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.     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

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 Rees algebra of certain codimension two perfect ideals

 Suppose ? is a set of arbitrary number of smooth points in ℙ² its defining ideal. In this paper, we study the Rees algebras of the ideals generated by I _t , t ≥α. When the points of ? are general, we give a set of defining equations for the Rees algebra . When the points of ? are arbitrary, we show that for all t≫ 0, the Rees algebra is Cohen-Macaulay and its defining ideal is generated by quadratics. A cohomological characterization for arithmetic Cohen-Macaulayness of subvarieties of a product space is also given. Received 4 April 2001     

Determination of uranium and thorium isotopes in soil samples by coprecipitation

Summary The paper presents a procedure to prepare soil samples for U and Th isotope measurement by alpha-spectrometry after coprecipitation with LaF₃. In this procedure the reduction of U(VI) to U(IV) was performed by Zn metal in 4M HCl solution. The recoveries of chemical separation equal to e_U-chemistry = 78±4% for uranium and e_Th-chemistry = 82±4% for thorium. Canberra alpha-spectrometer was used with PIPS detectors of A-1200-37-AM Model of 1200 mm² active area. The counting efficiency of the measuring system equals to e_counting = 18% and the total efficiencies were e_U = e_counting ^.e_U-chemistry = 14.0±0.7% for uranium and e_Th = e_counting ^.e_Th-chemistry = 14.7±0.7% for thorium. The recoveries of chemical separation were rather high (about 80%), that leads to the use of a small weight of soil sample (about 0.5 g). The efficiencies were also stable, that allows analyzing the soil sample without using radiotracers. They are advantages of the sample preparation procedure of this work.     

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.     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality

Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with K_ε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.     

Graph bisection algorithms with good average case behavior

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n ^{1?1/[(d+1)/2]}), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n ^2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:

1. the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
2. whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
3. the algorithm works well both theoretically and experimentally,
4. the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
5. the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).

     

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.