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.     

Universal point sets for planar three-trees

For every $n\in \mathbb{N}$, we present a set $S_n$ of $O(n^{3/2}\log n)$ points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of $S_n$. This is the first subquadratic upper bound on the cardinality of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.     

Genotyping of exons 1 to 20 in Duchenne muscular dystrophy by universal multiplex PCR and short‐end capillary electrophoresis

One rapid CE method was established to diagnose Duchenne muscular dystrophy (DMD). DMD is a severe recessive inherited disorder frequently caused by gene deletions. Among them, exons 1–20 account for nearly 30% of occurrences. In this study, the universal multiplex PCR was used to enhance the fluorescently labeling efficiency, which was performed only by one universal fluorescent primer. After PCR, a short‐end injection CE (short‐end CE) speeded up the genotyping of the DMD gene. This method involved no extra purification, and was completed within 9 min. The CE conditions contained a polymer solution of 1.5% hydroxylethylcellulose in 1× TBE buffer at 6 kV for separation. This method was applied to test six DMD patients and one healthy male person. The results showed good agreement with those of multiplex ligation‐dependent probe amplification. This method can be applied for clinical diagnosis of DMD disease. Accurate diagnosis of the DMD gene is the best way to prevent the disease.     

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.     

Exact solutions to a class of differential equation and some new mathematical properties for the universal associated-Legendre polynomials

The exact solutions to a class of differential equation are studied. Some special cases are discussed for the central potentials, single ring-shaped potential and the angular Teukolsky equation. A new expression to the associated Legendre polynomials is found. Some new properties of the universal associated-Legendre polynomials (UALPs) including the generating function, Rodrigues’ formula, parity, some special values and the recurrence relations are presented. A new different Rodrigues’ formula of associated Legendre polynomials is also obtained.     

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.     

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.     

长余辉发光材料研究进展

长余辉发光材料是一类重要的光-光转换和节能材料。这类材料在工农业生产、军事、消防和人们生活的许多方面得到广泛应用。本文主要结合本课题组近年在长余辉发光材料领域的研究工作,综述长余辉发光材料的研究进展,并对今后的发展方向进行展望。