查询词典 dimensional equation

The problems of point - line - plane - volume; the facts of square - circle - triangle; the mysteries of central - peripheral - frontal - oblique - concave - convex; the right angle and perpendicular; of scale and position; the interest in post- lintel, wall-slab, vertical-horizontal; the arguments of two-dimensional and three-dimensional space; the extent of a limited field; the meaning of implied extension; the meaning of plan, of section, of spatial expansion - spatial contraction - spatial compression - spatial tension; the direction of regulating lines, of grids; the relationships of figure to ground, or number to proportion, of measurement to scale, of symmetry to asymmetry, of diamond to diagonal; the hidden forces, the ideas of configuration; the static, the dynamic: all these begin to take on the form of a vocabulary.

点-线-面-体的课题；正方形-圆形-三角形的事实；中央-边缘-正对-倾斜-凹入-凸出的奥秘；直角与垂直；尺度与位置；柱-梁、墙-板、竖直-水平的旨趣；两维与三维空间的思辩；局促场所的极限；暗示延伸的含意；平面、剖面、空间扩充-空间收缩-空间挤压-空间张拉的意义；控制线与网格的方向；图与底、数字与比例、尺寸与尺度、对称与非对称、菱形与对角线的关系；暗藏的力量、构型的想法；静态、动态━这一切都将发展成为语汇的形式。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

In addition,the authors propose that for a multi peaked one dimensional search problem its optimum solution can be obtained by ordinary optimization methods only when the convexity or concavity of the objective function matches the step length determining the one dimensional search region and the method of finding the optimum step length factor.

另外 ，还提出了对于多峰一维搜索问题，只有当所求函数的凹凸性与确定一维搜索区问题的步长以及求解最优步长因子的方法匹配时，才能用一般方法得到搜索区间内的最优解

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

Construct the three-dimensional manifold element covering hexahedron, provide cover displacement function, strain matrix, stiffness matrix and stress matrix of the three-dimensional manifold element by the previous research work.

6在前人研究的基础上，构造了六面体有限覆盖的三维流形单元，推导了三维流形单元覆盖位移函数、应变矩阵、刚度矩阵、荷载矩阵等表达式。

It can get the three-dimensional profile of the object surface effectively. Because of the cragginess of the three-dimensional surface when sine grating is projected the image of the sine grating is modulated and the modulated image is taken by a CCD camera with an angel compared to projecting direction. After the phase shift measuring method, the phase is gotten. Because the phase is calculated by the phase shift measuring ranges from –π to +π it isn't continuous. The phase unwrapping is necessary to recover the continuous phase about the object shape.

这种方法采用结构光照明，将正弦光栅图像投影到被测物体表面，用与投影方向成一定角度的CCD摄像机获取受物体表面面形调制的变形光栅像，根据数字相移算法计算出相位分布，由于从相移计算的相位被截断在反三角函数的主值范围内，因而是不连续的，必须通过相位展开恢复出连续相位分布，由相位－高度关系最终求出物体轮廓的三维数据信息。

A three-dimensional anisotropic etch rate distribution of Si can be described by two-dimensional etch rate distribu-tions in a series of crystal planes.

硅各向异性腐蚀速率三维分布可由一系列晶面上的二维腐蚀速率分布表示。

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

Firstly, the concepts of dimensional element and dimensional element-chain are defined, and a geometric tolerancing model expressed by DE and its semantic mapping are also given. Secondly, the construction of DEC, the geometric measuring method for the calculation of error transfer coefficients of dimension-chain components and the realization of DECA are proposed.

首先定义尺素和尺素链等概念，并在此基础上建立尺寸公差的尺素表示模型及其语义映射；然后给出尺素链构造方法、计算误差传递系数的几何度量方法以及尺素链分析的实现方法。

By using the decomposability of graph, high-dimensional problem can be decomposed into some low-dimensional problems, and then we can analyze the independence relation, time sequence relation and causal relation among random variables by means of visual structure of graph.

利用图的可分解性，可将高维问题分解成低维问题，并借助图的直观结构对随机变量间复杂的独立性关系、时序关系或因果关系进行分析。

Aquatic or marsh-growing fern allies; known to have existed since the Cenozoic; sometimes included in Lycopodiales.

生活于水中或湿地的蕨类；从新生代生存至今；有时归于石松目之中。

The engine was uprated from a 90hp Franklin to a 125hp Lycoming.

改良过的引擎是从90hp到125hp莱康明富兰克林。