Universal canonical entropy for gravitating systems

The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.     

气体节流膨胀过程的热力学分析

探讨气体节流膨胀过程中的熵(S)的变化,指出任何气体的节流膨胀都是熵增过程,并且是不可逆的。在此基础上,讨论和总结了节流膨胀过程的全部热力学特征。     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Entropy numbers in ‐Banach spaces

Let X be a quasi‐Banach space, Y be a γ‐Banach space and T be a bounded linear operator from X into Y . In this paper, we prove that the first outer entropy number of T lies between and ; more precisely, , and the constant is sharp. Moreover, we show that there exist a Banach space X ₀, a γ‐Banach space Y ₀ and a bounded linear operator such that for all positive integers k . Finally, the paper also provides two‐sided estimates for entropy numbers of embeddings between finite dimensional symmetric γ‐Banach spaces.     

Mass,momentum and total excess energy transported by a weak planeN wave

A weakly nonlinear plane acoustic wave is emitted into an ideal gas of semi-infinite extent from an infinite plate by its sinusoidal motion of single period. The wave develops into anN wave in the far field, as long as the energy dissipation is negligible everywhere except for discontinuous shock fronts. The third-order effects at shock fronts are evaluated, i.e., the generation of reflected acoustic wave as a result of the interaction of shock and expansion wave and the production of entropy by the energy dissipation at shock fronts. Consideration of these effects enables one to estimate the whole mass, momentum and total excess energy (sum of the kinetic energy and excess of internal energy over an initial undisturbed value) transported by theN wave to the accuracy of third order of wave amplitude. It is shown that the mass and total excess energy transported by theN wave increase and the momentum decreases to asymptotic limits as the wave propagates. The result shows good agreement with a numerical result obtained by solving the Euler equations with a high-resolution TVD upwind scheme.     

局部归一化融合EW-Gabor特征的光照变化人脸识别

针对光照变化人脸识别问题,提出了一种基于局部归一化融合熵加权Gabor特征方法。首先,计算类熵加权向量;然后,对图像进行局部归一化,并且计算输入图像的Borda计数,从而消除低值Gabor jet比较矩阵;最后,利用投票得分策略和k近邻分类器完成人脸识别。在扩展YaleB和AR人脸数据库上进行实验评估,在AR上的识别率可接近100%,相比其它几种较新的局部特征方法,本文方法取得了更高的识别精度,并且在一定程度上减少了计算开销。     

A simplified prediction of entropy of melting for energetic compounds

A new widely applicable model for the prediction of the entropy of melting of organic compounds is presented. The use of three simple geometry based parameters: rotational symmetry, flexibility, and eccentricity enables the simple and accurate prediction of this important property. This paper demonstrates the use of the model for energetic compounds.     

On the Hughes' model for pedestrian flow: The one-dimensional case

In this paper we investigate the mathematical theory of Hughes' model for the flow of pedestrians (cf. Hughes (2002) [17]), consisting of a non-linear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task. For such an approximated system we prove existence and uniqueness of entropy solutions (in one space dimension) in the sense of Kru?kov (1970) [22], in which the boundary conditions are posed following the approach of Bardos et al. (1979) [7]. We use BV estimates on the density ρ and stability estimates on the potential ? in order to prove uniqueness. Furthermore, we analyze the evolution of characteristics for the original Hughes' model in one space dimension and study the behavior of simple solutions, in order to reproduce interesting phenomena related to the formation of shocks and rarefaction waves. The characteristic calculus is supported by numerical simulations.