查询词典 finite dimensional

This article mainly simulates gradually damage destruction process of rock, major in determinationg the definition of rock three-dimensional damage tensor, simplify to the damage tensor and obtain its engineering calculation method, and obtains the basic expression form of equivalent stress by equivalent stress assumption, symmetrization to the actual stress, thus obtains construction relation of the festival principle of three-dimensional damage rock mass, finally couples elasticity- plasticity with damage in the finite element equation, with reference to elasticity-plasticity gradually degenerated method thought, simulates rock damage to advance gradually the destruction process in finite element method, draws up elasticity - plasticity and damage coupling two-dimension finite element procedure with the C language in the VC contact surface, by simulating experiment destroyed process, acquires destruction image and the axial load distortion curve of model, agreement with the experimental result.

本文主要模拟岩石渐进损伤破坏过程，确定岩石三维损伤张量的定义，对损伤张量进行简化计算并得出其工程计算方法，采用等效应力假设得出有效应力的基本表达形式，对有效应力进行对称化，得出节理损伤岩体的三维本构关系，在有限元方程中实现弹塑性和损伤耦合；借鉴弹塑性渐进退化方法的思想，采用有限元的方法模拟岩石损伤渐进破坏过程，用C++语言在VC界面编制了弹塑性和损伤耦合的二维有限元程序，通过模拟已有的实验破坏过程，得出模型的破坏图像和轴向荷载变形曲线，与实验结果基本一致。

Quadratic finite volume element method s for the air pollution model in one-dimensional;2. The two-grid algorithm of the finite volume element method for second-order indefinite elliptic problems;3. A fally discrete finite volume element method is given for one-dimensional two-phase incompressible flow in porous media.

在初始网格剖分上采取分段线性函数空间作为有限体积元方法的试探函数空间，在相应的对偶网格上采取分段常数函数空间作为其检验函数空间，对一维不可压缩两相渗流驱动问题提出了全离散有限体积元方法，并得到L2-模误差估计。

This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.

回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。

The inconsistencies of dimensional reduction and naive dimensional regularization in dealing withChern-Simons-matter theory are analyzed.The consistent dimensional regularization combiningwith higher covariant derivative regularization is adopted to consider Chern-Simons field theorycoupled to complex scalar and spinor field.All the local parts of one-loop two-point functionsand three-point functions are computed.Slavnov-Taylor identity is combined with these explicitcalculation results to give the one-loop local effective action.The finite gauge invariant quantumcorrection is shown and finite wave function renormalization constant for each field is defined.Thelocal part of one-loop three gauge field vertex is especially evaluated and it is verified that thereexists a renormalization choice compatible with BRST symmetry.

然后计算了所有的两点函数和三点函数单圈修正的定域部分，利用S-T恒等式给出了单圈定域有效作用量，定义了场的重正化常数，发现物质场和规范场都存在有限的规范不变的量子修正，并讨论了这些有限的规范不变的量子修正的物理意义，进而通过考察单圈三规范场顶角，表明存在与BRST对称性相容的重正化选择。5、在背景场方法的框架下，选择高阶协变导数正规化与维数正规化的杂化正规化方案计算了背景场两点函数的两圈量子修正，结果表明，标志紫外发散的极点项恰好抵消；进一步利用背景场方法中明显的规范对称性，证明背景场三点函数的两圈图贡献也是有限的。

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. The key techniques used in numerical simulation of the three-dimensional extrusion from dies such as decision of boundary conditions, creation of initial velocity field, selection of penalty factor, high Weissenberg number problem , regeneration of the free surface were studied in detail.

中文题名聚合物异型材口模挤出三维流动研究副题名外文题名 Study on three-dimensional flow of polymer melts during the process of profile extrusion from dies 论文作者涂志刚导师柳和生包忠诩教授学科专业材料加工工程研究领域\研究方向学位级别博士学位授予单位南昌大学学位授予日期2001 论文页码总数148页关键词挤出成型聚合物材料挤出口模聚合物异型材馆藏号BSLW /2003 /TQ320 /9 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。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

This thesis begins with a problem which appears when applying Graphic Design to the three-dimensional space, giving an analysis on the visual apperceiving orderliness of two-dimensional, three-dimensional and four-dimensional, then tries to talk about the possibility of the crossing, superposition and transformation among Graphic Design, Three-dimensional space Design and Tridimensional Design.

论文从平面设计在空间中应用时出现的问题入手，对视觉的二维、三维、四维的感知规律进行分析，探讨平面、立体、空间设计语言的交叉、重叠与转换的可能性。

The method is realized via the following steps: first to apply Isomap or LLE to get the embeddings of the original data set in the low dimensional space; then to obtain support vectors, which are the most significant and intrinsic data for the final classification result, by using support vector machine on these low dimensional embedding data; subsequently to get support vectors in the original high dimensional space based on the corresponding labels of the obtained low dimensional support vectors; finally to apply support vector machine again on these high dimensional support vectors to gain the final classification discriminant function.

数据挖掘是数据库知识发现中最重要的步骤之一，其目标是从获取的数据中高效准确地挖掘出我们所需要的信息。在实际应用中，数据往往呈现海量、高维、非线性等特性，这些特性给数据挖掘带来了很多问题，例如海量特性导致的计算效率低下问题、高维特性带来的维数灾难问题和非线性特性引起的线性模型失效问题等。幸运的是，实际中高维数据的属性之间往往存在一定的规律性和相关性，即实际数据经常存在着外在与内在两个维数。

Using finite fields , the classical groups give rise to finite groups , intensively studied in relation to the finite simple groups ; and associated finite geometry , which has both combinatorial and algebro-geometric sides.

利用有限领域，古典的群体产生有限的群体，深入研究有关的有限简单群体；及相关有限几何，这两个组合和algebro几何双方。

The number of polynomial function over a finite commutative ring. This paper is on the basis of the research for the first question.With the structure of finite commutative ring,we know that a finite commutative ring can be expressed by direct sum of some finite commutative local rings.

本文主要基于对问题一的研究，并由有限交换环的构造可以知道，有限交换环可以由一些有限交换局部环的直和表示，于是就将问题简化到对有限交换局部环上多项式的判定。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。