毕业设计外文文献翻译院系：数学与计算机科学学院
年级专业：12级数学与应用数学
姓名：施钰桢
学号：121301025
有限维向量空间
本文译自：Paul R.Halmos. Finite-Dimensional Vector Spaces. Library of Congress Cataloging in Publication Data, 1916.
§2.向量空间
现在我们来到了这本书的基本概念这里.有如下的定义，令F是一个数域; F中的元素叫做标量.
定义：向量空间V满足以下公理.
（A）对于任意的x和y，在V中有唯一确定的向量与它们对应，称为x与y的和，并记作x+ y，满足：
（1）交换律，x+ y= y+x.
（2）结合律，x+（y+z）=(x+y)+z.
（3）在V中存在一个独特的向量0（称为原点），对于任意向量x使得+0.
x
x=
（4）对于任意向量x，V中存在一个向量-x与之对应，使得x+（- x）= 0. （B）对于任意α和x，其中α是一个标量，x是V中的向量，在V中有唯一确定的向量与它们对应，称为α和x的积，记作αx，有如下公式：（1）乘法结合律，α（βx）=（αβ）x.
（2）对每个向量x有，1x=x.
（C）（1）向量乘法分配律，α（x+ y）=αx+αy.
（2）标量乘法分配律，（α+β）x=αx+βx.
这些公理在逻辑上不要求是独立的，它们只是其中的一个特性，为了方便我们研究.向量空间V和数域F之间的关系通常被描述为V是F上的向量空间.如果F是实数域R，V被称为实数向量空间;同样，如果F是Q或者是E，我们称V为有理向量空间或复数向量空间.
§3.实例
在讨论关于公理的影响前，我们举一些例子.在整个操作中我们将一遍又一遍参考这些例子，并利用现有的符号.
（1）让1E （=E ）为复数的集合，如果我们令x +y 和αx 为普通的复数加 法和乘法，则1E 为复数域上的向量空间.
（2）p 为所有多项式的集合，变量t 为复数系.我们解释到复数多项式的加法和乘法能写成向量加法和乘法，就称p 为复数向量空间；原点在多项式p 中恒等于零.
这本书的典型例子即实例（1）太过简单实例（2）太复杂.我们再举一个例子，复数向量空间（我们将在后面看到）一般足够为我们所用.
（3）设n E ,n =1,2,…, 是所有n 元复数的集合.如果x =（1ξ，...,n ξ）和 y =（1η，...,n η），根据定义,有
x +y = (1ξ+1η,…, n ξ+n η),
x α= (α1ξ,…, αn ξ),
0 = (0,…,0),
-x = (-1ξ,…,- n ξ).
这些§2中的真理（A ），（B ）与（C ）都很容易满足，所以n E 是一个复数向量空间，被称为n 维复坐标空间.
（4）对于每个正整数n ，设n P 为所有多项式的集合（复系数，如实例（2））当维≤n -1时，多项式恒等于零. （通常都是以维来讨论的，这多项式的维是没有定义，所以我们不能说维≤n -1）跟线性运算的解释一样（加法和标量乘法）如（2）n P 是一个复数向量空间.
(5)与n E 相近的所有n 维实数为n R ，它跟n E 的加法和标量乘法的定义相同，但现在我们只考虑实数标量α，空间n R 是一个实数向量空间，它会被称为n 维
实坐标空间.
（6）前述所有实例可以进行推广.例如，（1）中的一个明显的概括，可以说每个所述的数域可以被视为其自身的向量空间.一个常见的推广（3）和（5）是由任意数域F和n维F元素构成集合n
F;相同情况下线性运算的正式定义为F=E.
（7）根据定义，数域至少具有两个元素;一个是向量空间.由于每个向量空间包含原点，实际上（即除符号）一个向量空间只具有一个向量，这个是最简单的向量空间将用 来表示.
（8）如果在所有实数域R中，加法和有理实数乘法的定义跟之前是一样的，那么R为实数向量空间.
（9）如果在所有复数的集合E中，加法和复实数乘法的定义跟之前是一样的，那么E为复数向量空间. （将此例与（1）对比，他们有很大的不同）
§4.评论
公理和符号的评论.数域和向量空间的公理存在惊人的相似之处（和同样惊人的差异）.在这两种情况下，公理（A）中描述了该系统的加法结构，公理（B）描述了其乘法结构，公理（C）说明两种结构的联系，（在§1和§2）中的公理（A）的交换律是代数中较为熟悉的术语; （§2）中公理（B）及（C）中承认了标量作为运算的符号.我们顺便提下，如果标量是元素（而不是数域），相应的向量空间的广义概念称为模.
特殊实向量空间（如2R和3R）是熟悉的几何图形.似乎在这个阶段坚持R以外的数域显然是没有任何理由的，特别是复数域E.我们希望读者愿意去相信它，我们后面尽量使用复数性质（共轭，代数包闭），并且，我们的研究结果为希尔伯特空间的复数的推广在向量空间中的两个应用程序现代（量子力学）物理和数学中发挥重要的作用.它的一大缺点就是画图难度大.对普通图（阿根图）1E和2R 图是无法区别的，用图形表示似乎是超出人能达到的范围.因此我们不得不使用
E和n R，例如将2E称为平面.
一些图像语言来区分n
最后，我们对符号评论.我们观察到的符号0具有两个含义：一个作为标量，一个作为向量.为了使情况变的不那么糟，我们将在后面引入线性泛函与线性变换来给它下定义.幸运的是，0 的各种解释由此可得知，紧记这句话，我们就不会混淆了.
练习
1.证明，如果x 和y 是向量，α是一个标量，则下面的关系成立.
0),(00),(0),(=?=-=+αc b x
x a
00),(=?x d (观察到相同的符号被用在这个等式的两边;左侧它表示的是标量，右侧它表示的是向量.)
