矩阵的秧下界与方阵的非异性

<正> 在[2]、[3]、[4]中,已给出一串矩阵秩的下界估计式,并相应地讨论了几类所谓“迹占优”的方阵的非异性。但在理论上以及某些应用问题上,还需判断下列两类方阵的非异性:一是当方阵的主对角元出现负元,然其绝对值较大时;二是方阵之迹并不“占优”.但每一行的不同列上各有一个元素,使这些元素之绝对值的和“占优”。本文将首先讨论两个     

On some generalization of the area theorem with applications to the problem of rolling balls

This publication contributes to the series of RCD translations of Sergey Alexeevich Chaplygin’s scientific heritage. Earlier we published three of his papers on non-holonomic dynamics (vol. 7, no. 2; vol. 13, no. 4) and two papers on hydrodynamics (vol. 12, nos. 1, 2). The present paper deals with mechanical systems that consist of several spheres and discusses generalized conditions for the existence of integrals of motion (linear in velocities) in such systems.     

Editorial: Hierarchical and bilevel programming

Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical developments and terms of the diversity of the applications. The collection of seven papers in this issue covers a diverse number of topics and provides a good picture of recent research activities in the field of bilevel and hierarchical programming. The papers can be roughly divided into three categories; Linear bilevel programming is addressed in the first two papers by Gendreau et al and Moshirvaziri et al; The following three papers by Nicholls, Loridan & Morgan, and Kalashnikov & Kalashnikova are concerned with nonlinear bilevel programming; and, finally, Wen & Lin and Nagase & Aiyoshi address hierarchical decision making issues relating to both biobjective and bilevel programming.     

Exploring the dynamics of journal citations: Modelling with s-curves

This paper reports on an exploratory analysis of the behaviour of citations for management science papers over a 14-year period. Citations often display s-curve type behaviour: beginning slowly, rising in response to previous citations, and then declining as the material becomes obsolete. Within the context of citation research such functions are known as obsolescence functions. The paper addresses three specific questions: (i) can collections of papers from the same journal all be modelled using the same obsolescence function? (ii) Can we identify specific patterns of behaviour such as ‘sleeping beauties’ or ‘shooting stars’? (iii) Can we predict the number of future citations from the pattern of behaviour in the first few years? Over 600 papers published in six leading management science journals are analysed using a variety of s-curves.     

Re-sourcing curriculum materials: in search of appropriate frameworks for researching the enacted mathematics curriculum

This article provides a commentary to the eight papers of this issue of ZDM entitled “Researching the enacted mathematics curriculum.” It is structured around three main questions concerning (1) the layers of the curriculum addressed in the eight papers; (2) an identification of the main theoretical framework used, and an appreciation of this as compared to another European framework; and (3) challenges for future research on the enacted mathematics curriculum. The author outlines her views derived from a particular European perspective.     

An inverse spectral problem for rational matrix functions and minimal divisibility

The present paper serves as an introduction to the papers [BR 2], [BGR] and [GKLR]. For rational matrix functions a concise account is given of the recent results about inverse spectral problems and minimal divisibility appearing in these three papers.     

Scheduling of corrugated paper production

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.     

On Solving the Transportation Problem

The Hitchcock transportation problem is perhaps one of the ‘most solved’ linear programming problems in existence. We shall propose yet another computation for the problem....¹The current computational status of the transportation problem is reviewed, and the claims of three papers that recently appeared in this journal are put into perspective.     

Tautological Classes of the Stack of Rational Nodal Curves

This is the second in a series of three papers in which we investigate the rational Chow ring of the stack 𝔐₀ consisting of nodal curves of genus 0. Here we define the basic classes: the classes of strata and the Mumford classes.     

On characterizing properties of the value sets and the equilibrium point sets of non-cooperative two-person games

In this paper, for certain subfamilies of the family of bounded measurable two-person games in normal form, the value sets are characterized by three properties, called the maximum property, the minimum property and the adjunction property. Furthermore, one of the papers of Vilkas is critically discussed. Finally, for bimatrix games, two systems of characterizing properties for the equilibrium point sets are given.     

