A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

The generalized beta- and F-distributions in statistical modelling

The univariate generalized beta- and generalized F-distributions are frequently in recent statistical modellings and applications. They have richer properties than the standard beta- and Snedecor F-distributions and provide more flexibility than these distributions, of which they are natural extensions. Their connection with the Gauss hypergeometric function and Lauricella functions leads to further generalizations and important properties. This article gives a unified and up-to-date treatment of these two generalized distributions using only simple arguments. Proofs are given for some original results and a complete reference to their source is provided for established ones. The important problem of parameter estimation is also studied.     

On the Smoothness of a Generalized Solution of the First Initial Boundary-Value Problem for Strongly Parabolic Systems in a Cylinder with Nonsmooth Base with Respect to Time Variable

We consider the first initial boundary-value problem for strongly parabolic systems in an infinite cylinder with nonsmooth boundary. We establish conditions for the existence of generalized solutions, an estimate for this solutions, and an estimate for the derivative of the solution.     

Hyperfine structure and isotope shift investigations in202–222Rn for the study of nuclear structure beyond Z=82

The hyperfine structure (hfs) and isotope shift (IS) in the isotopic chain of the radioactive element radon have been studied for the first time. The measurements were carried out by collinear fast-beam laser spectroscopy at the mass separator facility ISOLDE at CERN. The IS between 16 isotopes in the mass range 202A222 and the hfs of 7 odd-A isotopes were determined in the transitions 7s [3/2]₂-7p [5/2]₃ (745 nm) of Rn I. The nuclear spins and moments, as well as the observed inversion of the odd-even staggering for^218–222Rn, can be associated with the effects of octupole instability around N=134.This work was supported by the Bundesministerium für Forschung und Technologie and the Deutsche Forschungsgemeinschaft.     

A simple method for assigning multiple immunogens to their protein on a two-dimensional blot and its application to asthma-causing allergens

A "one-step" procedure, that not only removes the color and blocking proteins used in the colorimetric immunodetection step but also stains the proteins originally on the blot, is presented. Following immunostaining and recording of immunoreactive spots, the blot was allowed to air-dry overnight (or longer) at room temperature and then counterstained with a colloidal gold solution. This "air-drying" process apparently altered the affinity of the blocking proteins (and possibly other proteins added subsequently to the blotting step) towards the nitrocellulose membrane causing them to be removed by the acidic colloidal gold solution while the "blotted" proteins were being stained. The sensitivity of this counterstained blot was comparable to that of the blot without going through the immunodetection process. Since both immunodetection and protein staining were carried out on the same blot, this allowed easy identification of many immunoreactive spots to their corresponding proteins when the two profiles were superimposed. Using this procedure, we have detected 25 immunoreactive spots (or allergens) from the whole body extract of the German cockroach (Blattella germanica) that contribute to asthma and assigned them to their corresponding proteins on a two-dimensional (2-D) protein map. The apparent Mr and pI for each of the allergens were determined. We have also located one of the major cockroach allergens, Bla g 5 (glutathione S-transferase). Two-dimensional zymography revealed the presence of ten gelatinase-type proteolytic enzymes. Only one of the ten proteases comigrated with the immunoreactive proteins indicating that unlike other allergen-producing systems, most of the cockroach allergens do not possess protease activity.     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.