A Priestley Sum of Finite Trees is Acyclic

We show that the Priestley sum of finite trees contains no cyclic finite poset. The first author would like to express his thanks for support from project LN 1M0021620808 of the Ministry of Education of the Czech Republic. The second author would like to express his thanks for support from project 1M0021620808 of the Ministry of Education of the Czech Republic, from the NSERC of Canada and from a PROF grant from the University of Denver. The third author would like to express his thanks for the support from the NSERC of Canada and for partial support from the project 1M0021620808 of the Ministry of Education of the Czech Republic.     

A Strategy for Writing Equations of Graphs

A strategy for writing equations of graphs is introduced to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. The strategy helps students and teachers weave the conceptual fabric of equations and graphs by (a) moving from unknown graphs to known graphs rather than from known to unknown graphs and by (b) moving from spatial representations to algebraic representations rather than from algebraic to spatial representations. Beginning with the unknown graph is distinctly different from present practices and can lead to significant and useful change in curriculum and instructional practices.     

国内外投资对制造业技术进步影响的行业分化特征

本文首先采用1996年-2008年中国制造业分行业数据,选择随机前沿生产函数模型测度了制造业各行业的全要素生产率变化率,通过调整得到技术进步率,在此基础上,利用2001年-2007年国内外投资的数据基于面板数据模型,研究了制造业各行业国内外投资对技术进步影响的问题,旨在揭示改革开放以来尤其是经济发展较快的最近几年制造业技术进步的源泉,并进一步探讨技术进步来源不同的两类行业的行业分化特征。实证结果表明,制造业绝大多数行业的技术进步来源于国内投资或外商投资,个别行业甚至同时受国内外投资的双重影响,当行业特征表现为市场竞争程度高且外商投资对国内投资比重偏高时,技术进步更倾向来源于国内投资,反之则更倾向来源于外商投资。     

Challenges of β-deformation

We briefly review problems arising in the study of the beta deformation, which turns out to be the most difficult element in a number of modern problems: the deviation of ?? from unity is connected with the ??exit from the free-fermion point?? in two-dimensional conformal theories, from the symmetric graviphoton field with ??₂ = ???₁ in instanton sums in four-dimensional supersymmetric Yang-Mills theories, with the transition from matrix models to beta ensembles, from HOMFLY polynomials to superpolynomials in the Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras, and so on. We mainly attend to issues related to the Alday-Gaiotto-Tachikawa correspondence and its possible generalizations.     

Problems Identifying Independent and Dependent Variables

This paper discusses one step from the scientific method—that of identifying independent and dependent variables—from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of independent and dependent variables. It then outlines four rationales (two from science and two from mathematics) for identifying independent and dependent variables. Finally, it reports the results of a textbook analysis that used these rationales to examine the extent to which typical mathematics textbook problems support or supplant a sensible view of independent and dependent variables. The findings indicate that often, mathematics textbook problems misrepresent the sense‐making aspect of identifying independent and dependent variables, possibly setting students up to develop misconceptions about this step from the scientific method.     

Maximal order codes over number fields

We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.     

20世纪之数学

20世纪数学的重点从局部转移到整体，从低维转移到高维，从交换转移到非交换，以及从线性转移到非线性．几何学和代数学的对立统一依然存在，从哲学上反映了空间与时间之对立统一．与同调论、K-理论和李群有关的技巧和概念被广泛运用．在最近的20年间，量子场论和弦理论为数学注入新观念．理论物理学对数学的影响还将在21世纪延续下去．     

Instability in Porous Layers with Depth-Dependent Viscosity and Permeability

The paper is concerned with a multicomponent porous horizontal layer L with depth-dependent viscosity and permeability, heated from below and salted partly from below and partly from above. The instability of the thermal conduction solution, due to the growth of the gradient of temperature or of the gradient of chemical species salting L from above, is investigated.     

Parallel assimilation of observed data in the hydrodynamic model of the ocean circulation

The parallel use of the Kalman ensemble filter technique for assimilating data from observations in theHYCOMmodel of theWorldOcean is described. Data from satellite observations of the sea’s surface temperature and the sea’s surface height are assimilated both separately and conjointly. Numerical experiments on correcting model calculations using data from observations are performed. The results from the corrections are compared to model calculations without assimilation. The effectiveness of the employed parallelization algorithm is confirmed.     