Nicolai Nicolaevich Luzin and the Moscow school of the theory of functions

Shortly before the revolution of 1917, four papers written by participants in N. N. Luzin's analysis seminar at Moscow University appeared in the Comptes Rendus of the Paris Academy of Sciences. The publication of these papers--written by A. Ya. Khinchin, D. E. Menshov, P. S. Aleksandrov and M. Ya. Suslin--and Luzin's monograph, The Integral and Trigono-metric Series 1915, marked the emergence of Moscow University as a center of research in the theory of functions of a real variable. This paper describes Luzin's early mathematical education at Moscow University and the three year period he spent abroad (mainly in Paris) where he wrote a series of papers whose results form the core of his influential and widely praised monograph. Finally, we will show how Luzin's ideas formed the basis for the early investigations of a series of young Moscow mathematicians.     

Historical Overview of the Kepler Conjecture

This paper is the first in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. After some preliminary comments about the face-centered cubic and hexagonal close packings, the history of the Kepler problem is described, including a discussion of various published bounds on the density of sphere packings. There is also a general historical discussion of various proof strategies that have been tried with this problem.     

On the Degeneration, Regeneration and Braid Monodromy of T×T

This paper is the first in a series of three papers concerning the surface T×T. Here we study the degeneration of T×T and the regeneration of its degenerated object. We also study the braid monodromy and its regeneration.     

基于灰色统计模型的试题内容效度测量方法研究

首先从内容效度的构成要素以及影响内容效度的诸要素入手,从一般的角度上,构建了试题内容效度的测量指标,然后运用灰色统计方法将专家的主观评估结果进行综合,得到了试题内容效度数量化的评价结论.最后以实例说明其应用.     

The mean value of the product of class numbers of paired quadratic fields III

This is the final part in a series of three papers. In this part, we evaluate the previously unevaluated local densities at dyadic places that appear in the density theorem stated in the first part. For this purpose we introduce an invariant, the level, attached to a pair of ramified quadratic extensions of a dyadic local field. This invariant measures how close the fields are in their arithmetic properties and its evaluation may be of interest independent of its application here.     

A Formulation of the Kepler Conjecture

This paper is the second in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. The top level structure of the proof is described. A compact topological space is described. Each point of this space can be described as a finite cluster of balls with additional combinatorial markings. A continuous function on this compact space is defined. It is proved that the Kepler conjecture will follow if the value of this function is never greater than a given explicit constant.     

Enumeration of one-nodal rational curves in projective spaces

We give a formula computing the number of one-nodal rational curves that pass through an appropriate collection of constraints in a complex projective space. The formula involves intersections of tautological classes on moduli spaces of stable rational maps. We combine the methods and results from three different papers.     

Remembering Mel Henriksen and (some of) his theorems

The author selects theorems from three papers co-authored by Mel Henriksen, proves some of those, and offers some consequences and commentary. Also included are some comments, mathematical and social, on Mel Henriksen as a colleague, a co-author, and a forceful presence in the wider political and mathematical community.     

Sphere Packings, VI. Tame Graphs and Linear Programs

This paper is the sixth and final part in a series of papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. In a previous paper in this series, a continuous function f on a compact space is defined, certain points in the domain are conjectured to give the global maxima, and the relation between this conjecture and the Kepler conjecture is established. In this paper we consider the set of all points in the domain for which the value of f is at least the conjectured maximum. To each such point, we attach a planar graph. It is proved that each such graph must be isomorphic to a tame graph, of which there are only finitely many up to isomorphism. Linear programming methods are then used to eliminate all possibilities, except for three special cases treated in earlier papers: pentahedral prisms, the face-centered cubic packing, and the hexagonal-close packing. The results of this paper rely on long computer calculations.     

R-trees and laminations for free groups I: algebraic laminations

This paper is the first of a sequence of three papers, wherethe concept of a real tree dual to a measured geodesic laminationin a hyperbolic surface is generalized to arbitrary real treesprovided with a (very small) action of a free group by isometries.Laminations for free groups are defined with care in three differentapproaches: algebraic laminations, symbolic laminations, andlaminary languages. The topology on the space of laminationsand the action of the outer automorphisms group are detailed.