Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...

Evaluation of the cardiovascular system of canine pediatrics requires awareness of the anatomical and physiological changes occurring from birth to six months of age. The aim of this study was to report electrocardiographic changes in the littermate mongrel dogs from birth tosix months. Serial six-lead electrocardiograms were recorded from ten normal littermate mongrel dogs kept on right latera...

We investigate the life time distribution P (τ, t) in one dimensional and two dimensional coarsening processes modelled by Ising-Glauber dynamics at zero temperature. The life time τ is defined as the time that elapses between two successive flips in the time interval (0, t) or between the last flip and the observation time t. We calculate P (τ, t) averaged over all the spins in the system and ...

We construct a locally linearly independent basis for the space S 1 q (() (q 5). Bases with this property were available only for some subspaces of smooth bivariate splines. x1. Introduction Let IR 2 be a simply connected polygonal domain, and let denote a triangulation of consisting of N triangles, V vertices and E edges. Given 0 r < q, consider the linear space of bivariate polynomial splines...

This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems    −4pu = λa1(x)|u|q−2u + b(x)Fu(u, v), in Ω, −4pv = λa2(x)|v|q−2v + b(x)Fv(u, v), in Ω, u = v = 0, on ∂Ω, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω; 1 < q < p < N , p∗ = Np N−p ; 4pw = div(|∇w|p−2∇w) denotes the p-Laplacian operator; λ > 0 is a positive pa...

The bigraded Frobenius characteristic of the Garsia-Haiman module M μ is known [7] [10] to be given by the modified Macdonald polynomial˜H μ [X; q, t]. It follows from this that, for μ n the symmetric polynomial ∂ p1˜H μ [X; q, t] is the bigraded Frobenius characteristic of the restriction of M μ from S n to S n−1. The theory of Macdonald polynomials gives explicit formulas for the coefficients...

We prove the existence of a unique large-data global-in-time weak solution to class models form \begin{document}$ \boldsymbol{u}_{tt} = \mbox{div }\mathbb{T} + \boldsymbol{f} $\end{document} for viscoelastic bodies exhibiting strain-limiting behaviour, where constitutive equation, relating linearised stra...

We consider the generalized Gierer-Meinhardt system ><>: ∂uj ∂t = dj4uj − ajuj + gj (x, u) in Ω× [0, T ) , ∂uj ∂ν = 0 on ∂Ω× [0, T ) , uj (x, 0) = φj (x) in Ω where Ω is a smooth bounded domain in Rn with ν its unit outer normal, j = 1, 2, u = (u1, u2) and <: g1 (x, u) = ρ1 (x, u) u p 1 u q 2 + σ1 (x) , g2 (x, u) = ρ2 (x, u) u1 u2 + σ2 (x) . Here dj , aj are positive constants, ρ1 ≥ 0, ρ2 > 0, ...