The first,the biggest,and other such considerations

We investigate the relation between the underlying dynamics of randomly evolv ing systems and the extrema statistics for such systems. Independent processes, Fokker-Planck processes and Lévy processes are considered.     

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained.     

Correlation integral as a tool for distinguishing between dynamics and statistics in time series data

We propose a new test for time series data for proper choice of processing technique: dynamical or statistical. It is based upon the normalized slope of the correlation integral (, m) = m⁻¹d(ln C()) /d ln , where m is the embedding dimension. It is shown that when does not tend to 0 on the resolved range of scales as m grows, then there will be serious limitations for dynamical methods even if the data are dynamical by nature. In the latter case it means that the length of time series does not allow to resolve small scales, and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques, such as estimating Lyapunov exponents or predicting time series.     

Development of boundary element method to dynamic problems for porous media

Biot's consolidation theory is extended to a general class of viscoelastic bodies defined by Riemann-Stieltjes integral convolutions. From a new reciprocity theorem, proved for the governing equations including the inertia terms, the basic integral representations of the displacement fields and pore pressure are obtained. It is shown that, in the absence of internal inputs, a formulation of the dynamic problem in terms of the boundary unknown fields only is possible.     

Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations

In this paper, the nonlinear Volterra-Fredholm integro-differential equations are solved by using the homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of a series which its components are computed easily . The existence and uniqueness of the solution and the convergence of the proposed method are proved. A numerical example is studied to demonstrate the accuracy of the presented method.     

高压下FCC相金属氢结构稳定性和非谐效应的理论研究

利用第一性原理分子动力学方法研究金属氢体系的非简谐效应, 给出金属氢的声子谱, 讨论金属氢声子谱的温度效应。计算得到氢的同位素氕、氘和氚的FCC相在非零温下的声子谱, 不同温度下的声子谱对比发现零温下3.6 TPa为热力学稳定的临界压强点, 而有限温度下(100 K)临界压强点降到2.8 TPa, 非简谐效应显著地改变了体系的结构稳定性和声子振动性质。     

V掺杂二维MoS_2体系气体吸附性能的第一性原理研究

以芥子气和沙林为代表的毒剂具有毒性强、扩散快的特点,是一类杀伤力强、难以防护的化学战剂,对其快速高效检测是一项具有挑战性的课题.本文基于第一性原理计算方法研究了V掺杂对二维MoS_2气敏性能影响的机理,发现V原子向二维MoS_2的掺杂过程为自发的放热反应, V原子可以稳定掺杂于二维MoS_2超胞结构中的S空位上.掺杂进入二维MoS_2体系的V原子作为施主中心向周围Mo原子给出电子,从而提高了材料的导电能力.吸附能、吸附距离和吸附过程中的电子转移计算结果表明V的掺杂提高了二维MoS_2对气体分子的吸附能力,增强了吸附质分子与基底表面的电子相互作用,从而提高了二维MoS_2的气敏性能.     

奇异积分方程理论在迁移方程中的应用

本文利用奇异积分方程理论，对于具有非零边界条件的球对称模型的散射裂为函数，给出了直接求妥方法并给出了解的明显表达式。     

无穷限积分的控制收敛理论

本文根据有限区间上Ｒｉｅｍａｎｎ积分的Ａｒｚｅｌａ控制收敛定理［１］，给出无穷限积分的控制收敛定理，并做了相应的推广。