一个求总极值的实现算法及其收敛性

1978年,郑权等首先提出了一种用积分─水平集求总极值的方法及用Monte－Carlo随机投点实现的实现其法,其实现算法是否收敛未解决的问题．本文提出一种用数论方法实现的实现算法,并证明了该实现其法是收敛的．初步的数值结果表明,该实现其法是较有效的．     

Implementable and ex-post IR rules in bilateral trading with discrete values

We study bargaining problems between one buyer and one seller for a single object when each set of valuations is finite. We derive a necessary and sufficient condition for interim-implementable trading rules, analogous to the result in Myerson and Satterthwaite (1983), and a necessary condition for mechanisms that are free from ex post regret on and off equilibrium path. Based on these two theorems, our contribution is three-fold. First, we illustrate the results by means of three examples. Second, in contrast to the continuous model, there always exist strictly positive probability mass functions such that ex post efficiency and interim-implementability is feasible. Third, we show the difference between interim- and ex post-implementation. In the class of threshold trading rules, interim-implementation only precludes inefficient trade, while ex post-implementation is equivalent to posted price implementation.     

修正积分水平集算法的一个实现算法及其收敛性证明

郑权等（1978）在“一个求总极值的方法”一文中给出了一个积分水平集求总极值的概念性算法及Monte-Carlo随机投点的实现算法,其收敛性一直未得以解决,本文在张连生,邬冬华等提出的修正算法的基础上,利用数论中一致分布佳点集列,给出了一个实现算法及全局收敛性的证明,为了提高算法的计算效率,文中对算法进行了并行化处理。     

Leading Learning: Science Departments and the Chair

In this article, we have considered the role of the chair in leading the learning necessary for a department to become effective in the teaching and learning of science from a reformed perspective. We conceptualize the phrase “leading learning” to mean the chair's constitution of influence, power, and authority to intentionally impact the conceptual, pedagogical, cultural, and political aspects of teachers’ work. The data for this article are based on our ongoing work with one science department, over the past nine years, and have been woven into a longitudinal narrative study of a chair who has led the learning of an effective department since 2000. In considering the data, we can reach two major conclusions. First, for a chair to lead learning is to build a professional commitment to a vision of science education, not a particular program. Second, in leading learning, chairs afford opportunities for teacher empowerment. This affordance, however, is only half the issue. It is commitment to a vision that drives a desire to take advantage of opportunities as they arise. In leading learning that reflects changes in the broader science education community, learning opportunities are opened beyond the department.     

Fluid thermodynamics: Qualitative consideration

We consider the thermodynamics of fluids (i.e., of a gas-liquid region where gas is indistinguishable from liquid). Using the methods of distribution theory for Diophantine equations, we find an explanation of certain old experiments. We disprove some old postulates and hypotheses, including the mathematical axiom that distributions of independent events are mutually multiplied. In the weakly nonideal case, we propose that the complex germ method should be used to avoid using the previously disproved Kac hypothesis on the conservation of chaos.     

Investigating equality: The poverty and riches indices

As noise is omnipresent, real-world quantities measured by scientists and engineers are commonly obtained in the form of statistical distributions. In turn, perhaps the most compact representation of a given statistical distribution is via the mean-variance approach: the mean manifesting the distribution’s ‘typical’ value, and the variance manifesting the magnitude of the distribution’s fluctuations about its mean. The mean-variance approach is based on an underlying Euclidean-geometry perspective. So very often real-world quantities of interest are non-negative sizes, and their measurements yield statistical size distributions. In this paper, and in the context of size distributions, we present an alternative to the Euclidean-based mean-variance approach: a mean-equality approach that is based on an underlying socioeconomic perspective. We establish two equality indices that score, on a unit-interval scale, the intrinsic ‘egalitarianism’ of size distributions: (i) the poverty equality index which is particularly sensitive to the existence of very small “poor” sizes; (ii) the riches equality index which is particularly sensitive to the existence of very large “rich” sizes. These equality indices, their properties, their computation, their application, and their connections to the mean-variance approach – are explored and described comprehensively.     

On Linking Approaches to Decision-Aiding: Issues and Prospects

This paper arises from some current attempts to being together several approaches designed to help decision-makers faced with complex, ‘messy’ problems. These include, inter alia, the strategic choice methodology, hypergame analysis and other game-based approaches, and methods making use of cognitive mapping.Some general issues pertinent to ‘linkage’ are discussed: differences in theoretical background between the approaches are noted, and some implications of these explored. With these in mind, a number of possible forms of linkage are suggested. Within this general framework, the paper discusses some specific pieces of work already done, and considers the prospects for further progress. Though it concentrates on work involving certain specific approaches, the issues raised are relevant to the linkage and/or classification of other decision-aiding methods.     

