正态分布在学生学习成绩评估中的应用

本文将正态分布应用于学生学习成绩评估中，将原始分数转换为标准分数后，各科的分数方可比较或相加，从而改变了将原始分数直接相加比较的那种不够科学也不甚合理的传统做法。     

Some Geometrical Aspects of Efficient Points in Vector Optimization

We study efficient point sets in terms of extreme points, positive support points and strongly positive exposed points. In the case when the ordering cone has a bounded base, we prove that the efficient point set of a weakly compact convex set is contained in the closed convex hull of its strongly positive exposed points, thereby extending the Phelps theorem. We study also the density of positive proper efficient point sets. This research was supported by a Central Research Grant of Hong Kong Polytechnic University, Grant G-T 507. Research of the first author was also supported by the National Natural Science Foundation of P.R. China, Grant 10361008, and the Natural Science Foundation of Yunnan Province, China, Grant 2003A002M. Research of the second author was also supported by the Natural Science Foundation of Chongqing. Research of the third author was supported by a research grant from Australian Research Counsil.     

On the compactly locally uniformly rotund points of Orlicz spaces

In this paper, locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.     

The fractal structures of the exceptional sets of Lévy processes

In this paper we review some results on the fractal geometry properties of the sets of thick points, thin points, fast points and slow points derived from Lévy processes. This work was supported by National Natural Science Foundation of China (Grant No. 10871200)     

多目标规划的ak—较多有效点与ak—较多最优点

在[1]中,作引入了多目标规划的较多有效点及较多最优点的概念,并讨论了它们的性质,本首次提出了ak-较多有效点与ak-较多最优点的概念,并讨论了ak-较多有效点,ak-较多最优点、ak-较多有效解,ak-较多最优解的相关性质。     

严有效点与Henig真有效点

文章证明了严有效点等价于Henig真有效点．利用这个等价关系，得到了局部凸空间中Henig真有效点的存在性条件。纯量化特征和稠密性定理．并且改进了已知的有关结果．     

On the Existence of Focal Points near Closed Geodesics on Surfaces

We establish some criteria for the existence or nonexistence of focal points near closed geodesics on surfaces. These criteria are in terms of the curvature of the manifold along the closed geodesic and the average values of the partial derivatives of the curvature in the direction perpendicular to the geodesic. Our criteria lead to a new family of examples of surfaces with no focal points. We also show that if S is a compact surface with no focal points and an inequality relating the curvature of the surface to the curvature of the horocycles holds, then the horocycles (considered as curves in S) are uniformly C ^2+Lipschitz.     

拓扑空间中集网收敛性的非标准刻画

在非标准扩大模型下,给出了拓扑空间中集网收敛性的非标准刻画.首先,由非标准扩大模型的充要条件,证明了拓扑空间中集网的极限点和聚点的非标准刻画;然后,利用这些非标准特征,刻画了拓扑空间中集列、网和点列的极限点和聚点;最后,以自然的方式讨论了拓扑空间中集网上极限和下极限的一些重要性质.     

On generalized equilibrium points

Generalizations of the usual definition of saddle point and equilibrium point are introduced in this paper. The existence of these points is shown to be related to a class of functions that we call perturbed convex functions. First and second order conditions regarding the existence of these points are also proved.     

Density of the set of positive proper minimal points in the set of minimal points

One of the important problems of vector optimization concerns the density of the set of positive proper minimal points in the set of minimal points. We use the concepts of dentable point and approximating cones to derive sufficient conditions guaranteeing that the set of minimal points is contained in the closure of the set of positive proper minimal points. The result can be applied to obtain a density result for the unit ball in 1 ^p , 1<p<+, which does not follow from any other well-known density theorem.The author would like to thank Professor W. T. Fu for helpful comments. Moreover, the author is grateful to Professor H. P. Benson and the referees for valuable remarks and suggestions concerning a previous draft of this paper.     

Comparison of Existence Results for Efficient Points

Existence results of maximal points with respect to general binary relations were stated by Hazen and Morin (Ref. 1) and by Gajek and Zagrodny (Ref. 2). In this paper, we point out that the natural framework for this problem is that of transitive and reflexive relations (preorders). The aim of this paper is to discuss existence results for maximal points with respect to general transitive relations in such a way that, when considering them for preorders defined by convex cones, we are able to recover most known existence results for efficient points; the quasi-totality of them, with their (short) proofs, is presented, too.     

