A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

Proton conductivity of phosphoric acid derivative of fullerene

The proton conductive property of methano [60] fullerene diphosphoric acid has been investigated under various humidity conditions at the temperature range between 15 and 45 °C. It shows proton conductivity as high as 10⁻² S cm⁻¹ at 25 °C under relative humidity of 95%. Thermal analyses including TG–DTA and thermal desorption mass spectroscopy (TDS) confirm that the compound is thermally stable up to 200 °C. Proton conduction of the compound depends very much on humidity or water content. The logarithmic conductivity at 25 °C is increased linearly with increasing relative humidity. The activation energy (E_a) estimated from the slope of log(σT) vs. 1/T is decreased from 1.08 to 0.52 eV, as the relative humidity is increased from 40% to 75%. The humidity dependence of conductivity is discussed in the light of the observed hydration isotherm.     

关于NA情况下重对数律收敛速度的一般形式

研究了NA序列重对数律收敛速度的一般形式，把Davis和Gut的结果推广到了NA的情形，并使梁汉营等人关于对数律一个结果成为特例；作为推论，得到了关于NA序列重对数律收敛速度的充分条件．     

Measurement of elastin hydrolysis by reverse-phase HPLC with on-line post-colum derivatization

Summary Excessive breakdown of elastin, a structural protein, may be related to aortic disease and emphysema. Since L-valyl-L-proline occurs in high concentrations in elastin, a rapid and sensitive method using HPLC with post-column on-line derivatization was used to measure the dipeptide from swine aortic tissue, and the amount of elastin present was determined. Elastin was extracted by alkaline hydrolysis. After neutralization and filtration, the sample was injected onto a ODS-2 gel column, and the dipeptide was eluted by a linear gradient of 0 to 10% of 1-propanol in 50 mM heptafluorobutyrate, pH 3, at a flow rate of 1 ml/min. The eluent was reacted with fluorescamine at pH 8.6, and fluorescence was detected at an excitation wavelength of 395 nm and a 455 nm cutoff emission filter.Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.     

The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Modelling of an underground waste disposal site by upscaling

In this paper, we study the global behaviour of an underground waste disposal in order to have an accurate upscaled model suitable for the computations involved in safety assessment processes. We start from a detailed model describing the transport of pollutant leaking from a high number of units. Using the method of homogenization, going to the limit, we obtain first a macroscopic model where the sources are now appearing globally. Then we compute a first‐order matched asymptotic expansion and we give the error estimates for this approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Gaussian Chaos Laws on Banach Function Spaces

We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ _∞ ⁿ 's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces. __________ Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005.     

一类暂留稳定过程的极限定理

本文研究了Ａ型暂留稳定过程在无穷远处的收敛速度，给出了一个重对数律．同时我们也得出了这类过程在起始点附近的一些性质．这些性质推广了［１］中的结果