(e) 如果αx =0，那么α=0或x =0（或α=0且x =0）
(f) –x =(-1) x
(g) y +(x -y )=x (这里x -y =x +（-y ）)
2. 如果P 是素数，则n
P Z 是向量空间（cf. §1，例3）;在这个向量空间里有多少个向量？
3. 设V 是所有（命令）对数或实数的集合.如果),(21ξξ=x 和),(21ηη=y 为V 中的元素，有
x +y = ），（2211ηξηξ++
αx = ）
，（01αξ 0 =（0,0） -x = ），（21--ξξ
在线性操作的这些定义中V 是一个向量空间吗？为什么？
4. 有时一个向量空间中的一个子集,本身就是一个向量空间(线性操作已经给出).例如,向量空间3E 和3E 中子集V 组成的向量）
，，（321ξξξ，有
（a ）1ξ是实数
（b ）1ξ=0
（c ）1ξ=0或2ξ=0
（d ）1ξ+2ξ=0
（e ）1ξ+2ξ=1
在这种情况下V 是向量空间？
5. 考虑到向量空间p 和p 中的子集V 组成的向量(多项式)x ,有
（a ）x 有3维
（b ）2x （0）=x （1）
（c ）x （t ）≥0，（0 ≤ t ≤ 1）
（d ）x （t ）=x （1-t ），t 取任意数
在这种情况下V 是向量空间？
§5.线性关系
既然我们已经描述了向量空间,我们一定会对空间中的元素关系感到兴趣. 我们对求和符号描述几句.如果一组向量被赋于相应的一组指标i 即为i x ,如果没有必要或者不方便对指标进行详细说明,我们将简单地讲一组向量{i x }.(我们承认相同的向量可能有两个不同的指标与之相对应.因此,应该说,重要的不是向量出现在{i x }中,而是它们是如何出现的.) 如果考虑指标集是有限的,我们就把相应的向量之和记为i i x ∑（或者，可更加明确的记为∑=n
1i i x ）.为了避免频繁和繁琐,承认i i x ∑作为一般理论的总结是一个好主意，即使之前没有指标i 作总结,或者更准确地说,即考虑指标集是空的.（当然,在这种情况下是没有向量和，或者更准确地说, {i x }也是空的）.这种“空的和”很显然定义为向量0.
定义：如果存在一组相对应的标量{i a },且它们不全为0，使得
0=∑i
i i x a 则称有限向量组{i x }是线性相关.另一方面,如果使0=∑i
i i x a 当且仅当i a =0(对于任意i ),则称{i x }是线性无关.
这个定义的说法是指在空集情况下,虽然可能产生矛盾,但其它部分的理论还是相对吻合的.其结果表明，空集向量是线性无关的.实际上,如果没有指标i ,那么从向量中挑出一部分并分配给选定的非零标量使其之和消失是不可能的.问题不在于避免赋值为零,而在于分配指标.注意,这种观点表明,空集不是线性相关;线性无关的定义与直接否定线性相关的定义是等价的，这个说法还是需要一些直观理由.最简单的说法是“0=∑i
i i x a 当且仅当i a =0(对于任意i )”.假使没有指标i ，则另有说法：“如果0=∑i
i i x a 没有指标i ，则i a ≠0”,如果不存在指标i ，这个版本显然是如此.
线性相关和无关是向量集的属性，它是司空见惯的,然而对于向量本身的形容词应用,我们有时会说“一组线性无关的向量”而不是“线性无关的一组向量”.它也可以简单的说向量x 的线性相关和无关，并不一定要是有限集.
为了深入了解线性相关的意义，我们用已有的向量空间的例子来学习.
(1) 如果x 和y 是1E 中的任意两个向量,则x 和y 是一组线性相关.如果
x = y =
0，这个并不重要;如果不是这样的,那么我们有y x +(-x )y =0的关系.很明显, 因为每组包含一个线性相关的子集本身就是线性相关,这表明在1E 的各个组中包含多个元素是一组线性相关.
(2) 在空间P 情况下，向量y x ,和z 的定义，有
,
1)(),1()(,
1)(2t t z t t t y t t x -=-=-=
例如,当x +y -z =0则线性相关.然而对于无限的向量集,,,,210 x x x 的定义，有
,,)(,)(,1)(2210 t t x t t x t x ===
是一组线性无关的,如果存在形式
01100=+++n n x a x a x a
那么，我们就得到一个多项式的恒等式：
010=+++n n t a t a a
由此可得 010====n a a a
(3) 正如我们前面提到的,空间n E 是我们要研究的原型,让我们来看看,当n = 3，对于那些熟悉的高维几何,线性相关的概念 (或者,更确切的说,与其类似的(3R ))在这个领域有一个具体的几何意义.我们只提及在几何语言中若两个向量是线性相关的，当且仅当它们是共线.（如果有人认为一个向量不是作为空间中的一个点,而是作为一个箭头指向即从原点指向某个给定的点,由于两次忽略了“原点”，所以前面的句子应该修改下）.我们目前介绍了向量空间中线性流形（或向量子空间）的概念，并在这方面，我们将偶尔使用这类几何语言.
§6.线性组合
我们说，只要i
i i x a x ∑=，则x 是}{i x 一个线性组合;我们将没有任何进一步的解释，能使这个术语的所用语句更加简单.因此我们说,假如x 是}{i x 的线性组合,那么在{}i x 中x 是线性无关的；我们留给读者证明，如果{}i x 是线性无关的，它的充分必要条件是x 是}{i x 的一个线性组合.需要注意的是，按照空的和的定义，原点是空集的线性组合，而且这是此向量的唯一属性.
下面的定理是关于线性相关的基本结果.
定理：非零向量组)2(,,1n k x x k ≤≤ 是线性相关的，充分必要条件是向量组中至少有一个向量，可由其余个向量线性表示.
证明.假设)2(,,1n k x x k ≤≤ 是线性相关的，则存在一组不为零的a ，使
011=++k k x a x a
成立，我们不妨设0≠k a ，我们就可得到1-1,,k x x 之间是线性相关.即
111--++-=
k k
k k k x a a x a a x 因此k x 可由其余向量线性表示. 这证明了必要性条件;充分性是显而易见的,因为正如我们之前所说的,每组包含一个线性相关的子集其本身就是线性相关.
