查询词典 equations

Main contributions and achievements are as follows:A general non-equilibrium rigorous model for RDP is developed in this thesis. Based on the pseudo-homogenous assumption, two main factors reaction and separation are de-coupled, and an RDP model with the same format as that for a traditional distillation process is established. To solve the model with a large number of algebraic equations, modified M-K equations with tri-diagonal matrix form are developed based on the improved Separation Efficiency Functions, which greatly increases the iteration efficiency. This thesis also develops a general reactive distillation dynamic model. Through splitting of the differential variables based on SEFS, large-scaled differential algebraic equations can be solved with the improved Gear's algorithm which makes the dynamic model suitable for the on-line application. A simulation platform for the control loop design and evaluation of RDP by introducing control system equations into the dynamic model is also developed.A lactic acid purification pilot-scale RDP is investigated.

论文对热点问题——反应精馏过程的建模与优化控制相关技术进行了深入的研究，取得了一系列成果：1、建立了反应精馏过程机理模型，基于拟均相假设，将反应和分离过程进行解耦，推导出反应精馏过程的非平衡级稳态模型和动态模型，通过引入推广的分离效率函数，对模型变量进行了合理划分，显著提高了模型求解效率；将动态模型和控制系统方程结合，建立了反应精馏过程控制系统研究的辅助工具。2、全面分析了乳酸提纯反应精馏新工艺试验装置，利用本文建立的过程机理模型，对该试验装置进行了稳态和动态性能分析及水力学核算；设计和分析了单边质量控制方案，比较了间接和直接物料平衡控制两种方案的控制性能。

Since the different dynamics methods such as Newton-Euler method, Lagrange's equations and other methods can be used to develop the dynamic equations of global system, the two different forms of the dynamic equations are ordinary differential equations and differential algebra equations.

通过结合有限段法和多体系统动力学离散时间传递矩阵法，形成了非线性梁有限段离散时间传递矩阵法，该方法保留了有限段法适用于几何非线性大变形分析、自动考虑动力刚度项等优势，又保留了DT-TMM-MS建模方便灵活的特点。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

This course consists of three parts : A.The fundamental theory of gyroscopes. a.Kinematics and dynamics of gyroscopes, consisting of Coriolis acceleration, theorem of angular momentum, Euler's dynamical equations, dynamical explanation of gyroscopes' properties. b.Gyroscopes' motion equations, including the complete equations, technical equations and precession equations derived from Euler's dynamical equations, and the technical equations derived from static vs. dynamic method. c.Analysis of gyroscopes' motion. d.Coordinate systems and their mutual transformation. e.Gyroscope drift and its measurement. B.Principle of typical gyroscope instruments, such as gyro compass, gyro north finder, gyro horizon, platform compass, rate gyroscope and integrating gyroscope. C.Principles and applications of new-type gyroscpes, such as electrically suspended gyro, ring laser gyroscope, fiber optical gyroscope, hemispherical resonator gyro, dynamically tuned gyroscope and micro inertial sensors.

本课程教学内容由三部分组成：陀螺仪的基本理论，内容包括：陀螺力学基础（哥氏加速度、角动量定理和欧拉动力学方程、陀螺特性的力学解释）；陀螺仪运动方程和运动分析（用欧拉动力学方程建立完整方程、陀螺仪运动的技术方程和进动方程，用动静法建立技术方程）；坐标系及其变换；陀螺仪的漂移及其测试；典型陀螺仪器（包括陀螺罗经、陀螺找北仪、陀螺地平仪、平台罗经、速率陀螺仪和积分陀螺仪等）的工作原理；新型陀螺仪（包括静电陀螺仪、激光陀螺仪、光纤陀螺仪、半球谐振陀螺仪、挠性陀螺仪、微机械陀螺仪等）的原理及应用。

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。

The topics to be covered in the course are Integration and Economics Applications, Linear, First-Order Difference Equations, Nonlinear First-Order Difference Equations, Linear Second-Order Difference Equations, Linear First-Order Differential Equations, Nonlinear First-Order Differential Equations, Linear Second-Order Differential Equations, Simultaneous Systems of Differential and Difference Equations, and Optimal Control Theory.

讲授内容包括积分与经济的应用、线性一阶差分方程式、非线性一阶差分方程式、线性二阶差分方程式、线性一阶微分方程式、非线性一阶微分方程式、线性二阶微分方程式、差分与微分的联立方程式、最适控制理论。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

The nonparallel linear stability of the two-dimensional and three-dimensional disturbance waves are studied by the parabolized stability equations.

采用抛物化稳定性方程(Parabolized Stability Equations，PSE)研究了非平行流边界层二维、三维扰动波的线性稳定性问题。

Any high Re number flow over bodies consists of three basic flows: the flow with convection-dominant in all spatial directions, the flow with convection-diffusion competition in all directions and the flow with convection-dominant in part directions and convection-diffusion competition in part directions, which is called the interacting shear flow; the features of the three basic flows are different; their simplest conservation equations, i.e. the Euler equations, Navier-Stokes equations and diffusion parabolized NS equations, have different mathematical characteristics; there is a great disparity in domains of the three basic flows and the domains of NS equations are very small. Therefore, adopting Euler-DPNS-NS equation system to analyze and compute high Re number flows over bodies is a logical approach. There exists a mutual examined-complemented relationship of this approach with the usual one of adopting only NS equations.

主要内容如下：（1）高Re数绕流包含3种基本流动：所有方向对流占优流动、所有方向对流扩散竞争流动和部分方向对流占优部分方向对流扩散竞争流动，3个基本流动的特征彼此不同且在流场中所占领域大小彼此相差悬殊，NS方程区域很小，它们的最简单控制方程组Euler、Navier-Stokes和扩散抛物化NS方程组的数学性质彼此不同，因此利用Euler-DPNS-NS方程组体系分析计算高Re数绕流流动就是一个合乎逻辑的选择，该法与利用单一NS方程组的常用方法可以彼此检验和补充。

The masticatory mucosal thickness was measured in the hard palate by "bone sounding". A multiple regression model using the generalized estimating equations method was constructed to analyze the site-level data to investigate the association of the palatal mucosal thickness with the five selected factors and to analyze specifically differences among the 15 measurement points at site level.

收集43位台湾成人包括23位男性和20位女性（年龄从26岁至68岁），於硬颚区犬齿到第二大臼齿位置，每颗牙距离牙龈边缘4mm、8mm、12mm处，用牙周探针穿刺法来利量共15个点的黏膜厚度，并利用Generalized estimating equations method来进行统计分析。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。