查询词典 finite dimensional operator

In practice, such systems are simplified as finite dimensional systems, and then treated via existing finite dimensional control theory.

在工程应用中大多采用有限维近似模型，并应用现有的有穷维控制理论进行处理。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

Firstly, the study of the mechanical model. The three-dimensional finite element model is established, and it is condensed into M-dof interlamination structural model. The structural dynamic analysis is implemented by use of three-dimensional finite element model and M-dof interlamination structural model.

本文通过严谨的数学推导，得出"力学不耦合"的超高层结构顺风向和尾流旋涡干扰引起的横风向振动随机响应公式，并编制了相关计算程序，深入研究了应用随机振动理论进行结构风振反应分析的方法。

Methods One normal adult male was choosed, and his left elbow joint performed in pronation and extention position was scanned by spinal CT, and the two-dimensional image was dealed with Mimics 1 0 software, the three-dimensional finite element model was built up by Abaqus 6.7 software. Finite element calculation was performed to simulate the impact of 1 000 N on the elbow joint, and the stress distribution in the radial head and coronoid were analyzed.

选取1名正常成年男性为研究对象，使其左肘关节处于旋前伸直位，行螺旋CT断层扫描，得到CT数据二维图像，采用Mimics 10.0软件系统处理，利用Abaqus 6.7建立肘关节三维有限元模型，模拟施加1000 N冲击载荷，分析冠状突及桡骨小头内应力分布情况。

The results of numerical analysis show that the elastic modular and the poisson ratio have no effect on two-dimensional bearing capacity, but can affect the ultimate bearing capacity of three-dimensional foundations and control the convergence and precision of finite element calculation; the earth pressure coefficient controls the geostatic stress of foundation, sequentially affects the ultimate bearing capacity of foundations and the convergence of numerical calculation. When calculating the ultimate bearing capacity of undrained saturated foundation, the complete formulation exists shear locking, and reduce formulation exists hourglassing, so the hybrid formulation is suitable to imitate the geomaterial. When the soil obeys nonrelevent flow rule, the yielding function is different from potential function, and the elastic-plastic matrix of soil is asymmetric, so the unsymmetry numerical solver and appropriate finite element mesh is required.

研究结果表明，土体弹性模量和泊松比对二维基础极限承载力没有影响，但是影响着三维矩形基础的极限承载力，控制着ABAQUS数值算法的计算精度与收敛速度；地基土压力系数控制着地基土体中的地应力平衡，从而影响着二维条形基础和三维矩形基础的极限承载力和地基破坏包络面；对于不排水饱和软黏土地基，常规的完全积分单元会造成剪力自锁现象，而减缩积分单元则存在过于柔化的现象，故采用杂交单元来模拟较合适；当土体服从非关联流动法则时，屈服函数与塑性势函数之间存在差异，从而导致土体弹塑性矩阵呈现非对称性，在有限元计算中必须采用非对称数值解法，并且合理地划分单元才能对极限承载力进行准确求解。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory.

本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

There are fourteen chapters, including introduction, plane stress and plane strain, two-dimensional problems in rectangular coordinates, two-dimensional problems in polar coordinates, photoelastic and moire experimental methods, two-dimensional problems in curvilinear coordinates, analysis of stress and strain in three dimensions, general theorems, torsion, bending of bars, axisymmetric stress and deformation in a solid of revolution, thermal stress, the propagation of waves in elastic solid media, at last there is an appendix on the application of finite-difference equations in elasticity.

全书共十四章，包括绪论、平面应力和平面应变、直角坐标中的二维问题、极坐标中的二维问题、光弹性与云纹实验方法、曲线坐标中的二维问题、三维应力和应变问题、一般定理、简单的三维弹性问题、扭转、杆的弯曲、回转体中的轴对称应力和变形、热应力、弹性固体介质中波的传播，最后有一附录，讲述差分方程在弹性理论中的应用。

Chapter 5 and 6 are concentrated on the fundamental problem how to con-struct finite-dimensional and infinite-dimensional Liouville integrable Hamiltonsystem.Starting from two isospectral problems,Tu's scheme is applied to gen-erate the corresponding CKdV hierarohy and coupled Burgers hievachy,andthey are shown to be Liouville integrable Hamilton systems.Two spectral prob-lems,which contain three and four potentials respectively,are also studied byTu's scheme.Two new Liouville integrable Hamilton hierarchy are estab-lished.A new general approach using Lenard's gradient sequence is presentedto obtain Lax integrable hierarchy and their zero curvature representation,andsome examples are given.The nonlinearization procedure is applied to theeigenvalue problem of coupled Burgerrs hierarchy.It is shown that underBargmann constraint,the spatial part of the Lax pairs is nonlimearized to be afinite-dimensional Liouville completeiy integrable Hamilton system.

第五、六章研究如何从一个谱问题出发构造可积发展方程族及其零曲率表示、Hamilton结构和判断Liouville可积性：通过对二类具有2个位势的等谱问题直接研究，利用屠格式生成了耦合KdV族和耦合Burgers族，并证明它们均为Liouville可积的广义Hamilton方程族；而通过分别具有3个和4个位势的等谱问题，遵循屠格式构造了二族新的Liouville可积的广义Hamilton方程族；给出了利用Lenard梯度递推序列产生发展方程族及其零曲率表示的一种方法，作为应用，讨论了CKdV族，BPT族及耦合Burgers族的产生及其零曲率表示；应用非线性化技巧，证明了在Bargmann约束下，耦合Burgers族的Lax组可被线性化为Liou-ville完全可积的Hamilton系统。

Mandibular teeth and sustentacular tissues extracted from a healthy adult were treated using CT scanning to obtain two-dimensional image, and then a three-dimensional image was established using computer reconstruction technique. Simultaneously, a three-dimensional finite element model of rigid fixed bridge was established in abutments with mandibular 56 deletion.

采用CT扫描获取健康成人下颌牙及其支持组织的二维图像，通过计算机重建技术建立三维立体图像并获得了下颌56缺失后的双端单基牙固定桥的三维有限元数学模型。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。