芝麻杂种优势育种理论的研究

从芝麻的杂种优势表现,强优势形成,杂交组合的亲本组配与优化选择等方面的研究中,总结出一些原则,用以指导芝麻杂种优势育种,期能获得强优势杂交种。     

型如a^n-1或a^n＋1（n∈N＋）的标准分解式

探讨常见的型如a^n-1或a^n＋1（h∈N＋）的标准分解式．利用算术基本定理，对整数进行分解质因数是解决初等数论问题的重要途径．分解质因数的最基本方法是查质数表，但对于型如a^n-1或a^n＋1（n∈N＋）的数一般较大，要按此方法将其写成标准分解式并非易事，我们可以通过利用欧拉定理及同余性质探讨对这类数进行分解质因数的捷径．通过探讨研究得出解决此类数的标准分解式的两个定理，并推导型如2^n-1，2^2n＋1，2^3k＋1等特殊类型数的质因数的问题．利用得出的定理和推论对解决初等数论中的相关问题有着一定的意义．     

依赖于参数的泛函微分方程正周期解的存在性

考虑依赖于参数的泛函微分方程x′(t)=-a(t)g(x(t))x(t)+λb(t)f(t,x(t-τ_1(t)),x(t-τ_2(t)),…,x(t-τ_n(t))).利用不动点定理,得到了上述方程正周期解存在的充分条件。     

Number of soil profiles needed to give a reliable overall estimate of soil organic carbon storage using profile carbon density data

Abstract

Soil profile data are the basis for estimating soil organic carbon (SOC) storage and any changes in SOC storage, which are of great significance in terms of global climate change. Estimates based on various profile data have been made for SOC storage in China. Modeling studies have given contrasting results on changes in SOC storage in Chinese croplands. A certain number of measured soil profile data are needed to validate the modeled results. In the present study, we examined the relationships between sample size, population variance and detection limit using the central limit theorem and the statistical properties of the normal distribution. Based on the profile dataset from the Second National Soil Survey in China, we calculated that to derive a reliable estimate of the overall mean SOC density for all the soils of China, a sample size of 4,000 soil profiles is needed. In this case, a reliable estimate is defined as having a 95% confidence interval and allowing a ±5% detection limit of SOC. The necessary sample size for cropland soils is 1,250. Our results indicate that approximately 100 samples only are needed to validate a modeled SOC loss of 20–30% in cropland soils in China. By aggregating the soil profiles in the dataset into soil orders and calculating the variance of each soil order, we show that the sample sizes in the dataset are insufficient to give reliable estimates on the carbon densities of most soil orders; thus, we conclude that there is considerable uncertainty in the SOC distribution maps resulting from the Second National Soil Survey.     

Parseval定理在广义积分中的应用

本文从Fourier级数的展开式及Fourier变换两个角度出发，利用Parseval定理分别求解了在工程物理学及信号分析学中常用到的两类积分。这两类积分的求解，不仅给广义积分的求解提供了新的思路，而且丰富了Parseval定理的应用。     

一类三阶三点边值问题正解的存在性

研究具有非齐次三点边界条件的三阶三点边值问题u^m＋a（t）f（u（t））=0,t∈（0,1）,u（0）=u＇（0）=0,u＇（1）-αu＇（η）=λ正解的存在性,其中0〈α〈1,0〈η〈1,f：[0,＋∞）→[0,＋∞）连续,a：[0,1]→[0,＋∞）连续,λ〉0为参数.主要利用Schauder不动点定理给出了上述三阶三点边值问题存在正解的充分条件.     

三阶非线性常微分方程组三点边值问题的正解

研究一类三阶非线性常微分方程组三点边值问题,在满足假设条件下,利用锥拉伸压缩不动点定理得到了当f和g满足超线性或次线性时边值问题一个正解存在的充分条件．     

近完美匹配全覆盖点

利用匹配理论中的Gallai—Edmonds结构定理,首先得到了在一个有近完美匹配的图中判定一个顶点为近完美匹配全覆盖点的充要条件,然后对每一个顶点都为近完美匹配全覆盖点的图类给出了一个刻画．同时,也给出了一种构造这类图的方法．     

V a g u e集的F u z z y集分解

Vague集作为Fuzzy集的扩展,将其分解成Fuzzy集是一个值得探讨的问题.定义了Vague集的Fuzzy截集和数与Vague集的运算,在探讨了相应性质的基础上,给出了Vague集的Fuzzy集分解定理并进行了证明.     

一类四阶半正边值问题正解的存在性

运用锥上的不动点定理,讨论四阶常微分方程边值问题y(4)(t)-λf(t,y(t),y″(t))=0 t∈(0,1) y(0)=y(1)=0 ay″(ξ1)-by’’’(ξ1)=0 cy″(ξ2)+dy’’’(ξ2)=0正解的存在性,其中:0≤ξ1<ξ2≤1,f∈C([0,1]×[0,+∞)×(-∞,0],R).