比较定理

For the comparison equations, the sufficient conditions for the existence of nonoscillatory solutions are also given by using fixed point theorem.

对于比较方程，也用不动点定理给出了非振动解的存在的充分条件。

Mainly by means of the Hopf bifurcation theorem and the cone fixed point theorem in the functional differential equations.

本文对非线性项为两种形式的时滞Van der Pol方程分别加以比较，利用Hopf分支理论和锥不动点定理，得到相应方程在周期解和Hopf分支方面上的差异。

The stability and convergence for spectral methods and spectral element methods are presented, with the aid of the knowledge of functional analysis and calculus and with the help of the theorem of Lax-Milagram, the stability and convergence for steady problems, evolution equations and Navier-Stokes Equations are analyzed in detail.

利用泛函分析和微积分的基本知识，运用Lax-Milagram定理等，从理论上比较详细地分析了谱方法和谱元方法在定常问题、非定常问题以及求解Navier-Stokes方程方面的稳定性和收敛性问题，得出了Navier-Stokes方程谱近似的稳定性条件和收敛性准则。

Design and implement the experimental systems RM and GRM which are based on Reso-lution and Generalized Resolution respectively. Prove all the theorems in Section A and Section Bin Part Ⅰ of " Principia Mathematica " using RM and GRM respectively, and then compare andanalyze the efficiency of RM and GRM.

设计实现了基于归结和基于广义归结的实验系统RM和GRM，分别用RM和GRM证明了《数学原理》第一部分Section A和Section B中的全部定理(350个)，并对RM和GRM的效率进行了分析比较。

Compared with recovery algorithms which are based on Fourier transform, the interpolation formula of generalized sampling theorem one has much more highly accurate recovery result.

同其他基于Foureir变换理论的恢复算法进行了比较，计算结果表明：在相同条件下，定理一内插方式具有高得多的恢复精度。

Furthermore, when the system is a periodic system, sufficient conditions are obtained that guarantee the existence, uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Liapunov function.

利用比较原理给出了系统一致持久性的充分条件；当系统是周期系统时，应用Brouwer不动点原理和构造Liapunov函数的方法给出其存在惟一且全局吸引的ω-周期正解的充分条件，并通过实例验证了文中定理条件的可实现性。

It designs the assertion language and assertion calculus for Pointer Logic.

这在已存在的比较流行的定理证明器中是不曾实现过的。2。

The thesis first recommends the famous fuzzy Gaussian approximation system which is based on the Gaussian membership function, the fuzzy logic of product reasoning and the fuzzy law of weight approach. This thesis is discusses the general fuzzy Gaussian membership function that can approximate the form of triangular, trapezoid and Gaussian function , and its basic form is .The general fuzzy Gaussian membership function is to be generally used in the field of approximation .

模糊逼近是近年来发展比较迅速的一个新兴方向，论文首先给出了模糊理论中著名的基于高斯隶属函数、乘积推理模糊逻辑和重心解模糊法的模糊高斯型万能逼近定理，在此基础上本文进一步给出了可以用来逼近三角形、梯形和高斯形的广义高斯隶属度函数形式，它的基本形式是。

Based on the old algorithm, introduce new Linear Feedback Shift Register, new Central Limit Theorem, Maclaurin Equation to generate uniform distribution, gaussian distribution, exponential distribution's random number respectively and analyze them, compares the difference between new algorithm and old algorithm.

在原有算法的基础上，提出了改进型线性反馈移位寄存法、改进型中心极限定理法和麦克劳林展开法，并对其作测试仿真，比较传统算法与改进型算法之间的优缺点。

The main results can beexpressed as follows:(1)Based on πtheory, some affected factors about wave forces are given, and therelation between affected factors and wave forces is analysised by experimentalresults.(2) The distribution of wave press at representative time and reflection nature aregiven and their variety charactes are discussed by experimental results.(3)By comparing the wave forces of quarter-circular breakwater and semi-circularbreakwater under the same wave conditions,some approximately wave forcesexpressions of quarter-circular breakwater are given.(4)Based on VOF method to trace water free surface,solve numerical value ofRANS equation,and get the distributions of flow field and wave press ofquarter-circular breakwater at the same time during one period,the mechanism ofwave force is also discussed elementarily.(5) Based on the result that RANS equation of numerical simulation agree wellwith experimental results,a new approach to study hydraulic natures of quarter-circular breakwater is provided.

其主要结论如下：一、通过π定理，确定影响波浪力的无因次参变量，根据试验结果对其影响因素进行分析；二、基于模型试验，给出典型时刻圆弧面防波堤的同步波压分布和反射特性，讨论它们的变化特点；三、通过相同条件下圆弧面防波堤与半圆型防波堤两种堤型试验波浪力的比较，给出了圆弧面防波堤波浪力的近似方法；四、利用VOF法追踪自由水面，数值求解RANS方程，得到圆弧堤堤体周围的流场和压力场，初步分析了速度涡流与压力场的相互影响；五、对比数值分析与试验结果，探讨数值方法研究圆弧面防波堤水力特性的可行性，提供新的研究途径

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。