Bibliography 243

合集下载

参考文献(Bibliography)格式的具体说明

如果编著或论文集有多个编者，Ed.改为Eds.。如：
Starr,Paul.“The Electronic Reader.”InReadingin the 1980s.Eds. Stephen Braubard, Michael Jackson, and Michael Jodan.New York: Bowker,1983.
5.参考文献同一个条目内部不可中英文夹杂，一般应与文献使用的语种一致，要么用英文，要么用中文书写。
6.英文文献字体是Times New Roman，使用英文标点符号；汉语文献字体是宋体，采用中文标点符号。
7.参考文献须悬挂缩进，即每一条目的第二行开始缩进5字符。
8.参考文献按1.5倍行距排列，不同条目之间空一行。
3.编著、论文集中的论文
论文作者“论文名”，XXX（编者）编《书名》，出版社所在城市名：出版社名，出版年份，起止页码。如：
陈红霞“浪漫误读与贬抑性误读”，乐黛云编《独角兽与龙——中西文化交流中的误读》，北京：北京大学出版社，1996，第XX－XX页。
4.期刊论文
论文作者“论文名”，《期刊名》年份（期号），起止页码。如：
廖七一“庞德与胡适诗歌翻译的文化思考”，《外国语》2003（6），第54－59页。
五、网络文献：直接列出网址。
四、中文参考文献的格式
1.专著
作者《书名》，出版社所在城市：出版社名，出版年份。如：
桂诗春、宁春岩《XXXXX》，北京：外语教学与研究出版社，1997。
2.编著、论文集
XXX主编《书名》，出版社所在城市：出版社名，出版年份。如：
桂诗春、宁春岩主编《语言学方法论》，北京：外语教学与研究出版社，1997。
参考文献(Bibliography)格式和要求的具体说明

毕业论文的notes和bibliography格式

Notes格式：“Notes”居中，四号字，加粗。

每条注释数字上标，首行缩进4字符，注释内容用小四号字，1.5倍行距。

如下：Notes1 卫志强．当代跨学科语言学．北京：北京语言学院出版社，1992：2．2陈侠，黄希庭，白纲．关于网络成瘾的心理学研究．心里科学进展，2003，（11）：331．1)中文机构文件机构名．文件名．出版年代：页码．1中国国家教育部．关于加强高等院校德育教师队伍建设的决定．1998：2．2)中文著作，一个作者：作者名．书名．出版地：出版社，出版年代：页码．1卫志强．当代跨学科语言学．北京：北京语言学院出版社，1992：2．3)中文著作：两个或者三个作者：作者名（用逗号隔开）．书名．出版地：出版社，出版年代：页码．2陈侠，黄希庭，白纲．当代跨学科语言学．北京：北京语言学院出版社，1992：2．4)中文著作：三个以上作者：作者名（用空格隔开）等．书名．出版地：出版社，出版年代：页码．3陈侠等．当代跨学科语言学．北京：北京语言学院出版社，1992：2．5)中文期刊文章：（作者多人以上参照中文著作方式给作者名）作者名．文章名．期刊名，出版年代，（期数）：页码．4陈侠，黄希庭，白纲．关于网络成瘾的心理学研究．心里科学进展，2003，（11）：331．6)中文文集文章：作者名．文章名．文集主编名．文集名．文集出版地：出版社，出版年代：页码．5陈侠．关于网络成瘾的心理学研究．卫志强编．当代跨学科语言学．北京：北京语言学院出版社，1992：331．7)中文译著：作者名．书名．译者名译．出版地：出版社，出版年代：页码．6威廉•莎士比亚．罗密欧与朱丽叶．卫志强译．北京：北京语言学院出版社，1992：15．8)中文工具书：主编名（责任人名）编．书名．出版地：出版社，出版年代：页码．7简清国，林茂竹编．英汉多功能词典．北京：外语教学与研究出版社，1994：1134．9)英文专著，一个作者：作者名．书名．（出版地：出版社，出版年代）页码．8Wang Cunmei．The Investigation of Language Performance about Popular Language of Network．(Wuhan：Wuhan University Press, 2004) 6-7．10)英文专著，两个或者三个作者：作者名（用and连接）．书名．（出版地：出版社，出版年代）页码．9C. A. Dwyer and Zhou Ruanyan．The Investigation of Language Performance about Popular Language of Network．(Wuhan：Wuhan University Press, 2004) 6-7．11)英文专著，三个以上作者：作者名et al．书名．（出版地：出版社，出版年代）页码．10Wang Cunmei et al．The Investigation of Language Performance about Popular Language of Network．(Wuhan：Wuhan University Press, 2004) 6-7．12)英文期刊文章：（作者多人以上参照英文著作方式给作者名）作者名．文章名．期刊名，出版年代，（期数）：页码．11C. A. Dwyer．Assessment and Classroom Learning: Theory and Practice．Assessment in Education, 1998, (1)：111．13)英文文集文章：（包括TCLC, NCLC等大型文献性文集）作者名．文章名．文集主编名, Ed．文集名．(文集出版地：出版社，出版年代) 页码．12Qin Hui．On Localization of the Communicative Approach．Liu Shoulan and Qin Hui, Ed．Teaching English as a Foreign Language—Current Issues．V ol 2．(Kunming: Yunnan University Press, 2002) 9．14)英文工具书：主编名（责任人名）编．书名．（出版地：出版社，出版年代）页码．13Jian Qingguo．A Multifunction English-Chinese Dictionary．(Beijing: Foreign Language Teaching and Research Press, 1994) 1109．15)网络资源：作者名．文章名．网站名称．（网址）．14卫广新．新课程与角色的转换．香港大学图书馆．（http://sunzil.lib.hku.hk/view/32/3200054.pdf）．*只能接受以.pdf, .html, .htm, .php, .asp为结尾的网址。

