四边形

The quadrature formula about surface integral on any quadrilateral element is deduced by means of isoparametric transformation and bilinear interpolation.

通过对三维有界区域的边界曲面作四边形网格剖分，用有限元方法处理高斯公式中的曲面积分，由等参变换及双线性插值导出任意四边形单元上曲面积分的数值求积公式。

Secondly, for the boundary correspondence of affine stretch on hyperbolic regions, we prove that the above conclusion is also true. Finally, we pose a sufficient and necessary condition for the same conclusion.

最后利用退化的四边形序列，给出了拟对称同胚的极值拟共形延拓的最大伸缩商、四边形模之比的上确界及拟对称同胚的边界伸缩商三者相等的一个充要条件。

In Euclidean plane geometry terms, being a parallelogram is : affine transformations always take one parallelogram to another one.

用欧氏平面几何术语，平行就是：仿射变换总是将一个平行四边形变成另一个平行四边形。

In this article, aiming at a kind of elliptic problem, three types of preserving-symmetry finite volume schemes under quadrangle partition grids are firstly established . During the course of the establishing, the" vertex-centered" control volume are selected and the balance-equation is discretized by utilizing the finite volume element method.

本文首先对自共轭椭圆问题，在四边形剖分下，通过选取"vertex-centered"类型的控制体，并利用有限体积元方法对平衡方程进行离散，首次建立了四边形剖分下的三种保对称的有限体格式。

The theorems of Ibn al-Haytham, Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals , including the Lambert quadrilateral and Saccheri quadrilateral , were the first theorems on elliptical geometry and hyperbolic geometry , and along with their alternative postulates, such as Playfair's axiom , these works had a considerable influence on the development of non-Euclidean geometry among later European geometers, including Witelo , Levi ben Gerson , Alfonso , John Wallis , and Giovanni Girolamo Saccheri .

定理伊本Haytham，欧玛尔海亚姆和纳西尔基地丁铝土司上quadrilaterals ，包括德兰伯特四边形和萨凯里四边形，是第一个椭圆形的几何定理和双曲几何，并连同其替代假设，如普莱费尔的公理，这些作品有相当发展的影响非欧几里德几何之间稍后欧洲geometers ，包括Witelo ，列维本格森，阿方索，约翰瓦利斯和乔瓦吉罗拉莫萨凯里。

Firstly a square image is divided in- to two parts by diagonal and a parallelogram is reformed.

首先沿图像的对角线方向将正方形图分为上下两个部分并重新组合成一个平行四边形的图像；然后利用平行四边形图像的两列像素之间的像素数目差将某列中的像素插入到相邻下一列像素之间。

A solid with six faces, each a parallelogram and each being parallel to the opposite face .

每个底部是边数相同的多面形且其它面是不等边四边形或平行四边形的旁面三角台。

A prismatoid whose bases are polygons having the same number of sides and whose other faces are trapezoids or parallelograms.

每个底部是边数相同的多面形且其它面是不等边四边形或平行四边形的旁面三角台。

Bilinear quadrangular with reduced-dimension effect is used to simulate the real surface of the complex object, and a new hybrid basis function based on this quadrangular is presented.

采用具有降维效果的双线性四边形模型来模拟实际物体表面，提出了一种基于该四边形的混合域基函数，应用于金属物体的电磁散射特性的计算仿真中。

Some models were designed where the unique tetragon and hexagon grids borrowed from the wing structure were used as the basic elements, these models were analyzed numerically, it is shown that the model consisting of tetragon grids is much stiffer than that consisting of hexagon grids, while, more material is used in the first model;crinkling models based on tetragon grids or arched models consisting of hexagon grids become more stiffer than flat ones;hybrid models consisting of tetragon grids and hexagon grids can realize a proper balance between material saving and stiffness improving.

分别提取四边形、六边形的基本网格，建立结构模型，并对它们进行非线性数值分析。研究发现：四边形网格结构刚度大，六边形网格结构刚度小；而从材料利用率角度来讲，六边形网状结构更省材料；起皱对四边形网格结构刚度有加强，而起拱对六边形网格结构刚度有提高；如果将四、六边形的网格进行合理搭配，可以使结构刚度和材料利用率得到优化。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。