壳模型哈密顿量本征值的美与奇

本征值问题是自然科学中基本运算之一，对于超大矩阵的对角化是当今许多科学问题的瓶颈。在应用原子核壳模型理论研究较重的原子核结构时，因为壳模型组态太大，通常的方法是基于各种物理考虑做某些组态截断，另一个思路是利用新的算法和飞速发展的计算机资源对这些大矩阵对角化或者近似对角化。总结了本课题组近年来在壳模型哈密顿量本征值近似方面研究的主要结果，包括最低本征值半经验公式及多种外推方法、本征值与对角元的相关性等。The eigenvalue problem is one of the fundamental issues of sciences. Many research fields have been challenged by diagonalizing huge matrices. The nuclear structure theorists face this problem in studies of medium-heavynuclei in terms of the nuclear shell model, in which the configuration space is too gigantic to handle. Thus one usually truncates the nuclear shell model configuration space based on various considerations. Another approach is to make use of super computers by various algorithms, and/or to obtain approximate eigenvalues. In this paper we review our recent efforts in obtaining approximate eigenvalues of the nuclear shell model Hamiltonian, with the focus on our semi-empirical approach and a number of extrapolation approaches towards predicting the lowest eigenvalue, as well as strong correlation between the sorted eigenvalues and the diagonal matrix elements, and so on.     

Effects of ultra-strong magnetic field on electron capture rates of 55C0 and 56Ni in the magnetar surrounding

The electron capture rates of 55Co and 56Ni in the ultra-strong magnetic field at four typical temperature- density points have been calculated using the nuclear shell model and Landan energy levels quantized approximate correction. The results show that the electron capture rates of 55Co and 56Ni are increased greatly in the ultra-strong magnetic field, and even exceed two orders of magnitude in the range from 4.414×10^13G to 2.207×10^27 G. The change rate of electron abundance, ye, of 55Co and 56Ni under the condition of B=4.414×10^15G in the magnetar surrounding has been calculated and discussed, the proportions of ye of 55Co and 56Ni in the total Ye have been reduced by 50 percent in all more than the condition without a magnetic field.     

Chemoselective hydrogenation of α,β-unsaturated aldehydes with modified Pd/C catalyst

Selective hydrogenation of α, β-unsaturated aldehydes with modified Pd/C catalyst was developed.The reduction of C=O bond could be efficiently inhibited by the addition of carbonates,and high selectivity to the corresponding saturated aldehydes was achieved under mild conditions.This protocol provides an alternative for efficient preparation of saturated aldehydes.     

Calculations on polarization properties of alkali metal atoms using Dirac–Fock plus core polarization method

A semi-empirical atomic structure model method is developed in the framework of a relativistic case. This method starts from Dirac-Fock calculations using B-spline basis set. The core-valence electron correction is then treated in a semiempirical core polarization potential. As an application, the polarization properties of alkali metal atoms, including the static polarizabilities and long-range two-body dispersion coefficients, have been calculated. Our results are in good agreement with the results obtained from ab initio relativistic many-body perturbation method and the available experimental measurements.     

Environmental Impacts on Spiking Properties in Hodgkin-Huxley Neuron with Direct Current Stimulus

Based on the well accepted Hodgkin-Huxley neuron model, the neuronal intrinsic excitability is studied when the neuron is subject to varying environmental temperatures, the typical impact for its regulating ways. With computer simulation, it is found that altering environmental temperature can improve or inhibit the neuronal intrinsic excitability so as to influence the neuronal spiking properties. The impacts from environmental factors can be understood that,the neuronal spiking threshold is essentially influenced by the fluctuations in the environment. With the environmental temperature varying, burst spiking is realized for the neuronal membrane voltage because of the environment-dependent spiking threshold. This burst induced by changes in spiking threshold is different from that excited by input currents or other stimulus.     

不完全序关系信息下的双边匹配决策

针对不完全序关系信息下的双边匹配问题,提出了一种匹配决策方法。为了解决该问题,首先将不完全序关系信息转化为不完全Borda分值矩阵,并进行规范化处理;依据规范化Borda分值矩阵,构建综合Borda分值矩阵和离差矩阵,进而构建匹配度矩阵。基于匹配度矩阵构建优化模型,通过求解模型获得匹配方案。最后,以软件服务外包供需匹配为例说明本文所提方法的实用性和有效性。     

随机波动模型下算术亚式期权的Monte Carlo模拟定价

在随机波动模型下,研究亚式期权的定价问题.推导出了标的资产及其随机波动模型的路径,利用对偶变量法对亚式期权进行数值模拟计算,并对随机波动模型下与B-S模型下的欧式期权和亚式期权定价结果进行比较,最后给出了具有固定敲定价格和浮动敲定价格的算术亚式期权的数值计算结果.     

具有时滞的生态-传染病模型的定性分析

针对一类疾病在食饵中传播而把食饵分为易感和染病的时滞生态-传染病模型,以时滞(即传染病在食饵种群中的潜伏期)作为分支参数,讨论了系统正平衡点在时滞τ=0时的局部渐近稳定性,在τ0时在一列临界值处发生了Hopf分支,并且对保持正平衡点稳定时时滞的范围也给出了估计.     

太阳图的奇优美性和奇强协调性

设k_1,k_2,…,k_n是非负整数,C_n=v_v_2…v_nv_1是有n个顶点n条边的圈,则称图C_n+{v_1v_(11),v_1v_(12),…,v_1v_1k_1,v_2v_(21),…,v_2k_2,…,v_nv_(n1),…,v_nk_n}为(k_1,k_2,…,k_n)轮环图,简记为C(k_1,k_1,…,k_n).研究了太阳图1C_n的奇优美性及其奇强协调性,得到了太阳图1C_n在n为偶数时的奇优美标号算法和奇强协调标号算法,从而证明了太阳图1C_n在n为偶数时是奇优美图和奇强协调图的结论.     

我国企业R&D投入产出效率的评价分析

旨在研究企业RD投入产出效率评估.利用我国大陆31个地区企业RD活动的数据,RD经费和研发人员全时当量作为投入指标,专利申请数及新产品产值作为产出指标,基于DEA交叉评价模型来评估我国企业RD投入产出效率,发现我国企业RD活动的效率并不理想,全国仅有海南省是具有效率的,一半以上的地区效率值低于全国平均水平.同时根据全局空间自相关图及聚类地区得出,我国地区间企业RD效率水平差异较大.最后为我国企业RD投入产出水平的提高提出合理化建议.