§7.基
定义：在向量空间V 中，存在一组线性无关的集合x ，使得V 中的每个元素都可以用x 线性表示，则称集合x 为向量空间V 中的一个基.如果向量空间V 含有一个有限的基,则称V 是有限维的.
除了偶尔考虑这些例子以外,在这本书中,我们主要将注意力集中于有限维向量空间.
例如基，我们再次转向向量空间P 和n E .在向量空间P 中，集合}{n x 其中 2,1,0,)(n ==n t t x n ，是它的一个基;通过定义，每一个多项式是n x 的一个有限维的线性组合.此外P 有无限维的基，对给定的任意有限多项式，我们可以发现有比他们的维数高的多项式;后者多项式显然不是前者的线性组合.
关于基础一个例子，在n E 中向量n i x i ,,1, =,i x 的第j 个坐标定义成ij δ (在这里我们第一次使用克罗内克积δ;它是由当j i =，ij δ=1和当j i ≠，ij δ=0定义的).因此,我们认为,向量)1,0,0(),0,1,0(),0,0,1(321===x x x 是3E 中的一组基.不难看出,它们是线性无关的,公式
332211321),,(x x x x ξξξξξξ++==
证明了在3E 中每一个x 是它们的一个线性组合.
一般在有限维向量空间V 中，,基},,{n 1x x 中的每个x 可以写成如下形式：
i
i i x x ∑=ξ 我们断言，x 是由ξ唯一确定.这一说法的依据是线性相关理论中所使用到的论
证.如果我们有i
i i x x ∑=η，那么可以通过减法，可得 0)=-∑i i
i i x ηξ（ 由于i x 是线性无关的，这意味着0-i i =ηξ其中n i ,,1 =，换言之，η和ξ是一样的.
参考文献
[1] N.Bourbaki, Algebre; Chap.Ⅱ（Algebre lineaire ）, Paris, 1947,and Chap. Ⅲ
(Algebre mullilineaire), Paris, 1948.
[2] B.L. Van Der Waerden, Modern algebra, New York, 1953.
[3] S.Banch, Theorie des operations lineaires, Warszawa, 1932.
[4] F.Riesz and B. Sz.-Nagy, Functional analysis, New York, 1955.
[5] P.R.Halmos, Introduction to Hilbert space, New York, 1951.
[6] M.H.Stone,Linear transformations in Hilbert space, New York, 1932.
[7] R.Courant and D.Hilbert, Methods of mathematical phsics,New York,1953.
[8] J.V on Neumann,Mathematical foundations of quantum mechanics,
Princeton,1955.
Finite-Dimensional Vector Spaces
§2. Vector spaces
We come now to the basic concept of this book. For the definition that follows we assume that we are given a particular field F ; the scalars to be used are to be elements of F .
Definition. A vector space is a set V of elements called vectors satisfying the follo-wing axioms.
（A）To every pair , x and y，of vectors in ?there corresponds a vector x + y, called the sum of x and y , in such a way that
(1) addition is commutative , x + y = y + x
(2) addition is associative, x+(y+z)= (x+y)+z
(3) there exists in V a unique vector 0 (called the origin) such that x+ 0 =x
for every vector x, and
(4) to every vector x in V there corresponds a unique vector -x such that
x+(-x)=0
（B）To every pair , α and x，where α is a scalar and x is a vector in V, there corresponds a vector αx in V, called the product of α and x，in such
a way that
(1) multiplication by scalars is associative, α(βx)=(αβ) x, and
(2) 1x=x for every vector x.
（C）(1) Multiplication by scalars is distributive with respect to vector addition,α(x+y)= αx+αy, and
(2) multiplication by vectors is distributive with respect to scalar addition, (α+β)x=αx+βx
These axioms are not claimed to be logically independent ; they are merely a co-nvenient characterization of the objects we wish to study . the relation between a vector spaces V and the underlying field F is usually described by saying that V is a vector space over F . if F is the field R of real numbers , V is called a real vector space ; similarly if F is Q or if F is E, we speak of rational vector spaces or com-
plexvector space.
§3. Examples
Before discussing the implications of the axioms，we give some examples. We shall refer to these examples over and over again，and we shall use the notation established here throughout the rest of our work.
(1)Let 1E（=E）be the set of all complex numbers；if we interpret x+y and ax as ordinary complex numerical addition and multiplication.1E becomes
a complex vector space.
(2) Let p be the set of all polynomials , with complex coefficients, in a variable t. To make p into a complex vector space , We interpret vector addition and scal ar multiplication as the ordinary addition of two polynomials and the multiplication o
fa polynomial by a complex number; the origin in p is the polynomial identically zero.
Example (1) is too simple and example (2) is too complicated to be typical of the main contents of this book .we give now another example of complex vector spaces which ( as we shall see later ) is general enough for all our purposes.
(3)Let n E ，n =1,2,…, be the set of all n -tuples of complex numbers. if
x =(n ξξ，，
1) and y =(n ηη，， 1) are elements of n E ,we write ,by definition, x +y = (1ξ+1η,…, n ξ+n η),
x α= (α1ξ,…, αn ξ),
0 = (0,…,0),
-x = (-1ξ,…,- n ξ).
It is easy to verity that all parts of our axioms (A),(b).and(c), §2,are satisfied, so that n E is a complex vector space; it will be called n-adimensional comple x coordinate space.
(4) For each positive integer n , let n p be the set of all polynomials (with comple x coefficients , as in example (2)) of degree ≤n -1, together with the polynomial id entically zero . (in the usual discussion of degree ,the degree of this polynomial is no t defined , so that We cannot say that it has degree ≤n -1. ) With the same interpreta tion of the linear operations (addition and scalar multiplication ) as in ( 2 ) , n p i s a complex vector space.
