随机交通均衡配流模型及其等价的变分不等式问题

本文讨论了交通网络系统的随机用户均衡原理的数学表述问题.在路段出行成本是流量的单调函数的较弱条件下,对具有固定需求和弹性需求的模式,首次证明了随机均衡配流模型可表示为一个变分不等式问题,同时也说明了该变分不等式问题与相应的互补问题以及一个凸规划问题之间的等价关系.     

Electrochemical Impedance Spectroscopy in the Characterisation and Application of Modified Electrodes for Electrochemical Sensors and Biosensors

Electrochemical impedance spectroscopy is finding increasing use in electrochemical sensors and biosensors, both in their characterisation, including during successive phases of sensor construction, and in application as a quantitative determination technique. Much of the published work continues to make little use of all the information that can be furnished by full physical modelling and analysis of the impedance spectra, and thus does not throw more than a superficial light on the processes occurring. Analysis is often restricted to estimating values of charge transfer resistances without interpretation and ignoring other electrical equivalent circuit components. In this article, the important basics of electrochemical impedance for electrochemical sensors and biosensors are presented, focussing on the necessary electrical circuit elements. This is followed by examples of its use in characterisation and in electroanalytical applications, at the same time demonstrating how fuller use can be made of the information obtained from complete modelling and analysis of the data in the spectra, the values of the circuit components and their physical meaning. The future outlook for electrochemical impedance in the sensing field is discussed.     

Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.     

General construction of mean-field potential and its application to the multiphase equations of state of tin

The mean-field potential (MFP) approach is an efficient way to evaluate the free energy contribution of ion motions for both solid and liquid states. In this paper the MFP is generally constructed with a volume-dependent term and a shape function. The former is derived in accordance with quasi-harmonic approximation. The latter is given semi-empirically. Application to multiphase equations of state for β-, γ- and liquid-tin has been examined. The theoretical phase diagram and thermodynamic properties of isotherm, thermal expansion, heat capacity, Hugoniot states as well as phase transitions are all in excellent agreement with experiments.     

石墨烯纳米孔道内受限水介电常数影响因素的分子动力学模拟

受限水的介电特性对于石墨烯电容器的储能效率有着重大的影响.因此本文使用分子动力模方法,研究了不同石墨烯纳米孔道宽度(0.812～10 nm)下内受限水介电常数的分布及其影响因素.结果表明,在石墨烯纳米孔道内部受限水双电层结构可分为空隙层、界面层和体相层三个部分.其整体的介电常数随孔道大小的降低而线性减少.这是由内部体相层的宽度的降低而导致的.此外电极电压大小和石墨烯-水相互作用参数ε_CO的强弱也会显著改变电极表面的双电层(Electric Double Layers, EDLs)结构.其中电压的增大使得介电常数分布的震荡的程度也随之增加,最终导致了整体介电常数的减小.与之类似,亲水态的石墨烯表面(高ε_CO)下受限水分布的震荡程度也显著增加,这导致了整体介电常数的降低.     

Reinvestigation of the second negative (A 2 Π u−X 2 Π g) band system of O 2 +

TheA ² Π _ustate of O₂ ⁺ was earlier established as an inverted state contrary to previous assumptions. The rotational analysis of a few more bands of theA-X system of O₂ ⁺ has now been completed. These studies show that the spin-orbit coupling constantA in theA ² Π _ustate gradually varies with the vibrational quantum numberν and is found to be positive forν⩾6. It has also been observed that the spia-rotation interaction is not negligible in theA ² Π _ustate. The spin splitting constantγ is reported for various vibrational levels of this electronic state.     

IBr分子的多光子电离谱的分析

本文用多光子电离的方法,观察了IBr分子高电子态(E)的2光子共振跃迁,结合Franck-Condon原理,从IBr分子的振动谱分析,首次得到IBr(E)态的转动常数B’_(?)-(0.0653±0.0003)cm~(-1).     

一个基本的Hilbert型不等式

本文研究了一个新的、基本的不含参量的Hilbert型不等式.应用改进的Euler-Maclaurin求和公式以估算权系数,证明了其常数系数为最佳值以及此不等式的等价式.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

Some new results on planar harmonic mappings

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.