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.     

六六六异构体稳定碳同位素组成分析

采用GC-C-IRMS、EA-IRMS和Dual-inlet IRMS 3种稳定同位素比值质谱仪分别对六六六的α、β和γ3种异构体的稳定碳同位素组成进行了分析。对比3种分析系统测定的碳同位素组成数据表明GC-C-IRMS系统能够准确和精确地测定六六六碳同位素组成。应用GC-C-IRMS技术分析了水样品中α-和γ-六六六的碳同位素组成,结果表明六六六在溶解、稀释、萃取、挥发等过程碳同位素组成没有分馏现象。采用GC-C-IRMS技术分析环境样品中持久性有机氯农药稳定碳同位素组成可能得到广泛应用。     

非等熵气体动力学方程组大初值问题的放缩框架

非等熵气体动力学系统Cauchy问题弱解全局存在性有两个公开问题:一个是包含真空的小初值问题,另一个是任意大初值问题.本文通过引入一个放缩框架证明了上述两个问题的等价性,即对于粘性消失解,其包含真空小初值问题的一致BV估计蕴含着任意大初值问题弱解的全局存在性.该放缩框架对大多数具有物理背景的双曲守恒律系统亦成立.     

Determination of the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of stable atropisomeric PCBs on Chirasil-dex

Pure enantiomers of chiral (atropisomeric) polychlorinated biphenyls (PCBs) obtained by high-performance liquid chromatography were used to establish the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of six PCB atropisomers on Chirasil-Dex. The elution order was found to be (−/+) for PCBs 84, 132, 136, and 176 and (+/−) for PCBs 135 and 174. The retention characteristics of all 19 tri- and tetra-ortho atropisomeric PCBs were also investigated. Nine of the atropisomers could be separated using this chiral selector. PCBs 95, 132, and 149 were completely resovled and PCBs 84, 91, 135, 136, 174, and 176 were partially separated (R = 0.7–0.9). All of the separated congeners are 2,3,6-substituted in at least one ring, and conversely – none of the congeners that lacks 2,3,6-substitution could be separated. Thus, chiral recognition and enantiomer separation seems to be strongly governed by 2,3,6-substitution.     

三个不同领域实际问题相结合的教学方法探讨

通过建立肿瘤增长动力学模型,研究肿瘤增长动态规律时发现:肿瘤增长的全过程与龚珀兹增长曲线描述的经济增长过程完全相符;进一步给出了龚珀兹增长曲线与描述种群的增长与调节的逻辑斯蒂增长曲线完全相似.将上述三个属性完全不同的实际应用问题打包传授给学生的授课方法是有别于孤立地介绍三个具体问题的,学生的学习效果也会不同.     

Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

This paper reveals soliton solutions to magneto–optic waveguides that maintain parabolic–nonlocal law of refractive index. The unified Riccati equation expansion together with extended auxiliary equation approach together reveal bright, dark, singular as well as straddled optical solitons. These soliton solutions are obtained through a limiting process when the modulus of ellipticity approaches unity. Finally, the conservation laws are also listed.