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1.
快速遴选优胜者   总被引:1,自引:1,他引:0  
本文给出了一个行之有效的方案来确定某次竞赛的优胜者.首先,假定裁判是理想的(无误差的),我们提出了一个基本模型在几乎最短的时间内确定出前W名.在我们的方案中,用一个矩阵来记录从当前已知的裁判评分中所得到的“当前名次”,并且在一轮之后尽可能多地淘汰试卷.然后,我们考虑现实中的裁判(有误差的),估计了最后选出的W名中包含有非前2W名试卷的概率.进一步,考虑到打分方案中的系统偏差,我们用贝叶斯估计对模型做了改进,使不同裁判的评分有了一定的可比性.为检验模型的可行性,我们做了大量的计算机模拟,模型检验中我们发现,如果适当增加从第一轮中选拔出来的试卷数,将使我们的模型结果更好.我们还通过改变参数P,J,W对模型作了稳定性分析,并且得到了一个经验公式,可以用来预测在一定P,J,W值下评卷的总时间.接下来,我们采用了现实生活中的数据来检验模型,结果相当好当P=50,J=3时,若取W=2,用我们的方案得到了第一名和第三名若取W=3,得出的正是前三名.最后,我们总结出了一个灵活实用的方案,并提出了一些建议在模型推广中,我们还利用经验公式对开支做了预算.  相似文献   

2.
廖长高  李贤平  徐萍 《应用数学》2003,16(2):118-123
这篇文章中,我们建立了资产组合在受到约束时的期望效用优化问题,在我们特殊的指数效用函数下,我们发现最终的决策不依赖于具体的贴现函数,在文章的结尾部分,我们给出了几类常见约束下的最优消费和资产组合决策。  相似文献   

3.
在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理.利用这一定理,我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则.作为应用,我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理.也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果.我们的定理改进和推广了Szep,Mitchell-Smith,Cramer-Lakshmikantham,Lakshmikantham—Leela和丁的相应结果.  相似文献   

4.
在函数问题中,某些自变量或其函数值的特殊性在解题中有其独到之处,它不仅帮助我们解决了问题,且提高了我们的观察能力和分析能力.下面分二个方面举例加以阐述.  相似文献   

5.
王志华  张凤祥 《数学研究》1998,31(2):169-175
我们在无限维空间中研究微分包含的生存W—单调轨道的存在性.基于Zorn引理,我们给出了一个逼近方法,在较弱的条件下得到了一个存在性定理,其特殊情形则包含了已有的生存定理和微分方程理论中的若干结果作为应用,我们首先研究了微分包含生存解的整体存在性,得到了整体生存理.然后我们研究了微分包含解的稳定性,得到一些新的结果.  相似文献   

6.
为了改进我院的工程数学教学,我们讨论了工科工程数学教学中存在的问题,论述了工科工程数学教学改革的必要性和迫切性,并就工科工程数学教学改革问题提出了我们的看法。  相似文献   

7.
本文中,我们首先根据经典的Ricci曲率与Betti数的S.Bochner定理得到了ε-极小Riemann浸入子流形的数量曲率与Betti数的结果。然后,我们考虑了紧致连通Riemann流形中曲率与Betti数之间的关系,推广 了经典的S.Bochner定理。  相似文献   

8.
在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理。利用这一定理,我们对Banach空间中关于弱拓拟的非线性随机Volterra积分方程组给出了随机解的存在性准则,作为应用,我们得到了非线性随机微分方程的Cauchy问题弱随机解的存在定理,也得到了这些随机方程在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果。  相似文献   

9.
彭翕成 《数学通讯》2007,(11):12-13
前面我们介绍了超级画板中赋值语句,条件语句,循环语句和输出语句的基本用法,也列举了一些简单实例.本节我们将给出更多与中学数学教学相关的实例.  相似文献   

10.
马尔可夫骨架过程的有穷维分布(英文)   总被引:2,自引:0,他引:2  
在文献[1]和[2]中,我们引入了马尔可夫骨架随机过程的概念,并得到了向后方程和向前方程.同时还计算了这类过程的一维分布以及讨论了其它有关性质.在本文中,我们进一步给出马尔可夫骨架随机过程的有穷维分布的计算公式.  相似文献   

11.
In this article we study global in time (not necessarily small) solutions of the equation for the Higgs boson in the Minkowski and in the de Sitter spacetimes. We reveal some qualitative behavior of the global solutions. In particular, we formulate sufficient conditions for the existence of the zeros of global solutions in the interior of their supports, and, consequently, for the creation of the so-called bubbles, which have been studied in particle physics and inflationary cosmology. We also give some sufficient conditions for the global solution to be oscillatory in time.  相似文献   

