John Reynolds of the Mint: A mathematician in the service of king and commonwealth

In his youth, John Reynolds showed a talent for arithmetic and was destined for a career as a mathematician at the Tower Mint in London. He became skilled in the algorithms needed to determine the correct relationship between the weight and purity of coins and their values. This was a matter of national importance, and his work came to the attention of King James I, who reigned from 1603 to 1625, and his chief ministers, including Robert Cecil and Francis Bacon. It seemed that John might attain high office himself, but the murky administration of the early Stuart period cast its shadow over his career. Nevertheless, for the next forty years he continued to play a major part in the nation's affairs. He produced books of tables for the valuation of coins in the commercial world, and for the highly technical work of the assayers. Also, he was actively involved in the production of standard measures and instruments used by the excise officers. His life and works illustrate how mathematical ideas were employed by the English government in the period of the early Stuart kings and the Commonwealth.     

A method for efficiently computing the number of codewords of fixed weights in linear codes

The problem of computing the number of codewords of weights not exceeding a given integer in linear codes over a finite field is considered. An efficient method for solving this problem is proposed and discussed in detail. It builds and uses a sequence of different generator matrices, as many as possible, so that the identity matrix takes disjoint places in them. The efficiency of the method is achieved by optimizations in three main directions: (1) the number of the generated codewords, (2) the check whether a given codeword is generated more than once, and (3) the operations for generating and computing these codewords. Since the considered problem generalizes the well-known problems “Weight Distribution” and “Minimum Distance”, their efficient solutions are considered as applications of the algorithms from the method.     

Edgeworth expansion in partial linear models

In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of β in partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.     

复广义权与拟连续性

本文引入复广义权的外权的概念，讨论了某些与复广义权相关的函数的拟连续性。     

The law of one price in data envelopment analysis: Restricting weight flexibility across firms

The Law of One Price (LoOP) states that all firms face the same prices for their inputs and outputs under market equilibrium. Taken here as a normative condition for ‘efficiency prices’, this law has powerful implications for productive efficiency analysis, which have remained unexploited thus far. This paper shows how LoOP-based weight restrictions can be incorporated in Data Envelopment Analysis (DEA). Utilizing the relation between industry-level and firm-level cost efficiency measures, we propose to apply a set of input prices that is common for all firms and that maximizes the cost efficiency of the industry. Our framework allows for firm-specific output weights and for variable returns-to-scale, and preserves the linear programming structure of the standard DEA. We apply the proposed methodology to the evaluation of the research efficiency of economics departments of Dutch Universities. This application shows that the methodology is computationally tractable for practical efficiency analysis, and that it helps in deepening the DEA analysis.     

镀锡薄板单位面积镀锡量新的测定方法—贝尔德直读光谱仪分析技术的开发

本文利用贝尔德公司生产的ＳＶ－１０００型（ＤＶ－４）直读光谱仪测定镀锡薄板单位面积镀锡量，开拓了光电光谱仪在镀层领域的应用，通过选用基体铁元素作内标，在适宜的激发条件下获得锡元素涨强比与镀锡量间的线性关系。选择合适条件，解决了薄板易击穿，内标元素光强值稳定性等技术关键，采用容量法制作一套不同镀锡量的标准镀锡薄板，绘制校准曲线，建立了光电光谱分析测定镀锡薄板单位面积镀锡量的方法。方法精度ＲＳＤ小于５     

基于最大满意度的研究生录取问题

采用了模糊数学的知识和优化方法讨论解决了研究生的录取问题.首先对相关数据进行了合理的量化,然后定义了导师与学生之间的相互满意度,建立了择优录取和双向选择的优化模型,通过求解得到了理想的结果.     

模糊聚类与模糊识别理论模型研究

指出文 [1]模糊聚类与模糊识别模型的局限性 ,进一步研究模糊环境下的目标函数 ,修改模糊聚类中心的计算公式 ,提出计算权重的一个公式 ,拓广模糊聚类与模糊识别理论模型的应用范围     

小波变换传递误差、尺度、加权量化对分层树剖分编码图象压缩质量影响的研究

详细研究了小波变换传递误差、尺度、快速Mallat算法加权量化对分层树剖分(SPIHT)编码图象压缩质量的影响,并给出了基于VC++的仿真结果,结果表明,小波变换尺度对图象压缩编码效果有明显的影响,通常要在大于4的尺度上作图象压缩编码才可以得到较好的压缩效果,不同的边界延拓,不同尺度的取整重构、加权量化对图象压缩效果的影响是不同的,恰当选取加权量化步长能达到更好的图象压缩效果,一般而言,同一尺度下随加权量化步长的增加,压缩效果变差.     

Weak amenability and 2-weak amenability of Beurling algebras

Let be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of . This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of the derivation space. We apply these results to give examples of various classes of Beurling algebras which are weakly amenable, 2-weakly amenable or fail to be even 2-weakly amenable.