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.     

断裂问题特征根的重根探讨

利用特征矩阵的秩与特征根所对应的子特征函数空间维数之间的关系。确定了反平面断裂问题和平面断裂问题的特征根可能出现的最大重根数．利用Reissner型板特征根与反平面和平面断裂问题特征根的关系确定其可能出现的最大重根数．得到了反平面断裂问题、平面断裂问题和Reissner板断裂问题可能出现的最大重根数分别为1,2,3．     

含受弯根键的根式沉井承载性能分析

根据荷载传递法及Winkler地基梁理论,考虑根键弯曲及重叠折减效应,推导了含受弯根键的根式沉井承载性能的弹性解答,计算值在弹性范围内与实测值接近.给出了竖向位移和轴力随深度的分布曲线,并分析了根键的受力性状以及各部分土反力的分担比例等.结果表明,根式沉井的承载性能明显优于传统沉井基础,可应用于工程建设中,但根键的弯曲效应会降低基础的承载性能,故在设计中应提高根键的抗弯刚度.     

Computing the characteristic roots for delay differential equations

A new approach to computing the rightmost characteristic rootsof linear Delay Differential Equations (DDEs) with multiplediscrete and distributed delays is presented. It is based onthe discretization of the infinitesimal generator of the solutionoperators semigroup and it avoids the use of the characteristicequation. The approximated roots are obtained by a large sparsestandard eigenvalue problem.     

若干矩阵Γ分布的相关分布

本文研究了与矩阵Γ分布相关的若干分布的密度函数,利用矩阵Γ分布的特征函数和它的Bartlett分解等方法,获得了与矩阵Γ分布相关的几个分布的密度函数解析表达式,它们包括Γ分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度,进一步还得到了相关系数矩阵的分布密度函数形式.     

On roots of exponential terms

In the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms (with one variable). The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non-zero terms t(x) certain estimations concerning the location of roots of t(x) are given. MSC: 03C65, 03C60, 12L12.     

关于中立型泛函微分方程的一致渐近稳定性判别的两个定理

本文利用Ｌｙａｐｕｎｏｖ泛函方法和Ｐａｚｙμｘｕｈ函数方法的基本思想，将文（２）中某些结构推广到中立型泛函微分方程，得到中立型泛函微分方程的一致渐近稳定性的两个判别定理。     

15N Distribution in Wheat and Chemical Fractionation of Root-Borne 15N in the Soil

Abstract

Spring wheat plants were grown in split-root containers and labelled with ¹⁵N by fertilizing one compartment of the container with ¹⁵NH₄ ¹⁵NO₃ (95 at.-% ¹⁵N exc.). After the harvest, approx. 90% of the ¹⁵N incorporated by the plants were found in the shoots and 3% in the roots; approx. 7% had been released into the soil of the unlabelled compartment. The ¹⁵N in the soil of the unlabelled compartment was extracted with KCl and hydrolysed with HCl. Approx. 60% of the ¹⁵N was found in the hydrolysable organic N pool of the soil and 9% in the fraction of the soluble and exchangeable inorganic nitrogen.