A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids

Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived in previous work by Kröner, Noelle and Rokyta and a weaker condition on the grid, we can generalize and simplify the error estimates.

     

Light Amplification in a New Light Transducer Combining an Organic Electroluminescent Diode with Photoresponsive Organic Pigment Film

Light amplification was successfully demonstrated in an all-organic light transducer based on hybridization of an organic electroluminescent diode and a perylene pigment film as an electron photoinjecting electrode. Amplification gain of photon conversion from red to red light reached 25 with the assistance of effective electron photoinjection due to large photocurrent multiplication in a perylene film. Optical switching behavior caused by feedback of output-light to the photoconductive layer was observed.     

A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System

A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.     

非关联流动的安定性理论及在土力学中的应用

将Melan静力型安定定理加以推广，使其适用于非关联流动法则下的土工结构的安定性分析．应用Palmer的方法构造塑性势面，根据其性质，证明了静力型安定定理在非关联流动法则下同样成立．在非关联的Mok—Coulomb准则下，求解浅黏土层地基极限载荷，得到了比较合理的解答．最后，计算了非关联流动法则下的条形基础地基的安定裁荷．     

p－型空间中的Kolmogorov重对数律

主要说明了Ｋｏｌｍｏｇｏｒｏｖ重对数律对ｐ型Ｂａｎａｃｈ空间值独立、零均值的随机元列有类似于对实值的表现形式，从而揭示了空间的型ｐ与重对数律的开方指数之间有着密切的关系．     

Potential Symmetries and Associated Conservation Laws to Fokker-Planck and Burgers Equation

Kara and Mahomed have derived an identity, which does not rely on use of a Lagrangian as needed to obtain conservation laws by Noethers theorem. By using the identity and symbolic computation, conservation laws arising from nonlocal symmetries are obtained for Fokker-Planck equation and burgers equation.     

A comparison on failure pressures of cylindrical pressure vessels

In this work, the failure pressures of thick and thin walled cylindrical pressure vessels considering the Voce hardening law and plastic orthotropy effect are obtained. The solution presented is used to compare the failure pressures of copper and brass cylindrical pressure vessels.     

The Coefficient of Restitution Does Not Exceed Unity

We study a classical mechanical problem in which a macroscopic ball is reflected by a non-deformable wall. The ball is modeled as a collection of classical particles bound together by an arbitrary potential, and its internal degrees of freedom are initially set to be in thermal equilibrium. The wall is represented by an arbitrary potential which is translation invariant in two directions. We then prove that the final normal momentum can exceed the initial normal momentum at most by O(■mkT), where m is the total mass of the ball, k the Boltzmann constant, and T the temperature. This implies the well-known statement in the title in the macroscopic limit where O(■mkT) is negligible. Our result may be interpreted as a rigorous demonstration of the second law of thermodynamics in a system where a macroscopic dynamics and microscopic degrees of freedom are intrinsically coupled with each other.     

The strong law of large numbers for L-statistics with dependent data

We prove the strong law of large numbers for the linear combinations of functions of order statistics (L-statistics) based on weakly dependent random variables. We also establish the Glivenko-Cantelli theorem for ?-mixing sequences of identically distributed random variables.     

NA序列线性形式的强稳定性

本文研究了NA变量线性形式的强稳定性.利用随机变量的截尾术及强大数定律,得到了一般情况下不同分布NA变量具有强稳定性的充分条件,推广了NA列的Jamison型加权和具有强稳定性的充分条件.