Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

对数态Tavis-Cummings模型中辐射场的非经典性

本文研究了任意初态的双光子Tavis-Cummings模型的演化规律,作为例子,讨论了初始时刻两个原子均处于基态而光场为对数态时场的压缩效应,光子的聚束和反聚束效应.     

两指标B值鞅空间的对偶

通过引入新型两指标B值鞅空间, 利用两指标B值鞅的Fefferman不等式, 证明了当B为自反Banach空间时, 由p均方算子定义的两指标B值鞅空间_pH_α     

用MAPKOB链模拟月径流系列的尝试

水文统计中的月径流资料是非常重要的。月径流系列是一随机过程，由于水文现象的复杂性，难以用准确的分布函数来描述。但作出某些合理手假设后，可将其变为符合各态历经定理的平稳随机过程。用Ｍａｐｋｏｂ自回归模型可以生成人工月径流系列，以满足规划、设计等方面的要求。本文以三屯河为例，用Ｍａｐｋｏｂ模型模拟了该河的月径流系列。     

地价测算中的线性约束滚动模型

综合考虑影响地价的各种因素，结合目前土地价格评估中的各种理论方法，建立了描述土地价格变化的数学模型，并应用于宁波经济技术开发区新矸区域的地价评估工作中，取得较好的结果．     

感应耦合等离子体中原子发射光谱的非局部热平衡 Ⅰ.非玻尔兹曼分布

本文叙述了在感应耦合等离子体中,原子激发过程可以用台阶式模型来近似,从而证实了激发态粒子数的局部非玻尔兹曼分布是等离子体光学薄性质的必然结果。从理论上讨论了局部非玻尔兹曼分布公式以及分布曲线弯曲时的拐点能量。     

Heating mechanism in relation to the laser machining process

Laser workpiece interaction mechanism is an important phenomenon which will assist in the development of laser machining systems. The interaction mechanism is generally complicated and depends on the laser and workpiece properties. In the present study a mathematical analysis for the laser material removal by evaporation and radial ejection of liquid is carried out. In the analysis the time unsteady problem is solved and nucleation explosions are predicted.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

有向网络的复制机制及其相关网络分析

鉴于有向网络比无向网络包含了更多的内在信息, 而复杂网络中的基本统计量往往仅适用于无向网络, 使得有向网络的研究相对缺少, 由此提出了一个有向网络的统计量, 并分析该统计量在相关有向网络研究中的有效性. 考虑到复制是有向网络增长的一个主要动力, 定义了有向网络结点复制率和有向网络复制率的概念, 并利用结点入度分布和复制率研究了有向规则网络、复制模型网络及自然数网络. 结果显示, 完全复制模型和自然数网络的入度具有无标度特性, 其入度分布的幂律指数 都为2, 2个有向网络的复制率 , 而部分复制模型的复制率 . 因此, 有向网络的入度分布、复制率都能很好地解释完全复制模型与自然数网络的相关性, 可作为重要统计量广泛应用于有向网络研究中.