New series of AB2‐type hyperbranched polytriazoles derived from the same polymeric intermediate: Different endcapping spacers with adjustable bulk and convenient syntheses via click chemistry under copper(I) catalysis

In this article, according to the concept of “suitable isolation group,” six new AB₂‐type polytriazoles containing azo‐chromophore moieties, derived from the same hyperbranched polymer intermediate, were successfully prepared through click reaction under copper(I) catalysis by modifying the synthetic route, in which different isolation groups in different size were introduced to the periphery of the hyperbranched polymers as end‐capping moieties. With the different end‐capping groups, these hyperbranched polymers, P1 – P6 , exhibited different solubility and processability; also, their nonlinear optical properties were modified accordingly, realizing the adjustment of the properties of hyperbranched polymers through the structural design. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.     

一类多输出函数研究

本文研究和讨论了作为多输出函数的N级模2~M背包变换平衡特性,给出了N级模2~M平衡背包变换的结构、计数和函数性质,指出了N级模2~M平衡背包变换本身作为密码变换函数存在着除了第M路外,所有各路的输出函数都是不完全函数的弱点,从而得出了背包变换是密码学弱函数的结论.     

CsPbCl3 nanocrystals dispersed in the Rb0,8Cs0,2Cl matrix studied by far-infrared spectroscopy

The comparative far-infrared spectroscopy studies of Rb_0.8Cs_0.2Cl and Rb_0.8Cs_0.2Cl containing CsPbCl₃ nanocrystals between 170 and 320 K are reported. The effect of cesium lead chloride nanocrystals on the phonon modes of the host matrix, particularly manifested in different temperature behavior of LO–TO splitting and the temperature dependence of high frequency dielectric constant, are demonstrated.     

Separation of pinhole and tunneling electron transfer processes at self-assembled polymeric monolayers on gold electrodes

Self-assembled monolayers of poly(3-alkylthiophene) on gold electrodes are examined by cyclic voltammetry in solutions containing electroactive species. Two well-separated electron transfer processes, namely, electron tunneling through the monolayer and electron exchange at pinholes (defects) of the monolayer are observed. The voltammetric responses of the pinhole electron transfer process take place around the standard potential of the electroactive species and resemble those of a nanoelectrode ensemble of independent individual nanoelectrodes. The voltammetric characteristics of the electron tunneling agree well with predictions of the Marcus theory. Satisfactory values of tunneling coefficient, standard rate constant and organization energy are derived from the voltammetric data.     

Global existence of classical solutions to the Vlasov–Poisson–Boltzmann system with given magnetic field

This paper considers the Vlasov–Poisson–Boltzmann system with given magnetic field. The global existence of classical solutions was obtained when the initial data is a small perturbation around a global Maxwellian. The proof is based on the theory of compressible Navier–Stokes–Poisson equations with forcing and the macro–microdecomposition of the solution to the Boltzmann equation with respect to the local Maxwellian introduced in [T.-P. Liu, T. Yang, S.-H. Yu, Energy method for the Boltzmann equation, Physica D 188 (3–4) (2004) 178–192] and elaborated in [T. Yang, H.-J. Zhao, A new energy method for the Boltzmann equation, J. Math. Phys. 47 (2006)]. The result shows that the existence of solutions is independent of the magnetic field.     

Effects of power law logistic technologies on economic growth

Based on the S-shaped power law logistic technology, we set up an economic growth model in this paper. The solution of the model is given via hypergeometric functions. We show that the dynamics of the model is asymptotically stable. And, it is found that the dynamics of the model is actually controlled by the power law logistic function through an ordinary logistic function, as a power function of the power law logistic. From the statistical point of view, in this paper, three different types of power law index means three different types of skewness, giving three different types of growth and diffusion patterns of technology. Then, we show some comparison results of different types of technology and of different initial levels of capital, and their effects on economic growth. A numerical example is also given in this paper to illustrate the effects.     

A new space–time discretization for the Swift–Hohenberg equation that strictly respects the Lyapunov functional

The Swift–Hohenberg equation is a central nonlinear model in modern physics. Originally derived to describe the onset and evolution of roll patterns in Rayleigh–Bénard convection, it has also been applied to study a variety of complex fluids and biological materials, including neural tissues. The Swift–Hohenberg equation may be derived from a Lyapunov functional using a variational argument. Here, we introduce a new fully-discrete algorithm for the Swift–Hohenberg equation which inherits the nonlinear stability property of the continuum equation irrespectively of the time step. We present several numerical examples that support our theoretical results and illustrate the efficiency, accuracy and stability of our new algorithm. We also compare our method to other existing schemes, showing that is feasible alternative to the available methods.