A relativistic core-envelope model on pseudospheroidal space-time

A core-envelope model for superdense matter distribution with the feature- core consisting of anisotropic fluid distribution and envelope with isotropic fluid distribution is reported on the background of pseudospheroidal space-time. The physical plausibility of the model is examined analytically and numerically.     

Scenario of Inflationary Cosmology from the Phenomenological Λ Models

Choosing the three phenomenological models of the dynamical cosmological term Λ, viz., , and Λ∼ρ where a is the cosmic scale factor, it has been shown by the method of numerical analysis for the considered non-linear differential equations that the three models are equivalent for the flat Universe k=0 and for arbitrary non-linear equation of state. The evolution plots for dynamical cosmological term Λ vs. time t and also the cosmic scale factor a vs. t are drawn here for k=0,+1. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.     

Schur‐convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).     

Uncomputability and undecidability in economic theory

Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory[Noam Nisan, Tim Roiughgarden, Éva Tardos, Vijay V. Vazirani (Eds.), Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007] and Algorithmic Statistics[Péter Gács, John T. Tromp, Paul M.B. Vitányi, Algorithmic statistics, IEEE Transactions on Information Theory 47 (6) (2001) 2443-2463] are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory (The qualification ‘recursive’ here has nothing to do with ‘recursion theory’. Instead, this is a reference to the mathematical formalizations of the rational economic agent’s intertemporal optimization problems, in terms of Markov Decision Processes, (Kalman) Filtering and Dynamic Programming, where a kind of ‘recursion’ is invoked in the solution methods. The metaphor of the rational economic agent as a ‘signal processor’ underpins the recursive macroeconomic paradigm.), are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.     

GMPLS中基于子网保护的LSP保护机制探讨

主要探讨了GMPLS中基于子网保护的LSP保护机制。首先描述了子网保护机制的含义;然后,重点分析了子网保护机制的实现过程,并对子网保护机制中存在的入口问题提出了相应的解决方案;最后,通过比较说明了该保护机制的优点。     

A Tri-state Fluorescent Switch with “Gated” Solid-state Photochromism Induced by an External Force

Mr. Chen Qian, Dr. Zhimin Ma, Mr. Jianwei Liu, Mrs. Xue Zhang, Prof. Shitao Wang and Prof. Zhiyong Ma. In this article, we report a newly designed molecule composed of a dihydroazulene (DHA) group and a phenothiazine (PTZ) moiety, which achieves aggregation-induced emission enhancement (AIEE), mechanochromism and “gated” solid-state photochromism upon stimulation by an external force. Grinding loosens intermolecular interactions in the crystal and causes a red-shift of fluorescence from 570 nm to 600 nm. Meanwhile, the ring-opening reaction of DHA unit is activated by grinding and a remarkable photochromism could be observed from the grinded powder. The reddish emission of the grinded powder peaked at 600 nm weakened gradually and finally became dark, and a new absorption band at 470 nm emerged in the absorption spectra. Time-dependent density functional theory (TD-DFT) calculation results reveal that the intramolecular intramolecular charge-transfer (ICT) process is replaced by a locally excited (LE) emission on the DHA group, which leads to the quenching of fluorescence. Its impressive photochromic property inspired us to a simple but effective way to develop an encryption system which can let the correct information be displayed upon external stimulation.     

Electrical Potential Distribution around a Charged Colloidal Particle: Nonlinear Integral Equation

多电解质溶液中带电胶体粒子的电势分布由球形Ｐｏｉｓｓｏｎ－Ｂｏｌｔｚｍａｎｎ方程（ＰＢＥ）描述．ＰＢＥ是一个非线性的微分方程，且难以求得其解析解．本文采用非线性Ｐ－Ｂ积分方程，计算电势分布的数值解．首先，根据静电场和热力学系统中的物理定理，导出描述电势分布的Ｐ－Ｂ积分方程（ＰＢＩＥ）；其次，用迭代方法求ＰＢＩＥ的数值解．最后，计算了在３－１型电解液中无量纲半径κａ分别为０．１２和０．２２，无量纲表面电势ξ分别为１，２，４，６时球形胶体粒子外部的电势值．为了检验数值解的精度，计算了表面电荷密度，并与Ｌｏｅｂ（１９６１）和Ｏｓｈｉｍａ（１９９５）等人的结果比较，本文结果的相对误差小于１％，优于Ｏｓｈｉｍａ的结果．     

含时变分S 矩阵解得一般形式

推导出含时S散射矩阵变分表达式经基函数展开并优化后的解的一般形式。     

Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.     

Effects of High Salt Concentration and Residue on Copper and Aluminum Corrosion

Traditional researches on metal corrosion under salt solutions deposit conditions are usually carried out by visual, electron microscopic observations and simple electrochemical measurement via a traditional one-piece electrode. These techniques have difficulties in measuring localized corrosion that frequently occur in inhomogeneous media. This paper reports the results from the experiments using specially shaped coupons and a relatively new method of measuring heterogeneous electrochemical processes, namely, the wire beam electrode(WBE). Preliminary results from copper and aluminum corrosion in highly concentrated sodium chloride solutions with and without solid deposits show that the method is useful in simulating and studying corrosion especially localized corrosion in pipelines.