A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

1. Download : Download high-res image (151KB)
2. Download : Download full-size image

     

Temperature effects on surface activity and application in oxidation of toluene derivatives of CTAB-SDS with KMnO4

The γ_cmc values of CTAB-SDS decrease from 63.67 mN/m at 10‡C to 36.38 mN/m at 90‡C, slightly lower than those of either CTAB or SDS. Correspondingly, the CMC of CTAB-SDS decreases almost by half. The increase of surface activity of CTAB-SDS can be attributed to the relatively weak electrostatic interaction at high temperature, which is supported by the increase of solubility of CTAB-SDS with rise in temperature. Catalytic effect on oxidation of toluene derivatives with potassium permanganate follows the order CTAB-SDS > SDS > CTAB. This is not caused by the dissociative effect of CTAB-SDS with low surface activity at low temperature, as seen from the fact that almost all oxidative products can be retrieved for different toluene derivatives and surfactants by mimicking the conditions of reaction. In the emulsifications of toluene derivatives at 90‡C, the time that turbid water layers of surfactant solutions take to become clear is the same as that of the catalytic effect on oxidation of toluene derivatives. Thus, it can be inferred that surfactants can improve the oxidation yields of toluene derivatives by increasing the contact between two reacting phases.     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infinite paths in planar graphs III, 1‐way infinite paths

An infinite graph is 2‐indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4‐connected, 2‐indivisible, infinite, plane graph. It is known that G contains a spanning 1‐way infinite path. In this paper, we prove a stronger result by showing that, for any vertex x and any edge e on a facial cycle of G, there is a spanning 1‐way infinite path in G from x and through e. Results will be used in two forthcoming papers to establish a conjecture of Nash‐Williams. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Indeterminacy Criteria for the Stieltjes Matrix Moment Problem

In this paper, we obtain criteria for the indeterminacy of the Stieltjes matrix moment problem. We obtain explicit formulas for Stieltjes parameters and study the multiplicative structure of the resolvent matrix. In the indeterminate case, we study the analytic properties of the resolvent matrix of the moment problem. We describe the set of all matrix functions associated with the indeterminate Stieltjes moment problem in terms of linear fractional transformations over Stieltjes pairs.     

Polarization fluctuations in a dipolar medium in an electrostatic field

Radio Engineering and Electronics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1113–1124, September, 1989.     

Crystallographic report: Bis{[diacetyl‐bis(2,6‐isopropylphenylimine)]nickel(I)(µ‐chloro)}

The first α‐diimine nickel(I) complex having a chloro bridge is reported. The centrosymmetric dinuclear structure of {[ArN?C(Me)C(Me)?NAr]NiCl}₂[Ar?2,6?C₆H₃(i‐Pr)₂] features two chelating α‐diimine ligands and two bridged chlorine atoms, so that a distorted tetrahedral N₂Cl₂ coordination geometry for nickel results. Copyright © 2004 John Wiley & Sons, Ltd.     

Crystallographic report: catena‐Aqua(2,2′‐bipyrimidine)lithium(I) perchlorate

A lithium(I) coordination polymer has been formed from LiClO₄ and the 2,2′‐bipyrimidine (bpym) ligand in which each square pyramidal lithium(I) atom is coordinated in the basal plane by four nitrogen donor atoms derived from two bpym ligands and one water molecule at the apical position. These are connected into a layer structure via hydrogen‐bonding interactions involving the perchlorate anions. Copyright © 2004 John Wiley & Sons, Ltd.     

Accuracy analysis of airborne gravimeter calibration using repeated flight paths

Some possible errors in determining the gravity anomalies are discussed. Such errors may be caused by an inaccurate calibration of the gravimeter used in an airborne survey system. An approach based on wavelet decompositions is proposed for its additional calibration with the use of flight data obtained during repeated flights.