路径约束条件下车辆行为的时空演化模型

复杂地理环境下车辆运行线路具有空间三维特征, 它对车辆行为的约束是显然的, 非一维空间和二维空间所能描述. 将复杂地理环境下车辆运行线路抽象为空间曲线, 引入微分几何理论, 利用弧长、曲率和挠率等几何不变量参数建立沿空间曲线运动的Serret-Frenet活动标架; 然后, 对空间曲线上任意一点处Serret-Frenet标架具有时变属性的动态行为进行数学描述, 进而建立路径约束条件下车辆行为的时空演化模型, 并在数学上严格证明了所建时空演化模型适用于车辆(Serret-Frenet标架)直线运行和做匀速圆周运动的特殊情形. 为后续复杂地理环境中交通线路上的车辆跟驰、变道等微观行为和交通流宏观行为研究, 奠定了理论基础.     

逆Walsh序p值Walsh变换的演化生成及快速算法

本文利用二分演化思想和矩阵分解技术 ,重点讨论逆Walsh序三值Walsh变换的演化生成和快速算法 ,并将之推广至p值情形 .     

谱问题、发展方程族及Lax表示的等价性

讨论了四对谱问题、相应的保谱方程族以及它们Ｌａｘ表示的等价住，并利用这种等价关系可导出一些方程的Ｌａｘ表示．     

Zero-determinant strategy:An underway revolution in game theory

Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions according to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant(ZD) strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two players, indicating that a smart player can control her unwitting co-player’s payoff in a unilateral way [Proc. Acad. Natl. Sci.USA 109, 10409(2012)]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players,and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis,cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.     

Temperature evolution associated with dynamic phase transformation in shape-memory TiNi alloys

In this paper, temperature evolution in shape-memory TiNi alloys was in situ measured in the process of phase transition under shock loading tests. It was shown that the temperature increased during loading, while unloading, it would keep the maximum value constant or decreased, depending on the strain rate. The corresponding dynamic response indicated that the hardening property is related to phase transition strain and the transformation path has remarkable strain-rate effect. The reason for this phenomenon is essentially due to the temperature dependence of the phase transformation stress. Moreover, the evolution of temperature was consistent with the change of stress, suggesting that this dynamic phase transition deformation is uniform. The theoretical calculation shows that the mechanism of temperature evolution results from the release of latent heat and the hysteresis dissipated energy. The results of this investigation provide insight into intriguing strain-rate-dependent phenomena intrinsic of TiNi alloys.     

Cobalt Based Nanoparticles Embedded Reduced Graphene Oxide Aerogel for Hydrogen Evolution Electrocatalyst

Efficient water electrolysis catalyst is highly demanded for the production of hydrogen as a sustainable energy fuel. It is reported that cobalt derived nanoparticle (CoS₂, CoP, CoS|P) decorated reduced graphene oxide (rGO) composite aerogel catalysts for highly active and reliable hydrogen evolution reaction electrocatalysts. 7 nm level cobalt derived nanoparticles are synthesized over graphene aerogel surfaces with excellent surface coverage and maximal expose of active sites. CoS|P/rGO hybrid aerogel composites show an excellent catalytic activity with overpotential of ≈169 mV at a current density of ≈10 mA cm^?2. Accordingly, efficient charge transfer is attained with Tafel slope of ≈52 mV dec^?1 and a charge transfer resistance (R_ct) of ≈12 Ω. This work suggests a viable route toward ultrasmall, uniform nanoparticles decorated graphene surfaces with well‐controlled chemical compositions, which can be generally useful for various applications commonly requiring large exposure of active surface area as well as robust interparticle charger transfer.     

Sorting Using Complete Subintervals and the Maximum Number of Runs in a Randomly Evolving Sequence

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a string of 0’s, and then evolves by changing each 0 to 1, with the n changes done in random order. What is the maximal number of runs of 1’s? We give asymptotic results for the distribution and mean. It turns out that, as in many problems involving a maximum, the maximum is asymptotically normal, with fluctuations of order n ^1/2, and to the first order well approximated by the number of runs at the instance when the expectation is maximized, in this case when half the elements have changed to 1; there is also a second order term of order n ^1/3. We also treat some variations, including priority queues and sock-sorting. The proofs use methods originally developed for random graphs.     

Entanglement Evolution of a 2-Qutrit System Interacting with a Fermionic Bath

Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 (2002) 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybroken environment consisting of a fermionic bath. Entanglement of states will decrease or remain constant under the influence of environment, and the class of states which remain unchanged has been found out.     

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.     

非线性发展方程非局部初值问题解的存在性

本文讨论非线性方程的非局部初值问题，利用半群理论、单调算子理论以及Banach不动点定理，分别得到两个问题的温和解和弱解的存在唯一性定理．