A certain class of one-dimensional classical lattice models is considered. Using the method of abstract harmonic analysis explicit thermostatic properties of such models are derived. In particular, we discuss the low-temperature behavior of some of these models. 1 A class of one-dimensional models In this section we will characterize a certain class of lattice models in one dimension. This clas...

In this study, the thermal performance analysis of porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Haar wavelet collocation method. The effects of various parameters on the thermal characteristics of the porous fin are investigated. It is found that as the porosity increases, the rate of heat transfer from the fin increases and the th...

The strength of any conventional cipher system relies on the underlying cryptographic Boolean functions employed in the system. The design of such systems requires that the employed Boolean functions meet specific security criteria. Two of such criteria are the correlation immunity and resiliency of a given Boolean function. To determine whether such criteria are met, a designer needs the help ...

In this paper, Haar wavelet based identification of a continuous-time linear time-varying (LTV) system is proposed. For that purpose, input and output data are analyzed to derive an algebraic equation, leading to estimation of Haar wavelet coefficients for the impulse response. Finally, it is demonstrated that an LTV system can be effectively identified by solving the algebraic equation and by ...

In this paper, we develop an accurate and ef£cient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is con£rmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, ¤exible, convenient, small computation costs and computationally attract...

Let Γn = (γij)n×n be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n) or the symplectic group Sp(n). Given 1 ≤ m < n, a probability inequality for a distance between (γij)n×m and some mn independent F -valued normal random variables is obtained, where F = R, C or H (the set of real quaternions). The result is universal for the three cases. I...

In [6], M. Krishnapur and the authors considered the convergence of the empricial measure of (complex) eigenvalues of matrices of the form An = TnUn, where Un is Haar distributed on U(n), the unitary group of n×n matrices, and independent of the self-adjoint matrix Tn (which therefore can be assumed diagonal, with real non-negative entries s i ). That is, with λ (n) i denoting the eigenvalues o...

Let U be a Haar distributed matrix in U(n) or O(n). In a previous paper, we proved that after centering, the two-parameter process T (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge. In the present paper, we replace the deterministic truncation of U by a random one, where each row (resp. column) is chosen with probability s (resp. t) indepen...

We investigate the combinatorics of truncated Haar-distributed random unitary matrices. Specifically, if U is a random matrix from the unitary group U(d), let Uk denote its k × k upper left corner, where 1 ≤ k ≤ d. We give an explicit combinatorial formula for the moments ∫ U(d) |Tr(Uk)|dU in terms of pairs of Standard Young Tableaux on shapes that are not neccessarily the same. This formula ca...

as shown in [9, 31]. This law also arises as the Gibbs measure for n identical charged particles confined to lie on the circle and interacting via the 2-dimensional Coulomb law. For this reason, it is also known as the log-gas. An important example of (1.1) is as the distribution of eigenvalues of an n × n unitary matrix chosen at random according to Haar measure; this corresponds to β = 2. The...