A supraconvergent scheme for the Korteweg-de Vries equation

Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented.     

Multiple-scattering-theory analysis of XANES spectra of SO2 adsorbed on Cu(100)

The sulphur K-edge x-ray absorption spectra of SO₂ multilayer and of SO₂ submonolayer adsorbed on Cu(100) are analysed. It is found that the dominant spectral features are of a molecular origin. The results support earlier findings that the SO₂ molecule stands perpendicular to the surface. Use of non-selfconsistent potentials does not lead to a good quantitative agreement between theory and experiment.     

[VS_4Cu_6(Py)_8I_3]的合成和晶体结构

在(NH4)3VS4/CuI/Py反应体系中合成了新化合物 [VS4Cu6(Py)8I3]并测定其晶体结构。该化合物(C40H40N8Cu6I3S4V)属正交晶系, 空间群为Fdd2, 晶胞参数为: a = 29.924(6), b = 13.475(3), c = 25.853(5) , V = 10425(4) ?, Dc = 2.006 g/cm3, Mr = 1573.92, Z = 8, (MoK) = 4.546 mm-1, F(000) = 6048。结构由直接法解出, 用全矩阵最小二乘法修正, 最终偏离因子R = 0.023, wR = 0.069。簇合物分子是由6个带端基配体的Cu沿着四面体单元VS4的6条SS边配位而成, 6个Cu排列成了1个八面体, V基本位于八面体的中心, 整个分子具有C2对称性。     

Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Temperature modulated DSC study of the kinetics of free radical isothermal network polymerization

Temperature modulated differential scanning calorimetry (TMDSC) is used to study the kinetics of the free radical isothermal polymerization of triethyleneglycol dimethacrylate (TEGDMA). Azo-bis-isobutironitrile was used as initiator. The polymerization’s temperature is lower than the final glass transition temperature of the polymer network. The measurement of the average heat flow released and the heat capacity during the reaction allows identifying the different stages of the reaction. The presence of double peaks in the heat flow is ascribed to the autoacceleration. The influence of temperature, measuring conditions and oxygen are described. Vitrification is detected by the drop in heat capacity. It occurs at increasing conversion rates for increasing temperatures. After vitrification, the diffusion-controlled reaction continues.     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

Inferring mixed-culture growth from total biomass data in a wavelet approach

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Hölder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Hölder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Hölder exponent is no longer a useful parameter.     

Air-activated carbons from almond tree pruning: Preparation and characterization

In this work the results obtained in the preparation and characterization of carbons made from almond tree pruning by non-catalytic and catalytic gasification (using K and Co) with air are analyzed and discussed. The main aim was to obtain high quality activated carbons at the lowest possible cost. The variables studied have been the temperature (190-260 °C) and the time (1-10 h) in non-catalytic gasification and the influence of the catalyst type (K and Co, 1 wt.% referred to cation, at 190 °C and 1 h) and the time (1-4 h) in catalytic gasification with Co at 190 °C. The air flow rate used in all the series was 167 cm³ min⁻¹. In non-catalytic gasification the reaction normalized rate versus the conversion degree was maintained until a conversion value of 10% for the experiment made at 260 °C since, at lower temperatures, this rate drops quickly for low conversion values. The N₂ adsorption isotherms for the carbons of this series resemble type I, although there is an increase of N₂ adsorbed volume at relatively high pressures. A temperature rise produced an increase of the carbon porosity and BET specific surface (116-469 m² g⁻¹). The activation time has a positive effect on the N₂ volume adsorbed by the carbons. The isotherms shapes were similar to those previously commented. A concentration equal to 1 wt.% was used to study the influence of the catalyst type. Under the studied experimental conditions, Co drives to a bigger porosity development than K, although with both catalysts a very similar pore size distribution is obtained. The activation time, in the gasifications catalyzed with Co, gives rise to a very important porosity development in the carbons. This produces a strong increase of the carbon specific surface area with very high values in the 4 h experiment, in which a BET specific surface of 959 m² g⁻¹ was obtained.