12.
Given an undirected graph with edge weights, we are asked to find an orientation, that is, an assignment of a direction to each edge, so as to minimize the weighted maximum outdegree in the resulted directed graph. The problem is called MMO, and is a restricted variant of the well-known minimum makespan problem. As in previous studies, it is shown that MMO is in P for trees, weak NP-hard for planar bipartite graphs, and strong NP-hard for general graphs. There are still gaps between those graph classes. The objective of this paper is to show tighter thresholds of complexity: We show that MMO is (i) in P for cactus graphs, (ii) weakly NP-hard for outerplanar graphs, and also (iii) strongly NP-hard for graphs which are both planar and bipartite. This implies the NP-hardness for P4-bipartite, diamond-free or house-free graphs, each of which is a superclass of cactus. We also show (iv) the NP-hardness for series-parallel graphs and multi-outerplanar graphs, and (v) present a pseudo-polynomial time algorithm for graphs with bounded treewidth.  相似文献   

13.
The ratio of the largest eigenvalue divided by the trace of a p×p random Wishart matrix with n degrees of freedom and an identity covariance matrix plays an important role in various hypothesis testing problems, both in statistics and in signal processing. In this paper we derive an approximate explicit expression for the distribution of this ratio, by considering the joint limit as both p,n with p/nc. Our analysis reveals that even though asymptotically in this limit the ratio follows a Tracy-Widom (TW) distribution, one of the leading error terms depends on the second derivative of the TW distribution, and is non-negligible for practical values of p, in particular for determining tail probabilities. We thus propose to explicitly include this term in the approximate distribution for the ratio. We illustrate empirically using simulations that adding this term to the TW distribution yields a quite accurate expression to the empirical distribution of the ratio, even for small values of p,n.  相似文献   

14.
15.
A nation with its natural resources, human capabilities, research and educational institutions, government organizations, financial systems, and cultural and social values provides an environment in which firms are created, organized, and managed. The competitive environment a nation provides influences the performance of its firms at home and abroad. Therefore, it is of prime importance for both governments and firms to study the competitive environment of a country in comparison with those of the others. The World Competitiveness Report (WCR), a report annually produced by the Institute for Management Development (IMD) and the World Economic Forum (WEF), both based in Switzerland, is a study that rates and ranks the competitiveness of a certain group of countries (OECD plus 15 newly industrialized countries) and is a widely quoted study in the international media. Although some essence of its methodology is given for a general understanding, details are not provided, perhaps for proprietary reasons since the report is a commercial enterprise itself. The objective of this paper is to uncover the methodology used by the WCR. For this purpose, the methodological information provided in the WCR is used to the fullest extent. However, for the steps where the information is missing or when different interpretations are possible, an approach based on mathematical programming is employed to ‘guess’ the methodology.  相似文献   

16.
《偏微分方程通讯》2013,38(3-4):745-769
Abstract

We obtain an explicit representation formula for the sub-Laplacian on the isotropic, three-dimensional Heisenberg group. Using the formula we obtain themeromorphic continuation of the resolvent to the logarithmic plane, the existence of boundary values in the continuous spectrum, and semiclassical asymptotics of the resolvent kernel. The asymptotic formulas show the contribution of each Hamiltonian path in Carnot geometry to the spatial and high-energy asymptotics of the resolvent (convolution) kernel for the sub-Laplacian.  相似文献   

17.
The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F D (N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.  相似文献   

18.
We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture that the sine kernel also occurs in connection with the higher (even) shifted moments and show that this conjecture is closely related to a recent conjecture by Conrey, Farmer, Keating, Rubinstein, and Snaith (2003, 2005) [CFKRS1] and [CFKRS2].  相似文献   

19.
This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.  相似文献   

20.
On the validity of the Ginzburg-Landau equation   总被引:1,自引:0,他引:1  
Summary The famous Ginzburg-Landau equation describes nonlinear amplitude modulations of a wave perturbation of a basic pattern when a control parameterR lies in the unstable regionO(ε 2) away from the critical valueR c for which the system loses stability. Hereε>0 is a small parameter. G-L's equation is found for a general class of nonlinear evolution problems including several classical problems from hydrodynamics and other fields of physics and chemistry. Up to now, the rigorous derivation of G-L's equation for general situations is not yet completed. This was only demonstrated for special types of solutions (steady, time periodic) or for special problems (the Swift-Hohenberg equation). Here a mathematically rigorous proof of the validity of G-L's equation is given for a general situation of one space variable and a quadratic nonlinearity. Validity is meant in the following sense. For each given initial condition in a suitable Banach space there exists a unique bounded solution of the initial value problem for G-L's equation on a finite interval of theO(1/ε2)-long time scale intrinsic to the modulation. For such a finite time interval of the intrinsic modulation time scale on which the initial value problem for G-L's equation has a bounded solution, the initial value problem for the original evolution equation with corresponding initial conditions, has a unique solutionO2) — close to the approximation induced by the solution of G-L's equation. This property guarantees that, for rather general initial conditions on the intrinsic modulation time scale, the behavior of solutions of G-L's equation is really inherited from solutions of the original problem, and the other way around: to a solution of G-L's equation corresponds a nearby exact solution with a relatively small error.  相似文献   

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