Bibliography

Bibliography[1]H.L.Abbott,Lower bounds for some Ramsey numbers,Discrete Math.2(1972),289–293.[2] A.Agresti,Categorical Data Analysis,John Wiley and Sons,New York,1990,xvi+558pp.[3] D.Aldous,On the Markov-chain simulation method for uniform combinatorial simulationand simulated annealing,.Sci.1(1987),33–46.[4] D.Aldous,Some inequalities for reversible Markov chains,J.London Math.Soc.25(1982),564–576.[5]N.Alon,Eigenvalues and expanders,Combinatorica6(1986),86–96.[6]N.Alon and F.R.K.Chung,Explicit construction of linear sized tolerant networks,DiscreteMath.72(1988),15–19.[7]N.Alon,F.R.K.Chung and R.L.Graham,Routing permutations on graphs via matchings,SIAM J.Disc.Math.7(1994),513–530.[8]N.Alon,Z.Galil and man,Better expanders and superconcentrators,J.Algorithms8(1987),337–347.[9]N.Alon and man,λ1isoperimetric inequalities for graphs and superconcentrators,b.Theory B38(1985),73–88.[10]N.Alon,Z.Galil and O.Margalit,On the exponent of the all pairs shortest paths prob-lem,32nd Symposium on Foundations of Computer Science,IEEE Computer Society Press, (1991),569–575.[11]N.Alon and N.Kahale,Approximating the independence number via theθfunction,Math.Programming,80(1998),253–264.[12]N.Alon and J.H.Spencer,The Probabilistic Method,John Wiley and Sons,New York1991,xvi+254pp.[13]S.Arora and S.Safra,Probabilistic checking of proofs,a new characterization of NP.33rdSymposium on Foundations of Computer Science,IEEE Computer Society Press,(1992), 2–13.[14]L.Babai and M.Szegedy,Local expansion of symmetrical graphs,Combinatorics,Probabilityand Computing1(1991),1–11.[15]L.Babai,Automorphism groups,isomorphism,reconstruction,Handbook of Combinatorics(eds.R.L.Graham,M.Gr´o tschel and L.Lov´a sz),North-Holland,Amsterdam,(1996),1447–1540.[16] D.Bakry,L’hypercontractivit´e et son utilisation en th´e orie des semigroupes,In Ecole d’´e t´ede Saint Fleur1992,Springer Lecture Notes1581,1–114.[17]L.A.Bassalygo,Asymptotically optimal switching circuits,Problems Inform.Transmission17(1981),81–88.[18]J.Beck,On size Ramsey number of paths,trees and circuits I.,J.Graph Theory7(1983),115–129.[19]W.Beckner,Inequalities in Fourier analysis,Annals of Mathematics102(1975),159–182.[20]V.E.Ben˘e s,Mathematical Theory of Connecting Networks and Telephone Traﬃc,AcademicPress,New York1965,xiv+319pp.[21]J.C.Bermond and B.Bollob´a s,The diameter of graphs–a survey,Congressus Numerantium32(1981),3–27.[22]J.C.Bermond,C.Delorme and G.Farhi,Large graphs with given degree and diameter,III,Proc.Coll.Cambridge(1981),Ann.Discr.Math.13,North Holland,Amsterdam(1982), 23–31.[23] A.J.Berstein,Maximally connected arrays on the n-cube,SIAM J.Appl.Math.15(1967),1485–1489.201202BIBLIOGRAPHY[24]S.N.Bhatt and F.T.Leighton,A framework for solving VLSI graph layout problems,J.Comput.System Sci.28(1984),300–343.[25] F.Bien,Constructions of telephone networks by group representations,Notices Amer.Math.Soc.36(1989),5–22.[26]N.L.Biggs,Algebraic Graph Theory,(2nd ed.),Cambridge University Press,Cambridge,1993,xvi+205pp.[27]N.L.Biggs and M.H.Hoare,The sextet construction for cubic graphs,Combinatorica3(1983),153–165.[28]N.L.Biggs, E.K.Lloyd and R.J.Wilson,Graph Theory1736-1936,Clarendon Press,Oxford,1976,xi+239pp.[29]Y.Bishop,S.Fienberg,P.Holland,Discrete Multivariate Analysis,MIT Press,Cambridge,1975,x+557pp.[30]M.Blum,R.M.Karp,O.Vornberger,C.H.Papadimitriou,and M.Yannakakis,The complex-ity of testing whether a graph is a superconcentrator,Inf.Proc.Letters13(1981),164–167.[31] B.Bollob´a s,Random Graphs,Academic Press,New York(1985),xvi+447pp.[32] B.Bollob´a s and F.R.K.Chung,The diameter of a cycle plus a random matching,SIAM J.Disc.Math.1(1988),328–333.[33] B.Bollob´a s and I.Leader,Edge-isoperimetric inequalities in the grid,Combinatorica11(1991),299–314.[34] B.Bollob´a s and I.Leader,An isoperimetric inequality on the discrete torus,SIAM J.Disc.Math.3(1990),32–37.[35] B.Bollob´a s,and A.Thomason,Graphs which contain all small graphs,European J.of Com-binatorics2(1981),13–15.[36] B.Bollob´a s and W.F.de la Vega,The diameter of random regular graphs,Combinatorica2(1982),125–134.[37]J.A.Bondy and M.Simonovits,Cycles of even length in graphs,bin.Theory Ser.B16(1974),97–105.[38]R.B.Boppana,Eigenvalues and graph bisection:An average-case analysis,28th Symposiumon Foundations of Computer Science,IEEE Computer Society Press,(1987),280–285. [39]R.Bott and J.P.Mayberry,Matrices and trees,In Economic Activity Analysis,(O.Morgen-stern,ed.),John Wiley and Sons,New York(1954),391–340.[40] A.Broder, A.Frieze and E.Upfal,Existence and construction of edge disjoint paths onexpander graphs,Proc.Sym.Theo.on Computing,ACM(1992),140–149.[41]R.Brooks,The spectral geometry of k-regular graphs,Journal d’Analyse Math´e matique,57(1991),120–151.[42]N.G.de Bruijn,A combinatorial problem,Nederl.Akad.Wetensch.Proc.49(1946),758–764.[43] D.A.Burgess,On character sums and primitive roots,Proc.London Math.Soc.12(1962),179–192.[44]P.Buser,Cubic graphs and theﬁrst eigenvalue of a Riemann surface,Math.Z.162(1978),87–99.[45]P.Buser,Cayley graphs and planar isospectral domains,in Geometry and Analysis on Man-ifolds(T.Sunada,ed.),Springer Lecture Notes1339(1988),64–77.[46]P.Buser,Cubic graphs and theﬁrst eigenvalue of a Riemann surface,Math.Z.162(1978),87–99.[47]L.Caccetta,On extremal graphs with given diameter and connectivity,Ann.New York Acad.Sci.328(1979),76–94.[48] A.Cayley,A theorem on trees,Quart.J.Math.23(1889),376–378.[49]J.Cheeger,A lower bound for the smallest eigenvalue of the Laplacian,Problems in Analysis(R.C.Gunning,ed.),Princeton Univ.Press(1970),195–199.