Integral Operators Between Fock Spaces∗

In this paper, the authors study the integral operator Sφf(z) = Z C φ(z, w)f(w)dλα(w) induced by a kernel function φ(z, ·) ∈ F ∞α between Fock spaces. For 1 ≤ p ≤ ∞, they prove that Sφ : F 1 α → F p α is bounded if and only if sup a∈C kSφkakp,α < ∞, (?) where ka is the normalized reproducing kernel of F 2 α; and, Sφ : F 1 α → F p α is compact if and only if lim |a|→∞ kSφkakp,α = 0. When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness of Sφ : F q α → F p α . In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F 2 α, for 1 ≤ q < p < ∞, they show that Sφ : F p α → F q α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give sufficient conditions for the boundedness or compactness of the operator Sφ : F p α → F q α.     

基于新型核与灰度序列的时滞GM(1,N)模型及其应用

为了解决GM(1,N)模型在新型核与灰度的基础上,对驱动项的延迟作用机理不明确的问题,将时滞参数引入到GM(1,N)模型的驱动项中,构建了基于新型核与灰度的时滞GM(1,N)模型,分析了时滞参数的辨识方法,讨论了新模型的建模机理。为了更好地对该模型的有效性进行验证,将优化的时滞GM(1,N)模型对南京市的雾霾进行预测分析,选择GM(1,N)模型、一元回归模型与文中的优化模型进行对比。结果显示,优化模型对PM₁₀浓度的拟合精度更高,且误差均控制在5%之内,从而验证了提出的优化模型适用于具有时滞特征数据的模拟和预测。     

Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Retrieval and chaos in extremely dilutedQ-Ising neural networks

Using a probabilistic approach, the deterministic and the stochastic parallel dynamics of aQ-Ising neural network are studied at finiteQ and in the limitQ. Exact evolution equations are presented for the first time-step. These formulas constitute recursion relations for the parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis of the retrieval properties is carried out in terms of the gain parameter, the loading capacity, and the temperature. The results for theQ network are compared with those for theQ=3 andQ=4 models. Possible chaotic microscopic behavior is studied using the time evolution of the distance between two network configurations. For arbitrary finiteQ the retrieval regime is always chaotic. In the limitQ the network exhibits a dynamical transition toward chaos.     

On the extreme spectral properties of Toeplitz matrices generated byL 1 functions with several minima/maxima

In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue ₁ ⁽ⁿ⁾ of symmetric (Hermitian)n ×n Toeplitz matricesT _n (f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that ₁ ⁽ⁿ⁾ tends to essinff =m _f in the following way: ₁ ⁽ⁿ⁾ –m _f 1/n ^2k . These authors use three assumptions:A1)f –m _f has a zero inx =x ₀ of order 2k.A2)f is continuous and at leastC ^2k in a neighborhood ofx ₀.A3)x =x ₀ is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L ¹[–, ]. In this paper we further extend this theory to the case of a functionf L ¹[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m _f is the only parameter which characterizes the rate of convergence of ₁ ⁽ⁿ⁾ tom _f .     

Mass shifting roles of negative kernel mass in density estimation

f(x) is a univariate density in C ⁴ with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, –U, to any smooth unimodal symmetric kernel of order p=2 shifts expected estimator mass from regions where f(x)>0 to regions where f(x)<0. For large n, the mean automatic kernel adaptation induced by –U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of –U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f(x)|.     

Learning to align organizational design and data

The relationship between organizational learning and organizational design is explored. In particular, we examine the information processing aspects of organizational learning as they apply to a two-valued decision making task and the relation of such aspects to organizational structure. Our primary contribution is to extend Carley's (1992) model of this process. The original model assumes that all data input into the decision making processes are of equal importance or weight in determining the correct overall organizational decision. The extension described here allows for the more natural situation of non-uniform weights of evidence. Further extensions to the model are also discussed. Such organizational learning performance measures provide an interesting framework for analyzing the recent trend towards flatter organizational structures. This research suggests that flatter structures are not always better, but rather that data environment, ultimate performance goals, and relative need for speed in learning can be used to form a contingency model for choosing organizational structure.     

构建网络学习资源提高民族高校有机化学课程教学质量

High-quality online course materials were reconstructed through feedback from undergraduate students and online data analysis regarding constructed learning materials on the Chao Xing Learning Platform. They were used for studying organic chemistry courses online and offline in university for nationalities. This model, based on student-centered teaching, can effectively transform students from passively accepting knowledge to actively learning and internalizing knowledge. This strategy can also enhance the students' learning initiative and the effects of learning, and hopefully be helpful to the universities in multi-ethnic areas in developing fundamental disciplined construction of organic chemistry and other courses.