(5) A close relative of n E is the set n R of all n-tuples of real numbers. W ith the same formal definitions of addition and scalar multiplication as for n E , ex cept that now we consider only real scalar α, the space n R is A real vector spa-ce; it will be called n-dimensional real coordinate space.
(6) All the preceding examples can be generalized. Thus, for instance, an obviou s generalization of (1) can be described by saying that every field may be regarded as a vector space over itself. A common generalization of ( 3 ) and ( 5 ) atarts with a n arbitrary field F and forms the set F of n-tuples of elements of F ; the formal d efinitions of the Linear operations are the same as for the case F =E .
(7) A field , by definition , has at least two elements ; A vector space however, may have only one . Since every vector space contains an origin, there is essentially (i.e , except for notation ) only one vector space having only one vector . This most trivial vector space will be denoted by θ.
(8) If , in the set R of all real numbers, addition is defined as usual and multipli cation of a real number by a rational number is difined as usual, then R becomes a r ational vector space.
(9) If, in the set E of all complex numbers, addition is defined as usual and mu ltiplication of a complex number by a real number is defined as usual, then E beco mes a real vector space. ( Compare this example with (1); they are quite different.)
§4. Comments
A few comments are in order on our axioms and notation .There are striking simila rities ( and equally striking differences ) between the axioms for a field and the axio ms for a vector space over a field. in both cases, the axioms ( A ) describe the additiv e structure of the system , the axioms (B) describe Its multiplicative structure , and the axioms ( C ) describe the connection between the two structures, Those familiar with algebraic terminology will have recognized the axioms ( A ) (in both 1 and 2 ) as the defining conditions of an abelian ( commutative ) group; the axioms (
B ) and (
C ) (in §2 ) express the fact that the group admits scalars as operators. We mentio
n in passing that if the scalars are elements of a ring ( instead of A field) , the general ized concept corresponding to a vector space is called A module.
Special real vector spaces ( such as 2R and 3R ) are familiar in geometry. There seems at this stage to be no excuse for Our apparently uninteresting insistence on fiel ds other than R , and, in particular , on the fielde E of complex numbers .We hope that the reader is wulling to take it on faith that we shall have to make use of deep properties of complex numbers later ( conjugation , algebraic closure ) , and that in bo th the applications of vector spaces to modern (quantum mechanical ) physics and th e mathematical generalization of our results to Hilbert space complex numbers play an important role. Their one great disadvantage is the difficulty of drawing pictur es ; the ordinary picture ( Argand diagram ) of 1E is indistinguishable from that of 2
R , and a graphic representation of 2E seems to be out of human reach. On the occ asions when we have to use pictoral language we shall therefore use the terminolog
y of n R in n E , and speak of 2E, for example as a plane.
Finally we comment on notation . We observe that the symbol 0 has been used in two meanings : Once as a scalar and once as a vector. To make the situation worse, we shall later, when we Introduce linear functionals and Linear transformations , give it still other meanings. Fortunately the relations among the various interpretatio ns of 0 are such that , after this word of waning , no confusion should arise from
this practice.
Exercises
1.Prove that if x and y are vectors and if is a scalar，then the followi
ng relations hold.
0),(00),(0),(=?=-=+αc b x
x a
00),(=?x d （observe that the same symbol is used on both sides of this equation ；on the left it denotes a scalar, on the right it denotes a vector.）
(e) if αx =0，then either α=0 or x =0（or both ）
(f) –x =(-1) x
(g) y +(x -y )=x (Here x -y =x +（-y ）)
2. if P is a prime, then n P Z is a vector space over P Z (cf. §1,ex.3); how
many vectors are there in this vector space?
3. let V be the set of all (ordered) pairs or real numbers. If ),(21ξξ=x a ),(21ηη=y are elements of V , write
x +y = ），（2211ηξηξ++
αx = ）
，（01αξ 0 =（0,0）
-x = ）
，（21--ξξ Is V a vector space with respect to these definitions of the linear operations?why?
4. Sometimes a subset of a vector apace is itself a vector space (with respe ct to the linear operations already given). Consider, for example, the vector space 3E and the subsets V of 3E consisting of those vectors (321,,ξξξ) for which
（a ）1ξ is real,
（b ）1ξ=0,
（c ）either 1ξ=0 or 2ξ=0,
（d ）1ξ+2ξ=0
（e ）1ξ+2ξ=1
In which of these cases is V a vector space?
5. Consider the vector space p and the subsets V of p consisting of those vectors (polynomials) x for which
（a ）x has degree 3,
（b ）2x （0）=x （1）,
（c ）x （t ）≥0 whenever 0 ≤ t ≤ 1,
（d ）x （t ）=x （1-t ）for all t .
In which of these cases is V a vector space?
§5. Linear dependence
Now that we have described the spaces we shall work with, we must specify the relations among the element of those spaces that will be of interest to us.
We begin with a few words about the summation notation . if corresponding to each of a set of indices i there is gaven a vector i x , and if it is not necessary or n ot convenient to specify the set of indices exactly, we shall simply speak of a set {}i x of vectors . (we admit the possibility that the same vector corresponds to two di stinct Indices. in all honesty, therefore, it should be stated that what is important is not which vectors appear in {}i x , but how they appear. ) If the index-set under cons ideration is finite , we shall denote the sum of the corresponding vector by ∑i i x (or,when desirable , by a more explicit symbol such as ∑=n i i x 1) . In order to avoid freque nt and fussy case distinctions, it is a good Idea to admit Into the general theory sums s uch as ∑i i x even when there are no indices i to be summed over , Or , more precis ely , even when the index – setunder consideration is empty . ( in that case of cours e, there are no vectors to sum , or , more precisely , the set {}i x is also empty. ) The value of such an " empty sum " is defined , naturally enough, to be the vector 0.
Definition. A finite set {}i x of vectors is linearly dependent if there exists a c orresponding set {}i a of scalars, not all zero,such that
0=∑i i i
x a
If, on the other hand, 0=∑i i i x a implies that i a = 0 for each i , the {}i x is l inearly independent.
