黎曼浸没在全空间中的特征值估计

给出了一类黎曼浸没在全空间中第一特征值的下界估计．设π：M→N为黎曼浸没，其中M是个非紧致流形，N是个在无穷远点有一个极点的黎曼流形，而且Ric（M）≤-（n--1）k，这里k〉0，如果｜｜H｜｜≤c≤（n-1）,那么，λ1（M）≥{（n-1）k-c}^2/4，从而得到了著名的Mckean定理。     

On Hypothesis about the Second Eigenvalue of the Leontief Matrix

If an arbitrarily positive eigenvector is repeatedly premultiplied by a positive matrix, then the result tends towards a unique, positive (Frobenius) eigenvector. Brady has demonstrated that the expected absolute magnitude of the estimate of the second largest eigenvalue of a positive random matrix (with identically and independently distributed entries) declines monotonically with the increasing size of the matrix. Hence, the larger the system is, the faster is the convergence. Molnár and Simonovits examined Brady's conjecture in the case where entries of a stochastic matrix are close to 1/n. We prove this hypothesis for any stochastic and positive matrix.     

一阶常系数线性齐次微分方程组的两种解法

一阶常系数线性齐次微分方程组其中的求解,一般有两种解法。第一种,归结为求矩阵A的特征值和特征向量,微分方程组(1)的解的一般结构完全由代数问题的解所决定。第二种,归结为求矩阵A的Jordan标准形,从而可以写出,由其中为可逆矩阵,求出即为方程组(1)的解。     

TD-SCDMA系统中一种快速的下行波束形成技术

利用阵列天线系统接收信号的自相关矩阵的最大特征值所对应的本征向量的信号处理(PSM)思想，提出一种适用于TD—SCDMA系统的快速下行波束形成技术。此方法利用各个用户的扩频码进行目标用户的数据分离，并用迭代的方法代替用户信号的自相关矩阵的特征分解，降低了计算复杂度。计算机仿真验证了该方法的有效性。     

A Dynamic Leontief Model with Non-renewable Resources

In this paper we study a generalization of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously, the non-renewable stocks will decrease, exploiting primary resources. In this study we examine the controllability of this extended model by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate how long these scarce resources will cover the input needs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption. In doing so, we apply classic results from control theory and on eigenvalue problems in linear algebra.     

The effect of response scaling on the detection of linear dependencies among multiresponse data

Summary Box and Draper (1965) introduced a criterion for the estimation of parameters from a multiresponse model. This criterion can lead to misleading results in the presence of linear relationships among the responses. Box et al. (1973) proposed a procedure for detecting the existence of such relationships when the multiresponse data are subject to round-off errors. The procedure is applicable only when the round-off errors are identically distributed as uniform random variates. In many situations, however, the round-off errors can vary considerably. For example, the responses may have distinct physical meanings, and hence distinct scales of measurement with possibly widely different orders of magnitude. This article extends Box et al.’s procedure to cover these situations. Two examples are given to illustrate the implementation of the proposed methodology.     

Excel在水质资料整编特征值统计中的应用

Excel是一个数据处理功能很强的软件,其大量实用的函数库可以为各项统计工作提供全面的支持。本文结合笔者自身工作实践,针对水质资料整编工作中最大值、最小值、平均值和超标率四项特征值统计,提出了运用Excel函数实现数据批量快速处理的解决方案,在消除人为错误隐患的同时极大提高了整编工作效率,并成功应用于太湖流域2009~2012年水质资料整编工作中。     

基于Radarsat 2全极化数据的多种雷达植被指数差异分析

[目的]雷达植被指数(Radar Vegetation Index,RVI)作为评价雷达影像植被分布与生长状态的重要指标,对植被生长动态监测具有重要意义。然而,不同算法的雷达植被指数对于同一地物类型的表征往往存在一定的差异。文章通过对比分析3种常用RVI在多种类型地物上的差异,为其在SAR影像特征提取、分类、识别等应用提供指导性意见。[方法]实验基于武汉市Radarsat-2全极化数据,结合Google earth历史影像和实地调研数据,选取林地、灌丛、草地、耕地、水生植被、建筑、道路、裸地、湖泊、河流10种典型地物样本,从样本折线图分布、类内标准差等方面,对分别通过H/A/alpha分解、Freeman分解和后向散射系数计算得到的3种常用雷达植被指数Van_RVI、Freeman_RVI和Kim_RVI进行了测算分析。[结果] 3种雷达植被指数有着相似的折线图走势,对植被的监测能力良好,但对于不同地物的敏感性稍有差异:Freeman_RVI对林地等高密度植被区域敏感程度较高; Van_RVI对耕地与林地、灌木与林地具有一定的区分性; Kim_RVI对水体与建筑的敏感程度较高。[结论] Freeman_RVI对高密度植被识别能力最好,可用于林地提取、森林制图; Van_RVI对植被与非植被的区分能力最好,适用于植被提取; Kim_RVI数据预处理计算速度最快,但提取精度不高,可用于应急制图。     

Input–output evidence on the relative price effects of total productivity shift

This paper provides empirical evidence on the relative price effects of a notional shift in total productivity using data from ten Symmetric Input–Output Tables of five European economies. The results suggest that the direction of the price-movements is, more often than not, governed by the (traditional) labour cost condition and this could be connected to the effective ranks of the matrices of the relative shares of the capital goods.