定性关系及其应用

在已有的定性演算的基础上,引入了定性值集上的定性关系,讨论了定性关系的基本性质,并定义了定性关系的并、交、差及复合运算.在文后给出了定性综合评判的3个基本要素,着重给出了主因素决定型定性综合评判的步骤,并将其应用到具体的实例中.     

Continuous and Discrete Age-Replacement Policies

This paper considers the combined continuous and discrete age-replacement policies when units deteriorate with age and use: a unit is replaced preventively before failure at time T of age or at number N of uses, whichever occurs first. The expected cost rate C (T,N) is derived, and both optimum time T* and number N* to minimize C (T,N) are discussed. There exist finite and unique T* and N* when the use occurs in a Poisson process under suitable conditions.     

Personal Excursions: Investigating the Dynamics of Student Engagement

We investigate the dynamics of student engagement as it is manifest in self-directed, self-motivated, relatively long-term, computer-based scientific image processing activities. The raw data for the study are video records of 19 students, grades 7 to 11, who participated in intensive 6-week, extension summer courses. From this raw data we select episodes in which students appear to be highly engaged with the subject matter. We then attend to the fine-grained texture of students’ actions, identifying a core set of phenomena that cut across engagement episodes. Analyzed as a whole, these phenomena suggest that when working in self-directed, self-motivated mode, students pursue proposed activities but sporadically and spontaneously venture into self-initiated activities. Students’ recurring self-initiated activities – which we call personal excursions – are detours from proposed activities, but which align to a greater or lesser extent with the goals of such activities. Because of the deeply personal nature of excursions, they often result in students collecting resources that feed back into both subsequent excursions and framed activities. Having developed an understanding of students’ patterns of self-directed, self-motivated engagement, we then identify four factors that seem to bear most strongly on such patterns: (1) students’ competence (broadly construed); (2) features of the software-based activities, and how such features allowed students to express their competence; (3) the time allotted for students to pursue proposed activities, as well as self-initiated ones; and (4) the flexibility of the computational environment within which the activities were implemented.     

Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity

In this paper, we prove various qualitative properties of pulsating traveling fronts in periodic media, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov type or general monostable nonlinearities. Besides monotonicity, the main part of the paper is devoted to the exponential behavior of the fronts when they approach their unstable limiting state. In the general monostable case, the logarithmic equivalent of the fronts is shown and for noncritical speeds, the decay rate is the same as in the KPP case. These results also generalize the known results in the homogeneous case or in the case when the equation is invariant by translation along the direction of propagation.     

Morrey Spaces on Domains: Different Approaches and Growth Envelopes

We deal with Morrey spaces on bounded domains \(\Omega \) obtained by different approaches. In particular, we consider three settings \(\mathcal {M}_{u,p}(\Omega )\), \(\mathbb {M}_{u,p}(\Omega )\) and \(\mathfrak {M}_{u,p}(\Omega )\), where \(0<p\le u<\infty \), commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes \(\mathfrak {E}_{\mathsf {G}}(\mathcal {M}_{u,p}(\Omega ))\) as well as \(\mathfrak {E}_{\mathsf {G}}(\mathfrak {M}_{u,p}(\Omega ))\), and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether \(\frac{n}{u}\ge \frac{1}{p}\) or \(\frac{n}{u} < \frac{1}{p}\) plays a decisive role when it comes to the behaviour of these spaces.     

Kronecker's and Newton's Approaches to Solving: A First Comparison

These pages are a first attempt to compare the efficiency of symbolic and numerical analysis procedures that solve systems of multivariate polynomial equations. In particular, we compare Kronecker's solution (from the symbolic approach) with approximate zero theory (introduced by S. Smale as a foundation of numerical analysis). For this purpose we show upper and lower bounds of the bit length of approximate zeros. We also introduce efficient procedures that transform local Kronecker solutions into approximate zeros and conversely. As an application of our study we exhibit an efficient procedure to compute splitting field and Lagrange resolvent of univariate polynomial equations. We remark that this procedure is obtained by a convenient combination of both approaches (numeric and symbolic) to multivariate polynomial solving.