[50]S.Y.Cheng,Peter Li and S.-T.Yau,On the upper estimate of the heat kernel of a completeRiemannian manifold,American Journal of Mathematics103(1981),1021–1063.[51]R.Christensen,Log-Linear Models,Springer-Verlag,New York,1990,xii+408pp.[52] F.R.K.Chung,On concentrators,superconcentrators,generalizers and nonblocking net-works,Bell Systems Tech.J.58(1979),1765–1777.[53] F.R.K.Chung,A note on constructive methods for Ramsey numbers,J.Graph Th.5(1981),109–113.BIBLIOGRAPHY203 [54] F.R.K.Chung,Diameters of communications networks,Mathematics of Information Pro-cessing,AMS Short Course Lecture Notes(1984),1–18.[55] F.R.K.Chung,Diameters of graphs:Old problems and new results,Congressus Numeran-tium60(1987),295–317.[56] F.R.K.Chung,Diameters and eigenvalues,J.of Amer.Math.Soc.2(1989),187–196.[57] F.R.K.Chung,Quasi-random classes of hypergraphs,Random Structures and Algorithms1(1990),363–382.[58] F.R.K.Chung,Regularity lemmas for hypergraphs and quasi-randomness,Random Struc-tures and Algorithms2(1991),241–252.[59] F.R.K.Chung,Constructing random-like graphs,in Probabilistic Combinatorics and ItsApplications,(B.Bollobas ed.),Amer.Math.Soc.,Providence,1991,21–55.[60] F.R.K.Chung,Laplacians of graphs and Cheeger inequalities,in Combinatorics,Paul Erd˝o sis Eighty,Volume2,(D.Mikl´o s,V.T.S´o s,and T.Sz˝o nyi eds.),J´a nos Bolyai Mathematical Society,Budapest(1996),157–172.[61] F.R.K.Chung,V.Faber and T.A.Manteuﬀel,An upper bound on the diameter of a graphfrom eigenvalues associated with its Laplacian,SIAM.J.Discrete Math.7(1994),443–457.[62] F.R.K.Chung and M.R.Garey,Diameter bounds for altered graphs,J.of Graph Theory8(1984),511–534.[63] F.R.K.Chung and R.L.Graham,Quasi-random hypergraphs,Random Structures andAlgorithms1(1990),105–124.[64] F.R.K.Chung and R.L.Graham,Quasi-random tournaments,J.of Graph Theory15(1991),173–198.[65] F.R.K.Chung and R.L.Graham,Maximum cuts and quasirandom graphs,Random Graphs(A.Frieze and T.Luczak,eds.),John Wiley and Sons,New York(1992),23–33.[66] F.R.K.Chung and R.L.Graham,On graphs not containing prescribed induced subgraphs,in A Tribute to Paul Erd¨o s,(A.Baker et al.eds.)Cambridge University Press(1990),111–120.[67] F.R.K.Chung and R.L.Graham,Quasi-random set systems,J.Amer.Math.Soc.4(1991),151–196.[68] F.R.K.Chung and R.L.Graham,Quasi-random subsets of Z n,bin.Th.(A)61(1992),64–86.[69] F.R.K.Chung and R.L.Graham,Cohomological aspects of hypergraphs,Trans.Amer.Math.Soc.334(1992),365–388[70] F.R.K.Chung and R.L.Graham,Random walks on generating sets of groups,Electronicbinatorics,4,no.2,(1997),#R7,14pp.[71] F.R.K.Chung and R.L.Graham,Stratiﬁed random walks on an n-cube,Random Structuresand Algorithms,11(1997),199–222.[72] F.R.K.Chung,R.L.Graham and R.M.Wilson,Quasi-random graphs,Combinatorica9(1989),345–362.[73] F.R.K.Chung,R.L.Graham and S.-T.Yau,On sampling with Markov chains,RandomStructures and Algorithms9(1996),55–77.[74] F.R.K.Chung,A.Grigor’yan,and S.-T.Yau,Upper bounds for eigenvalues of the discreteand continuous Laplace operators,Advances in Mathematics117(1996),165–178.[75] F.R.K.Chung,A.Grigor’yan,and S.-T.Yau,Eigenvalues and diameters for manifolds andgraphs,Tsing Hua Lectures on Geometry and Analysis,International Press,Cambridge,MA, 1997,79–106.[76] F.R.K.Chung and C.M.Grinstead,A survey of bounds for classical Ramsey numbers,J.Graph Theory7(1983),25–37.[77] F.R.K.Chung,B.Kostant and S.Sternberg,Groups and the Buckyball,in Lie Theory andGeometry:In honor of Bertram Kostant(Eds.J.-L.Brylinski,R.Brylinski,V.Guillemin and V.Kac)PM123,Birkh¨a user,Boston,1994,97–126.[78] F.R.K.Chung and nglands,A combinatorial Laplacian with vertex weights,J.Comb.Theory(A)75(1996),316-327.[79] F.R.K.Chung and K.Oden,Weighted graph Laplacians and isoperimetric inequalities,Paciﬁc J.of Math.192(2000),257–273.[80] F.R.K.Chung and S.Sternberg,Laplacian and vibrational spectra for homogenous graphs,J.Graph Theory16(1992),605–627.204BIBLIOGRAPHY[81] F.R.K.Chung and S.Sternberg,Mathematics and the Buckyball,American Scientist81,No.1,(1993),56–71.[82] F.R.K.Chung and P.Tetali,Communication complexity and quasi-randomness,SIAM J.Discrete Math.6(1993),110–123.[83] F.R.K.Chung and P.Tetali,Isoperimetric inequalities for Cartesian products of graphs,Combinatorics,Probability and Computing,7(1998),141–148.[84] F.R.K.Chung and S.-T.Yau,A Harnack inequality for homogeneous graphs and subgraphs,Communications in Analysis and Geometry,2(1994),627–640.[85] F.R.K.Chung and S.-T.Yau,Eigenvalues of graphs and Sobolev inequalities,Combinatorics,Probability and Computing4(1995),11–26.[86] F.R.K.Chung and S.-T.Yau,Logarithmic Harnack inequalities,Mathematics ResearchLetters3(1996),793–812.[87] F.R.K.Chung and S.-T.Yau,Eigenvalue inequalities for graphs and convex subgraphs,Communications in Analysis and Geometry5(1997),575–623.[88] F.R.K.Chung and S.-T.Yau,A Harnack inequality for Dirichlet eigenvalues,J.of GraphTheory34(2000),247–257.[89] D.M.Cvetkovi´c,M.Doob and H.Sachs,Spectra of Graphs,Theory and Application,Aca-demic Press,1980,368pp.[90] D.M.Cvetkovi´c,M.Doob,I.Gutman,and A.Torga¨s ev,Recent results in the Theory ofGraph Spectra,North Holland,Amsterdam1988,xii+306pp.[91] E.B.Davies,Heat kernel bounds,conservation of probability and the Feller property,J.d’Analyse Math.58,(1992),99–119.[92]P.J.Davis,Circulant Matrices,John Wiley and Sons,New York,1979,xv+250pp.[93]P.Deligne,La conjecture de Weil I,Inst.Hautes Etudes Sci.Publ.Math43(1974),273–307.