标题: 数学名词站 [打印本页] 作者: lilianjie 时间: 2011-12-27 16:37 标题: 数学名词站 本帖最后由 lilianjie 于 2011-12-27 16:39 编辑 8 B, R7 i' ^% M8 `# w+ ^: x3 N( a) D e5 L. B, S
cut-the-knot。ORG 5 n$ h* y/ V1 y. D x 4 I, l/ m& v2 I+ X: dMaclaurin and Taylor series5 [% W4 R% P: O- ~
For a (real) function f under certain conditions (Taylor's Theorem) 8 N+ h; X$ M0 H" N% K- O( R7 U5 P9 S( Q/ `
f(x) = f(a) + (x - a)f'(a) + (x - a)2f(2)(a)/2! + ... + (x - a)nf(n)(a)/n! + Rn 1 `3 w$ e7 w7 Q
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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. * f8 c5 N( t% {4 a* p ! T' I4 ^# ]8 I' w) s' MThe remainder Rn looks very much like the expected next term, with the derivative evaluated at an intermediate point:, Z) O8 `5 p9 x& h
! Z2 A. i. w7 r) b Rn = (x - a)n + 1f(n + 1)(γ)/(n + 1)!, 7 d4 z1 f! x1 J / I* C3 y' `5 g- c* _where 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.# O6 ~+ X1 K# h, f) Q
0 v1 _& U2 u3 g& d% ^2 C# j3 x3 z一张学格的表： ' }( `* j" y* [3 C- q! F+ T1 A) T. U: T- ~
1. A boolean algebra is a complemented distributive lattice. (def)布尔代数是完全分配格 % |- i% e& U! Y7 L: t , _$ S0 Z* W" p8 ~2. A boolean algebra is a heyting algebra.[1]布尔代数是一个海廷代数+ j1 S' i& [' v* A8 n/ D! u
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3. A boolean algebra is orthocomplemented.[2]布尔代数是正交可补& Y- I# b0 [+ _
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4. A distributive orthocomplemented lattice is orthomodular.[3]分配正交可补格是正交模 $ U) X( Y. I$ r% W! `' l+ A2 l! B$ `8 S; l6 u2 N) r6 e
5. A boolean algebra is orthomodular. (1,3,4)布尔代数是正交模 ; Y/ d" F# m5 d % L; j2 B6 b2 ]7 W- \- T. }" \6 N3 v- f$ D9 s
6. An orthomodular lattice is orthocomplemented. (def)正交模格正交可补# g( c! i) ~# `& d6 |0 U4 d
; i+ D9 ]+ z4 V, I7. An orthocomplemented lattice is complemented. (def)正交可补格可补 4 I4 E c8 E1 L' L2 H5 V: N * d6 S: ]7 h I2 U& z+ v; e8 }- q8. A complemented lattice is bounded. (def)可补格有界 / j8 J# H& F' p9 a- c. o, C. C* }9 D7 e, V, X8 R, O8 C
9. An algebraic lattice is complete. (def)代数格是完全的 & K5 v% m# i* J* O9 G6 z* H F$ x9 f; d4 n6 d/ I( Z2 f' t8 l/ T8 ]
10. A complete lattice is bounded.完全格有界 ; G1 A# b0 h& L" N* \) G 4 t# J0 A) Y; w0 D8 T/ H0 \# V6 f11. A heyting algebra is bounded. (def)海廷代数有界0 G: Y# h9 l* _' l
% e& X* Z7 k6 u; T; |7 |12. A bounded lattice is a lattice. (def)有界格是格+ y$ ]8 S. Q, l6 g
3 B2 P; m' V4 k/ q3 p13. A heyting algebra is residuated.海廷代数是剩余的3 p" l" I" I( O: ], H' ]
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14. A residuated lattice is a lattice. (def)剩余格是格( S6 {/ g2 p+ {
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15. A distributive lattice is modular.[4]分配格是模; w! |+ ]4 ~. v2 t
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16. A modular complemented lattice is relatively complemented.[5]模可补格相关可补 . ?! `" A- ]. G( @$ M2 h. F; g3 g % V W+ L/ T9 L17. A boolean algebra is relatively complemented. (1,15,16)布尔代数相关可补' X0 b, J6 i, { D1 `; o V: m
+ W) ~8 f9 J' o0 _18. A relatively complemented lattice is a lattice. (def)相关可补格是格; \* P8 `; C" j% f# t) A! |
8 I: v0 L" n, Q2 e/ i$ d+ n) V* A* f2 h19. A heyting algebra is distributive.[6]海廷代数可分配 L6 i8 c6 j/ Q; k8 ]+ M & l- H+ t9 V2 C20. A totally ordered set is a distributive lattice.全序集是分配格3 c3 h; N+ O: m, H, O& w
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21. A metric lattice is modular.[7]度量格是模- K; I; G7 C; J, {, c/ B
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22. A modular lattice is semi-modular.[8]模格是半模 C) F2 c* S" ~' [$ O K$ \* I" ^
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23. A projective lattice is modular.[9]防射格是模 0 _' u; B% u* F) W+ [" K + H. H' q5 r. k0 J1 k) a24. A projective lattice is geometric. (def)防射格可几何度量 5 o. W) L$ o8 ^' q; Y# ^( b8 S. V6 m/ f1 j0 W4 U5 p2 A7 F, V
25. A geometric lattice is semi-modular.[10]几何度量格是半模 0 l/ N j- Y! t% s, S( _& Q/ P5 ~5 [+ }& j* j& X
26. A semi-modular lattice is atomic.[11]半模格是原子格 " Y0 s/ ?- N# S, z' E8 Z+ d% F5 P) u/ l
27. An atomic lattice is a lattice. (def)原子格是格9 ~2 d: |' o, o3 c( d/ D8 D. w0 }
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28. A lattice is a semi-lattice. (def)格是半格 % m6 W9 L+ N" d( J: j/ ~' |. {$ u# m) k2 r" B1 T. U
29. A semi-lattice is a partially ordered set. (def)半格是偏序集 . f$ `+ ^: J, g/ I$ T & l. U$ L4 x- M m
