单种群离散模型的全局稳定性

本文证明了■全局稳定的充要条件是方程无二点环.可以证明本文的结论与“C—R 定理是等价的.利用本文的结果不仅可以简化“C—R 定理”的证明,而且为推广到多个极值点的情形提供了方便的工具.     

Theoretical investigation on kinetics and thermochemistry of reaction of CHF2CF2OCH2CF3 with OH radicals and global warming potentials

Theoretical investigation has been carried out on the mechanism, kinetics and thermochemistry of the gas-phase reactions between CHF₂CF₂OCH₂CF₃ and OH radical using a new hybrid density functional M06-2X/6-31+G(d,p) and G2(MP2)//M06-2X/6-31+G(d,p) methods. The most stable conformer of CHF₂CF₂OCH₂CF₃ is considered in our study and the possible H-abstraction reaction channels are identified. Each reaction channel shows an indirect H-abstraction reaction mechanism via the formation of pre-reactive complex. The rate coefficients are determined for the first time over a wide range of temperature 250–1000 K. At 298 K, the calculated total rate coefficient of k_OH = 1.01×10^?14 cm³ molecule^?1 s^?1 is in good agreement with the experimental results. The heats of formation for CHF₂CF₂OCH₂CF₃ and CF₂CF₂OCH₂CF₃ and CHF₂CF₂OCHCF₃ radicals are estimated to be -1739.25, -1512.93 and -1523.94 kJ mol^?1, respectively. The bond dissociation energies of the two C-H bonds are C(-H)F₂CF₂OCH₂CF₃: 423.34 kJ mol^?1 and CHF₂CF₂OC(-H)HCF₃: 411.87 kJ mol^?1. The atmospheric lifetime of CHF₂CF₂OCH₂CF₃ is estimated to be around 4.5 years and the 100-year time horizon global warming potentials of CHF₂CF₂OCH₂CF₃ relative to CO₂ is estimated to be 601.     

水平变化双层波导声传播问题的耦合简正波解

为了验证现有模型的精度,导出了全反射下边界双层波导中简正波耦合矩阵的解析表达式,并将其应用到全局矩阵耦合简正波模型(Direct Global Matrix Coupled-Mode)中,使得该模型可以提供水平变化双层波导问题的标准解。文中首先利用COUPLE的简正波及耦合矩阵数值解验证了该简正波及耦合矩阵解析表达式的正确性;其次,采用改进的DGMCM模型求解了双层波导海山声传播损失,结果表明,改进后的DGMCM模型可以非常精确地求解水平变化双层波导问题,可作为求解此类问题的标准模型使用。     

基于有向网络的Email病毒传播模型及其震荡吸引子研究

基于有向Email网络和Email病毒传播特点,运用平均场方法建立Email病毒传播的时滞微分方程模型,研究Email病毒在有向网络中的震荡传播行为.理论上给出了震荡解的全局吸引子存在的充要条件,数值实验验证了吸引子的存在性和控制.研究表明,子图之间的传播概率决定吸引子的存在性,而有效传播率影响吸引子的振幅,因此这两个参数对于有效预测和控制Email病毒在网络上的传播规模具有重要意义.     

利用纠缠密度研究光子禁带系统的纠缠演化特性

研究了一个二能级原子在光子禁带模型中的原子与热库间及热库模式间的纠缠动力学行为.利用全局纠缠的方法,引出与热库模式相关的纠缠密度.研究发现,当禁带是完美带隙时,会出现稳态原子布居数俘获现象,从而抑制原子的自发辐射效应,防止了信息传输过程中信息的流失.原子与热库模式之间的纠缠密度以及热库模式与模式之间的纠缠密度会随着原子与热库之间耦合强度的增加而增大.当取长时极限时,原子与热库模式之间的纠缠减为零.热库模式与模式之间在强耦合情况下,由于拉比分裂的作用,在两个对称模式间会形成较强的纠缠;在弱耦合情况下,只能在中心频率处形成纠缠.     

PB- Und Sr-Isotopensignaturen AlS Herkunftsindikatoren Für Anthropogene Und Geogene Kontaminationen

Abstract

In isotope geochemistry, natural differences in isotope abundance ratios of heavy elements (e.g. Sr, Nd, Pb) allow the use of specific isotopic signatures as tracers for these and genetically related elements. Examples of such applications in the field of anthropogeochemistry will be presented for lead and strontium.     

Mechanism and kinetics of the atmospheric degradation of 2-formylcinnamaldehyde with O3 and hydroxyl OH radicals – a theoretical study

In the present investigation, the reaction mechanism and kinetics of 2-formylcinnamaldehyde (2-FC) with O₃ and hydroxyl OH radicals were studied. The reaction of 2-FC with O₃ radical are initiated by the formation of primary ozonide, whereas the reaction of 2-FC with the hydroxyl OH radical are initiated by two different ways: (1). H-atom abstraction by hydroxyl OH radical from the –CHO and –CH = CHCHO group of 2-FC (2). Hydroxyl OH addition to the –CH = CHCHO group to the ring-opened 2-FC. These reactions lead to the formation of an alkyl radical. The reaction pathways corresponding to the reactions between 2-FC with O₃ and hydroxyl OH radicals have been analysed using density functionals of B3LYP and M06-2X level of methods with the 6-31+G(d,p) basis set. Single-point energy calculations for the most favourable reactive species are determined by B3LYP/6-311++G(d,p) and CCSD(T)/6-31+G(d,p) levels of theory. From the obtained results, the hydroxyl OH addition at C8 position of 2-FC are most favourable than the C9 position of 2-FC. The subsequent reactions of the alkyl radicals, formed from the hydroxyl OH addition at C8 position, are analysed in detail. The individual and overall rate constant for the most favourable reactions are calculated by canonical variational transition theory with small-curvature tunnelling corrections over the temperature range of 278–350 K. The calculated theoretical rate constants are in good agreement with the available experimental data. The Arrhenius plot of the rate constants with the temperature are fitted and the atmospheric lifetimes of the 2-FC with hydroxyl OH radical reaction in the troposphere calculate for the first time, which can be applied to the study on the atmospheric implications. The condensed Fukui function has been verified for the most favourable reaction sites. This study can be regarded as an attempt to investigate the O₃-initiated and hydroxyl OH-initiated reaction mechanisms of 2-FC in the atmosphere.     

Global dynamics of a novel multi-group model for computer worms

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.     

最值理论中一个结论的证明

同济大学《高等数学》最值理论中有结论称“若一个函数在一个区间内可导且只有一个驻点,并且这个驻点是函数的极值点,那么此驻点也是该函数的最值点”,但并未给出证明。学生们对此频感好奇。受Fermat引理启发,利用反证法可获一个比此结论更为一般的定理。     

Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum

We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.