形式实模的核心

通过含单位元的交换环的实素理想构造出对应的模的实素子模,得到模的序存在的一个充要条件,并对模的所有序的支集的交集(文中称作"模的核心")作出一定的刻划,找到了判断模中的元素属于模的核心的充要条件.     

包含—受扭迴转轴的半空间的性质*

本文研究包含有一根部份嵌入的迴转轴的半空间的性质.不用知道一给定的嵌入的轴的扭转问题的精确解,这些性质能指出此半空间的位移或应力场的某些特点并且有时可以用来检查数值解.文中给出嵌入半空间的受扭的刚性圆柱的轴的表面上的正确的应力分布的检查的例子.     

几何学概论(三)

(四)罗氏几何的光辉照亮了科学前进的道路我们来分析他的学说的哲学意义.在罗氏的时代,哲学中占统治地位的思想是康德的"不可知论",按照这批人的说法,客观世界是存在的,但是不可知的,时间空间是人心的创造,是人心给经验安排的秩序,我们所确实知道的世界的规律性是人心按先天的原则所创造出来的,先天就是与经验无关的,这样,我们的空间观念就完全是人心的创造,     

映射与函数、指数函数

1　重、难点分析关于映射与函数的概念 ,重点是映射、函数的概念的理解与掌握 ,难点是对映射、函数概念 ,对函数符号 ｙ =ｆ(ｘ) ,以及对函数是一种特殊的映射的理解 ,对函数的定义域、值域的理解与掌握 .对于函数的单调性和奇偶性 ,重点是对函数的单调性、奇偶性的概念的理解 ,难点是对函数的单调性、奇偶性的判断与应用 .关于反函数 ,重点是反函数的概念的理解 ,难点是对求反函数的方法的掌握 .关于指数、指数函数 ,重点是分数指数幂的概念和分数指数幂的运算性质、指数函数的图象和性质的理解与掌握 ,难点是根式的概念和分数指数幂的概念…     

任意角的三角函数

1本单元重点、难点分析三角函数是中学数学的重要内容之一,也是高等数学的重要基础。本单元首先将角的概念进行推广,并引入弧度制的表示方式,再定义六种三角函数,然后探讨同角三角函数间的一些基本关系式及三角函数的诱导公式。角的概念的推广和角的度量单位的更新(引入弧度制)是本单元的第一个重点,它拓宽了三角函数的应用范围,简化了三角函数的研究,是进一步学习三角函数的基础,起到了承上启下的作用.任意角的三角函数的定义是进一步学习三角函数的根基,由此导出的三角函数的符号、同角三角函数间的基本关系式及三角函数的诱导公式是本单…     

微分差分方程解之稳定性

最近20—30年来在调节过程的研究中微分差分方程得到很多的应用.在调节理论和在很多其他具有时滞的过程的理论中所发生的基本问题中的一个问题是关于过程的稳定性的问题,一般化为关于微分差分方程解的稳定性的问题.这具问题吸引了非常多的工作者的注意(参考交末的目录),但据我们所知,这些零散的研究从未被有系统地综述过.这篇文章的目的是用简要的形式综述关于微分差分方程解的稳定性的工作的结果,也包括本文作者的若干研究在内.     

方程a~x=loga~x的解

一个方程的解可以看作两个函数的图象的交点的横坐标。反过来,方程的解又可以反映两个函数之间的某种关系,即它们的图象相交的情况。因此,可以利用函数的性质对方程的解,特别是直接求解很困难的某些超越方程的解的情况作出定性的讨论。也可以利用方程的解对函数的图象间的交点个数作出定量的研究,本文主要通过对函数y=x~(1/x)和y=x~x的性质的分析,就方程a~x=x和a~x=loga~x等的解的情况进行讨论。     

基于预期的损失厌恶的“报童式”推理

利用Koszegi与Rabin的参照依赖效用函数对报童问题进行了研究,不仅求得基于预期的损失厌恶报童的最优订货量而且讨论了它的性质.研究发现,基于预期的损失厌恶的报童的订货量要低于利润最大化的报童的订货量,而且,基于预期的损失厌恶的报童的订货量随预期利润、损失厌恶程度的增加而减少.     

