系数问题

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

This paper is mainly the dynamic input-output model that the time lag is one, which is base on the above models. After studying, we consider stochastic factor step by step in it, namely when consumption coefficient matrix is stochastic (when investment matrix is stochastic, it is almost same. So we dont research it), and they are both stochastic, then we research the stable increase solution. We utilize the means of the modern stochastic analysis and Markov process, that the stochastic dynamic input-output model don not exist the stable solution is proved. Namely, economic system must is adjusted constantly. The probability that the collapse time of the economic system is o is one.

本文对在上述基础上构造的一类时滞为1的动态投入产出模型，进行了深入研究，将随机因素逐步考虑进去，即对投入产出消耗系数矩阵为随机的情况(投资系数矩阵为随机的情况与投入产出消耗系数矩阵为随机的情况大致相同，这里就不再证明)，以及二者同时为随机矩阵时所得到的动态投入产出模型的稳定增长解问题，利用现代概率分析及马氏过程的工具，证明了不存在随机动态投入产出模型的稳定增长解；即投入产出模型反映的经济系统必须经常进行调整，其崩溃时间为无穷大的概率为零。

This article analyses the application conditions of freezing method, current research status and the problems in this field. It points that it's necessary to study deep freezing temperature field deeply and discusses the factors which influence the freezing wall such as soil's nature, moisture content, geological conditions, etc. It introduces the theory, process of freezing method, the distribution of temperature field of freezing method and key thermotics parameters influencing freezing temperature field. It simplifies the deep freezing temperature field model. Through ANSYS, this article founds the deep freezing temperature field model, and simulates the field on vary heat conductivities. It analyzes the results of ANSYS simulation, gains the theoretical value of thermometric holes which is needed by back-analysis. Using the simulation temperature and actual value, it gets the equivalent heat conductivity. Then it solves the deep freezing temperature field by the equivalent value, simulates the freezing wall development process and temperature change curve. Against the actual project, the results are favorable.

文中分析了冻结法施工的应用条件，目前对冻结法施工的研究现状和在此领域内存在的问题，指出了对深土冻结温度场进行深入研究分析的必要性；对影响冻结壁形成发展的因素如冻土土性、含水量、地质条件及施工方法等因素进行了论述；对冻结法施工的原理、过程，冻结法温度场的分布情况，影响冻结温度场分布的主要热学参数进行了综述；对深土冻土温度场模型进行了合理的简化，通过ANSYS大型有限元分析软件，建立了深土冻结温度场的模型，对不同导热系数情况下的深土冻结温度场进行了模拟；对ANSYS的模拟结果进行了定性的分析，通过对ANSYS结果的后处理取得了反分析时需要用到的测温孔理论温度值；经过对测温孔模拟温度值和实测温度值的分析，得到了冻结温度场的等效导热系数；使用等效导热系数对深土冻结温度场进行了求解，模拟了冻结壁发展情况和温度场中的温度变化曲线，用所得结果对比工程实际情况，取得了较好的效果。

This article analyses the application conditions of freezing method, current research status and the problems in thisiold. It, points that it" s necessary to study deep freezing temperature field deeply and discusses the factors which influence the freezing wall such as soil" s nature, moisture content, geological conditions, etc. It introduces the theory, process of freezing method, the distribution of temperature field of freezing method and key thermotics parameters influencing freezing temperature field, it simplifies the deep freezing temperature field model. Through ANSYS, this article founds the deep freezing temperature field model, and simulates the field on vary heat conductivities. It analyzes the results of ANSYS simulation, gains the theoretical value of thermometric holes which is needed by back analysis. Using the simulation temperature and actual value, it gets the equivalent heat conductivity. Then it solves the deep freezing temperature field by the equivalent value, simulates the freezing wall development process and temperature change curve. Against the actual project, the results are favorable.

