基本运算

In order to explore solutions to the problem, so the sample students learn to socialist modernization, and further Xuexi Suobi Xu of algebraic, geometric probability and basic knowledge and a rudimentary micro-integration, and forms the basic skills; further developing of thought Nengli , computing power, spatial imagination, the ability to solve practical problems and sense of innovation, from last year, to understand the science ...

为了探索解决问题的办法，使学生在高中阶段学好从事社会主义现代化建设和进一步学习所必需的代数、几何基础知识以及概率统计和微积分的初步知识，并形成基本技能；进一步培养学生的思维能力、运算能力、空间想象能力、解决实际问题的能力和创新意识，从去年起，为了解学。。。本文共有6999字

In this paper, based on the vector analysis and the warping torsion theory of curved thin-walled girders, a set of governing differential equations for the non-uniform torsion of thinwalled spatial helicoid girders is developed.

本文应用矢量运算及薄壁曲线梁翘曲扭转理论，建立了空间螺旋形的薄壁曲线梁基本微分方程，用初参数法解出翘曲扭转微分方程，为进一步进行薄壁螺旋曲线梁的空间结构分析提供理论基础。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

In this paper, we use Extended Cabor Function of simple cells as the basic functional units to have successfully set up a mathematical model of neural network, with the properties of overlap-formed receptive fields and of comparative operation, explaining hyperacuity.

本文用简单细胞广义Gabor函数为基本功能单元，以Marr提出的计算理论为框架，建立了一个感受野重叠的，具有比较运算性质的、可解释超视锐度现象的神经网络数学模型。

All other forces, moments, displacements and rotations can be expressed in terms of these basic unknowns by taking inverse of an operator and using the constitutive relations.

其余的内力、内力矩、位移和转角可通过运算子矩阵求逆和本构关系由这些基本未知量来表达。

Following the basic principles of Kraepelin's Continuous Addition,this study endeavord to work out a Continuous Addition Work Test based on the objective operation pattern developed by Uchida-Kraepelin Psychodiagnostic Test.

本研究遵循克雷佩林连续加算法的基本原则，充分吸收内田—克雷佩林心理测验的长处，参照其客观化的作业方式和操作方法，并加以改进，研究并编制出一套既科学又客观的连续加法运算作业测验，以编制者的名义命名为SK—克雷佩林心理测验。

In the method,based on the traditional ideas of maximal tree clustering method,the dyadic semantic representation is used to process the linguistic assessment information,and the clustering objects are classified.

该方法依据传统的最大树聚类分析方法的基本思想，采用二元语义概念对语言评价信息进行处理和运算，并对聚类对象进行分类，具有概念清晰、计算简单、信息处理较为精确的特点。

We expect it will benefit the industry field to break through the optical measuring limits at present by offering some new ideas. Optical measuring research based on moire interferometry has developed for several decades. The main idea of this research is to utilize the moire effect caused by two superimposed gratings of identical or similar spatial frequency. One is the reference grating and it is a virtual grating created by a computer program in this research; The other grating is the image of grating projected on the measured surface by the DLP projector, and this grating will distort because of the different sloped profile of the surface. To superimpose the program-created grating and the captured distorted grating will derive the so-called moire effect. This research combined the basic theory of optical interferometry and moire effect to project the different phases of the projected grating fringes by the phase-shifting method and compute the principal value of arguments between -π,π. In the end, the phase unwrapping program based on discrete Fourier transform of solving PDEs is used to unwrap the phase of the measured surface, and finally the surface profile is derived by the optical measuring system.

以叠纹干涉术为基础的光学检测研究之发展早已行之有年，而在本研究中所采用的投影叠纹法(Projection moiré)之主要精神在於藉由两道空间频率相近或相同的光栅相互叠加而成的效应，其中一道为参考光栅，而本研究中的参考光栅是以程式产生可调整不同空间频率的虚拟光栅；另一道则为投影至待测物表面的光栅影像，而在起伏高度不一的待测表面上的光栅影像会受到待测物表面起伏状况不同而在观测方向产生光栅投影条纹影像的歪曲变形，将电脑产生的参考光栅与由影像撷取装置所获取投影於待测物表面的光栅影像作叠合，便会产生所谓的叠纹效应；利用基本的光学干涉理论与叠纹效应结合，本研究中以相移法来改变投影於待测表面的光栅相位，再以相移法的理论反运算出在带有待测面各点高度资讯之介於-π，π相位主幅角，再以离散傅立叶转换解偏微分方程的相位重建程式还原待测面的相位值，以得知待测面之表面轮廓。

Disjunction normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

研究了模态逻辑系统S5中的析取范式定理的归纳证明，给出了在S5中用深度至多等于1的最简模态公式通过析取与合取运算表示含有多重模态词的公式的方法，作为范式定理的应用，讨论了知识库中的一个基本问题，证明了知识库能够回答KB命题式问题的充要条件是该知识库能够回答相关的非模态命题及其否定命题的问题。

Secondly, Study the basic concepts, theorems , fundamental nature and the computing formula of the interval number.

2研究了区间数有关性质概念、定理的基本性质及运算公式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。