The wording of this definition is intended to cover the case of the empty set; th e result in that case , though passibly paradoxical, dovetails very satisfactorily with the rest of the theory. The result is that the empty set of vectors is linearly ind ependent . indeed, if there are no indices i , then it is not possible to pick out some of them and to assign to the selected ones a non-zero scalar so as to make a certain sum vanish. The trouble is not in avoiding the assignment of zero ; it is infinding an index to which something can be as assigned. Note that this argument shows that th e empty set is not linearly dependent ; for the reader not acquainted with arguig by
华北电力大学科技学院 毕业设计（论文）附件 外文文献翻译 学号：121912020115姓名：彭钰钊 所在系别：动力工程系专业班级：测控技术与仪器12K1指导教师：李冰 原文标题：Infrared Remote Control System Abstract 2016 年 4 月 19 日
红外遥控系统 摘要 红外数据通信技术是目前在世界范围内被广泛使用的一种无线连接技术，被众多的硬件和软件平台所支持。红外收发器产品具有成本低，小型化，传输速率快，点对点安全传输，不受电磁干扰等特点，可以实现信息在不同产品之间快速、方便、安全地交换与传送，在短距离无线传输方面拥有十分明显的优势。红外遥控收发系统的设计在具有很高的实用价值，目前红外收发器产品在可携式产品中的应用潜力很大。全世界约有1亿5千万台设备采用红外技术，在电子产品和工业设备、医疗设备等领域广泛使用。绝大多数笔记本电脑和手机都配置红外收发器接口。随着红外数据传输技术更加成熟、成本下降，红外收发器在短距离通讯领域必将得到更广泛的应用。 本系统的设计目的是用红外线作为传输媒质来传输用户的操作信息并由接收电路解调出原始信号，主要用到编码芯片和解码芯片对信号进行调制与解调，其中编码芯片用的是台湾生产的PT2262，解码芯片是PT2272。主要工作原理是：利用编码键盘可以为PT2262提供的输入信息，PT2262对输入的信息进行编码并加载到38KHZ的载波上并调制红外发射二极管并辐射到空间，然后再由接收系统接收到发射的信号并解调出原始信息，由PT2272对原信号进行解码以驱动相应的电路完成用户的操作要求。 关键字：红外线；编码；解码；LM386；红外收发器。 1 绪论
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外文翻译 专业机械设计制造及其自动化学生姓名刘链柱 班级机制111 学号1110101102 指导教师葛友华
外文资料名称： Design and performance evaluation of vacuum cleaners using cyclone technology 外文资料出处：Korean J. Chem. Eng., 23(6), (用外文写) 925-930 (2006) 附件： 1.外文资料翻译译文 2.外文原文
应用旋风技术真空吸尘器的设计和性能介绍 吉尔泰金，洪城铱昌，宰瑾李， 刘链柱译 摘要：旋风型分离器技术用于真空吸尘器 - 轴向进流旋风和切向进气道流旋风有效地收集粉尘和降低压力降已被实验研究。优化设计等因素作为集尘效率，压降，并切成尺寸被粒度对应于分级收集的50％的效率进行了研究。颗粒切成大小降低入口面积，体直径，减小涡取景器直径的旋风。切向入口的双流量气旋具有良好的性能考虑的350毫米汞柱的低压降和为1.5μm的质量中位直径在1米3的流量的截止尺寸。一使用切向入口的双流量旋风吸尘器示出了势是一种有效的方法，用于收集在家庭中产生的粉尘。 摘要及关键词：吸尘器; 粉尘; 旋风分离器 引言 我们这个时代的很大一部分都花在了房子，工作场所，或其他建筑，因此，室内空间应该是既舒适情绪和卫生。但室内空气中含有超过室外空气因气密性的二次污染物，毒物，食品气味。这是通过使用产生在建筑中的新材料和设备。真空吸尘器为代表的家电去除有害物质从地板到地毯所用的商用真空吸尘器房子由纸过滤，预过滤器和排气过滤器通过洁净的空气排放到大气中。虽然真空吸尘器是方便在使用中，吸入压力下降说唱空转成比例地清洗的时间，以及纸过滤器也应定期更换，由于压力下降，气味和细菌通过纸过滤器内的残留粉尘。 图1示出了大气气溶胶的粒度分布通常是双峰形，在粗颗粒（>2.0微米）模式为主要的外部来源，如风吹尘，海盐喷雾，火山，从工厂直接排放和车辆废气排放，以及那些在细颗粒模式包括燃烧或光化学反应。表1显示模式，典型的大气航空的直径和质量浓度溶胶被许多研究者测量。精细模式在0.18?0.36 在5.7到25微米尺寸范围微米尺寸范围。质量浓度为2?205微克，可直接在大气气溶胶和 3.85至36.3μg/m3柴油气溶胶。
Optimum blank design of an automobile sub-frame Jong-Yop Kim a ,Naksoo Kim a,*,Man-Sung Huh b a Department of Mechanical Engineering,Sogang University,Shinsu-dong 1,Mapo-ku,Seoul 121-742,South Korea b Hwa-shin Corporation,Young-chun,Kyung-buk,770-140,South Korea Received 17July 1998 Abstract A roll-back method is proposed to predict the optimum initial blank shape in the sheet metal forming process.The method takes the difference between the ?nal deformed shape and the target contour shape into account.Based on the method,a computer program composed of a blank design module,an FE-analysis program and a mesh generation module is developed.The roll-back method is applied to the drawing of a square cup with the ˉange of uniform size around its periphery,to con?rm its validity.Good agreement is recognized between the numerical results and the published results for initial blank shape and thickness strain distribution.The optimum blank shapes for two parts of an automobile sub-frame are designed.Both the thickness distribution and the level of punch load are improved with the designed blank.Also,the method is applied to design the weld line in a tailor-welded blank.It is concluded that the roll-back method is an effective and convenient method for an optimum blank shape design.#2000Elsevier Science S.A.All rights reserved. Keywords:Blank design;Sheet metal forming;Finite element method;Roll-back method
A convection-conduction model for analysis of the freeze-thaw conditions in the surrounding rock wall of a tunnel in permafrost regions Abstract Based on the analyses of fundamental meteorological and hydrogeological conditions at the site of a tunnel in the cold regions, a combined convection-conduction model for air flow in the tunnel and temperature field in the surrounding has been constructed. Using the model, the air temperature distribution in the Xiluoqi No. 2 Tunnel has been simulated numerically. The simulated results are in agreement with the data observed. Then, based on the in situ conditions of sir temperature, atmospheric pressure, wind force, hydrogeology and engineering geology, the air-temperature relationship between the temperature on the surface of the tunnel wall and the air temperature at the entry and exit of the tunnel has been