Fuzzy测度的伪自连续性

为了克服ＳｕｇｅｎｏＦｕｚｚｙ测度的局限性，从而在更一般的情况下研究ＳｕｇｅｎｏＦｕｚｚｙ测度和Ｆｕｚｚｙ积分，王震源在文［１］中首次引进集函数的“自连续性、伪自连续性”等一系列重要概念，孙清河在文［３］中解决了文［１］中提出的“上自连续性”与“下自连续性”的等价问题，而本文则解决了文［１］中提出的“伪上自连续性”与“伪下自连续性”的等价问题，并得到有关伪自连续定义的一系列等价命题。     

Simulating Multivariate Extreme Value Distributions of Logistic Type

Methods are given for simulating from symmetric and asymmetric versions of the multivariate logistic distribution, and from other multivariate extreme value distributions based on the well known logistic model. We consider two general approaches. The first approach uses transformations to derive random variables with a joint distribution function from which it is easy to simulate. The second approach derives from a specification of conditionally independent marginal components, conditioning on positive stable random variables. This specification extends to models of nested or hierarchical type and leads to an efficient way of incorporating marginal censoring. The algorithms presented in Sections 2 and 3 are available on request from the author. They are also included in the R (Ihaka and Gentleman, 1996) package evd (Stephenson, 2002), which is available from http://www.maths.lancs.ac.uk/~stephena/.     

A constructive method for starlike harmonic mappings

Summary The idea initiated by Opfer for constructing conformal mappings from the disk onto starlike domains is generalized for univalent harmonic mappings. This is of some interest, since such mappings are not characterized by analytic means.This work was supported in partsby a Promotion of Research Grant from the TECHNION, Haifaby an Undergraduate Student Research A ward from the NSERCby grants from the NSERC and the FCAR     

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

This paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company’s pharmacy to patients’ homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks.     

A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem

This paper presents a genetic algorithm for solving the resource-constrained project scheduling problem. The innovative component of the algorithm is the use of a magnet-based crossover operator that can preserve up to two contiguous parts from the receiver and one contiguous part from the donator genotype. For this purpose, a number of genes in the receiver genotype absorb one another to have the same order and contiguity they have in the donator genotype. The ability of maintaining up to three contiguous parts from two parents distinguishes this crossover operator from the powerful and famous two-point crossover operator, which can maintain only two contiguous parts, both from the same parent. Comparing the performance of the new procedure with that of other procedures indicates its effectiveness and competence.     

The number of certain integral polynomials and nonrecursive sets of integers, Part 2

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, from recursion theory, and from the negative solution to Hilbert's 10th Problem.

     

Application of Banach limits to the study of sets of integers

The Kamae and Mendes France version of the Van der Corput equidistribution theorem is extended further to summability methods different from Cesàro summability and groups different from the circle. The theorem is shown to follow naturally from consideration of Banach limits and spectral theory.     

Issues arising on the use of hand‐held calculators in schools†

This paper considers the use of hand‐held calculators (HHCs) in schools from the pedagogical and sociological viewpoints. Using arguments based on the observed pattern of mathematical education, we discuss the effect of the use of HHCs, from the learning viewpoint and from the viewpoint of providing students with a ready competence in arithmetical manipulation. We shall also discuss the effects of the adoption of HHCs in undeveloped countries and for deprived minorities.

The topics are developed from philosophical/psychopedagogical reasoning and from developmental policy. Strategies designed to make mathematical education more immediately useful are discussed. An example is provided, and the relationship between Polya's problem‐solving approach and the use of HHCs is examined.     

基于酉几何的等概的具有仲裁的认证码的构造

具有仲裁的认证码既要防止敌手的欺骗,又要防止收入和发方的互相欺骗,本文给出一种由酉几何构造等概的具有仲的认证码的方法,并计算了有关参数,分析了各种攻击成功的概率。     

On the Weak Semi-continuity of Vector Functions and Minimum Problems

Lower semi-continuity from above or upper semi-continuity from below has been used by many authors in recent papers. In this paper, we first study the weak semi-continuity for vector functions having particular form as that of Browder in ordered normed vector spaces; we obtain several new results on the lower semi-continuity from above or upper semi-continuity from below for these vector functions. Our results generalize some well-known results of Browder in scalar case. Secondly, we study the minimum or maximum problems for vector functions satisfying lower semi-continuous from above or upper semi-continuous from below conditions; several new results on the existence of minimal points or maximal points are obtained. We also use these results to study vector equilibrium problems and von Neumann’s minimax principle in ordered normed vector spaces.     

Übersiedlung eines deutschen Mathematikers von Braunschweig nach Kazań im Jahre 1807/08: Zur Biographie von M. Bartels,Des Lehrers von Gauss und Lobačevskij

The emigration of a German mathematician from Braunschweig to Kazan in 1807–1808. On the biography of M. Bartels, the teacher of Gauss and Lobachevskii. An unpublished letter from M. Bartels to Heinrich Zschokke written in Petersburg 11 (23) December, 1807, and 24 January (5 February), 1808, accompanied by commentary, notes, and an excerpt from a letter from Bartels to Zschokke of 10 (22) January, 1810.