矩阵力学与波动力学等价性证明的历史分析

矩阵力学和波动力学是量子力学的两种早期形态.前者由海森堡、约当、玻恩提出,后者由薛定谔提出.1926年,薛定谔给出二者之间等价性的证明.随后,泡利、狄拉克、约当、冯·诺伊曼等人或是为等价性证明给出新的版本,或是给出了间接的论证.这两种力学现在已被表述为海森堡绘景和薛定谔绘景,而数学家近来又从量子化问题出发对其等价性做出...     

关于建立面向应用的规范词异名库的若干理论探讨

收集整理规范术语的异名,用于开发面向应用的术语纠错工具,可使规范科技术语的宣传与推广工作达到事半功倍的效果。规范词异名是指与国家审定公布的规范科技术语＂正名＂表达相同概念,但词形不同的非推荐名。规范词异名的认定需经过收词和审词两个阶段。收词方法包括人工收集和自动抽取。通过规则和统计并举的自然语言处理技术进行自动抽取,可以有学科领域关联、英文术语一词多译关联、语义网络关联三种路径。规范词异名的人工收集和审词重在确保语义等价。     

A Proof of the Duality of the DINA Model and the DINO Model

The Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model are two popular cognitive diagnosis models (CDMs) for educational assessment. They represent different views on how the mastery of cognitive skills and the probability of a correct item response are related. Recently, however, Liu, Xu, and Ying demonstrated that the DINO model and the DINA model share a “dual” relation. This means that one model can be expressed in terms of the other, and which of the two models is fitted to a given data set is essentially irrelevant because the results are identical. In this article, a proof of the duality of the DINA model and the DINO model is presented that is tailored to the form and parameterization of general CDMs that have become the new theoretical standard in cognitively diagnostic modeling.     

Counterfactuals and Non-locality of Quantum Mechanics: The Bedford–Stapp Version of the GHZ Theorem

In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford.     

论多种语言间术语翻译之策略

随着中国改革开放的不断深入与全球化进程的加快,中国各行各业都面临着与一国或数国打交道的问题。在这一过程中,翻译,尤其是多语种间的翻译就显得非常重要和必要。但是相关翻译研究却严重滞后。文章拟从以下几个方面就多语间术语翻译的策略问题进行探讨:(1)多语种术语不等值是客观存在;(2)针对多语种术语不等值问题拟采取的翻译策略;(3)多语种术语翻译展望。     

黎曼猜想什么时候会被证明出来?

首先从对数学猜想证明的理解得出了影响证明数学猜想的两个重要因素,即数学猜想的证明依赖于必要的数学进展和合适的数学家;接着对这两个因素进行分析;由于对黎曼猜想的证明来说,无论是所需要的数学知识和方法是否具备还是是否有合适的数学家二者都是不确定的,因而无法肯定该猜想什么时候才能被证明出来。     

公安术语汉译英：对等的维度

公安术语翻译的难点在于寻求“对等”，翻译的灵魂在于译意。在译意的基础上，译者要尽量寻求形式上的对应，从而形成“形意兼备，得意保形，得意忘形”三种类型的对等维度。     

公安术语汉译英：对等的维度

公安术语翻译的难点在于寻求“对等”，翻译的灵魂在于译意。在译意的基础上，译者要尽量寻求形式上的对应，从而形成“形意兼备，得意保形，得意忘形”三种类型的对等维度。     

浅析房地产术语的俄译

中国房地产领域经历了纷繁复杂的变化,随之产生的复杂的房地产术语是翻译界面临的一大课题。文章从房地产术语的俄译特点出发,将房地产术语分为一般性房地产术语和无对等词的房地产术语,进而通过实例来分析平行文本与翻译补偿法在翻译过程中的重要性。旨在实现术语翻译的概念对等与语义对等。     

A comparison between two distance-based discriminant principles

A distance-based classification procedure suggested by Matusita (1956) has long been available as an alternative to the usual Bayes decision rule. Unsatisfactory features of both approaches when applied to multinomial data led Goldstein and Dillon (1978) to propose a new distance-based principle for classification. We subject the Goldstein/Dillon principle to some theoretical scrutiny by deriving the population classification rules appropriate not only to multinomial data but also to multivariate normal and mixed multinomial/multinormal data. These rules demonstrate equivalence of the Goldstein/Dillon and Matusita approaches for the first two data types, and similar equivalence is conjectured (but not explicitly obtained) for the mixed data case. Implications for sample-based rules are noted.     

A Note on K-modes Clustering

Recently, Chaturvedi, Green and Carroll (2001) presented a nonparametric approach to deriving clusters from categorical data using a new clustering procedure called K-modes. Huang (1998) proposed the K-modes clustering algorithm. In this note, we demonstrate the equivalence of the two K-modes procedures.     

