三四面体

Each atom behaves like a tiny bar magnet, and when the crystal is cooled to near absolute zero, the atom-magnets align.

有时候，四面体四个角中的三个排列在一起，使得四面体的中心产生磁单极子。

Nutlets 4, semiglobose-tetrahedral or subulate trigonous-tetrahedral, shiny, glabrous or pubescent, rarely tuberculate, adaxial 3 surfaces subequal in size or bottom smaller than 2 lateral surfaces, longitudinal vein at juncture of 2 lateral surfaces, sessile or with a short carpophore from corner of 3 adaxial surfaces, abaxial surfaces flattened or convex, acute or obtuse ribbed, rarely narrow winged; attachment scar at bottom of carpophore or at corner of 3 adaxial surfaces when sessile.

小坚果4，三棱四面体，发亮的半球形四面体或钻形，无毛或被短柔毛，具瘤，正面3 表面大小近等或者最后的小于2侧面的很少，在2侧面的接合的纵向脉，角落的3正面的在底部附件痕的果瓣柄或什么时候无梗。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

The variable geometry truss mechanisms have been studied extensively and systematically by this project. The research plan has been completed all sidedly, and expected results have been obtained. Three new kinds of combination decahedrons and a new class of variable geometry truss mechanism, which is composed of an octahedron and three tetrahedrons connected in parallel form, are proposed. The position analyses for decahedrons, dodecahedrons, triple-octahedrons, combinations decahedron and a new type of structure of variable geometry truss mechanisms are presented by introducing additional extra linear displacement sensors and using resultant elimination and homotopy continuation algorithms. The method of kinematical analysis of variable geometry truss mechanisms is established.

课题组对变几何桁架机构进行了深入的研究，全面地完成了研究计划，取得了预期的成果；提出了三种新的十面体组合机构以及由一个八面体和三个四面体组成的新型变几何桁架机构的结构形式；应用结式消元、附加传感器和同伦方法等提出了十面体、十二面体、三重八面体、组合十面体和新型变几何桁架机构的位置分析方法；建立了变几何桁架机构运动分析的一般方法；建立了简洁的凯恩和拉格伦日动力学的模型；应用有限元和子结构方法，提出了变几何柞架机构弹性动力学模型，导出了逆动力学方程的显式形式；设计和研制了一台可折叠的八面体变几何杵架机构装置等。

Then loading the models in both feet standing body posture, gain stress distribution figures of the models, record stress numerus of weight bearing dome, anterior wall and posterior wall in condition of different areas posterior wall fractures. Results 1、Normal 3D finite element model of acetabulum Obtain 3D visible model of pelvic by restituting CT fault images with Mimics10.01; gain 3D visible model of haunch bone by splitting the pelvic model with FreeForm software.

结果 1、正常髋臼三维有限元模型通过Mimics10.01软件对骨盆断层CT图像进行三维重建，获得骨盆三维可视模型；然后在FreeForm软件系统中对模型进行修饰，平滑模型表面，设定各受力面与界线；并成功截取出髋骨三维可视模型；再将模型导入Ansys8.0中进行各部分材料赋值及网格划分，建立了正常髋臼三维有限元模型，共含节点69440个，三维四面体单元45209个。

By means of estimates for three-dimensional discrete derivative Green's function , the theory of the interpolation operator of projection type and the technique of cancellation of elements, for several usual elements in the three-dimensional setting, including rectangular parallelepiped elements, tetrahedr.

借助三维离散导数Green函数的估计，投影型插值算子理论和单元合并技术，本文详细讨论了几种常用三维单元(包括长方体元，四面体元和三棱柱元)的有限元解梯度的最大模超逼近，均获得了高精度的超逼近结果。

The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial maps are discussed and proved.

从理论上分析并证明了三维多项式映射满足等变的条件，精确地给出了关于正四面体群和正八面体群具有旋转不变对称性的两类三维等变映射的具体公式，在此基础上讨论并证明了三维多项式映射的广义Julia集所具有的性质。

This structure took threefold-symmetric Bricard linkages,composed of six tetrahedrons,as fundament,and implemented retractability through tetrahedrons' rotation around the adjacent hinges.

这种结构以6个四面体构件形成的三向对称环形连杆机构为基础，通过四面体绕相邻铰转动实现结构的闭合和开启。

The conception of the edge element was firstly proposed by Whitney in 1957. At the beginning of 1980\'s, Bossavit and Verite put it to practical application to three-dimensional eddy-current problems. In 1987, Barton and Cendes applied the tetrahedral element to three-dimensional magnetic calculation.

棱边元的构想，最早由Whitney在1957年提出。80年代初期，Bossavit和Verite将四面体棱边元应用于三维涡流问题，1987年，Barton和Cendes将四面体棱边元首次应用于三维磁场计算揭开了基于棱边的有限元方法在电磁问题中应用的序幕。

Cutting process of soft tissue and organs is very important in virtual surgery simulation. Tetrahedron is widely used to construct the geometric model of virtual organs. Efficient methods must be developed to split or merge tetrahedrons in order to adapt to topology changes during cutting process. The main parts of this thesis are the two chapters on "Reconstruction of Tetrahedrons" and "Stability of Tetrahedrons".Main research work I have done is listed as follows:1 Reconstruction of Tetrahedrons.

人体软组织及器官的切割仿真是虚拟手术仿真的重要组成部分，软组织及器官的几何模型普遍采用四面体模型，切割的同时，软组织及器官的拓扑结构发生变化，模型中的部分四面体基元必须能够通过分裂或合并以适应上述变化，医学数据在三维场景中的交互和可视化是手术仿真的基本要求，因此，第二章&四面体重构&以及第三章&四面体单元稳定性&是本文重点讨论的两个部分。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