In this paper, Haar wavelet operational matrix method is proposed to solve a class of fractional partial differential equations. We derive the Haar wavelet operational matrix of fractional order integration. Meanwhile, the Haar wavelet operational matrix of fractional order differentiation is obtained. The operational matrix of fractional order differentiation is utilized to reduce the initial ...

We show that the empirical eigenvalue measure for sum of d independent Haar distributed n-dimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed n-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes t...

The war between colloids and crystalloids wages on. In a large multinational survey of fluid prescribing practices in critically ill patients, we have a new and intriguing snapshot of global fluid resuscitation practices. Colloids are more often used for impaired perfusion or low cardiac output, and the choice of colloid or crystalloid varies enormously between countries. Why are some ICUs pres...

This is the abstract. The problem of statement of SaintVenant’s Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of SaintVenants Principle of elasticity is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant’s Principle is suggested to fit and ...

In this paper, we present the estimation of Poisson intensity based on hypothesis testing in the wavelet domain for any dimensional data. The testing framework for wavelet-based Poisson intensity estimation was first introduced by Kolaczyk, where a thresholding estimator, which realizes the hypothesis testing, is derived for Haar wavelet coefficients. Here we propose for the same wavelet a new ...

In this paper we are proving that Sawyer type condition for boundedness work for individual Haar multipliers, as well as for the Haar shift and other “well localized” operators.

Most of the physical systems exhibit some degree of time-varying behavior. Physical phenomena exhibit time-varying behavior for a number of reasons. Some of the systems are inherently time-varying and can not effectively be modeled using time invariant models. This paper deals with the identification of time-varying systems using Haar basis functions. Basis functions approach involves expanding...