Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI _h models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor. PACS: 04.20.-q 95.30.Sf 98.80.Jk     

Theoretical insight of adsorption thermodynamics of multifunctional molecules on metal surfaces

Adsorption thermodynamics based on density functional theory (DFT) calculations are exposed for the interaction of several multifunctional molecules with Pt and Au(1 1 0)-(1 × 2) surfaces. The Gibbs free adsorption energy explicitly depends on the adsorption internal energy, which is derived from DFT adsorption energy, and the vibrational entropy change during the chemisorption process. Zero-point energy (ZPE) corrections have been systematically applied to the adsorption energy. Moreover the vibrational entropy change has been computed on the basis of DFT harmonic frequencies (gas and adsorbed phases, clean surfaces), which have been extended to all the adsorbate vibrations and the metallic surface phonons. The phase diagrams plotted in realistic conditions of temperature (from 100 to 400 K) and pressure (0.15 atm) show that the ZPE corrected adsorption energy is the main contribution. When strong chemisorption is considered on the Pt surface, the multifunctional molecules are adsorbed on the surface in the considered temperature range. In contrast for weak chemisorption on the Au surface, the thermodynamic results should be held cautiously. The systematic errors of the model (choice of the functional, configurational entropy and vibrational entropy) make difficult the prediction of the adsorption-desorption phase boundaries.     

Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.     

树映射的分布混沌

设T是个有限树,f是T上的连续映射．证明了f是分布混沌的当且仅当它的拓扑熵是正数．一些已知结论得到了改进．     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

吸附树脂对对甲苯胺的静态吸附行为及其热力学性质的研究

对比 Amberlite XAD-4与两种新型吸附树脂 NK和新 H对对甲苯胺的静态吸附行为 ,根据吸附等温线研究并讨论吸附热力学性质 .两种新型吸附树脂对对甲苯胺的吸附能力明显强于 Amberlite XAD-4 ,微孔作用机制及表面部分极性起决定作用 .吸附焓变 ΔH<0表明吸附为放热过程 ,降低温度有利于吸附 .对吸附焓变和自由能变的讨论同时表明树脂对对甲苯胺的吸附为多层物理吸附过程 .吸附熵变 ΔS表明吸附树脂表面的不均匀性和吸附质分子在树脂表面的分布及其局域运动与吸附有密切关系 .     

Characterisations of function spaces of generalised smoothness

We investigate function spaces of generalised smoothness of Besov and Triebel–Lizorkin type. Equivalent quasi-norms in terms of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is proved. Mathematics Subject Classification (2000) 46E35