Finite-Part Integrals and Modified Splines

We first state a uniform convergence theorem for finite-part integrals which are derivatives of weighted Cauchy principal value integrals. We then give a two-stage process to modify approximating splines and optimal nodal splines in such a way that the conditions of this theorem are satisfied. Consequently, these modified splines can be used in the numerical evaluation of these finite-part integrals.     

Critical evaluation of gas standards based on hydrogen

Summary Six commercial hydrogen standards containing helium, oxygen, nitrogen, methane and carbon dioxide at trace levels were analyzed by gas chromatography, for periods up to 105 days. The concentrations, in the range of 0–120 μmol mol⁻¹, were stable (with the exception of oxygen) but often significantly different from the certified values provided by the suppliers, especially for helium, oxygen and nitrogen. Concurrently, some experiments were carried out to verify the stability of gas mixtures based on hydrogen stored in cylinders submitted to different chemical and physical treatments. The causes that led to the deviations observed, as well as the decreases in oxygen, are discussed. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996.     

Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere.     

双障碍问题阻尼牛顿法的二阶收敛性

本文研究由双障碍问题导出的一类B可微函数的性质，并在一定条件下证明了求解相应的B可微方程阻尼牛顿法的全局收效性和二阶收效性．数值例子表明这一算法是有效的．     

Numerical analysis of a model of cure process for composites

We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β₁, β₂) ε [0, 1]² which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β₁, β₂) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd.     

Gas-liquid chromatography of perfluorocarboxylic thioesters

Perfluorocarboxylic thioesters R_FC(O)SR (R_F=CF₃(CF₂)_j, R=CH₃(CH₂)_i, i andj=0–5) were studied for the first time by GLC on packed columns using SE-30, SKTFT-50X, and XE-60 as the stationary phase. The values of thermodynamics functions of sorption were calculated. The correlations between these functions and the molecular structures as well as the conditions of analysis were established. The insertion of the S atom into the molecules of derivatives of perfluorocarboxylic acids causes a decrease in the contribution of the orientation interaction and an increase in the dispersion interaction of thioesters with the stationary phases compared to esters and amides of perfluorocarboxylic acids studied previously. For Part 1, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1165–1168, June, 1997.     

OSCILLATION CONVERGENT THEOREMS FOR THE V^2-INTEGRAL

The V^t-integral as defined in[2], which is eqnivalent to M^2-integrsl as defined in Trigonometre series by Zygmund is used to sum trigonometric seies in[1]. In this paper, some convergent theorems of V^2-integral are established.     

The variation of carrier gas viscosities with temperature

After describing simplified equations exspressing the temparature dependency of the viscosity of carrier gases (helium, nitrogen and hydrogen ) relative to a base value, absolute relationships based on the kinetic theory of gases are discussed. Comparative data obtained using various calculation methods are given and are compared to measured values. Based on the kinetic relationshipsm, of viscosity. Finally, the influence of pressure on the viscosity is also briefly discussed. As a supplement, Viscosity data are tabulated for the three gases in the range of 0°C to 400°C in increments of 2 K, calculated using the kinetic relationships.     

多元K-拟全纯函数及其正规定则

研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作．引进多元K-拟全纯函数的定义，并给出了多元K-拟全纯函数族的一个正规定则．