一种简单的基于固定网格的空间直线索引算法

介绍了空间索引的功能，建立了空间索引的方法．针对地理信息系统中空间索引的重要性，以及在地理信息系统空间元素中直线和由直线组成的复合元素占了绝大部分的现象，改进了一种图形学中常用的直线生成算法，以快速建立基于固定网格的直线空间索引的算法，并分4种情况进行分析．本算法具有原理简单、易于实现等特点，并且在作者开发的一个GIS项目中得到了具体应用．     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

古巴比伦人求算术平方根的探究

分析了古巴比伦人求算术平方根的算法，证明了其正确性。然后将其算法推广到求n次算术根，并证明了其正确性。     

环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.     

改进的神经网络并行算法及其在地震初至拾取中的应用

针对经典BP神经网络易于陷入局部极小点、易于产生振荡等缺点,提出了神经网络初始权值的二分法,改进了一种网络结构自动确定算法,并将随机算子和遗忘因子引入BP神经网络中.在提高全局寻优能力的同时,加快了网络的收敛速度.在分析了神经网络内在并行性的基础上,基于MPI实现了改进算法的并行化,将算法应用于地震资料的初至拾取,并取得了良好的应用效果,验证了算法的有效性.     

关于Euler-Maclaurin公式的一个注记

利用梯形公式的余项,将被积函数的二阶导数做幂级数展开,证明了余项是关于求积区间长度的奇数次幂级数.推导出了复合梯形公式的一类渐近展开式,从另一方面印证了Euler-Maclaurin公式.