An efficient computational method is presented for state space analysis of singular systems via Haar wavelets. Singular systems are those in which dynamics are governed by a combination of algebraic and differential equations. The corresponding differential-algebraic matrix equation is converted to a generalized Sylvester matrix equation by using Haar wavelet basis. First, an explicit expressio...

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. Introduction A basic question in functional analysis is to find axioms for quantum groups, which ensure the existence of a Haar measure. In the compact case, this ...

Drie belangrike konsepte word bespreek, naamlik die rol van die eenheidsuster, die gehalte van sorg en verantwoordbaarheid. ’n Model word voorsien waarin die rolle van die eenheidsuster uitgebeeld word — die fokus van haar werk (die pasiënt, span, agentskap, genteenskap en die professie) word aangetoon sowel as die inhoudsgebiede (kliniese sorg, bestuur, onderwys en beleidsbepaling). Die doelwi...

For a given group with a generating set A a dipole with jAj parallel directed edges labeled by elements of A gives rise to a voltage graph whose covering graph denoted by H A is a bipartite regular graph called a bi Cayley graph In the case when is abelian we refer to H A as a Haar graph of with respect to the symbol A In particular for cyclic the above graph is referred to as a cyclic Haar gra...

Bent Boolean functions play a very significant role in the design of strong symmetric cryptosystems. In this paper, we present an analysis of Bent functions in the Haar domain. We first present a brief overview of Bent Boolean functions and then derive expressions for the Haar spectrum of Bent functions. The Haar spectral coefficients of Bent functions are given in two ways namely; in terms of ...