a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...

This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of...

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

Given n vectors {~ αi}i=1 ∈ [0, 1), consider a random walk on the ddimensional torus T = R/Z generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q) between the k-th step distribution of the walk and Haar measure is bounded below byD(Q) ≥ C1k, where C1 =...

A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

Let H be a Hilbert space, U an unitary operator on H and K a cyclic subspace for U . The spectral measure of the pair (U,K) is an operator-valued measure μK on the unit circle T such that ∫ T zdμK(z) = ( PKU k ) ↾K , ∀ k ≥ 0 where PK and ↾ K are the projection and restriction on K, respectively. When K is one dimensional, μ is a scalar probability measure. In this case, if U is picked at random...

Following Schweiger’s generalization of multidimensional continued fraction algorithms, we consider a very large family p-adic which include Schneider’s algorithm, Ruban’s and the Jacobi–Perron algorithm as special cases. The main result is to show that all transformations in are ergodic with respect Haar measure.

Less than continuum many translates of a compact nullset may cover any infinite profinite group Abstract We show that it is consistent with the axioms of set theory that every infinite profinite group G possesses a closed subset X of Haar measure zero such that less than continuum many translates of X cover G. This answers a question of Elekes and Tóth and by their work settles the problem for ...

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.