空间关联白噪声影响下小世界神经元网络系统的同步动力学

以电耦合的Terman-Wang小世界神经元网络系统为研究对象, 研究了空间关联白噪声影响下神经元网络系统的同步动力学. 首先将动力学平均场近似理论扩展到受空间关联白噪声影响下的小世界网络系统中, 将描述网络系统动力学演化的2N维随机微分方程简化为11个确定性的矩微分方程. 其次, 基于动力学平均场近似理论所推导的矩方程, 讨论了空间关联噪声、网络结构参数对神经元网络系统同步动力学的关键影响, 发现较大的噪声空间关联系数、耦合强度及节点平均度均对神经元网络系统同步放电具有积极作用. 进一步地, 利用计算机仿真数值模拟原神经元网络系统的同步动力学, 并与基于动力学平均场近似理论所得到的结果进行比较, 发现二者具有较好的一致性.     

Structural and spectroscopic properties of small Pun （n= 2-5） molecules

The equilibrium structures and the electronic, spectroscopic and thermodynamic properties of small Pu_n (n=2-5) molecules are systematically investigated using the methods of general gradient approximation (GGA) of density functional theory (DFT). The results show that the bond length of the lowest-energy structure of Pu₂ is 2.578 AA. The ground state structure of Pu₃ is a triangle with D_3h symmetry, whereas for Pu₄, the ground state structure is a square (D_4h) and the spin polarization of 16 for molecule Pu₅ with square geometry (D_4h) is the most stable structure. For the ground state structures, the vibrational spectra as well as thermodynamic parameters are worked out. In addition, the values for the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) along with the energy gap of all the Pu_2-5 structures are presented. The relevant structural and chemical stabilities are predicted.     

Theoretical studies on the structural, electronic, and optical properties of Ag2HgSnSe4

We investigate the electronic structure of Ag₂HgSnSe₄ in a wurtzite-stannite structure with the first principles method. This crystal is a direct band-gap compound. In addition the dielectric function, absorption coefficient, reflectivity, and energy-loss function are studied using the density functional theory in the generalized gradient approximation. We discuss the optical transitions between the valence bands and the conduction bands in the spectrum of the imaginary part of the dielectric function at length. We also find a very high absorption coefficient and a wide absorption band for this material. The prominent structures in the spectra of reflectivity and the energy-loss function are discussed in detail.     

Density-functional study of CO adsorbed on RhN （N = 2-19） clusters

We investigate the structural, electronic and adsorption properties of one single CO molecule adsorbed on Rh_N (N = 2-19) clusters, using the density-functional theory in the spin-polarized generalized gradient approximation. It is found that the structural growth model of the Rh_N clusters transforms from double layers (N = 12-16) to three layers (N = 17-19). Three different adsorption types are the atop site adsorption for N = 6, 8, 9, 11, 12, the bridge site adsorption for N = 2-5, 7, 10, 13-15, 17 and the face adsorption for N = 16, 18, 19. The adsorption abilities of Rh_N clusters are related to C-O bond length, vibrational frequency, adsorption energy and the charge transfer between CO and Rh clusters as well as the electronic density of state. With the increase of Rh cluster size, the adsorption energy of CO adsorbed on Rh_N clusters tends to be 2.2 eV-2.3 eV, which is 0.2 eV-0.3 eV larger than the theoretical value (about 2.0 eV) of CO molecule adsorption on clean Rh (111) surface.     

混凝土复合介质爆炸的不确定优化设计及其高效求解方法

研究不确定因素对炸药在混凝土复合介质中爆炸的影响,并在不确定因素的影响下进行优化设计。用区间数模型来描述系统中的不确定参数,建立相应的区间数优化模型;通过高维代理模型的引入,以及对其中二层嵌套优化问题进行直接解耦,得到了一种高效的求解方法。研究表明：算法经过8个迭代步收敛到最优解,最优解得到的最佳炸药装填深度约为64cm,最佳姿态角约为30°;经过三个迭代步就能迅速定位到最优解附近。算法保证了在最大化毁伤面积的同时,尽量地追求不确定因素影响最小,即综合考虑了毁伤最大和偏差最小。该不确定优化设计方法能有效地推广到相关领域的优化设计,为处理爆炸系统的装药设计和爆炸初始状态参数设计等方面提供了新思路。     

再生核空间W_2~1[a,b]中线性微分方程组初值问题的数值求解

再生核方法在某些方程(组)解的表示和逼近中具有独特的优势,用一种新的再生核讨论线性微分方程组初值问题解的精确表示与近似计算.较之以往的同类文章,对一些重要定理进行了更简单有效的证明.另外本文的再生核由于其结构简单,易于算法实现.最后的算例充分的显示了基于的再生核方法的有效性.     

决策信息系统中的拓扑学方法

在决策信息系统中引入拓扑结构,借助拓扑学的基本概念(拓扑、内部和闭包等)研究决策问题,用它们刻画决策信息系统中的一些重要概念(决策协调集、决策约简集、下近似协调集、下近似约简集、上近似协调集、上近似约简集),并利用它们把这些重要概念推广到最一般的情况,建立起相应的约简理论.     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

Lévy型算子所生成马氏过程的稳定性

利用Lévy型算子积分微分型表示形式和拟微分型表示形式,以寻求Lévy型算子生成的马氏过程各种稳定性的精确且可验证的充分条件.给出了由符号函数直接判定的Lévy型过程非爆炸的充分条件,这个条件包括了扩散过程非爆炸的线性增长条件;当Lévy型算子生成马氏过程对应半群的符号函数已知时,得到了由该符号函数直接表达的常返性充分条件,它推广了关于Lévy过程经典的Chun-Fuchs常返性准则.     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.