[94] E.D’Hoker and D.H.Phong,On determinants of Laplacians on Riemann surfaces,Comm.Math.Phys.104(1986),537–545.[95]J.-D.Deuschel and D.W.Stroock,Hypercontractivity and spectral gap of symmetric diﬀu-sions with applications to the stochastic Ising models,J.Funct.Anal.92(1990),30–48. [96]P.Diaconis,Group Representations in Probability and Statistics,Institute of Math.Statistics,Hayward,California,1988,vi+198pp.[97]P.Diaconis,R.L.Graham and J.Morrison,Asymptotic analysis of a random walk on ahypercube with many dimensions,Random Structures and Algorithms1(1990),51–72. [98]P.Diaconis and L.Saloﬀ-Coste,Comparison theorems for reversible Markov chains,Annalsof Applied Prob.3(1993),696–730.[99]P.Diaconis and L.Saloﬀ-Coste,Comparison techniques for random walks onﬁnite groupsAnnals of Applied Prob.4(1993),2131–2156.[100]P.Diaconis and L.Saloﬀ-Coste,An application of Harnack inequalities to random walk on nilpotent quotients,J.Fourier Anal.Appl.(1995),189–207.[101]P.Diaconis and L.Saloﬀ-Coste,Logarithmic Sobolev inequalities forﬁnite Markov chains, Ann.Appl.Prob.6(1996),695–750.[102]P.Diaconis and L.Saloﬀ-Coste,Walks on generating sets of groups,Prob.Theory Related Fields105(1996),393–421.[103]P.Diaconis and D.W.Stroock,Geometric bounds for eigenvalues of Markov chains,Annals Applied Prob.1(1991),36–61.[104]P.Diaconis and B.Sturmfels,Algebraic algorithms for sampling from conditional distribu-tions,Ann.Statist.26(1998),363–397.[105]M.J.Dinneen,M.R.Fellows and V.Faber,Algebraic constructions of eﬃcient broadcast networks,Lecture Notes in Comput.Sci.,539,Springer,Berlin,1991,152–158.[106]J.Dodziuk and L.Karp,Spectral and function theory for combinatorial Laplacians,in Geometry of Random Motion,Contemp.Math73,AMS Publication(1988),25–40. [107]M.Dyer,A.Frieze and R.Kannan,A random polynomial time algorithm for approximating the volume of convex bodies,JACM38(1991),1–17.[108]M.Eichler,Quaternary quadratic forms and the Riemann hypothesis for congruence zeta functions,Arch.Math.5(1954),355–366.[109] B.Elspas,Topological constraints on interconnection limited logic,Switching Circuit Theory and Logical Design5(1964),133–147.[110]P.Erd˝o s,Some remarks on the theory of graphs,Bull.Amer.Math.Soc.53(1947),292–294.BIBLIOGRAPHY205 [111]P.Erd˝o s,Some remarks on chromatic graphs,Colloquium Mathematicum16(1967),253-256.[112]P.Erd˝o s,S.Fajtlowicz and A.J.Hoﬀman,Maximum degree in graphs of diameter2, Networks10(1980),87–90.[113]P.Erd˝o s and A.Hajnal,On spanned subgraphs of graphs,Betrage zur Graphentheorie und deren Anwendungen,Kolloq.Oberhof(DDR)(1977),80–96.[114]P.Erd˝o s and A.R´e nyi,On a problem in the theory of graphs,Publ.Math.Inst.Hungar.Acad.Sci.7(1962),623–641.[115]P.Erd˝o s,A.R´e nyi and V.T.S´o s,On a problem of graph theory,Studia Sci.Math.Hungar.1(1966),215–235.[116]P.Erd˝o s and H.Sachs,Regul¨a re Graphen gegenebener Teillenweite mit minimaler Knoten-zahl,Wiss.Z.Univ.Halle–Wittenberg,Math.Nat.R.12(1963),251–257.[117]P.Erd˝o s and V.T.S´o s,On Ramsey-Tur´a n type theorems for hypergraphs,Combinatorica 2(1982),289–295.[118]P.Erd˝o s and J.Spencer,Imbalances in k-colorations,Networks1(1972),379–385. [119]P.Erd˝o s and J.Spencer,Probabilistic Methods in Combinatorics,Academic Press,New York(1974),106pp.[120]R.J.Faudree and M.Simonovits,On a class of degenerate extremal graph problems,Com-binatorica3(1983),83–93.[121]U.Feige,Randomized graph products,chromatic numbers,and the Lov´a szθ-function,Proc.Sym.Theo.on Computing,ACM(1995),635–640.[122]U.Feige,S.Goldwasser,L.Lov´a sz,S.Safra,and M.Szegedy,Approximating clique is al-most NP-complete,32nd Symposium on Foundations of Computer Science,IEEE Computer Society Press,(1991),2–12.[123]M.Fiedler,Algebraic connectivity of graphs,Czech.Math.J.23(98)(1973),298–305. [124]J.A.Fill,Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process,Ann.Appl.Prob.1(1991)62–87.[125]L.R.Ford and D.R.Fulkerson,Flows in Networks,Princeton Univ.Press(1962),xii+194 pp.[126]P.Frankl,A constructive lower bound for some Ramsey numbers,Ars Combinatoria3 (1977),297–302.[127]P.Frankl and V.R¨o dl,Forbidden intersections,Trans.AMS300(1987),259–286. [128]P.Frankl,V.R¨o dl and R.M.Wilson,The number of submatrices of a given type in a Hadamard matrix and related results,binatorial Th.(B)44(1988),317–328. [129]P.Frankl and R.M.Wilson,Intersection theorems with geometric consequences,Combina-torica1(1981),357–368.[130]M.L.Fredman,New bounds on the complexity of the shortest path problem,SIAM J.Computing5(1976),83–89.[131]J.Friedman,On the second eigenvalue and random walks in random d-regular graphs, Combinatorica11(1991),331–362.[132]J.Friedman and N.Pippenger,Expanding graphs contain all small trees,Combinatorica7 (1987),71–76.[133]G.Frobenius,¨Uber die Charaktere der alternierenden Gruppe,Sitzungsberichte Preuss.Akad.Wiss.(1901),303–315.[134]G.Frobenius,¨Uber Matrizen aus nicht negative Elementen,Sitzber.Akad.Wiss.Berlin (1912),456–477.[135]Z.F¨u redi and J.Koml´o s,The eigenvalues of random symmetric matrices,Combinatorica1 (1981),233–241.[136]O.Gabber and Z.Galil,Explicit construction of linear-sized superconcentrators,put.System Sci.22(1981),407–420.[137] A.Galtman,Spectral characterizations of the Lov´a sz number and Delsarte number of a graph,bin.12(2000),131–143.[138] F.R.Gantmacher,The Theory of Matrices,Vol.1,Chelsea Pub.Co.,New York(1977), x+374pp.[139]M.R.Garey and D.S.Johnson,Computers and Intractability,A Guide to the Theory of NP-Completeness,W.H.Freeman and Co.,San Francisco,1979,x+338pp.