obtained, and the freeze-thaw conditions at the Dabanshan Tunnel which is now under construction is predicted. Keywords: tunnel in cold regions, convective heat exchange and conduction, freeze-thaw. A number of highway and railway tunnels have been constructed in the permafrost regions and their neighboring areas in China. Since the hydrological and thermal conditions changed after a tunnel was excavated，the surrounding wall rock materials often froze, the frost heaving caused damage to the liner layers and seeping water froze into ice diamonds，which seriously interfered with the communication and transportation. Similar problems of the freezing damage in the tunnels also appeared in other countries like Russia, Norway and Japan .Hence it is urgent to predict the freeze-thaw conditions in the surrounding rock materials and provide a basis for the design，construction and
外文翻译 原文 Foreign T rade o f China Material Source:W anfang Database Author:Hitomi Iizaka 1.Introduction On December11,2001,China officially joined the World T rade Organization(WTO)and be c a me its143rd member.China’s presence in the worl d economy will continue to grow and deepen.The foreign trade sector plays an important andmultifaceted role in China’s economic development.At the same time, China’s expanded role in the world economy is beneficial t o all its trading partners. Regions that trade with China benefit from cheaper and mor e varieties of imported consumer goods,raw materials and intermediate products.China is also a large and growing export market.While the entry of any major trading nation in the global trading system can create a process of adjustment,the o u t c o me is fundamentally a win-win situation.In this p aper we would like t o provide a survey of the various institutions,laws and characteristics of China’s trade.Among some of the findings, we can highlight thefollowing: ?In2001,total trade to gross domestic pr oduct(GDP)ratio in China is44% ?In2001,47%of Chinese trade is processed trade1 ?In2001,51%of Chinese trade is conduct ed by foreign firms in China2 ?In2001,36%of Chinese exports originate from Gu an gdon g province ?In2001,39%of China’s exports go through Hong Kong to be re-exported elsewhere 2.Evolution of China’s Trade Regime Equally remarkable are the changes in the commodity composition of China’s exports and imports.Table2a shows China’s annu al export volumes of primary goods and manufactured goods over time.In1980,primary goods accounted for 50.3%of China’s exports and manufactured goods accounted for49.7%.Although the share of primary good declines slightly during the first half of1980’s,it remains at50.6%in1985.Since then,exports of manufactured goods have grown at a much
文献出处：Thronson P. Toward Comprehensive Reform of America’s Emergency Law Regime [J]. University of Michigan Journal of Law Reform, 2013, 46(2). 原文 TOWARD COMPREHENSIVE REFORM OF AMERICA’S EMERGENCY LAW REGIME Patrick A. Thronson Unbenownst to most Americans, the United States is presently under thirty presidentially declared states of emergency. They confer vast powers on the Executive Branch, including the ability to financially incapacitate any person or organization in the United States, seize control of the nation’s communications infrastructure, mobilize military forces, expand the permissible size of the military without congressional authorization, and extend tours of duty without consent from service personnel. Declared states of emergency may also activate Presidential Emergency Action Documents and other continuity-of-government procedures, which confer powers on the President—such as the unilateral suspension of habeas corpus—that appear fundamentally opposed to the American constitutional order.
南京理工大学 毕业设计(论文)外文资料翻译 教学点：南京信息职业技术学院 专业：电子信息工程 姓名：陈洁 学号： 014910253034 外文出处：《 Pci System Architecture 》 (用外文写) 附件： 1.外文资料翻译译文；2.外文原文。 指导教师评语： 该生外文翻译没有基本的语法错误，用词准确，没 有重要误译，忠实原文；译文通顺，条理清楚，数量与 质量上达到了本科水平。 签名： 年月日 注：请将该封面与附件装订成册。
附件1：外文资料翻译译文 64位PCI扩展 1.64位数据传送和64位寻址：独立的能力 PCI规范给出了允许64位总线主设备与64位目标实现64位数据传送的机理。在传送的开始，如果回应目标是一个64位或32位设备，64位总线设备会自动识别。如果它是64位设备，达到8个字节（一个4字）可以在每个数据段中传送。假定是一串0等待状态数据段。在33MHz总线速率上可以每秒264兆字节获取（8字节／传送＊33百万传送字／秒），在66MHz总线上可以528M字节／秒获取。如果回应目标是32位设备，总线主设备会自动识别并且在下部4位数据通道上（AD[31::00]）引导，所以数据指向或来自目标。 规范也定义了64位存储器寻址功能。此功能只用于寻址驻留在4GB地址边界以上的存储器目标。32位和64位总线主设备都可以实现64位寻址。此外，对64位寻址反映的存储器目标（驻留在4GB地址边界上）可以看作32位或64位目标来实现。 注意64位寻址和64位数据传送功能是两种特性，各自独立并且严格区分开来是非常重要的。一个设备可以支持一种、另一种、都支持或都不支持。 2.64位扩展信号 为了支持64位数据传送功能，PCI总线另有39个引脚。 ●REQ64#被64位总线主设备有效表明它想执行64位数据传送操作。REQ64#与FRAME#信号具有相同的时序和间隔。REQ64#信号必须由系统主板上的上拉电阻来支持。当32位总线主设备进行传送时，REQ64#不能又漂移。 ●ACK64#被目标有效以回应被主设备有效的REQ64#（如果目标支持64位数据传送），ACK64#与DEVSEL#具有相同的时序和间隔（但是直到REQ64#被主设备有效，ACK64#才可被有效）。像REQ64#一样，ACK64#信号线也必须由系统主板上的上拉电阻来支持。当32位设备是传送目标时，ACK64#不能漂移。 ●AD[64::32]包含上部4位地址／数据通道。 ●C/BE#[7::4]包含高4位命令/字节使能信号。 ●PAR64是为上部4个AD通道和上部4位C/BE信号线提供偶校验的奇偶校验位。 以下是几小结详细讨论64位数据传送和寻址功能。 3.在32位插入式连接器上的64位卡
