具有最小度距离的双圈图

记G（n）为所有n阶连通简单双圈图所构成的集合．本文主要讨论G（n）按其度距离从小到大进行排序的问题，并确定了该序的前两个图及其相应的度距离，其中具有最小度距离的图是由星图K1,n-1的一个悬挂点与另外两个悬挂点之间各连上一条边所得的图Sn．     

Carrier-envelope phase of ultrashort pulsed Laguerre-Gaussian beam

The carrier-envelope phase of the ultrashort pulsed Laguerre-Gaussian beam is studied.The order of Laguerre function affects seriously the variations of the carrier-envelope phase with the propagation distance increasing.The beam waist also affects the carrier-envelope phase in a few Rayleigh distances.The variation of the carrier-envelope phase is larger on the axis than on the beam periphery in propagation.     

A note on the number of different inner products generated by a finite set of vectors

This note aims to introduce a new problem in combinatorial geometry. What is the minimum number of distinct inner products determined by n distinct vectors in R^d? We use some elementary methods to derive upper and lower bounds giving a good impression of where the answer might lie and show how it is connected to various known problems.     

某个单点值给定的Copula最优界的不可交换性度量

通过研究某个单点值给定的Copula(相关结构函数)的最佳上下界的不可交换性度量,构造了4个奇异的Copula,它们具有最大的不可交换性,揭示了最大不可交换Copula的结构特点和性质.定义了非径向对称和非联合对称意义下的随机变量的不可交换性,指出对于4个最大不可交换的C叩ula,3种不可交换性度量是相同的.另一方面,研究了在一般的Lp距离定义下的不可交换性度量的计算公式,确定了其中的标准化系数kp=3p 1(p 1)p 2/4,特别地k1=27/2和k2=81的计算公式可以作为常用的不可交换性度量.     

Globally flexible functional forms: The neural distance function

The output distance function is a key concept in economics. However, its empirical estimation often violates properties dictated by neoclassical production theory. In this paper, we introduce the neural distance function (NDF) which constitutes a global approximation to any arbitrary production technology with multiple outputs given by a neural network (NN) specification. The NDF imposes all theoretical properties such as monotonicity, curvature and homogeneity, for all economically admissible values of outputs and inputs. Fitted to a large data set for all US commercial banks (1989–2000), the NDF explains a very high proportion of the variance of output while keeping the number of parameters to a minimum and satisfying the relevant theoretical properties. All measures such as total factor productivity (TFP) and technical efficiency (TE) are computed routinely. Next, the NDF is compared with the Translog popular specification and is found to provide very satisfactory results as it possesses the properties thought as desirable in neoclassical production theory in a way not matched by its competing specification.     

偏正态数据下众数回归模型的统计诊断

为了更好地拟合偏态数据,充分提取偏态数据的信息,针对偏正态数据建立了众数回归模型,并基于Pena距离统计量对众数回归模型进行统计断研究,得到了众数回归模型的Pena距离表达式以及高杠杆异常点的诊断方法.利用EM算法与梯度下降法给出了众数回归模型参数的极大似然估计,根据数据删除模型计算似然距离、Cook距离和Pena距离统计量,绘制诊断统计图.通过Monte Carlo模拟试验和实例分析比较,说明文章提出的方法行之有效,并在一定条件下Pena距离对异常点或强影响点的诊断优于似然距离和Cook距离.     

Derivation of quantum Chernoff metric with perturbation expansion method

We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.     

A possible resolution of tension between Planck and Type Ia supernova observations

There is an apparent tension between cosmological parameters obtained from Planck cosmic microwave background radiation observations and that derived from the observed magnitude-redshift relation for the type Ia supernova(SNe Ia).Here,we show that the tension can be alleviated,if we first calibrate,with the help of the distance-duality relation,the light-curve fitting parameters in the distance estimation in SNe Ia observations with the angular diameter distance data of the galaxy clusters and then re-estimate the distances for the SNe Ia with the corrected fitting parameters.This was used to explore their cosmological implications in the context of the spatially flat cosmology.We find a higher value for the matter density parameter,m,as compared to that from the original SNLS3,which is in agreement with Planck observations at 68.3%confidence.Therefore,the tension between Planck measurements and SNe Ia observations regarding m can be efectively alleviated without invoking new physics or resorting to extensions for the standard concordance model.Moreover,with the absolute magnitude of a fiducial SNe Ia,M,determined first,we obtained a constraint on the Hubble constant with SNLS3 alone,which is also consistent with Planck.     

数字全息显微系统结构参量对再现像质的影响

为了获取高质量的数字全息显微再现像,分析了同轴相移数字全息显微系统结构参量对再现像质的影响.首先经过计算得出理想成像时,像空间物光波频率完全由物体面形结构频率和系统放大倍率决定.然后基于显微成像时物光波的所有频率分量都应该被有效记录的分析,得出在同轴相移系统中放大倍率必须使物光波的空间频率缩小到满足采样要求|并得出在相同的放大倍率下记录距离会影响有效记录的物体尺寸,记录器件离开像平面的距离越小,有效记录的物体尺寸越大,在像平面上时有效记录的物体尺寸最大.计算机仿真和光学实验都证明了上述结论的正确性.     

大气信道紫外光通信系统通信距离的增程方法

介绍了紫外光大气传输理论和非直视单散射模型.在此模型基础上,针对紫外光通信系统的结构设计对信道能量损耗的影响进行了理论上的定性分析.对不同天气、不同通信模式、不同几何结构参量条件下,大气信道所产生的能量损耗进行了定量仿真.仿真结果表明:能量衰减随通信距离的增加而增大;不同能见度条件下,能量衰减随通信距离的递增程度不同,能见度越高能量衰减越小,可实现的通信距离越远;通信距离随发射仰角的减小而增加,随接收仰角的减小而增加,且发射仰角对通信距离的影响程度大于接收仰角;通信距离随发射束散角的增加而增加,随接收视场角的减小而增加,且接收视场角对通信距离的影响程度远大于发射束散角.