Is the Conventional Interpretation of the Anisotropic Effects of CC Double Bonds and Aromatic Rings in NMR Spectra in Terms of the π‐Electron Shielding/Deshielding Contributions Correct?

Based on the nucleus‐independent chemical shift (NICS) concept, isotropic magnetic shielding values have been computed along the three Cartesian axes for ethene, cyclobutadiene, benzene, naphthalene, and benzocyclobutadiene, starting from the molecular/ring center up to 10 Å away. These through‐space NMR spectroscopic shielding (TSNMRS) values, which reflect the anisotropic effects, have been broken down into contributions from localized‐ and canonical molecular orbitals (LMOs and CMOs); these contributions revealed that the proton NMR spectroscopic chemical shifts of nuclei that are spatially close to the C?C double bond or the aromatic ring should not be explained in terms of the conventionally accepted π‐electron shielding/deshielding effects. In fact, these effects followed the predictions only for the antiaromatic cyclobutadiene ring.     

二元Block-Basu型指数分布的独立性与不相关性

若（X,Y）服从二元Block-Basu型指数分布,则X,Y相互独立与不相关是等价的．还给出了X,Y的相关系数和尾部相关系数．     

图的上可嵌入性与独立顶点的新度和

Let G be a k(k ≤3)-edge connected simple graph with minimal degree ≥ 3,girth g,r=g12.For any independent set {a1,a2 , . . . , a 6/(4 k)} of G,if,then G is up-embeddable.     

Massive and massless neutrinos on unbalanced seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM).A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L x U(1)y gauge symmetry.The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix.Given p＞q,the rank of M is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues.The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model,independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M,and the q x q heavy Majorana neutrino mass matrix MR.In other words,the numbers of massive left- and right-handed neutrinos are fairly matched.A good example to illustrate this "seesaw fair play rule"is the minimal seesaw model with p ＝ 3 and q ＝ 2,in which one masslese neutrino sits on the unbalanced seesaw.     

一种数字全息图零级项消除的新方法

针对离轴数字全息图中的零级项问题,提出用独立分量分析方法对零级项进行压缩.首先通过CCD获取同一物体的两幅干涉强度不同的全息图构成观测信号,然后采用独立分量分析方法(Independent Component Analysis(ICA))从观测信号中分离出零级项和共轭项,再从获得的共轭项中减去残余的零级项分量,实现零级项的有效压缩,并用模拟结果论证该方法在处理零级项压缩方面的优越性和有效性.     

Independent N-Electron Method and High Accuracy Calculations of the Ground State Energy of the Nonrelativistic Light Atoms (3≤Ne≤10)

A new method based on the independent electron-pair approximation is developed to calculate the correlation energy and the basis size truncation error. The formalisms for the nondegenerate systems are described in this paper. Because all important terms are very efficiently selected and the calculations can be separated into several parts, this new method gives very accurate results and does not require expensive computing facilities. As a test, the ground state energies (GSE) of the nonrelativistic atoms for 3≤N_e≤10 are calculated using this new method. The calculated results are found to be in close agreement with the most recent available version of the exact GSE which is derived from the experimental data after subtracting the contributions from the relativistic effect, QED radiative corrections, finite nucleon mass corrections, and the finite radius of the nuclear size. Those accurate results have not been reproduced for N_e≥5 by any direct theoretical calculations in literatures. Since this method is not restrained to nonrelativistic or Coulomb systems, it should become powerful to study other quantum interacting systems.     

An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs

The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Directed Acyclic Graph) approach, an O(kn ²) time sequential algorithm is designed in this paper to solve the maximum weight k-independent set problem on weighted trapezoid graphs. The weights considered here are all non-negative and associated with each of the n vertices of the graph.     

关于B值行独立随机元阵列部分和的完全收敛性的注记

讨论了p型Banach空间（1≤p≤2）下,B值行独立随机元阵列部分和的完全收敛性,得到了几个充分条件的结果,它们是实值随机变量阵列完全收敛性的推广。     

Join-Independent and Meet-Independent Sets in Complete Lattices

In this paper join-independent and meet-independent sets in a complete lattice are defined. The relations between them are presented and substructures of a complete lattice induced by such sets are investigated.     

Independent mistakes in large games

Economic models usually assume that agents play precise best responses to others' actions. It is sometimes argued that this is a good approximation when there are many agents in the game, because if their mistakes are independent, aggregate uncertainty is small. We study a class of games in which players' payoffs depend solely on their individual actions and on the aggregate of all players' actions. We investigate whether their equilibria are affected by mistakes when the number of players becomes large. Indeed, in generic games with continuous payoff functions, independent mistakes wash out in the limit. This may not be the case if payoffs are discontinuous. As a counter-example we present the n players Nash bargaining game, as well as a large class of “free-rider games.” Received: November 1997/Final version: December 1999