翻译文献：INVESTIGATION ON DYNAMIC PERFORMANCE OF SLIDE UNIT IN MODULAR MACHINE TOOL （对组合机床滑台动态性能的调查报告） 文献作者：Peter Dransfield, 出处：Peter Dransfield, Hydraulic Control System-Design and Analysis of TheirDynamics, Springer-Verlag, 1981 翻译页数：p139—144 英文译文： 对组合机床滑台动态性能的调查报告 【摘要】这一张纸处理调查利用有束缚力的曲线图和状态空间分析法对组合机床滑台的滑动影响和运动平稳性问题进行分析与研究，从而建立了滑台的液压驱动系统一自调背压调速系统的动态数学模型。通过计算机数字仿真系统，分析了滑台产生滑动影响和运动不平稳的原因及主要影响因素。从那些中可以得出那样的结论，如果能合理地设计液压缸和自调背压调压阀的结构尺寸. 本文中所使用的符号如下： s1-流源，即调速阀出口流量； S el—滑台滑动摩擦力 R一滑台等效粘性摩擦系数： I1—滑台与油缸的质量 12—自调背压阀阀心质量 C1、c2—油缸无杆腔及有杆腔的液容； C2—自调背压阀弹簧柔度； R1, R2自调背压阀阻尼孔液阻， R9—自调背压阀阀口液阻 S e2—自调背压阀弹簧的初始预紧力； I4, I5—管路的等效液感 C5、C6—管路的等效液容： R5, R7-管路的等效液阻； V3, V4—油缸无杆腔及有杆腔内容积； P3, P4—油缸无杆腔及有杆腔的压力 F—滑台承受负载， V—滑台运动速度。本文采用功率键合图和状态空间分折法建立系统的运动数学模型，滑台的动态特性可以能得到显著改善。
204/JOURNAL OF BRIDGE ENGINEERING/AUGUST1999
JOURNAL OF BRIDGE ENGINEERING /AUGUST 1999/205 ends.The stress state in each cylindrical strip was determined from the total potential energy of a nonlinear arch model using the Rayleigh-Ritz method. It was emphasized that the membrane stresses in the com-pression region of the curved models were less than those predicted by linear theory and that there was an accompanying increase in ?ange resultant force.The maximum web bending stress was shown to occur at 0.20h from the compression ?ange for the simple support stiffness condition and 0.24h for the ?xed condition,where h is the height of the analytical panel.It was noted that 0.20h would be the optimum position for longitudinal stiffeners in curved girders,which is the same as for straight girders based on stability requirements.From the ?xed condition cases it was determined that there was no signi?cant change in the membrane stresses (from free to ?xed)but that there was a signi?cant effect on the web bend-ing stresses.Numerical results were generated for the reduc-tion in effective moment required to produce initial yield in the ?anges based on curvature and web slenderness for a panel aspect ratio of 1.0and a web-to-?ange area ratio of 2.0.From the results,a maximum reduction of about 13%was noted for a /R =0.167and about 8%for a /R =0.10(h /t w =150),both of which would correspond to extreme curvature,where a is the length of the analytical panel (modeling the distance be-tween transverse stiffeners)and R is the radius of curvature.To apply the parametric results to developing design criteria for practical curved girders,the de?ections and web bending stresses that would occur for girders with a curvature corre-sponding to the initial imperfection out-of-?atness limit of D /120was used.It was noted that,for a panel with an aspect ratio of 1.0,this would correspond to a curvature of a /R =0.067.The values of moment reduction using this approach were compared with those presented by Basler (Basler and Thurlimann 1961;Vincent 1969).Numerical results based on this limit were generated,and the following web-slenderness requirement was derived: 2 D 36,500a a =1?8.6?34 (1) ? ??? t R R F w ?y where D =unsupported distance between ?anges;and F y =yield stress in psi. An extension of this work was published a year later,when Culver et al.(1973)checked the accuracy of the isolated elas-tically supported cylindrical strips by treating the panel as a unit two-way shell rather than as individual strips.The ?ange/web boundaries were modeled as ?xed,and the boundaries at the transverse stiffeners were modeled as ?xed and simple.Longitudinal stiffeners were modeled with moments of inertias as multiples of the AASHO (Standard 1969)values for straight https://www.doczj.com/doc/6a4196369.html,ing analytical results obtained for the slenderness required to limit the plate bending stresses in the curved panel to those of a ?at panel with the maximum allowed out-of-?atness (a /R =0.067)and with D /t w =330,the following equa-tion was developed for curved plate girder web slenderness with one longitudinal stiffener: D 46,000a a =1?2.9 ?2.2 (2) ? ? ? t R f R w ?b where the calculated bending stress,f b ,is in psi.It was further concluded that if longitudinal stiffeners are located in both the tension and compression regions,the reduction in D /t w will not be required.For the case of two stiffeners,web bending in both regions is reduced and the web slenderness could be de-signed as a straight girder panel.Eq.(1)is currently used in the ‘‘Load Factor Design’’portion of the Guide Speci?cations ,and (2)is used in the ‘‘Allowable Stress Design’’portion for girders stiffened with one longitudinal stiffener.This work was continued by Mariani et al.