文中分析了冻结法施工的应用条件，目前对冻结法施工的研究现状和在此领域内存在的问题，指出了对深土冻结温度场进行深入研究分析的必要性；对影响冻结壁形成发展的因素如冻土土性、含水量、地质条件及施工方法等因素进行了论述；对冻结法施工的原理、过程，冻结法温度场的分布情况，影响冻结温度场分布的主要热学参数进行了综述；对深土冻土温度场模型进行了合理的简化，通过ANSYS大型有限元分析软件，建立了深土冻结温度场的模型，对不同导热系数情况下的深土冻结温度场进行了模拟；对ANSYS的模拟结果进行了定性的分析，通过对ANSYS结果的后处理取得了反分析时需要用到的测温孔理论温度值；经过对测温孔模拟温度值和实测温度值的分析，得到了冻结温度场的等效导热系数；使用等效导热系数对深土冻结温度场进行了求解，模拟了冻结壁发展情况和温度场中的温度变化曲线，用所得结果对比工程实际情况，取得了较好的效果。

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。

In the fourth, the formulation for anisotropically undrained strength is used in the theory of slip lines for evaluating the bearing capacity of strip footings placed on the anisotropically consolidated clays The bearing capacity factors and correction factors for strength anisotropy can be given for various shear tests.

针对不同试验条件下各向异性地基承载力系数与各向同性地基承载力系数的差异，考虑不排水剪强度的修正问题，导出不排水剪强度各向异性修正系数。

In this paper, a new conflict coefficient is presented. First, the deficiency of the classical conflictive coefficient is analyzed. Then, the distance function between evidences is introduced. A new model to represent conflict is constructed with the distance function and the classical conflictive coefficient. Finally, numerical examples verify the efficiency of the proposed method.

针对这一问题，首先分析了证据理论中经典冲突系数的不足，引入证据距离函数表示证据之间的差异性，结合经典冲突系数一起提出了一种新的证据冲突表示方法，克服了经典证据理论冲突系数的不足，能更有效地度量证据的冲突程度，最后通过算例验证了该方法的有效性。

In chapter Ⅰ, a historial review of structure control is given; In chapter Ⅱ, A discussion of the controllability and observablity of flexible structures is given, Two kinds of controllability and observablity index are defined, and applied to actuator allocation; chapter Ⅲ considers the reduction of high order flexible structure mode; the content of chapter Ⅳ is about the basic problem of distributed parameter control system design. It is proved that a stable controllor in mode space may be unstable in real use in distributed paramater systems, also, by closed loop mode concept, a pole assignment method of flexible structure controllor design is given; chapter Ⅴ is about the low-authority controllor design, it is pointed out by use of high order eigenvalue/eigenvector perturbation, a better controllor can be designed; chapter Ⅳ considers flexible structure reduced order control; chapter Ⅶ disscusses the basic problem of flexible structure computer control, analyses discreate controllablity and observablity and its computing, the sample period and coefficient wordlength; chapter Ⅷ is on the problem of low flexibility compensation; chapter Ⅸ is a design example.

在第一章简要回顾了挠性结构控制的历史，并且指出控制中的一些问题；第二章讨论了挠性结构的能控性与能观性，定义了两类能控性程度和能观性程度指标，还将能控性程度概念应用于执行器位置的确定；第三章论述了高阶模型的降价问题，比较了适于挠性结构模型降阶的方法，指出其适用范围；第四章内容是分布参数系统设计的基本问题，首先证明在模态空间中设计的稳定的控制器在实际分布系统上可能是不稳定的，进而根据闭环模态的概念，获得挠性结构控制器设计的极点配置方法；第五章的内容是关于低权控制器的设计问题，指出利用特征值高价摄动和特征向量的摄动，可以设计出更加完善的低权控制器；第六章讨论挠性结构降阶控制问题；第七章讨论挠性结构计算机控制的基本问题，分析了时间离散化模型的能控性和能观性及其计算问题，讨论了采样周期选择和系数字长问题；第八章讨论低挠性结构的补偿问题；第九章的设计例子用来说明第二章和第四章的结果。

In order to improve the accuracy of the existing transformation ratio model of the hydraulic transformer, a mathematical model is established by introducing the friction coefficient, the viscous drag friction coefficient and the laminar leakage coefficient.

为解决已有的液压变压器变压比模型与实际结果偏差较大的问题，通过对实际工作过程中不应忽略的摩擦与泄漏损失进行研究，引入机械摩擦损失系数、黏性摩擦损失系数和层流泄漏系数，建立了液压变压器变压比模型。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。