厚薄板通用三角形位移元

本文构造出了一种具有九个自由度的厚薄板通用三角形位移单元，并给出了单元刚度矩阵显式。这种单元以其简洁的常规位移元列式可在相当宽的板厚变化范围内（包括板厚为零）获得很高的计算精度，其结果可与相应的矩形单元相比。而且不会出现剪切自锁。     

Information theory of D‐dimensional hydrogenic systems: Application to circular and Rydberg states

The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the familiar variance and its generalization, the power and logarithmic moments, and, more appropriately, the Shannon entropy and the Fisher information. These complementary uncertainty measures have a global or local character, respectively, because they are power‐like (variance, moments), logarithmic (Shannon) and gradient (Fisher) functionals of the corresponding probability distribution. Here we explicitly discuss all these spreading measures (and their associated uncertainty relations) in both position and momentum for the main prototype in D‐dimensional physics, the hydrogenic system, directly in terms of the dimensionality and the hyperquantum numbers which characterize the involved states. Then, we analyze in detail such measures for s‐states, circular states (i.e., single‐electron states of highest angular momenta allowed within an electronic manifold characterized by a given principal hyperquantum number), and Rydberg states (i.e., states with large radial hyperquantum numbers n). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

特征值问题的预变换方法(I): 杨辉三角阵变换与二阶PDE 特征多项式

本文提出一类求解特征值问题的下三角预变换方法, 目标是通过相似变换后矩阵下三角元素平方和明显减少、且变换后的特征值及其特征向量较易求解, 使变换后的对角线可作为全体特征值很好的一组初值, 其作用如同对于解方程组找到好的预条件子, 加速迭代收敛. 以二阶PDE 数值计算为例,对于以Laplace 方程为代表的特征波向量组及正交多项式组有广泛的应用前景.
杨辉三角是我国古代数学家的一项重要成就. 本文引入杨辉三角矩阵作为预变换子, 给出一般矩阵用杨辉三角矩阵作为左、右预变换子时变为上三角矩阵的充要条件, 给出了元素为行指标二次多项式的两个矩阵类(三对角线阵与五对角线阵) 中特征值何时保持二次多项式的充要条件, 并应用于构造新的二元PDE 正交多项式.     

Correlation and entanglement of a three-level atom inside a dissipative cavity

We discuss the correlation and entanglement of a three-level atom with a single-mode quantized field in a coherent state inside a phase-damped cavity. We analyze the influence of dissipation on the quantum and classical entropy. It has been shown that the quantum, classical and nonextensive entropy are sensitive to any change in the initial state setting of the atom and the quantized field. The relation between the long lived entanglement and dissipation is observed. On the other hand, a short disentanglement can be generated through special values of the atomic motion parameter.     

Integrating across Pascal's triangle

Sums across the rows of Pascal's triangle yield n² while certain diagonal sums yield the Fibonacci numbers which are asymptotic to ?n where ? is the golden ratio. Sums across other diagonals yield quantities asymptotic to cn where c depends on the directions of the diagonals. We generalize this to the continuous case. Using the gamma function, we generalize the binomial coefficients to real variables and thus form a generalization of Pascal's triangle. Integration over various families of lines and curves yields quantities asymptotic to cx where c is determined by the family and x is a parameter. Finally, we revisit the discrete case to get results on sums along curves.     

On Information Processes in Statistical Experiments with Distributed Observations

Using stochastic integration theory in topological vector spaces general formulas for the Hellinger processes are derived. Feynman–Kac type formulas are obtained for the related Hellinger integrals in terms of the Hellinger processes and the geometric mean measures. The expected logarithmic utility from data, characterized as the Shannon information, is also considered.     

On the Helly Number for Line Transversals to Parallel Triangles

We prove two results about the problem of finding the Helly number for line transversals to a family of parallel triangles in the plane: (1) If each three triangles of a family of parallel right triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all     

杨辉三角形的若干性质

研究了杨辉三角中的D av id星恒等式,给出了n阶星恒等式的定义,证明了n(n 3)阶星恒等式的存在性,并且给出了构造n阶星恒等式的方法.     

一种快速求红移和证认谱线的新方法--伪三角法

对于河外天体，谱线证认和红移确定是光谱分析的第一步。本文在仔细分析天体光谱特点的基础上，提出了一种全新的求红移和证认谱线的新方法--伪三角法。该方法利用最强的三根谱线的波长信息构造“三角形”，通过将最大角的“余弦”与已知模板的“余弦”表相匹配，反推得到相应的标准谱线波长，并进而得到红移值。通过这个红移值，可以得到所有的谱线的标准位置，这就相当于谱线证认。结果表明：这种方法在大大减少运算量的同时，保持了较高的正确识别率和极低的误识率。这对海量光谱数据的处理具有重要的意义。同时，该方法立意新颖，简单明了，容易实现。缺点是对于谱线少于3根的光谱以及噪声很大的光谱不能有效地处理。