A_2H_n(n=2-6)的成键情况

本文讨论了含A-A键的A_2H_n(n=2-6)体系的成键规则,导出了相应能级和波函的成对定理。得出了A_2H_n中成键情况、价电子填充情况以及A-A键和A-H键的键级。结果表明:A_2H_n中A原子的杂化状态由价电子数决定。价电子数相同的A_2H_n,不仅几何构型相似,而且键级也相同。     

Asymptotic normality of a weighted integrated squared error of kernel regression estimates with data-dependent bandwidth

Let (X, Y) be a bivariate random vector and let be the regression function of Y on X that has to be estimated from a sample of i.i.d. random vectors (X₁, Y₁),…,(X_n, Y_n) having the same distribution as (X, Y). In the present paper it is shown that the normalized integrated squared error of a kernel estimator with data-driven bandwidth is asymptotically normally distributed.     

ON CROSS-VALIDATION FOR SMOOTHING SPLINES IN THE CASE OF DEPENDENT OBSERVATIONS

Cross-validation, as a popular tool for choosing a smoothing parameter, is generalized to the case of dependent observations. A general version of the ‘deletion theorem’ for representation and simplified calculation of cross-validatory criteria is given. Finally cross-validation is discussed in terms of penalized likelihoods as a method for model choice analogous to the Akaike information criterion.     

Optimum invariant tests for random manova models

Consider the canonical-form MANOVA setup with X: n × p = (+ E, X_i n_i × p, i = 1, 2, 3, M_i: n_i × p, i = 1, 2, n₁ + n₂ + n₃) p, where E is a normally distributed error matrix with mean zero and dispersion I_n (> 0 (positive definite). Assume (in contrast with the usual case) that M₁i is normal with mean zero and dispersion I_n1) and M₂2 is either fixed or random normal with mean zero and different dispersion matrix I_n2 (being unknown. It is also assumed that M₁ E, and M₂ (if random) are all independent. For testing H₀) = 0 versus H₁: (> 0, it is shown that when either n₂ = 0 or M₂ is fixed if n₂ > 0, the trace test of Pillai (1955) is uniformly most powerful invariant (UMPI) if min(n₁, p)= 1 and locally best invariant (LBI) if min(n₁ p) > 1 underthe action of the full linear group Gl (p). When p > 1, the LBI test is also derived under a somewhat smaller group G_T(p) of p × p lower triangular matrices with positive diagonal elements. However, such results do not hold if n₂ > 0 and M₂ is random. The null, nonnull, and optimality robustness of Pillai's trace test under Gl(p) for suitable deviations from normality is pointed out.     

Locally minimax tests for multiple correlations

Let X be a normally distributed p-dimensional column vector with mean μ and positive definite covariance matrix σ. and let X α, α = 1,…, N, be a random sample of size N from this distribution. Partition X as ( X ₁, X ₍₂₎', X '₍₃₎)', where X₁ is one-dimension, X₍₂₎ is p₂- dimensional, and so 1 + p₁ + p₂ = p. Let ρ₁ and ρ be the multiple correlation coefficients of X₁ with X₍₂₎ and with ( X '₍₂₎, X '₍₃₎)', respectively. Write ρ2/2 = ρ² - ρ2/1. We shall cosider the following two problems     

积分第一中值定理中间点集稳定性的注记

引入积分第一中值定理本质中间点的概念讨论中间点集的稳定性问题：证明了[a,b]上大多数连续函数（在Baire分类意义下）的中间值点集是稳定的;得到[a,b]上连续函数的中间点集是本质连通区的一个充分条件.     

Preference Aggregation With Incomplete Information

We show in an environment of incomplete information that monotonicity and the Pareto property applied only when there is common knowledge of Pareto dominance imply (i) there must exist a common prior over the smallest common knowledge event, and (ii) aggregation must be ex ante and ex post utilitarian with respect to that common prior and individual von Neumann–Morgenstern utility indices.     

论马克思创立的实践人类学哲学

马克思实现了哲学视域的转换1.从“一切存在”转换到“人的社会存在”;2.从“人的类本质”转换到人类的生产交往共同体;3.确认“人类活动”是实践人类学哲学的思考框架;4.明确了哲学的目标理念人类的个体自由、生存合理性与发展规律性;5.强调了哲学的理论旨归从实践上改变“非人世界”,走向“自由人的联合体”;6.创立了哲学的实践批判原则以实践作为观察世界和社会历史批判的本源;7.确立了实践人类学哲学的边际关系与中心法则等。这几方面共同形成了马克思“改变世界”的实践人类学哲学,这是马克思一生理论关怀的总体特质。     

关于勾股定理的起源

本文对勾股定理的起源作了初步的探讨，纠正了一些错误说法，并给出了一些新的见解。     

Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division

In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal.