7 n# m1 Y8 L, r1 c( u$ ~* eMaclaurin and Taylor series7 J0 _) `9 D% L9 F
For a (real) function f under certain conditions (Taylor's Theorem) " T* k$ p \, Z D8 G3 s( i 8 r x' a4 {; k: j' e f(x) = f(a) + (x - a)f'(a) + (x - a)2f(2)(a)/2! + ... + (x - a)nf(n)(a)/n! + Rn 5 E* L; F. S6 g4 v3 C, m- f: r4 P* r) i6 [3 i- N
One obtains a Maclaurin series when a = 0. However, introducing g(x) = f(x + a) one gets f(n)(a) = g(n)(0), and so the Maclaurin series for g at x = 0 coincides with the Taylor series of f at x = a.. d, Z. O+ A$ R- G }7 \% `# j9 P
+ w4 P, u! g( ~4 m) F' `3 d! `+ LThe remainder Rn looks very much like the expected next term, with the derivative evaluated at an intermediate point: 0 H% y! {) F4 }2 ?7 l( D2 F+ K Z" A+ E3 E f- t5 B, s
Rn = (x - a)n + 1f(n + 1)(γ)/(n + 1)!, . k4 K* a; S) P0 ` $ Q" ~3 f6 m) O; ^: @1 uwhere γ is a point between a and x. For the derivation of this form for the remainder of the series f is required to have at least n + 1 continuous derivatives.$ u. A3 Y! z7 H l6 n& ~" W
7 S6 q9 X$ f. n; RLocal homeomorphism局部同胚 7 b) B+ l+ A" _. q1 e& ~8 OHomotopy同伦 % I- ~# a }, g4 UIsotopy同痕是同伦的加细版0 V& r4 W8 ~7 \! {9 m7 G
homology同调 3 J* V) P% z6 p1 ~+ m, k8 ]7 M, ^# t9 H
Cohomology上同调 ; y# l* r9 a. E/ b* U8 d; T7 p
同调和上同调的唯一区别是上同调中的链复形以逆变方式依赖于X，因此其同调群（在这个情况下称为上同调群并记为Hn）构成从X所属的范畴到可换群或者模的范畴的逆变函子。% N* @( s( V2 E1 ]' o! Z
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4 d8 L/ S+ x! i1 K- H 作者: lilianjie 时间: 2011-12-29 16:03
semi homomorphism半同态 $ x- N& J$ g/ k5 [: M Zupper semi homomorphism3 K, \$ f8 m0 Y- Y
上半同态 ' z0 W" _' M6 Y% I% fDual semi homomorphism ) \0 U3 @ M# I对偶半同态* y. }# ~$ o. v+ V
Dual semi AUTOhomomorphism 0 {3 B0 V( ?3 v
对偶半自同态$ [+ Q" h4 G2 G3 X7 F3 j
+ p1 W# O! D' C! n4 w' v5 K
LATTICE ntersection homomorphism 6 P, ?8 o/ \/ i: A/ j5 ~4 K8 h, `3 }
格的交同态 , R. ~! i) M; j% E/ s
LATTICE UNION homomorphism $ Z, j. p) G9 Y3 n
格的并同态作者: zxl911816294 时间: 2011-12-30 15:04
顶哈哈。。。。。。。。。。作者: lilianjie 时间: 2011-12-30 19:06 本帖最后由 lilianjie 于 2012-1-4 17:01 编辑 2 U) M( \: R, K! x2 ]' W
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看看晕不晕。。。。7 d! Y% V* u: O: h# K
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associative algebra 结合代数 % t6 o# G* ~+ o2 f& h6 H8 Q' pcommutative algebra 交换代数 9 F J- {% M5 O7 C
Quotient algebra 商代数 ) O @( ^/ s5 e% G, HLie algebra 李代数 . }$ f& G# ` {1 N0 r) }9 ~李代数是一个代数结构，主要用于研究象李群和微分流形之类的几何对象。李代数因研究无穷小变换的概念而引入。“李代数”（以索甫斯·李命名）一词是由赫尔曼·外尔在1930年代引入的。在旧文献中，无穷小群指的就是李代数。 9 t% u n" ^/ r% Z李超代数 # S7 G9 m3 l) s' D V& g李余代数 1 X0 Y+ ?: }& [3 b李双代数(Lie bialgebra) " N( U3 k! v9 t( T
泊松代数 $ K( f. a0 d( |; g, d. S+ Danyonic李代数 0 K7 W6 t( q) f5 J- vHomological algebra 同调代数 / B4 x( U/ w) i/ i* [, ~( N# t6 ZUniversal algebra泛代数 & J. y; r: _" @$ U. j: cBCK algebra# ?- X% _2 s/ i: y( o2 H
Stone algebra & e, ^% `/ w6 B5 A |, F# UTerm algebra2 _% W! }; _5 a* S+ r4 A/ \! b( J$ {/ |
Graph algebra 图代数$ o1 N* f a' v. f# @+ J
group algebra群代数 w% K* b7 Q& P
RING algebra 环代数9 h4 C' Z D$ x
FIELD algebra 域代数 / a* C' i; Q1 p( g- C; `波莱尔子代数 ) o) _2 U, L, W5 JRelational algebra 有理代数+ w! B, O* y' O* h5 X/ P/ s
Subdirectly irreducible algebra 4 P- W8 v% _: w0 R3 a! \' gClifford代数、2 u& f3 o! r, F9 i# C+ l7 [: s/ L8 v
约当代数 / I& J6 }& T V2 T) s# q8 |Banach algebra 巴拿赫代数 $ E3 V" g5 x* S3 `" }6 ~5 S6 x- wHidden algebra - ?6 v5 [9 K% S4 fDiagram algebras 图形代数5 u- h A, v- ~' K: M* U
Differential algebra 微分代数 , N* H! S, u# x) `4 {8 mBoolean algebra 布尔代数 Y1 ~7 p, N' G" N
Topological algebra 拓扑代数. G' ?1 B, E3 \
Computer algebra ! @, M. D" A& e6 ]0 F8 MCoalgebra * ?) l1 v% l5 B3 z `) S3 KBialgebra 生物代数 $ @. {- j3 j& m# {3 e8 y8 PHopf algebra 霍普夫代数 5 c8 F! A F- T$ B0 L1 L( rSubalgebra 子代数( F6 R! r# t+ {) C$ Z
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平凡子代数 , J3 k4 {3 H/ b, H; n# u真子代数% B7 x4 @: ~% l/ V) F% J
( `9 C* \ y. O$ `# p. ?# O v5 f积代数 : _. }6 \! s! L9 O% o/ W海廷代数! |# {/ J: X' |% D6 l5 n
A algebra 一个代数 -------------向量可加也可乘 . ?" r8 e. _ U3 I; dBanach algebra 除代数3 t" |" a# b; X* p
symmetric algebra 辛代数作者: lilianjie 时间: 2011-12-30 19:39 本帖最后由 lilianjie 于 2012-1-3 12:07 编辑 4 G" u& y: L7 D1 v , l1 ~ X8 O; u" O. _( T" m% }heyting algebra 海廷代数* Q5 Y+ n& \7 A& {" A, K$ t* I* |
, w0 ?3 |5 x1 K8 Q! q* P3 qVirasoro 代数 - @/ J" b! ~* h# B8 y5 V5 ]6 j1 o, b* p1 z
5 b" R# e7 a) \& w* y
coalgebras or cogebras 余代数 ' y5 ?+ Q4 ?' G$ k. t- U' b2 r" a余代数是带单位元的结合代数的对偶结构，后者的公理由一系列交换图给出，将这些图中的箭头反转，便得到余代数的公理。- N+ \0 Z! Q2 Q# Q
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余代数的概念可用于李群及群概形等领域中。4 O! M( h" k9 I k6 D* I
/ V# G/ T- o6 v" o/ L7 E ; U9 D, i( I/ k' }$ |+ d' J李余代数2 b& ^: Z) S4 U$ i
# G% M r) q% t5 T2 q一张学格的表： 7 l. L6 r* u/ A% o. F: c: ?. ]" v3 `( x
1. A boolean algebra is a complemented distributive lattice. (def)布尔代数是完全分配格, g! C- ^$ ?& h2 a) c2 Q9 \
9 E+ n! \1 \/ C* Q2. A boolean algebra is a heyting algebra.[1]布尔代数是一个海廷代数 ( ^) W0 K$ `. }+ |# p 3 u: u) [; l' h k3 o2 {: W: ~$ y: c0 D: r% O1 l6 g: }' D; B# F
3. A boolean algebra is orthocomplemented.[2]布尔代数是正交可补) q k x) `; K% }8 z8 s" O- A* m
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4. A distributive orthocomplemented lattice is orthomodular.[3]分配正交可补格是正交模7 D: U/ v: l% U# f4 [/ h$ x; }9 g( Z
3 _" d! I8 v& v; `5. A boolean algebra is orthomodular. (1,3,4)布尔代数是正交模1 J- e+ P; W' x5 ?
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6. An orthomodular lattice is orthocomplemented. (def)正交模格正交可补 9 @# y/ a0 H8 H4 A+ n) {4 S# C , n5 W* {$ w$ M1 p: L2 d$ [" i6 t7. An orthocomplemented lattice is complemented. (def)正交可补格可补' H* Z5 ]' f9 D9 v/ L
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8. A complemented lattice is bounded. (def)可补格有界 1 H9 N# L6 j2 D5 c* [% q% v/ u2 M$ C9 N0 J- \
9. An algebraic lattice is complete. (def)代数格是完全的! h; }# I7 q A5 e2 c% d
% |; ]7 r- I9 h; K2 o10. A complete lattice is bounded.完全格有界 : s2 N/ K6 N2 Q3 Q/ m: r' `" u( R w" x' q; E. d* I- Y
11. A heyting algebra is bounded. (def)海廷代数有界: h: x4 r' u2 v K
& m7 h8 n( d- @) m# {& v12. A bounded lattice is a lattice. (def)有界格是格 : g3 }5 q6 n5 s& |2 S9 G- Z+ ~# i) V
13. A heyting algebra is residuated.海廷代数是剩余的 : T! ]# l$ U+ A 6 r s& I( ]4 [7 u z, T14. A residuated lattice is a lattice. (def)剩余格是格 " s4 f+ I0 r. Q 8 j5 Y9 u: i! n/ m. ]* ?. p# P) L15. A distributive lattice is modular.[4]分配格是模# ^4 R. n" R2 f* |. _" l( I9 I
$ |2 k6 h' s7 x2 a( K0 Q5 u
16. A modular complemented lattice is relatively complemented.[5]模可补格相关可补 / O- E' T- }7 T5 M ! s8 ~+ E) I, I) ~6 u+ B( I0 ?17. A boolean algebra is relatively complemented. (1,15,16)布尔代数相关可补3 c3 s, m7 M7 W& j3 ?5 i) }; [* ?
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18. A relatively complemented lattice is a lattice. (def)相关可补格是格9 a$ u0 B. h, L8 O
# w/ L9 m( H* i) m1 `1 o A( m19. A heyting algebra is distributive.[6]海廷代数可分配3 Y- V+ @2 x. V7 a, d/ F
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20. A totally ordered set is a distributive lattice.全序集是分配格, m9 i/ D) K- G+ W5 K+ ^" U( p
9 c- ~2 o+ i) _: k# B. u21. A metric lattice is modular.[7]度量格是模 % H1 S3 d1 \' g. B + ?; M$ I* i, \22. A modular lattice is semi-modular.[8]模格是半模 : _ Y, Y/ C9 J 1 _6 Q' }; K0 Y( E) n2 r23. A projective lattice is modular.[9]防射格是模 , }4 f# E5 D+ U; Q9 ^9 Q 3 p$ E: G; s% c. X$ f) x; {24. A projective lattice is geometric. (def)防射格可几何度量) W' W8 [' K ~3 N I0 i
& |6 o: K4 }0 Z0 P25. A geometric lattice is semi-modular.[10]几何度量格是半模& P: C. S) ?) e7 S2 L3 I% k( k8 L
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26. A semi-modular lattice is atomic.[11]半模格是原子格 3 h. W1 P6 V6 Y% K% F8 L & e7 l8 U4 j0 }& ]' B; w" [7 H4 q27. An atomic lattice is a lattice. (def)原子格是格 8 g$ k8 l5 E6 z: x. V, L" t+ C: t2 y# M7 [7 G( U ~/ {
28. A lattice is a semi-lattice. (def)格是半格0 w* K. A6 m1 V: L+ V3 Y& \6 \ g
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29. A semi-lattice is a partially ordered set. (def)半格是偏序集 , e* r' |( j, Q3 e+ i9 u6 X" u5 L1 \1 E% Z$ z; x! v