《吕氏春秋》术语英译研究

以《吕氏春秋》的两个英译本,即翟江月译本和汤博文译本为研究对象,从全额等值和选择性等值两个方面探讨中国典籍中术语译法统一的可行性,并分析目前存在的音译、意译和释译的优缺点,最终认为音译和意译仍是目前实现术语译法统一的最佳途径。     

论古代科学发现优先权的确立原则与判定标准——以勾股定理与毕达哥拉斯定理的发现为例

通过对勾股定理与毕达哥拉斯定理发现与证明方法比较,考证了中西方对勾股定理的发现均符合现代科学发现的定义,提出了中国与西方几乎同时独立发现勾股定理。根据时间敏感性差异原理,指出了古代科学发现优先权的确立原则和判定标准,中西方这种独立的发现开辟了中西方科学发展的不同模式。     

Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data,Contingency Tables and Ratio-Scale Measurements

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyze the ratios of the data values. A common approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property and can be applied to a wider class of methods. This weighted log-ratio analysis is theoretically equivalent to “spectral mapping”, a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modeling. The weighted log-ratio methodology is used here to visualize frequency data in linguistics and chemical compositional data in archeology. The first author acknowledges research support from the Fundación BBVA in Madrid as well as partial support by the Spanish Ministry of Education and Science, grant MEC-SEJ2006-14098. The constructive comments of the referees, who also brought additional relevant literature to our attention, significantly improved our article.     

Structural Similarity: Spectral Methods for Relaxed Blockmodeling

In this paper we propose the concept of structural similarity as a relaxation of blockmodeling in social network analysis. Most previous approaches attempt to relax the constraints on partitions, for instance, that of being a structural or regular equivalence to being approximately structural or regular, respectively. In contrast, our approach is to relax the partitions themselves: structural similarities yield similarity values instead of equivalence or non-equivalence of actors, while strictly obeying the requirement made for exact regular equivalences. Structural similarities are based on a vector space interpretation and yield efficient spectral methods that, in a more restrictive manner, have been successfully applied to difficult combinatorial problems such as graph coloring. While traditional blockmodeling approaches have to rely on local search heuristics, our framework yields algorithms that are provably optimal for specific data-generation models. Furthermore, the stability of structural similarities can be well characterized making them suitable for the analysis of noisy or dynamically changing network data.     

The Surveyability of Long Proofs

The specific characteristics of mathematical argumentation all depend on the centrality that writing has in the practice of mathematics, but blindness to this fact is near universal. What follows concerns just one of those characteristics, justification by proof. There is a prevalent view that long proofs pose a problem for the thesis that mathematical knowledge is justified by proof. I argue that there is no such problem: in fact, virtually all the justifications of mathematical knowledge are ‘long proofs’, but because these real justifications are distributed in the written archive of mathematics, proofs remain surveyable, hence good.     

A Formal Proof of a Paradox Associated with Cohen’s Kappa

Suppose two judges each classify a group of objects into one of several nominal categories. It has been observed in the literature that, for fixed observed agreement between the judges, Cohen’s kappa penalizes judges with similar marginals compared to judges who produce different marginals. This paper presents a formal proof of this phenomenon.     

Numerical taxonomy and the principle of maximum entropy

The standard procedure in numerical classification and identification of micro-organisms based on binary features is given a justification based on the principle of maximum entropy. This principle also strongly supports the assumption that all characteristics upon which the classification is based are equally important and the use of polythetic taxa. The relevance of the principle of maximum entropy in connection with taxonomic structures based on clustering and maximal predictivity is discussed. A result on asymptotic separateness of maximum entropy distributions has implications for minimizing identification errors.The work was partially supported by the Bank of Sweden Tercentenary Foundation, The Swedish Council for Forestry and Agricultural Research, The Carl Trygger Foundation, and the Swedish Cancer Foundation.     

The generation of random ultrametric matrices representing dendrograms

Many methods and algorithms to generate random trees of many kinds have been proposed in the literature. No procedure exists however for the generation of dendrograms with randomized fusion levels. Randomized dendrograms can be obtained by randomizing the associated cophenetic matrix. Two algorithms are described. The first one generates completely random dendrograms, i.e., trees with a random topology, random fusion level values, and random assignment of the labels. The second algorithm uses a double-permutation procedure to randomize a given dendrogram; it proceeds by randomization of the fixed fusion levels, instead of using random fusion level values. A proof is presented that the double-permutation procedure is a Uniform Random Generation Algorithmsensu Furnas (1984), and a complete example is given. This work was supported by NSERC Grant No. A7738 to P. Legendre and by a NSERC scholarship to F.-J. Lapointe.