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In Chapter 3, we discuss the other orthogonalities in in Banach space, and give some properties of them. The emphase of the chapter is to study the relations of Birkhoff orthogonality, Isosceles orthogonality and Pythagorean orthogonality, and it is proved that if one of these induces another, then the space is an inner product space.

第三章研究其它几种正交性问题，讨论Birkhoff正交性、Isosceles正交性与Pythagorean正交性之间的关系，证明了：如果这三种正交性的任一种都蕴含另一种，那么此空间就是内积空间。

We paid special attention to the complex linear space consisting of all linear mappings from dimensional complex inner product space into dimensional complex inner product space .

2是与基的选择无关的概念。容易验证内积(2)满足内积的公理，从而是一个位的复内积空间。当是的正交归一基，是的正交归一基，可以证明构成的正交归一基。

Strengthening visual effects of caisson ceiling ,in vertical space .The contrast of painted pattern and large space of inoccupation which mixing the light ,shadow and the emotions, enhanced the enthusiasm atmosphere ,fulfill the space.

疏密的纹饰对比与大块面的留白，使光与影巧妙地结合，溶入诸多的情感，因而大大增强了气氛的煽情，使空间变得有情景，有情绪，人在情景中体验生活，接受一种由外而内的温情呵护，在不自觉中感受到东方气息的人文关怀。

But as Fermi project scientist Steve Ritz (NASA/Goddard Space Flight Center) notes, GRBs give us a chance to conduct the experiment in space by letting gamma rays run a very long race across the vast distances of intergalactic space.

不过根据费米望远镜项目科学家史蒂夫·里茨（美国航空航天局/戈达德宇宙飞行中心）的说法，伽马射线爆发提供了一个在太空进行实验的机会，因为伽马射线需要穿过广阔的星系空间，这是一段非常遥远的距离。

Based on the theory of isomorphic mapping and singular value decomposition theorem, the maximum of the kernel Fisher discrimination criterion can be skillfully acquired by solving the minimum of its reciprocal in a small space, and the final solution is acquired without taking account of the null space and non-null space of the kernel within-class scatter matrices separately.

基于同构映射原理和奇异值分解定理，在一个更小的空间内将核Fisher描述准则函数的极大值问题转化为其倒数的极小值问题，使最终的解不需要分开考虑核类内散度矩阵的零空间和非零空间。

In this algorithm, multiple lag parameters and the spectrum correlation property are used to exploit the cyclic statistical information and time domain characteristics of signals sufficiently and ef-fectively. Moreover, this method remedies the lack of space domain information, and it is an extension from space domain to space-time domain. Therefore the ability to select the desired signals and supress the noise and interfering signals is improved.

该算法在利用信号的谱相关特性的同时使用了多个时延，将波束形成技术从空域扩展到了时空域，弥补了空域信息的不足，充分利用了信号的循环统计信息和信号的时域特征，提高了信号的选择能力和对干扰、噪声的抑制能力。

After constrcting the perfective space , prove that this space is just the space of lebesgue integratiable function , thus explain that lebesgue integral is the form of the perfective riemann integral

在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。

We proved that this kind of operators were bounded from Hardy space to Lebesgue space, and they were bounded operators on the Hardy space if they satisfied some special conditions.

利用Hardy空间和Herz型Hardy空间的原子和分子分解特征，文中首先给出了此类算子从Hardy空间到Lebesgue空间上的有界性，而且，在满足一定的消失矩时，它又是Hardy空间上的有界算子。

This is a project to use the three-dimensional space vector/point type and related functions, they can be defined using a space vector/point, the realization of vector translation, scaling and rotation, the use of correlation function can also be the realization of the two vectors fork x, the absolute length of a vector, a vector unit, and get a three-point decision to the vertical plane of the vector, be the distance between two points in space, by the two vectors point multiplication by the two vectors angle, such as operations, for the use of user-friendly, each function are detailed notes, I hope all of you useless.

详细说明：这是一个项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，希望对大家有所用处。

As a result of the sound appearance, in two kind of space and times relations, between the lens space and time relations as well as the lens and between the lens space and time relations boundary further weakened.

由于声音的出现，两种时空关系、镜头内的时空关系以及镜头与镜头之间的时空关系之间的界限进一步地削弱了。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。