查询词典 one dimensional differential equation

By the numerical analysis of the ultimate bearing capacity of two- and three-dimensional footing under combined loading mode, the results show that the effect of alteration of underground water lever on bearing capacity of three-dimensional foundation is more than on that of two-dimensional foundation, the effect of soil gravity on bearing capacity of three-dimensional foundation is more than that of two-dimensional foundation. At the same time, the numerical calculation process of ABAQUS indicates that whether the geostatic stress is balanced or not has great effect on the numerical convergence. In view of the effect extent of dilation angle of soil on the ultimate bearing capacity and the failure pattern of foundation, the condition of two-dimensional plane strain is higher than that of the three-dimensional foundation.

复合加载模式下，通过对三维矩形基础和二维条形基础进行数值分析，结果表明：黏性土地基中地下水位的变化，对三维矩形基础极限承载力的影响程度高于对二维条形基础的影响；在求解地基极限承载力的过程中，土体重度对三维矩形基础的影响明显高于对二维条形基础的影响，同时ABAQUS数值计算过程表明，地基土体地应力能否合理平衡，对数值求解过程中是否收敛有很大的影响；就土体剪胀角对地基极限承载力的影响程度而言，二维平面应变情况下土体剪胀角对极限承载力的影响比三维情况下的影响更明显，即土体剪胀角对条形基础极限承载力的影响高于三维矩形基础。

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

This article use the improved integral inequalities with the deviate variable and some skills of inequalities as well as related knowledge about second-order differential equation,to obtain the following results: the classification of limit point case or limit circle case and boundedness for second order differential or difference equation with deviative variable,discussed the classification for certain n-order differential equations,Criteria for the classification of second order differential equation with deviative variable.

本文利用推广的具有偏差变元的积分不等式，结合不等式的一些技巧以及常微分方程的相关知识对一类二阶具有偏差变元的微分方程及一类二阶差分方程极限圆型的分类问题作了相关的研究工作，并且讨论了一类n阶具有偏差变元的常微分方程解的平方可积性与有界性和一类二阶非线性具有偏差变元的微分方程解的有界性。

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

The traffic momentum differential equation and Euler's equation for the ramp junction is founded by means of differential calculus in this paper,the traffic momentum differential coupled equation is solved by characteristic curve method,two groups of characteristic curves and corresponding related equation in high speedstates and low speedstates are presented.

采用特征线法对运动微分方程组进行分析求解，在高速低密度区和低速高密度区分别得到了两组特征线和对应的特征关系式。

All the compounds are characterized by IR and elemental analysis.we design and prepare a bipyridinium supramolecular compound and six coordination compounds, which are also characterized by IR, elemental analysis and X-ray structure analysis. According to X-ray structure analysis, hydrogen bonds and n-n stocking interactions participate in the architecture of three-dimensional framework [H2L1 (NO3)2 (H2O)2]n; one-dimensional zigzag coordination polymer [Hgl21.5CH3OH]n; binuclear metallamacrocycle (HgI2L2)2 3H2O; helical double-stranded one-dimensional coordination polymer [Co2(L2)2-2CH3OH]n; double-stranded one-dimensional coordination polymer [Co2(L3)2-CH3OH-CH3CN]n; and three-dimensional compound [Cu(C5H4NCOO)2(H2O)2]-H2O with hydrogen bonds, three-dimensional coordination polymer {[Cd(C5H6NCOO)2H2O]-DMF}n, which are indirectly obtained from the precursor ligand L3 through metal ion induced the hydrolysis of diamide and self-assembled with the hydrolyzate.

我们首次合成了一个双吡啶鎓超分子化合物和六个过渡金属配合物，并通过IR谱，元素分析和X-ray晶体衍射分析对它们进行了表征。X-ray晶体结构分析表明：超分子化合物[H_2L1·(NO_3)_2·(H_2O)_2]_n是由多种氢键和芳香环间的π-π堆积作用构建的三维无限结构；[HgI_2(L1)·1.5CH_3OH]_n是一维锯齿状配位聚合物；(HgI_2L2)_2·3H_2O是双核金属大环化合物；[Co_2(L2)_2·2CH_3OH]_n是具有一维双螺旋结构的配位聚合物；[Co_2(L3)_2·CH_3OH·CH_3CN]_n为一维双链结构的配位聚合物；以及由非直线形配体L3在金属离子Cu和Cd的诱导作用下发生水解，并且金属离子与水解产物——异烟酸根离子自组装，形成了三维氢键超分子化合物[Cu(C_5H_4NCOO)_2(H_2O)_2]·H_2O和三维配位聚合物{[Cd(C_5H_6NCOO)_2H_2O]·DMF}_n。

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

A quasi one-dimensional, time dependent system model based on the parallel compressor theory was used to compute the effect of inlet distortion on turbine engine stability; Through Modifying steady state continuum equation, momentum equation and energy equation, the effect of power extraction and additional bleed on turbine engine running line was computed. Unsteady state continuum equation, momentum equation and energy equation were solved for computing the effect of acceleration on turbine engine running line.

其中，进气畸变对发动机气动稳定性影响的计算采用平行压气机模型，基于李亚普诺夫理论的方法完成；附加引气、功率提取对发动机气动稳定性的影响采用通过对发动机转子间质量、动量、能量守恒方程进行修正的方法进行；加速过程对发动机气动稳定性的影响采用欧拉方法求解动态的质量、动量、能量守恒方程的方法完成；最后采用&层迭&的方法进行各种降稳因素的综合评估。

The equation of one dimensional mathematical model i human lung is built. The study is transformed from three-dimensional space one dimensional problem. This paper is base on the test of single breath washout. According the law of Pick and convction-difussion, we have t equation of one dimensional mathematical model.

论文以一次深呼吸氮清洗实验为研究基础，根据Fick定律和扩散对流定律得出一维一层喇叭口模型内气体传输和扩散方程，计算得出的模拟结果肺泡高坡区为一条水平直线，也没有明显的第Ⅳ区域。

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。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。