An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

The Crossing Number of P(N, 3)

 It is proved that the crossing number of the Generalized Petersen Graph P(3k+h,3) is k+h if h∈{0,2} and k+3 if h=1, for each k≥3, with the single exception of P(9,3), whose crossing number is 2. Received: May 7, 1999 Final version received: April 8, 2000     

Energy and number of collision fluctuations in inelastic gases

The two-dimensional Inelastic Maxwell Model (IMM) is studied by numerical simulations. It is shown how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations. These fluctuations are associated to a shrinking of the available phase space. We find the asymptotic scaling of these energy fluctuations and show how they affect the tail of the velocity distribution during long time intervals. We stress that these fluctuations relax like power laws on much slower time scales than the usual exponential relaxations taking place in kinetic theory.     

Regioselective Ring‐Opening Polymerization of a Polyhydroxycarboxylic Acid for the Synthesis of a Nanoscale Carrier Material with pH‐Dependent Stability and Sustained Drug Release

Synthetic polyesters are usually composed of monohydroxycarboxylic acids to avoid the problem of regioselectivity during ring‐opening polymerization. In contrast, the linear polyester BICpoly contains four secondary OH groups and is nevertheless esterified regioselectively at only one of these positions. Neither the synthesis of the tricyclic monomers nor the ring‐opening polymerization requires protecting groups, making BICpoly an attractive novel and biocompatible polymer. BICpoly nanoparticles can be loaded with low‐molecular weight drugs or coated onto surfaces as thin films. The release of loaded compounds makes BICpoly an attractive depot for drug release, as shown herein by loading BICpoly with dyes or the cytostatic drug doxorubicin. BICpoly is distinguishable from other polymers by its characteristic pH‐dependent degradation.     

On the Pseudolinear Crossing Number

A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph.     

Synthesis of homo- and heteronuclear ruthenium-gold clusters with diphosphine and thiolato bridged ligands. Single crystal molecular structure of [Ru3(CO)10(μ-AuPPh3)(μ-SC5H4N)] and [Ru3(CO)8(μ-H)(μ-SC5H4N)(μ-dppe)]

The reaction between [Ru₃(CO)₁₀(NCMe)₂] and [AuClPPh₃] gave compound [Ru₃(CO)₁₀(μ-Cl)(μ-AuPPh₃)] (1) in quantitative yield under very mild conditions. The reaction of 1 with 4-mercaptopyridine (4-pyS) using ultrasonic reaction conditions gave the heteronuclear compound [Ru₃(CO)₁₀(μ-AuPPh₃)(μ-SC₅H₄N)] (2) in moderate yield. There was no spectroscopic evidence that indicates the formation of the hydride isolobal analog in this reaction. The homonuclear cluster [Ru₃(CO)₈(μ-H)(μ-SC₅H₄N)(μ-dppe)] (3) was prepared by a selective reaction employing the ruthenium-diphosphine derivative [Ru₃(CO)₁₀(μ-dppe)] (dppe = 1,2-bis(diphenylphosphine)ethane) with 4-pyS in THF solution. The isolobal analog to compound 3, compound [Ru₃(CO)₈(μ-AuPPh₃)(μ-SC₅H₄N)(μ-dppe)] (4) was synthesized by the reaction between compound 2 and dppe in refluxing dichloromethane. Compounds 1-4 were characterized in solution by spectroscopic methods and the molecular structure of compounds 2 and 3 in the solid state was obtained by single crystal X-ray diffraction studies.     

Inverse estimation for unknown fouling geometry on inner wall of forced-convection pipe

A conjugate gradient method (CGM) based on the inverse algorithm is used to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It is assumed that no prior information is available about the functional form of the unknown profile. Therefore, the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined using the simulated exact and inexact temperature measurements. The results show that the excellent estimation of the fouling-layer profile can be obtained for the test case considered in this study. The technique presented in this study can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a predefined criterion.     

Site-diluted quantum Heisenberg spin model applied to the magnetic properties of Fe–Al disordered alloys

In this work we present a theoretical study of the magnetic behavior of disordered Fe–Al alloys on the basis of a simple-diluted quantum Heisenberg spin model with the assumption that the exchange interaction J depends on the Al concentration q. We calculated the critical temperature and exponents through the mean field renormalization group method. An acceptable fit to the experimental phase diagram for Al concentration in the range 0.30q0.45 is obtained.     

Nearly light cycles in embedded graphs and crossing‐critical graphs

We find a lower bound for the proportion of face boundaries of an embedded graph that are nearly light (that is, they have bounded length and at most one vertex of large degree). As an application, we show that every sufficiently large k‐crossing‐critical graph has crossing number at most 2k + 23. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 151–156, 2006