A Posteriori Estimators for the Finite Volume Discretization of an Elliptic Problem

We analyze a residual error estimator for a finite volume discretization of a linear elliptic boundary value problem. The error estimator consists of the residual of the strong equation and the jumps across the inter-element boundaries of a primal triangulation. Some numerical experiments are presented.     

The influence of the periodic disturbance on the local heat transfer in separated and reattached flow

A numerical study based on the large eddy simulation methodology was made of heat transfer in locally disturbed turbulent separated and reattached flow over a backward facing step. The local disturbance was given to the flow by a sinusoidally blowing/suction of the fluid into a separated shear layer. The Reynolds number was fixed at 33,000 and Richardson number at 0.5. The disturbance frequency was varied in the range 0 ≤ St ≤ 2, where St is the Strouhal number of disturbance. The obtained results revealed the existence of an optimum perturbation frequency value, St = 0.25, in terms of the reduced reattachment length. At this frequency the heat transfer is significantly enhanced in the recirculation zone. The influence of the frequency and the amplitude of disturbance, in the maximum heat transfer positions and the maximum local Nusselt number, is analysed.     

Diverse stereocontrol effects induced by weakly coordinating anions. Stereospecific olefin polymerization pathways at archetypal C(s)- and C(1)-symmetric metallocenium catalysts using mono- and polynuclear halo-perfluoroarylmetalates as cocatalysts

Counteranion effects on propylene polymerization rates and stereoselectivities are compared using Cs-symmetric Me2C(Cp)(Flu)ZrMe2 (1; Cp = C5H4,eta5-cyclopentadienyl; Flu = C13H8, eta5-fluorenyl) and C1-symmetric Me2Si(OHF)(CpR*)ZrMe2 (2; OHF = C13H16, eta5-octahydrofluorenyl; CpR* = eta5-3-(-)-menthylcyclopentadienyl) precatalysts activated with the mononuclear and polynuclear perfluoroarylborate, -aluminate, and -gallate cocatalysts/activators B(C6F5)3 (3), B(o-C6F5C6F4)3 (4), Al(C6F5)3 (5), Ph3C+B(C6F5)4- (6) Ph3C+FAl(o-C6F5C6F4)3- (7), Ga(C6F5)3 (8), and recently reported mono- and polymetallic trityl perfluoroarylhalometalates Ph3C+FB(C6F5)3- (9), Ph3C+FB(o-C6F5C6F4)3- (10), (Ph3C+)xFx[Al(C6F5)3]yx- (x = 1, y = 1, 11; x = 1, y = 2, 12; x = 2, y = 3, 13), Ph3C+(C6F5)3AlFAl(o-C6F5C6F4)3- (14), Ph3C+XAl(C6F5)3- (X = Cl, 15; X = Br, 16), and Ph3C+F[Ga(C6F5)3]2- (17). Temperature, propylene concentration, and solvent polarity dependence are surveyed in polymerizations catalyzed by 1 activated with cocatalysts 3-16 and with a 1:2 ratio of Ph3CCl and 5, and with a 1:2 ratio of Ph3CBr and 5, and by 2 activated with 3, 6, 7, 12, and 14. Remarkable stereocontrol with high activities is observed for 1 + 12 and 1 + 14. Polypropylene samples produced using C1-symmetric precatalyst 2 are subjected to microstructural analyses using stochastic models describing the relative contributions of enantiofacial misinsertion and backskip processes. A powerful technique is introduced for calculating interparametric correlation matrices for these nonlinear stochastic models. The collected results significantly extend what is known about ion-pairing effects in the case of Cs-symmetric precatalyst 1 and allow these findings to be applied to the case of C1-symmetric precatalyst 2 as an agent of isospecific propylene polymerization.     

Some actinide complexes of pyridin-, pyrrol-, furan- and thiophen-aldazine Schiff bases

Actinide chloride complexes with pyridinaldazine (PAA), pyrrolaldazine (PyAA-H₂), furanaldazine (FAA), and thiophenaldazine (TAA): An(L)Cl_n·m-H₂O, where An = Th, UO₂; L = PAA, PyAA-H₂, FAA, TAA; n = 2, 4; m = 0, 2, 3, 5 (also, mononuclear with 2L, dinuclear and trinuclear complexes) have been prepared by the reaction of ThCl₄, UO₂Cl₂ or UO₂(Ac)₂·2H₂O with PAA, PyAA-H₂, FAA or TAA and characterized by spectral data, electrical conductance, thermal and elemental analysis.     

Molecular Conformation and Mobility of Polyamines Adsorbed on Silica Studied by Spin Labeling

Poly(ethyleneimine) and poly(4-vinylpyridine) chains adsorbed on Nucleosil silica have been randomly labeled with nitroxide free radicals. The EPR signal is very sensitive to the molecular Brownian motion of the segments and shows generally at least two different environments: trains adsorbed on the surface with a restricted mobility, and loops and tails protruding into the solution with a fast motion. The rotational correlation times and the relative fraction of each population are given as functions of the coverage achieved and of the specific surface area of the silica for the samples in contact with methanol and sometimes water. The overall picture is consistent with a diffuse layer for the PEI and a more compact one with some heterogeneities for the P4VP. Copyright 1999 Academic Press.     

Fixed point theorems for the sum of ( ws)-compact and asymptotically $${\Phi}$$-nonexpansive mappings

In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.     

Leray–Schauder alternatives for weakly sequentially continuous mappings and application to transport equation

Motivated by the study of a general radiative transfer problem, we state some new variants of Leray–Schauder type fixed point theorems for weakly sequentially continuous operators. Further, we apply our results to establish some new existence and locality principles for a source problem in L₁‐setting with generally boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd.