vibration structure is presented. Utilizing properties of Haar functions, a computational method to find optimal vibration control for the engine-body system is developed. It is shown that the optimal state trajectories and optimal vibration control are c...

A non-linear transform, called ‘Sign Hadamard-Haar transform’ is introduced. The transform is unique and converts ternary vectors into ternary spectral domain. Recursive definition and fast transform have been developed. Formulae to represent Sign Hadamard-Haar spectra for basic logic functions and their variables for two different codings are shown. New transform is extremely effective in term...

In our previous work, we showed empirically that independent (Haar) wavelet models were parsimonious, computationally efficient and accurate in modeling heterogeneous network traffic measured by both autocovariance functions and buffer loss rate. We also proved analytically that such models were capable of capturing any decay rate of auto-covariance functions at large lags. In this work, we foc...

The main purpose of this article is to demonstrate the use of the two Dimensional Walsh and Haar functions with Operational Matrix for solving nonlinear Volterra-Fredholm integral equations. The approximate solution is represented in the form of series. The approximate solution is obtained by two Dimensional Walsh and Haar series. The operational matrix and direct method for solving the linear ...

We propose an algorithm e ciently implementing TD( ) using (the in nite tree of) Haar basis functions. The algorithm can maintain and update the information of the in nite tree of coe cients in its nitely compressed form by taking advantage of the fact that the information obtained from nite training data is nite. Our algorithm computes the whole updating at each time step in time linear in the...