[140]M.Goemans and D.Williamson,Improved approximation algorithms for maximum cut and satisﬁability problems using semideﬁnite programming,J.ACM42(1995),1115–1145.206BIBLIOGRAPHY[141]P.Ginsbarg,Applied Conformal Field Theory,les Houches(1988),1–168.[142]W.Goddard,private communication.[143]R.L.Graham and V.R¨o dl,Numbers in Ramsey theory,Surveys in Combinatorics(1987),(C.Whitehead,ed.)London Math.Soc.Lecture Notes Series123,111–153.[144]S.W.Graham and C.Ringrose,Lower bounds for least quadratic nonresidues,Analytic Number Theory,(edited by B.Berndt,H.Halberstam,H.Diamond and A.Hildebrand), Birkh¨a user,Boston1990,264–309.[145]R.L.Graham and J.H.Spencer,A constructive solution to a tournament problem,Canad.Math.Bull.14(1971),45–48.[146] A.Grigor’yan,Integral maximum principle and its applications,Proc.of Royal Society, Edinburgh Sect.A,124(1994),353–362.[147]M.Gromov,Groups of polynomial growth and expanding maps,Publ.IHES,53(1981), 53–73.[148]L.Gross,Logarithmic Sobolev inequalities,Amer.J.Math.97(1975),1061-1083. [149]L.Gross,Logarithmic Sobolev inequalities and contractivity properties of semigroups, Springer Lecture Notes1563,(1993),54–88.[150]M.Grotschel,L.Lov´a sz and A.Schrijver,The ellipsoid method and its consequences in combinatorial optimization,Combinatorica1(1981),169–197.[151]M.Grotschel,L.Lov´a sz and A.Schrijver,Geometric Algorithms and Combinatorial Opti-mization,Springer-Verlag,Berlin,1988,xii+362pp.[152]W.Haemers,Eigenvalue methods in Packing and Covering in Combinatorics,(A.Schrijver ed.),Mathematisch Centrum,Amsterdam(1982),15–38.[153]M.M.Halldorsson,A still better performance guarantee for approximating graph coloring, Information Processing Letters45(1993),19–23.[154]L.H.Harper,Optimal numberings and isoperimetric problems on graphs,J.of Comb.Theory1(1966),385–393.[155]S.Hart,A note on the edges of the n-cube,Discrete Math.14(1976),157–163.[156]J.Hastad,Clique is hard to approximate within n1− ,37th Symposium on Foundations of Computer Science,IEEE Computer Society Press,(1996),627–636.[157]J.Haviland and A.Thomason,Pseudo-random hypergraphs,Discrete Math.75(1989), 255–278.[158]W.Hebisch and L.Saloﬀ-Coste,Gaussian estimates for Markov chains and random walks on groups,Ann.Probab.21(1993),673–709.[159] A.J.Hoﬀman,Eigenvalues of graphs,in Studies in Graph Theory II(D.R.Fulkerson,ed.), M.A.A.Studies in Math,Washington D.C.,(1975),225–245.[160] A.J.Hoﬀman and R.R.Singleton,On Moore graphs with diameter2and3,IBM J.of Res.Development4(1960),497–504.[161]R.A.Horn and C.R.Johnson,Matrix Analysis,Cambridge University Press,New York, 1985,xii+561pp.[162]J.Igusa,Fibre systems of Jacobian varieties III,American J.of Math.81(1959),453–476. [163]W.Imrich,Explicit construction of regular graphs without small cycles,Combinatorica4 (1984),53–59.[164]K.Ireland and M.Rosen,A Classical Introduction to Modern Number Theory,Springer-Verlag,New York1982,xiii+341pp.[165]M.Jerrum and A.J.Sinclair,Approximating the permanent,SIAM puting18(1989), 1149–1178.[166] F.Juh´a sz,On the spectrum of a random graph,Colloq.Math.Soc.J´a nos Bolyai25,Alge-braic Methods in Graphs Theory,Szeged(1978),313–316.[167]N.Kahale,Isoperimetric inequalities and eigenvalues,SIAM J.Discrete Math.,10(1997), 30–40.[168] D.Karger,R.Motwani,and M.Sudan,Approximate graph coloring by semi-deﬁnite pro-gramming,35th Symposium on Foundations of Computer science,IEEE Computer Society Press,1994,2–13.[169] B.S.Kashin and S.V.Konyagin,On systems of vectors in a Hilbert space,Trudy Mat.Inst.imeni V.A.Steklova157(1981)64–67.English translation in Proceedings of the Steklow Institute of Math.AMS(1983),67–70.[170]G.O.H.Katona,A theorem ofﬁnite sets,Theory of Graphs,Proc.Colloq.Tihany,Academic Press,New York,1966,187–207.BIBLIOGRAPHY207 [171]N.M.Katz,An estimate for character sums,J.Amer.Math.Soc.2(1989),197–200. [172] F.Kirchhoﬀ,¨Uber die Auﬂ¨o sung der Gleichungen,auf welche man bei der Untersuchung der linearen Verteilung galvanischer Str¨o me gef¨u hrt wird,Ann.Phys.chem.72(1847),497–508 [173]M.Klawe,Non-existence of one-dimensional expanding graphs,22nd Symposium on Foun-dations of Computer Science,IEEE Computer Society Press,(1981),109–113.[174] D.E.Knuth,The Art of Computer Programming,vol.3,Addison-Wesley,Reading,MA, 1973,xi+722pp.[175] D.E.Knuth,The sandwich theorem,Electronic J.of Combinatorics1(1994),A1,48pp. [176]J.B.Kruskal,The number of simplices in a complex,Mathematical Optimization Tech-niques,(ed.R.Bellman),University of California Press,Berkeley,1963,251–78,.[177]nglands and Y.Saint-Aubin,Algebro-geometric aspects of the Bethe equations, Strings and Symmetries,Lecture Notes in Phys.447,Springer,Berlin,1995,40–53. [178] zebnik,timenko and A.J.Woldar,A new series of dense graphs of high girth, Bull.Amer.Math.Soc.32(1995),73–79.[179] F.T.Leighton,Introduction to Parallel Algorithms and Architectures:Arrays,Trees,Hy-percubes,Morgan-Kauﬀman,San Mateo,CA,1992,xx+831pp.[180] F.T.Leighton and S.Rao,An approximate max-ﬂow min-cut theorem for uniform multi-commodityﬂow problem with applications to approximation algorithms,29th Symposium on Foundations of Computer Science,IEEE Computer Society Press,(1988),422–431. [181]T.Lengauer and R.E.Tarjan,Asymptotically tight bounds on time-space trade-oﬀs in a pebble game,put.Mach.29(1982),1087–1130.[182]H.Lenstra,personal communication.[183]G.Lev,Size bounds and parallel algorithms for networks,Ph.D.Thesis,Department of Computer Science,University of Edinburg.[184]W.Li,Character sums and abelian Ramanujan graphs,J.Number Theory41(1992),199–217.[185]P.Li and S.