查询词典 sufficient condition

Another Two Forms of Necessary and Sufficient Condition of Differentiable Complex Function;2. The paper introduces a kind of differentiable fractal interpolation function,discusses its generating mechanismas well as the sufficient condition that generates its IFS.

文章介绍一类可微的分形插值函数，探讨了它的产生机理以及生成它的迭代函数系所满足的充要条件，在此基础上给出样条分形插值函数的定义，并讨论它所具有的部分收敛性质。

We obtain a sufficient condition and a essential - sufficient condition about convergence at the end point of the convergence interval of power series.

通过对阿贝尔定理的深入探讨，获得了幕级数在其收敛区间端点收敛的一些判别条件。

In this paper, we give a new sufficient condition and describe some semicomplete multipartite digraphs demonstrating that this sufficient condition is independent and in some sense, it is best posssible.

本文将针对此问题给出一个新的充分条件，并举例说明该充分条件的独立性以及它在某种意义下的最佳可能性。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

In this paper, the theoretical analysis of matrix's triangular decomposition is mainly discussed, including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition,the necessary and sufficient condition of existence and so on.

本文主要对矩阵的三角分解理论分析作了比较全面的统述，它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件、存在性的充分条件等。

In order to study the effects of water supply intensity, soil bulk density, initial soil moisture and soil texture on infiltration ponding time under the condition of non-sufficient water supply, and build mathematical relation on infiltration ponding time and each factor, infiltration experiments with eight kinds of homogenized soils under non-sufficient water supply condition were conducted indoors.

为了研究供水强度、土壤容重、初始含水率、土壤质地等因素对非充分供水入渗积水时间的影响，建立入渗积水时间与单一因素的数学关系，在室内进行了8种均质土壤的非充分供水入渗试验。

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

As the development that studies to structure of protective screen of kidney spherule filtration and function, it is normal to realise VEGFR of sufficient cell surface shares sufficient cell gradually of structure and function maintain, mix in injury sufficient cell wither dies certain effect is produced in the process.

随着对肾小球滤过屏障结构和功能探究的深入，逐渐熟悉到足细胞表面VEGFR参和足细胞正常结构和功能的维持，在损伤和足细胞凋亡过程中发挥一定功能。

First of all,we tested the germination and water uptake rate of 47 species typical xerophil seeds grow up in north China from 20 families,38 genuses under sufficient water and different Grads water stress by high-molecular-weight polyethylene glycol(PEG6000).The results show that Xerophil seeds from the same habitat exhibited similar patterns in response to water stress.Xerophil seeds from arid community were stronger in germination and imbibition than that from other two communities under serious water stress,whereas Xerophil seeds from humid community were sensitive to any degree of water stress.Namely,the seeds live in arid habitat possessed high germination and quickly water uptake in sufficient water or any degree of water stress,but the others grow up in humid habitat shown significant difference which germination and water uptake well under sufficient water but inhibited even if slight water stress.

首先，我们通过对20个科，38属，47种旱生植物种子在水分充足和不同梯度的干旱处理(聚乙二醇PEG6000)条件下的萌发率及吸水率实验发现，当水分胁迫强烈时，分布于干旱沙漠地区的植物种子其吸水率和萌发率都高于半干旱和湿润地区的植物群落，相反，湿润地区植物种子的吸水率和萌发率对任何的水分胁迫都表现出敏感的响应趋势，也就是说，生境恶劣的植物种子在较强的干旱胁迫下，仍然保持了较高较快的萌发率及吸水率，水分充足与水分缺乏时无显著差异，而生境相对较好的植物种子在水分充足情况下萌发与吸水良好，但在干旱胁迫时则受到明显抑制，水分充足与水分缺乏时差异显著。

World War II: Battle of Saipan - Americans take Saipan.

1944年的今天，美国在塞班战役中拿下塞班岛。

When the scorner, the rejecter of truth, has become presumptuous; when the routine of work in the various money-making lines is carried on without regard to principle; when the student is eagerly seeking knowledge of everything but his Bible, Christ comes as a thief.{DA 635.3

当讥诮和拒绝真理的人，到了任意妄为时，当追求财利者罔顾按道义经营谋利时，当学人正在兢兢业业地研究各种知识，而单把圣经丢在一边时，基督要像贼一样来临。