摘要： Let K be a field;let P subset of K '' be a finite set and let J(P) subset of K[x(1),...,x(n)] be the ideal of P. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K[x(1),...,x(n)]/J(P) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order less than or equal to(i.t.). It is also shown how this algorithm can be extended to the case in which P is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grobner basis of J(P) with respect to less than or equal to(i.t.) without using Buchberger's algorithm).

关键词： 机械设备   折旧   计算   数学模型  

摘要： 长期以来,我国固定资产折旧方法采用平均年限法(即直线法)和工作量法,这种计提方法有其不足之处。设备原值在计提年限内,货币因市场的波动会贬值,如仍按原值来计算提取折旧费,势必造成原有资产的衰减,而使企业萎缩。为此,笔者认为,在设备折旧计提的各个年度中,必须考虑一个该年度的保值系数来进行校正,才能确保企业再生产的能力。 采用双倍余额递减法提取折旧,能加快设备投资的回收,促进设备更新,对经济发达的国家来说能适应其科技飞速发展的需要,而对我国来说。

关键词： 数学形态学   灰值图像   并行处理  

摘要： 在灰值数学形态学的阴影算法的基础上，提出了采用表面点集代替阴影来代表灰值结构核的改进算法，大大降低了二值邻城互连的数量。光学实现采用一个光学非相干相关器与阈值器件结合的二值数学形态学系统，并设计了一种数字空间编码技术使这二维系统能实现算法要求的有限三维操作。

关键词： 数学形态学   细化算法  

摘要： 本文主要讨论了细化算法的定义与条件，二值图像细化的数学原理和基于数学形态学的细化算法。文中对结构模式类型和细化算法的逻辑运算描述提出新的见解，可望深化和丰富基于数学形态学细化算法的内容。

摘要： It is shown that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincaré groups. Using these symmetries, it is shown that the intricate sums appearing in the calculation of the high-temperature expansion of the magnetic susceptibility can be performed, at least up to the fourth order, using elementary algebraic manipulations which can be implemented with a computer. These symmetries appear more clearly if we use the two-adic fractions to label the sites. Then the new algebraic methods are applied to the calculation of quantities having a random walk interpretation. In particular, it is shown that the probability of returning to the starting point after m steps has poles at D=–2,–4,...,–2m, where D is a free parameter playing a role similar to the dimensionality in nearest neighbor models.

关键词： 刘徽   割圆术   中国   数学   π   古算法  

摘要： 本文首先阐述了刘徽的割圆术。然后,在述评π的密率求法的基础上,认为祖冲之的求法实质上使用了连分数方法,并作了较为合乎情理的论证。最后,结合π的古算法,初步分析了中国传统数学内部固有的缺陷。

关键词： SENSORS   SURFACE TECHNIQUES   HUMIDITY CORRECTION ALGORITHM  

摘要： Nitrobenzene and water adsorption isotherms were obtained on an aminopropyltriethoxysilane coated surface acoustic wave sensor (SAWS) at < 5, 17, 33 and 47% relative humidity (RH) at 6, 13, 25 and 47 degrees C. The nitrobenzene isotherms were BDDT type 1 (Langmuir) and water isotherms BDDT type 3. The nitrobenzene isotherms were fitted to a series of algorithms based on Langmuir theory and the coefficients of the algorithms derived from the experimental data. The derived model was then used to predict the original isotherms, achieving a good match (better than the +/- 12% predicted by error analysis) in the mid-ranges, increasing to as much as minus 35% at 6 degrees C, 47% RH approaching the saturation vapour pressure of nitrobenzene, and minus 20% at 47 degrees C, 47% RH approaching the isotherm plateau region. The theoretical model indicates that the nett heat of adsorption of nitrobenzene (isosteric heat of adsorption minus enthalpy of condensation) is the critical parameter affected by RH and temperature. The effect of this on the heat of adsorption is however not readily quantifiable and the corrections needed to model the isotherms had to be derived empirically, rather than based on those two thermodynamic quantities. The results of the work underline the necessity to compensate for changes in RH and temperature, and indicate important selection criteria for coatings to be used with not only an SAWS, but any other sensor which relies on vapour adsorption as part of its response mechanism.

关键词： 计算机专业人才   研究生培养   知识结构   人才培养   场经济   数学算法   市场竞争   数学基础   培养人才   创造性  

摘要： 计算机专业人才的知识结构及市场经济与研究生培养王选我主要讲一下十多年来科研和人才培养方面的体会，且．限于以计算机为主的专业。通过十多年来对周围学生的观察，我觉得计算机专业人才需要三方面的基础知识：第一是数学知识，第二是软件知识，第三是接口和电路方面的...

关键词： 电力分配   数学模型   算法   多目标决策  

摘要： 用电分配涉及整个社会的各行各业和千家万户,评价分配方案优劣既要考虑经济效益又要考虑社会效益,因此属于多目标决策分析问题。本文运用目标规划原理建立了用电分配数学模型,其中包括利润、产值、电业局收入及各种电量限制等96个目标,按5个优先级进行优化。文中所用算法的基础是单纯形方法,为给出有实用价值的优化分配方案,本文提出以上一年同期实际用电指标为基础研究现行分配方案的基本思想,并采取若干相应措施。