-T.Yau,On the parabolic kernel of the Schr¨o dinger operator,Acta Mathematica 156(1986),153–201.[186]P.Li and S.-T.Yau,Estimates of eigenvalues of a compact Riemannian manifold,Amer.Math.Soc.Proc.Symp.Pure Math.36(1980),205–239.[187]J.H.Lindsey,Assignment of numbers to vertices,Amer.Math.Monthly71(1964),508–516. [188]R.J.Lipton and R.E.Tarjan,A separator theorem for planar graphs,SIAM J.Appl.Math.36(1979),177–189.[189]L.Lov´a sz,On the Shannon capacity of a graph,Transactions on Information Theory-IT-25,IEEE Computer Society Press,(1979),1–7.[190]L.Lov´a sz,Perfect graphs,in Selected Topics in Graph Theory2,(eds R.L.Wilson and L.W.Beineke),Academic Press,New York(1983),55–87.[191]L.Lov´a sz and M.Simonovits,Random walks in a convex body and an improved volume algorithm,Random Structures and Algorithms4(1993),359–412.[192] A.Lubotzky,R.Phillips and P.Sarnak,Ramanujan graphs,Combinatorica8(1988),261–277.[193]G.A.Margulis,Explicit constructions of concentrators,Problemy Peredaci Informacii9 (1973),71–80(English transl.in Problems Inform.Transmission9(1975),325–332. [194]G.A.Margulis,Arithmetic groups and graphs without short cycles,6th Internat.Symp.on Information Theory,Tashkent(1984)Abstracts1,123–125(in Russian).[195]G.A.Margulis,Some new constructions of low-density parity check codes,3rd Internat.Seminar on Information Theory,convolution codes and multi-user communication,Sochi (1987),275–279(in Russian).[196]G.A.Margulis,Explicit group theoretic constructions of combinatorial schemes and their applications for the construction of expanders and concentrators,Problemy Peredaci Infor-macii(1988)(in Russian).[197]J.C.Maxwell,A Treatise on Electricity and Magnetism I,Oxford,Clarendon Press(1892), 403–410.[198]R.J.McEliece, E.R.Rodemich,and H.C.Rumsey,Jr.,The Lov´a sz bound and some generalizations,binatorics,Inform.Syst.Sci.3(1978),134–152.[199] B.Mohar,Isoperimetric number of graphs,J.of Comb.Theory(B)47(1989),274–291. [200]H.L.Montgomery,Topics in Multiplicative Number Theory,Lecture Notes in Math.227, Springer-Verlag,New York(1971),ix+178pp.208BIBLIOGRAPHY[201]J.W.Moon,Counting Labelled Trees,Canadian Mathematical Monographs,Canadian Mathematical Congress,Montreal,1970,x+113pp.[202]Z.Nagy,A constructive estimate of the Ramsey number,pok23(1975),301–302. [203] A.Nilli,On the second eigenvalue of a graph,Discrete Math.91(1991),207–210.[204] B.Osgood,R.Phillips,and P.Sarnak,Extremals of determinants of Laplacians,J.Funct.Anal.80(1988),148-211.[205] B.Osgood,R.Phillips,and P.Sarnak,Moduli space,heights and isospectral sets of plane domains,Ann.Math.129(1989),293–362.[206] E.M.Palmer,Graphical Evolution,John Wiley and Sons,New York(1985),xvii+177pp. [207]W.J.Paul,R.E.Tarjan and J.R.Celoni,Space bounds for a game on graphs,Math.Systems.Theory10(1977),239–251.[208]O.Perron,Zur Theorie der Matrizen,Math.Ann.64(1907),248–263.[209]M.Pinsker,On the complexity of a concentrator,7th Internat.Teletraﬃc Conf.,Stockholm, June1973,318/1–318/4.[210]N.Pippenger,Superconcentrators,SIAM put.6(1977),298–304.[211]N.Pippenger,Advances in pebbling,Internat.Collo.On Automation Languages and Pro-gramming9(1982),407–417.[212]G.Poly´a and S.Szeg¨o,Isoperimetric Inequalities in Mathematical Physics,Annals of Math.Studies,no.27,Princeton University Press,(1951),xvi+279pp.[213] A.M.Polyakov,Quantum geometry of bosonic strings,Phys.Letters B103(1981),207–210. [214]S.Ramanujan,On certain arithmetical functions,Trans.Cambridge Philos.Soc.22(9) (1916),159–184.[215] F.P.Ramsey,On a problem of formal logic,Proc.London Math.Soc.30(1930),264–286. [216] D.Ray and I.M.Singer,Analytic torsion for complex manifolds,Ann.Math.98(1973), 154–177.[217] D.K.Ray-Chaudhuri and R.M.Wilson,On t-designs,Osaka J.Math.12(1975),737–744. [218] A.R´e nyi,On the enumeration of trees,in Combinatorial Structures and their Applications (R.Guy,H.Hanani,N.Sauer,and J.Schonheim,eds.)Gordon and Breach,New York(1970), 355–360.[219]V.R¨o dl,On universality of graphs with uniformly distributed edges,Discrete Math.59 (1986),125–134.[220]P.Sarnak,Determinants of Laplacians,Comm.Math.Phys.110(1987),113–120. [221]P.Sarnak,Some Applications of Modular Forms,Cambridge University Press,Cambridge, 1990,x+111pp.[222] A.Schrijver,A comparison of the Delsarte and Lov´a sz bounds,IEEE Transactions on Information Theory IT-25,(1979),425–429.[223]J.J.Seidel,Graphs and their spectra,Combinatorics and Graph Theory,PWN-Polish Scientiﬁc Publishers,Warsaw(1989),147–162.[224]R.Seidel,On the all-pairs-shortest-path problem,Proc.Sym.Theo.on Computing,ACM (1992),745–749.[225]M.Simonovits and V.T.S´o s,Szemer´e di’s partition and quasirandomness,Random Struc-tures and Algorithms2(1991),1–10.[226] A.J.Sinclair,Algorithms for Random Generation and Counting,Birkhauser,Boston,1993, vi+146pp.[227] A.J.Sinclair and M.R.Jerrum,Approximate counting,uniform generation,and rapidly mixing markov chains,Information and Computation82(1989),93–133.[228]R.Singleton,On minimal graphs of maximum even girth,bin.Theory1(1966), 306–332.[229]J.Spencer,Optimal ranking of tournaments,Networks1(1971),135–138.[230]J.Spencer,Ramsey’s theorem–A new lower bound,binatorial Theory18(1975), 108–115.[231]S.Sternberg,Group Theory in Physics,Cambridge University Press,Cambridge,1994.xiv+429pp.[232] D.W.Stroock,Logarithmic Sobolev inequalities for Gibbs states,Springer Lecture Notes 1563,Berlin,(1993),194–228.[233]J.J.Sylvester,On the change of systems of independent variables,Quarterly Journal of Mathematics1(1857),42–56.Collected Mathematical Papers,Cambridge2(1908),65–85.。