关于矩阵的外逆及矩阵的两个外逆的线性组合

本文研究了矩阵A的外逆的表达式,利用外逆及分块矩阵的秩的性质,得出了A的两个外逆的线性组合还是A的外逆的完全分类,不仅证明了A的两个外逆的和与差,而且A的外逆的几个充要条件,推广了Jerzy K.Baksalary和Oskar Maria Baksalary的结果.     

三棱锥体积在解题中的应用

三棱锥是一种特殊的棱锥;它的每一个顶点都可为棱锥的顶点,它的每一个面均可为棱锥的底面,而体积总是不变的。利用这一特点,可以把求多面体的体积和多边形的面积分别转化为求三棱锥的体积和三校锥的底面积;把求点到平面的距离、直线和平面的距离以及两条异面直线的距离转化为求三棱锥的高等等。一求多面体的体积多面体的体积,可以转化成若干个三棱锥的体积和,由于三棱锥的底面具有轮换性,可适当选取三棱锥的底面,较容易地求出三棱锥的体积,进而求出多面体的体积。     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

On the dependence of the growth rate on the length of the defining relator

Let { } be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999.     

On the rational approximation of the sum of the reciprocals of the Fermat numbers

Let $\mathcal{G}(z):=\sum_{n\geqslant0} z^{2^{n}}(1-z^{2^{n}})^{-1}$ denote the generating function of the ruler function, and $\mathcal {F}(z):=\sum_{n\geqslant} z^{2^{n}}(1+z^{2^{n}})^{-1}$ ; note that the special value $\mathcal{F}(1/2)$ is the sum of the reciprocals of the Fermat numbers $F_{n}:=2^{2^{n}}+1$ . The functions $\mathcal{F}(z)$ and $\mathcal{G}(z)$ as well as their special values have been studied by Mahler, Golomb, Schwarz, and Duverney; it is known that the numbers $\mathcal {F}(\alpha)$ and $\mathcal{G}(\alpha)$ are transcendental for all algebraic numbers α which satisfy 0<α<1. For a sequence u, denote the Hankel matrix $H_{n}^{p}(\mathbf {u}):=(u({p+i+j-2}))_{1\leqslant i,j\leqslant n}$ . Let α be a real number. The irrationality exponent μ(α) is defined as the supremum of the set of real numbers μ such that the inequality |α?p/q|<q ^?μ has infinitely many solutions (p,q)∈?×?. In this paper, we first prove that the determinants of $H_{n}^{1}(\mathbf {g})$ and $H_{n}^{1}(\mathbf{f})$ are nonzero for every n?1. We then use this result to prove that for b?2 the irrationality exponents $\mu(\mathcal{F}(1/b))$ and $\mu(\mathcal{G}(1/b))$ are equal to 2; in particular, the irrationality exponent of the sum of the reciprocals of the Fermat numbers is 2.     

On the depth of the tangent cone and the growth of the Hilbert function

For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.

     

On the summation of the Laguerre series by the Euler-Knopp method in the problem of inverting the Laplace transform

A method for inverting the Laplace transform based on expanding the original in Laguerre polynomials as $ f(t) = \sum\limits_{k = 0}^\infty {a_k L_k (bt)} $ is suggested. The representation of the Laguerre series by a linear-fractional mapping is reduced to a power series of the form $ \sum\nolimits_{k = 0}^\infty {a_k z^k } A method for inverting the Laplace transform based on expanding the original in Laguerre polynomials as is suggested. The representation of the Laguerre series by a linear-fractional mapping is reduced to a power series of the form , which is summed by the well-known Euler-Knopp method. The summation parameter is chosen in the complex plane so that the new expansion of the original corresponding to the Euler-Knopp transformation converge at a maximum rate. On the basis of geometric representations, the influence of the requirement that the Euler-Knopp transformation must be regular on the choice of the summation parameter is discussed. Numerical experiments are performed, which demonstrate the high efficiency of the method of choosing a complex parameter suggested in this paper. Original Russian Text ? M.M. Kabardov, 2008, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2008, No. 4, pp. 84–89.     

On choosing the location of the sources in the MFS

The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work we investigate this issue by means of two algorithms, one based on the satisfaction of the boundary conditions and one based on the leave-one-out cross validation algorithm. By applying these algorithms to several numerical examples for the Laplace and biharmonic equations in a variety of geometries in two and three dimensions, we obtain locations of the sources which lead to highly accurate results, at a relatively low cost.