The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs

The most popular weight restrictions are assurance regions (ARs), which impose ratios between weights to be within certain ranges. ARs can be categorized into two types: ARs type I (ARI) and ARs type II (ARII). ARI specify bounds on ratios between input weights or between output weights, whilst ARII specify bounds on ratios that link input to output weights. DEA models with ARI successfully maximize relative efficiency, but in the presence of ARII the DEA models may under-estimate relative efficiency or may become infeasible. In this paper we discuss the problems that can occur in the presence of ARII and propose a new nonlinear model that overcomes the limitations discussed. Also, the dual model is described, which enables the assessment of relative efficiency when trade-offs between inputs and outputs are specified. The application of the model developed is illustrated in the efficiency assessment of Portuguese secondary schools.     

Multicriteria sorting using a valued preference closeness relation

To define a metric or a similarity relation with good properties is a crucial issue in most analogy and rule induction oriented methods for multicriteria sorting. Here, we propose a valued indifference (closeness) relation which is inspired on concordance and discordance measures. The criterion “weights” are obtained from the preferential information embedded in a reference set. This proposal performs very well in several practical problems.     

全寄宿学校学生微量元素营养状况分析

测定了两所全寄宿学校一、二年级学生头发微量元素锌、铜、锰、铅和宏量元素钙的含量，并研究了上述元素与学生身高、体重及学习成绩的相关关系。结果表明：招生条件相似的两所寄宿学校的锌水平存在着显著性差异，两所学校一年级学生平均发锌含量分别为（115．3±27．3）×10-6和（83.5±31.9）×10-6，二年级学生平均发锌含量分别为（12．1±25．3）×10-6和（97．6±31．8）×10-6，锌水平较高的学校学生的身高、体重亦显著高于低锌学校学生，由此可见全寄宿学校膳食结构的不同对学生身体微量元素水平及身体的发育有着极大影响。     

Extension of Hilbert's inequality

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.     

Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials. We also obtain some non-trivial results about these Sobolev spaces with respect to measures; in particular, we prove a main result in the theory: they are Banach spaces. J.M. Rodriguez supported in part by three grants from M.E.C. (MTM 2006-13000-C03-02, MTM 2006-11976 and MTM 2007-30904-E), Spain, and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain. J.M. Sigarreta supported in part by a grant from M.E.C. (MTM 2006-13000-C03-02), Spain, and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain.     

Weighted Vector Valued Inequalities for Generalized Singular Integral Operators on Spaces of Homogeneous Type

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A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3

In this paper, by estimating the weight function, we give a new Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3 with the best constant factor and the reverse form is considered.     

关于Hardy-Hilbert积分不等式的推广

本文通过引入适当的参数，及如下形式的权系数（ｘ＋β）１－ｔｋｔ（ｒ）－ｌｎ２α＋βｘ＋β１－１／ｒ，ｘ∈［α，∞）（α－β，ｒ＞１，１－１／ｒ＜ｔ１）．而使Ｈａｒｄｙ－Ｈｉｌｂｅｒｔ积分不等式得到有意义的推广．这里ｋｔ（ｒ）＝∫∞０１（１＋ｕ）ｔ１ｕ１／ｒｄｕ，常数ｌｎ２＝０．６９３１４７１８＋．     

Quantum M-P Neural Network

Quantum Neural Network (QNN) is a young and outlying science built upon the combination of classical neural network and quantum computing. Making use of quantum linear superposition, this paper presents a quantum M-P neural network based on the analysis of the conventional M-P neural network. Moreover, the working principle of this proposed network and its corresponding weight updating algorithm are expatiated in the two cases of input state being in the orthogonal and non-orthogonal basic set, respectively. In addition, this paper not only validates that this quantum M-P network can realize some network functions, such as “XOR”, but also verifies the feasibility and validity of its weight learning algorithm by some simple examples.     

三维七元线性码的重量谱与改进的遗传算法

[n,3,7]线性码的重量谱与其差序列是一一对应的。本文改进了[1]结构4的条件（iv),从而得到了不满足链条件的[n,3;7]线性码的差序列的充要条件,并应用改进的遗传算法搜索满足链条件的[n,3;7]线性码的差序列,取得了较好的结果。