We consider the initial value problem for the filtration equation in an inhomogeneous medium ρ(x)ut = ∆u, m > 1. The equation is posed in the whole space R, n ≥ 2, for 0 < t < ∞ ; ρ(x) is a positive and bounded function with a certain behaviour at infinity. We take initial data u(x, 0) = u0(x) ≥ 0, and prove that this problem is well-posed in the class of solutions with finite “energy”, that is...

The time and place that Brownian motion on a Riemannian manifold first exits a normal ball of radius e is considered and a general procedure is given for computing asymptotic expansions, as e decreases to zero, for joint moments of the first exit time and place random variables. It is proven that asymptotic versions of exit time and place distribution properties that hold on harmonic spaces are...

We study the pion form factor F πγγ ∗ (Q2) in the light-cone sum rule approach, accounting for radiative corrections and higher twist effects. Comparing the results to the CLEO experimental data on F πγγ ∗ (Q2), we extract the the pion distribution amplitude of twist-2. The deviation of the distribution amplitude from the asymptotic one is small and is estimated to be a2(μ) = 0.12± 0.03 at μ = ...

The sequence A of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be written as the sum of h elements of A . Let MhA denote the set of elements that have more than one representation as a sum of h elements of A . It is proved that there exists an asymptotic basis A such that MhA (x) = O(x1-1 11 +E) for every e > 0. An asymptotic basis A of order h ...

Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different ...

BACKGROUND Plants of Euphorbiaceae are used in folkloric medicines in variety of ailments and well known for chemical diversity of their isoprenoid constituents. This study was carried out to explore the preliminary wound healing potential of four Euphorbia species (E. consorbina 1, E. consorbina 2, E. inarticulata, E. balsamifera and E. schimperi). MATERIALS AND METHODS Excision wound surfac...

We investigate some real time behaviour of a (discrete time) single server system with nonpreemptive LCFS task scheduling . The main results deal with the probability distribution of a random variable SRD(T), which describes the time the system operates without any violation of a fixed task service time deadline T . A tree approach, similar to those already used for the derivation of the same q...

Saunders, Natasha R., and Michael E. Tschakovsky. Evidence for a rapid vasodilatory contribution to immediate hyperemia in rest-to-mild and mild-to-moderate forearm exercise transitions in humans. J Appl Physiol 97: 1143–1151, 2004. First published May 21, 2004; 10.1152/japplphysiol.01284.2003.—Controversy exists regarding the contribution of a rapid vasodilatory mechanism(s) to immediate exerc...

Let ∆(T ) and E(T ) be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function in the critical strip, respectively. We show that ∆(T ) and E(T ) are asymptotic integral transforms of each other. We then use this integral representation of ∆(T ) to give a new proof of a result of M. Jutila.

This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identi…ed with regular bounds. When the bounds are just identi…ed along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an e¢ cient lower bound estimator plus the half of the known interval le...