bibliography

bibliographyBibliographyIntroduction:In the academic and research world, the importance of a bibliography cannot be overstated. A bibliography is a comprehensive list of the sources used in a research paper, thesis, or any other written work. It serves multiple purposes, including acknowledging the original authors and their contributions, avoiding plagiarism, providing additional sources for readers to explore, and establishing the credibility of the work.Purpose of a Bibliography:The primary purpose of a bibliography is to give credit to the authors of referenced works. By citing the sources used, researchers show respect for the original authors' ideas and expertise. Additionally, a bibliography allows readers to verify the information presented in the paper and delve deeper into the topic. It also serves as a roadmap for future researchers who want to explore the same or related subjects.Components of a Bibliography:A bibliography typically includes various components, depending on the citation style used. The most common elements found in a bibliography are:1. Author's Name: The surname and first name or initials of the author should be provided. In the case of multiple authors, all their names should be listed.2. Title of the Work: The title of the book, article, or document being referenced should be included. If it is an article or chapter within a larger work, it should be enclosed in quotation marks.3. Publication Information: This includes the name of the book or journal, the publisher, and the publication date. For journals, the volume and issue numbers, as well as the page range, should also be mentioned.4. Web Sources: When citing online sources, the URL, access date, and any associated digital object identifier (DOI) shouldbe included. In some cases, if the webpage does not provide the author's name or publication date, it may be omitted.5. Additional Information: Depending on the citation style, additional information such as the edition, translator's name, or specific page numbers may be required.Citation Styles:There are various citation styles used in different academic disciplines. The most widely used citation styles include:1. APA (American Psychological Association): Commonly used in social sciences, education, and psychology-related fields.2. MLA (Modern Language Association): Primarily used in humanities and liberal arts subjects.3. Chicago/Turabian: Used for history, social sciences, and natural sciences.4. Harvard: Widely used in the sciences and social sciences.5. IEEE (Institute of Electrical and Electronics Engineers): Mainly used in engineering, computer science, and information technology.Each citation style has specific guidelines for formatting the bibliography and in-text citations, so it is crucial to adhere to the specific style required by the institution or publisher.Benefits of a Bibliography:Apart from acknowledging the original sources and preventing plagiarism, a well-constructed bibliography offers several benefits to both the writer and the reader. These include:1. Enhancing Credibility: By providing a comprehensive list of references, the author demonstrates that their work is built upon a sound foundation and relies on accurate and reliable information.2. Extending Knowledge: Readers can use the bibliography to explore additional sources related to the topic. This not onlyimproves their understanding but also allows them to explore different perspectives and build their own knowledge base.3. Simplifying the Research Process: Researchers can save time and effort by referring to the bibliography of a well-written paper. Often, the bibliography itself directs readers to key works, eliminating the need for them to search for relevant sources from scratch.Conclusion:In conclusion, a bibliography is an indispensable component of any academic or research paper. It serves as a testament to the author's academic integrity, provides a roadmap for further exploration, and allows readers to verify and extend their knowledge. By understanding the purpose and components of a bibliography and adhering to the appropriate citation style, researchers can ensure that their work remains credible and contributes to the existing body of knowledge.。