Gap sequences of 1-Weierstrass points on non-hyperelliptic curves of genus 10

In this paper, we compute the 1-gap sequences of 1-Weierstrass points of non-hyperelliptic smooth projective curves of genus 10. Furthermore, the geometry of such points is classified as flexes, sextactic and tentactic points. Also, upper bounds for their numbers are estimated.     

A Simple Multistart Algorithm for Global Optimization

1.IntroductionConsidertheunconstrainedoptimizationproblem:findx*suchthatf(x*)~caf(x),(1)wheref(x)isanonlinearfllnctiondefinedonW"andXCR".Ourobjectiveistofindtheglobalminimizeroff(x)inthefeasibleset.Withoutassuminganyconditionsonf(x)globaloptimizationproblemsareunsolvableinthefollowingsensefnoalgorithmcanbeguaranteedtofindaglobalminimizerofageneralnonlinearfunctionwithinfinitelymanyiterations.Supposethatanalgorithmappliedtoanonlinearfunctionf(x)producesiteratesxlandterminatesafterKiterations.…     

Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces

For vector-valued functions, cone saddle points are defined, and some existence theorems for them are established in infinite-dimensional spaces. Most of our results rely on Condition 2.1, which has been given by Sterna-Karwat. In particular, it shows that the scalarization of vector-valued functions plays an important role for the condition. Some interesting examples in infinite-dimensional spaces are presented. Moreover, necessary conditions for the existence of cone saddle points are investigated.The author would like to thank the referees for their valuable suggestions on the original draft.     

Weierstrass points on cyclic covers of the projective line

We are interested in cyclic covers of the projective line which are totally ramified at all of their branch points. We begin with curves given by an equation of the form , where is a polynomial of degree . Under a mild hypothesis, it is easy to see that all of the branch points must be Weierstrass points. Our main problem is to find the total Weierstrass weight of these points, . We obtain a lower bound for , which we show is exact if and are relatively prime. As a fraction of the total Weierstrass weight of all points on the curve, we get the following particularly nice asymptotic formula (as well as an interesting exact formula):

where is the genus of the curve. In the case that (cyclic trigonal curves), we are able to show in most cases that for sufficiently large primes , the branch points and the non-branch Weierstrass points remain distinct modulo .

     

随机Dirichlet级数的奇异点和Picard点

本文研究系数为鞅差序列的随机Ｄｉｒｉｃｈｌｅｔ级数的奇异点和Ｐｉｃａｒｄ点。     

有效点、弱有效点和真有效点的锥刻画

利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画.     

Saddle Points and Pareto Points in Multiple Objective Programming

In this paper relationships between Pareto points and saddle points are studied in convex and nonconvex multiple objective programming. The analysis is based on partitioning the index sets of objectives and constraints and splitting the original problem into subproblems having a special structure. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. In the nonconvex case, a saddle point characterization of Pareto points is possible under assumptions that guarantee existence of Pareto points and stability conditions of single objective problems. Essentially, these conditions are not stronger than those in analogous results for single objective programming.This research was partially supported by ONR Grant N00014-97-1-784AMS Subject Classification: 90C29, 90C26     

Global Optimization: Local Minima and Transition Points

We consider the minimization of smooth functions of the Euclidean space with a finite number of stationary points having moderate asymptotic behavior at infinity. The crucial role of transition points of first order (i.e., saddle points of index 1) is emphasized. It is shown that (generically) any two local minima can be connected via an alternating sequence of local minima and transition points of first order. In particular, the graph with local minima as its nodes and first order transition points representing the edges turns out to be connected (Theorem A). On the other hand, any connected (finite) graph can be realized in the above sense by means of a smooth function of three variables having a minimal number of stationary points (Theorem B).     

Global optimality of extremals: An example

The question of the existence and the location of Darboux points (beyond which global optimality is lost) is crucial for minimal sufficient conditions for global optimality and for computation of optimal trajectories. Here, we investigate numerically the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, horizontal aircraft turns to capture a line. This simple second-order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories.The authors are indebted to G. Moyer for his constructive comments. This research was supported, for the first author, by a National Research Council Associateship at NASA Ames Research Center.on leave from the Technion, Israel Institute of Technology, Haifa, Israel.