On the numerical analysis of nonlinear twofold saddle point problems

We provide a general abstract theory for the solvability andGalerkin approximation of nonlinear twofold saddle point problems.In particular, a Strang error estimate containing the consistencyterms arising from the approximation of the continuous operatorsinvolved is deduced. Then we apply these results to analysea fully discrete Galerkin scheme for a twofold saddle pointformulation of a nonlinear elliptic boundary value problem indivergence form. Some numerical results are also presented.     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Asymptotic expansions of the generalized Epstein-Hubbell integral

The generalized Epstein–Hubbell integral recently introducedby Kalla & Tuan (Comput. Math. Applic. 32, 1996) is consideredfor values of the variable k close to its upper limit k = 1.Distributional approach is used for deriving two convergentexpansions of this integral in increasing powers of 1 –k². For certain values of the parameters, one of these expansionsinvolves also a logarithmic term in the asymptotic variable1 – k². Coefficients of these expansions are given interms of the Appell function and its derivative. All the expansionsare accompanied by an error bound at any order of the approximation.Numerical experiments show that this bound is considerably accurate.     

一类可解的（q）－群

有限群Ｇ叫（ｑ）－群，如果Ｇ中每个次正规子群均为拟正规子群，群Ｇ叫Ｅｑ－群，若Ｇ中每个子群在Ｇ中拟正规或自正规，有限群Ｇ叫内Ｅｑ－群，如果Ｇ本身不是Ｅｑ－群，但Ｇ的每个真子群是Ｅｑ－群，本文确定了Ｅｑ－群的结构与内Ｅｑ－群的分类．     

Extended range field emission spectroscopy

We have measured the energy distribution of field emitted electrons by first accelerating them to about 20 keV and then directly energy analyzing these high energy electrons with a high-performance magnetic prism spectrometer. Our preliminary results indicate that it may be possible to extend the energy range of field emission spectroscopy to more than 5 eV below the Fermi level. This work was supported by the U.S. Energy Research and Development Administration     

New Potentialities in Producing Composites Reinforced with High-Strength High-Modulus Polyethylene Fibers

A concept of physical and chemical stages of interaction between the matrix and reinforcing fibers during the production of composite materials is introduced. A strong bond between these constituents is formed at the stage of chemical interaction, which is characterized by a certain value of activation energy. The activation energy of such an interaction for high-strength high-modulus polyethylene fibers used for reinforcing composites is estimated. Based on these estimates, conditions for fiber activation with cold plasma are found. The application of plasma-activated polyethylene fibers for reinforcing an epoxy matrix allows one to produce light-weight composites with high physicomechanical indices. The failure mode of such composites points to a high strength of the bond between the fibers and matrix. The data on treating the fiber surface with cold plasma above the activation energy of chemical interaction may be utilized to create new types of organic composites from other kinds of organic fibers and matrices.     

Catalytic Behaviour of Carbonate β-CD Entrapped in PEEK-WC Membranes

O-octyloxycarbonyl cyclodextrins were immobilised in flat sheetPEEK-WC membranes. The membranes were prepared by phase inversion methodand characterised. cyclodextrin (CD) catalytic action in thep-nitrophenylacetate (PNPA) hydrolysis to p-nitrophenol (PNP) was studied. The CD acylic carbonate derivative shows an effective catalytic action whenincorporated in PEEK-WC membranes, by showing an enzyme-like behaviour. Themembranes were tested at different temperatures and substrate concentrations and thevalue of activation energy for the reaction was estimated. It is well known that CDhave a catalytic action, but their immobilisation in a polymeric matrix enhances thereaction rate, in fact the entrapment optimises the interaction with the substrate andincreases the chemical stability of the catalyst. In addition, CD show morestability when incorporated in the membrane, because of their chemical resistanceto alkaline attack.     

Existence of ∈-Minima for Vector Optimization Problems

The -generalized minima for vector optimization problems are defined and a sufficient condition for the existence of -generalized minima for vector optimization problems is established.     

Determination of the Elemental Composition of Chalcogenide Powders by the X‐Ray Fluorescence Method

A procedure of xray spectral fluorescence analysis of the elemental composition of As _x S_100–x chalcogenide powder samples is developed and its metrological characteristics are established. In determining the content of the components in an As₅₀S₅₀ sample, the relative standard deviation was 0.0030 for As and 0.0035 for S. The results of the xray spectral fluorescence analysis are in good agreement with the data of a gravimetric method.