Zhiber-Shabat方程的多辛几何和多辛隐式格式研究

Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性.     

Phase Systems and Post-Column Dithizone Reaction Detection for the Analysis of Organo-Mercurials by HPLC

Abstract

The suitability of HPLC (normal and reversed phase adsorption) with UV or post-column reaction detection for the analysis of organomercurials was investigated systematically. The separation of organomercurials is best carried out on a reversed phase system with a C-8 bonded phase material as the stationary phase and acetonitrile-aqueous sodium bromide mixtures as the mobile phase.

The precision and detection limit of the method and the efficiency of the extraction procedure were established. For the alkylmercury compounds the lowest limit of detection (80ppb) was obtained with the dithizone reaction detection and for the phenylmercury compounds with UV detection (60ppb). A chromatogram of a spiked fish (2ppmHg) and a river water sample (50ppbHg) is shown.     

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

On feedback and stable price adjustment mechanisms

Given an excess demand function of an economy, say Z(p)$Z(p)$, a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,_p0)$p(t,p_0)$ to an equilibrium _peq$p_{\mathit{eq}}$ solution of Z(p)=0$Z(p)=0$. Besides, all equilibrium points of Z(p)$Z(p)$ are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.     

On the discontinuous Galerkin computation of N‐waves focusing

Sonic boom focusing phenomenon can be predicted using the solution to the nonlinear Tricomi equation which is a hybrid (hyperbolic‐elliptic) second‐order partial differential equation. In this paper, the hyperbolic conservation law form is derived, which is valid in the entire domain. In this manner, the presence of two regions where the equation behaves differently (hyperbolic in the upper and elliptic in the lower half‐plane) is avoided. On the upper boundary, a new mixed boundary condition for the acoustic pressure is employed. The discretization is carried out using a discontinuous Galerkin (DG) method combined with a Runge–Kutta total‐variation diminishing scheme. The results show the accuracy of DG methods to solve problems involving sharp gradients and discontinuities. Comparisons with analytical results for the linear case, and other numerical results using classical explicit and compact finite difference schemes and weighted essentially non‐oscillatory schemes are included. Copyright © 2010 John Wiley & Sons, Ltd.     

Does the Electrical Conductivity of W/O Microemulsions Follow a Percolative Behaviour?

Abstract

The conductivities of different microemulsions prepared with triethanolamine were measured as a function of concentration for several temperatures. The goal of this work has been to test the degree of accuracy of the application of the scaling laws used in the literature. Our conclusion is that there is no general validity even though the abrupt variation of conductivity with concentration may be seen as a percolative phenomenon.     

Isotopes in groundwater as indicators of climate changes

Isotopes of the water molecule (δ¹⁸O and δ²H) are a well-used tool for investigating groundwater origin and history (i.e. tracing the recharge conditions over time, processes occurring during infiltration of rainwater towards aquifers and those involved in the water-rock interaction, and mixing of different waters).This review covers several large European aquifers (Portugal, France, UK, Switzerland, Germany, Hungary, and Poland), which were investigated in terms of their recharge conditions, and the story of the groundwater at a large scale, involving recent, Holocene and Pleistocene components and their eventual mixing.