矢量积

Using bi-imaginary number representation, complex multiplication is simplified into two multiplication, instead of four ones in the previous method.

为克服空间带宽积的限制，提出了利用有限的外积乘法单元，通过矩阵分块和矢量循环流动进行任意维数矩阵与矢量运算算法，处理器利用率高。

In the system, any complex number can be uniquely expressed by a single digit string, and the subtraction involved in the original complex multiplication is eliminated essentially.

二、在矩阵-矢量运算算法方面，提出了以负二进制编码为代表的全并行内积算法，一步得到混合进制表示的乘积矢量结果。

It is compact in structure, stable and efficient for practical uses with high package density. 7. Based on negative binary coding method, a modified two-dimensional crossed-ring interconnection network and four subarrays outproduct technique, an optoelectronic parallel martix-vector complex multiplication processor is presented.

借助负二进制数字表达、空间编码加权-移位四区域复数外积乘法技术和改进的矩阵-矢量啮合算法，研制了光电混合并行处理的矩阵-矢量乘法器。

The vactrix method is further developed, a vectrix Skew-symmetric crossproduct identity is presented and the dyadic form of the derivative of a vector with respect to another vector in terms of vectrix is also offered.

进一步发展了矢阵方法，提出了矢阵叉积算子恒等式及矢量相对于矢量的导数以矢阵表示的并矢形式，并给出了若干应用实例。

The dot product of vectors a and b .

矢量 a 和矢量 b 的点积。

The dot product of the ▽operator with a vector defines the divergence of that vector .

算子▽与一个矢量的点积定义为这个矢量的散度。

Fast Line Integral Convolution with constant filter kernels as well as with triangular filter kernels are presented,which are faster than the original Line Integral Convolution approach about an order of magnitude in rendering actual vector fields.

针对这个问题实现了基于常数滤波卷积核的快速线积分卷积算法，提出并论证了基于三角形滤波卷积核的快速线积分卷积算法，对于实际矢量场，上述两种方法均将运算速度提高了一个数量级，而基于三角形滤波卷积核的快速线积分卷积算法的结果使图像更加平滑。

This network's multidimensional wavelet basis function is built by substituting norm of the vector for that vector, not scalar product function of the vector, thus the cost of calculation of high dimensionalities is decreased nearly to the situation of one dimensionality.

此网直接用矢量的范数代替矢量来构造多维小波基函数，而不是采用通常的矢量的标量积函数的方法构造多维基函数，这样多维情况的运算量被降低到几乎和一维的情况基本相当的程度。

First, structure tensor is calculated to gain vector field for characterizing local structure of image. And then, total variation partial difference equation is imposed for smoothing vector field. Based on this we use line integral convolution for guide the stroke to generate virtual special effect image with fluctuant sense. Last, mergering with original real image, cylindrical panorama with virtualized relationship controlled by time can be generated, which accomplished the character of surpass the time and space in virtual reality system.

该方法通过计算结构张量获得图像曲线走向矢量场，以此刻画图像局部结构；并采用全变分偏微分方程对曲线走向矢量场自适应滤波平滑处理；在此基础上利用线积分卷积指导画笔走向模拟生成线条波动感虚化效果图像；最后结合原始真实图像和虚化效果图像，实现了一种基于时间变量的柱面场景虚化关联算法，并为虚拟现实系统超越现实时空的需要提供了一种新思路。

The definition of work suggests a third process of vector algebra, namely, scalar multiplication of two vectors

功的定义用到矢量代数的第三种运算，即两个矢量的标积。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。