Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

A non-linear transform, called ‘‘sign Haar transform’’ has recently been introduced. The transform is unique and converts binary/ternary vectors into ternary spectral domain. Recursive definitions for the calculation of sign Haar transform are developed. Essential properties of logic functions and variables in the spectral domain of a quantized transform based on Haar functions are presented. S...

This paper presents various algorithms for motion detection, object classification, object tracking and action recognition. It is an essential benchmark in the fields of video surveillance, traffic monitoring, border security etc. A novel approach is presented for detecting vehicles and pedestrians based on haar features. Haar feature value is calculated by using the rectangle integral, each re...

A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate...

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...

in this short note, we have given a short proof for the existence of the haar measure on commutative locally compact hypergroups based on functional analysis methods by using markov-kakutani fixed point theorem.

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

In the present paper Haar wavelet method is implemented on advectiondispersion equation representing one dimensional contaminant transport through a porous medium. Non uniform flow is considered by assuming velocity and dispersion varying with time as an exponentially increasing function. Expressing the Haar wavelets in advection-dispersion equation into Haar series provides the main advantage ...