(1973),where the optimum trans-verse stiffener rigidity was determined analytically. During almost the same time,Abdel-Sayed (1973)studied the prebuckling and elastic buckling behavior of curved web panels and proposed approximate conservative equations for estimating the critical load under pure normal loading (stress),pure shear,and combined normal and shear loading.The linear theory of shells was used.The panel was simply supported along all four edges with no torsional rigidity of the ?anges provided.The transverse stiffeners were therefore assumed to be rigid in their directions (no strains could be developed along the edges of the panels).The Galerkin method was used to solve the governing differential equations,and minimum eigenvalues of the critical load were calculated and presented for a wide range of loading conditions (bedding,shear,and combined),aspect ratios,and curvatures.For all cases,it was demonstrated that the critical load is higher for curved panels over the comparable ?at panel and increases with an increase in curvature. In 1980,Daniels et al.summarized the Lehigh University ?ve-year experimental research program on the fatigue behav-ior of horizontally curved bridges and concluded that the slen-derness limits suggested by Culver were too severe.Equations for ‘‘Load Factor Design’’and for ‘‘Allowable Stress Design’’were developed (respectively)as D 36,500a =1?4?192(3)? ?t R F w ?y D 23,000a =1?4 ?170 (4) ? ? t R f w ?b The latter equation is currently used in the ‘‘Allowable Stress Design’’portion of the Guide Speci?cations for girders not stiffened longitudinally. Numerous analytical and experimental works on the subject have also been published by Japanese researchers since the end of the CURT project.Mikami and colleagues presented work in Japanese journals (Mikami et al.1980;Mikami and Furunishi 1981)and later in the ASCE Journal of Engineering Mechanics (Mikami and Furunishi 1984)on the nonlinear be-havior of cylindrical web panels under bending and combined bending and shear.They analyzed the cylindrical panels based on Washizu’s (1975)nonlinear theory of shells.The governing nonlinear differential equations were solved numerically by the ?nite-difference method.Simple support boundary condi-tions were assumed along the curved boundaries (top and bot-tom at the ?ange locations)and both simple and ?xed support conditions were used at the straight (vertical)boundaries.The large displacement behavior was demonstrated by Mi-kami and Furunishi for a range of geometric properties.Nu-merical values of the load,de?ection,membrane stress,bend-ing stress,and torsional stress were obtained,but no equations for design use were presented.Signi?cant conclusions include that:(1)the compressive membrane stress in the circumfer-ential direction decreases with an increase in curvature;(2)the panel under combined bending and shear exhibits a lower level of the circumferential membrane stress as compared with the panel under pure bending,and as a result,the bending moment carried by the web panel is reduced;and (3)the plate bending stress under combined bending and shear is larger than that under pure bending.No formulations or recommendations for direct design use were made. Kuranishi and Hiwatashi (1981,1983)used the ?nite-ele-ment method to demonstrate the elastic ?nite displacement be-havior of curved I-girder webs under bending using models with and without ?ange rigidities.Rotation was not allowed (?xed condition)about the vertical axis at the ends of the panel (transverse stiffener locations).Again,the nonlinear distribu-
提高塔式复合人工湿地处理农村生活污水的 脱氮效率1 摘要： 努力保护水源，尤其是在乡镇地区的饮用水源，是中国污水处理当前面临的主要问题。氮元素在水体富营养化和对水生物的潜在毒害方面的重要作用，目前废水脱氮已成为首要关注的焦点。人工湿地作为一种小型的，处理费用较低的方法被用于处理乡镇生活污水。比起活性炭在脱氮方面显示出的广阔前景，人工湿地系统由于溶解氧的缺乏而在脱氮方面存在一定的制约。为了提高脱氮效率，一种新型三阶段塔式混合湿地结构----人工湿地（thcw）应运而生。它的第一部分和第三部分是水平流矩形湿地结构，第二部分分三层，呈圆形，呈紊流状态。塔式结构中水流由顶层进入第二层及底层，形成瀑布溢流，因此水中溶解氧浓度增加，从而提高了硝化反应效率，反硝化效率也由于有另外的有机物的加入而得到了改善，增加反硝化速率的另一个原因是直接通过旁路进入第二部分的废水中带入的足量有机物。常绿植物池柏（Taxodium ascendens），经济作物蔺草（Schoenoplectus trigueter），野茭白（Zizania aquatica），有装饰性的多花植物睡莲（Nymphaea tetragona），香蒲（Typha angustifolia）被种植在湿地中。该系统对总悬浮物、化学需氧量、氨氮、总氮和总磷的去除率分别为89%、85%、83%、83% 和64%。高水力负荷和低水力负荷（16 cm/d 和32 cm/d）对于塔式复合人工湿地结构的性能没有显著的影响。通过硝化活性和硝化速率的测定，发现硝化和反硝化是湿地脱氮的主要机理。塔式复合人工湿地结构同样具有观赏的价值。 关键词： 人工湿地；硝化作用；反硝化作用；生活污水；脱氮；硝化细菌；反硝化细菌 １. 前言 对于提高水源水质的广泛需求，尤其是提高饮用水水源水质的需求是目前废水深度处理的技术发展指向。在中国的乡镇地区，生活污水是直接排入湖泊、河流、土壤、海洋等水源中。这些缺乏处理的污水排放对于很多水库、湖泊不能达到水质标准是有责任的。许多位于中国的乡镇地区的社区缺乏足够的生活污水处理设备。由于山区地形、人口分散、经济基础差等原因，废水的收集和处理是很成问题的。由于资源短缺，经济欠发达地区所采取的废水处理技术必须低价高效，并且要便于施用，能量输入及维护费用较低，而且要保证出水能达标。建造在城市中基于活性污泥床的废水集中处理厂，对于小乡镇缺乏经济适用性，主要是由于污水收集结构的建造费用高。 1Ecological Engineering，Fen xia ，Ying Li。