二维向量空间

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

"Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces."

二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间

Image sequence of images for each frame along the horizontal and vertical direction integral projection formed two integral projection Vector and applications based on the one-dimensional gradient estimated translation technology, thereby obtaining accurate two-dimensional space on the volume of translation.

将图像序列中的每一帧图像分别沿水平和垂直方向进行积分投影形成两个积分投影向量，并应用基于梯度的一维平移估计技术处理，从而精确地获取二维空间上的平移量。

In order to calculation Lyapunov exponent spectrum of unknown system,firstly,reconstruct phase space of observed one-dimensional time series,secondly,use Least-Squared Support Vector Machine approximate dynamical equation of reconstruction system and calculation Lyapunov exponent spectrum by Jacobian matrix.

为了计算未知系统的Lyapunov指数谱，首先，对一维观测数据序列进行相空间重构，然后，利用最小二乘支持向量机逼近重构系统的动力学方程，再通过雅克比矩阵计算Lyapunov指数谱。

The stochastic expansions given here depend only on the independent normal random variables and curvature arrays, therefore they are easy to understand and to deal with.

f'(0)一f(二'，0)。二'为已知的自变量，相应的因变量和随机误差为y'和。'，0为p维未知参数，其参数空间为R中的子集习。在约束方程(2)中，甲(0)为k维向量k

Basing on the analysis of 1 dimension observation,2 dimensions and 3 dimensions points confidence region,a general formular is proposed in this paper,which can be used to calculate the semidiameter of P dimensions super space ellisposid by using some important probability distributions.

在分析一维观测量、二维和三维坐标点置信区间、区域的基础上，利用几个重要的数学分布，导出了线、面这一p维随机向量的置信区域——p维超空间误差椭球半径的计算公式，同时应用实例验证了该通式与常规公式的一致性。

The universal expression of Laue equation and two theorems on reciprocal space and reciprocal vector are obtained and proved.

讨论和研究了干涉函数对衍射的影响，提出并证明了Laue方程的一般表达式和有关倒易空间与倒易向量的2个定理，研究了作为三维晶体特例的二维晶体的衍射，讨论了二维晶体倒易点阵的物理内容和点阵点的权重。

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。