Bibliography

BibliographyAlmqvist Norbelie, Barbro. “Oppressive Narrowness”: A Study of the Female Community in George Eliot’s Early Writings. Philadelphia: Coronet Books Inc.,1992.Anolik, Ruth B. and Douglas L. Howard, eds. The Gothic Other: Radical and Social Constructions in the Literary Imagination. Jefferson, N. C.: McFarland & Co.,2004.Bernstein, Susan David. Confessional Subjects: Revelations of Gender and Power in Victorian Literature and Culture. Chapel Hill: U of North Carolina P, 1997. Bourke, Joanna. Fear: A Culture History. London: Virago, 2005.Briggs, Asa. Victorian People: A Reassessment of Persons and Themes, 1851-67.Chicago: U of Chicago P, 1970.Day, William P. In the Circles of Fear and Desire: A Study of Gothic Fantasy. Chicago: U of Chicago P, 1985.Eliot, George. Adam Bede. New York: Penguin, 2008.Fisher, Trevor. Scandal: the Sexual Politics of Late Victorian Britain. Gloucestershire: A.Sutton, 1995.Gregg, Melissa and Gregory J. Seigworth, eds. The Affect Theory Reader. Durham: Duke UP, 2010.Hardy, Thomas. Tess of the d’Urbervilles. Oxford: Oxford UP, 1983.Hallissy, Margaret. Venomous Woman: A Fear of the Female in Literature. New York: Greenwood Press, 1987.Hancock, Stephen. The Romantic Sublime and Middle-Class Subjectivity in the Victorian Novel. New York: Routledge, 2005.Harré, Rom and Fathali M. Moghaddam, eds. The Self and Others: Positioning Individuals and Groups in Personal, Political, and Cultural Contexts. Westport,Ct.: Praeger, 2003.Hebblethwaite, Kate and Elizabeth McCarthy, eds. Fear: Essays on the Meaning and Experience of Fear. Dublin: Four Courts Press, 2007.Jaffe, Audrey. Scenes of Sympathy: Identity and Representation in Victorian Fiction.Ithaca: Cornell UP, 2000.Kalaga, Wojciech, ed. Civilisation and Fear: Anxiety and the Writing of the Subject.Newcastle: Cambridge Scholars Publishing, 2012.Marck, Nancy A. “Narrative Transference and Female Narcissism: the Social Message of Adam Bede.” Studies in the Novel. 35.4 (2003): 447-70.Meyers, Helene. Femicidal Fears: Narratives of the Female Gothic Experience. Albany: State U of New York P, 2001.Mitchell, Judith. The Stone and the Scorpion: the Female Subject of Desire in the Novels of Charlotte Brontë, George Eliot, and Thomas Hardy. Westport, Ct.: Greenwood Press, 1994.Navarette, Susan J. The Shape of Fear: Horror and the Fin de Siècle Culture of Decadence. Lexington: UP of Kentucky, 1998.Parks, Tim. “Fear and Courage Versus Good and Evil: Warring Polarities in the Writings of Thomas Hardy and D. H. Lawrence.”Thomas Hardy Journal. 26 (2010): 151-72.Panek, Jennifer. “Constructions of Masculinity in Adam Bede and Wives and Daughters.”Victorian Review. 22.2 (1996): 127-51.Ragussis, Michael. “Tess of the d’Urbervilles.” Acts of Naming: the Family Plot in Fiction. New York: Oxford UP, 1986.Tague, Gregory. Character and Consciousness: George Eliot, Thomas Hardy, E. M.Forster, D. H. Lawrence (Phenomenological, Ecological, and Ethical Readings).Bethesda, Md.: Academica, 2005.Young, Kay. Imagining Minds: the Neuro-Aesthetics of Austen, Eliot, and Hardy.Columbus: Ohio State UP, 2010.。

bibliography格式--论文参考文献格式

Bibliography FormatsA bibliography should cite all the sources used in preparing a speech — including Internet documents, personal interviews, and television programs, as well as print materials such asbooks,newspaper and magazine articles,reference works,government documents,and the like.There are a number of bibliographical formats,and you should check with your instructor to see which she or he wants you to follow. Examples of the two major formats—from the American Psychological Association (APA) and the Modern Language Association(MLA) —are provided below.Book: Single AuthorMLA Ramos, Jorge.Dying to Cross: The Worst Immigrant Tragedy in American History. New York: Harper, 2005.APARamos, J. (2005).Dying to cross: The worst immigrant tragedy in American history. New York: HarperCollins.Book: Two or More AuthorsMLA Levitt, Steven D., and Stephen J. Dubner.Freakonomics: A Rogue Economist Explores the Hidden Side of Everything. New York: Morrow-Harper, 2005.APA Levitt, S. D., & Dubner, S. J. (2005).Freakonomics: A rogue economist explores the hidden side of everything. New York: William Morrow.Book: Second or Later EditionMLAFishman, Stephen.The Public Domain: How to Find & Use Copyright-Free Writings, Music, Art & More. 2nd ed. Berkeley: Nolo, 2004.APA Fishman, S. (2004).The public domain: How to find & use copyright-free writings, music, art, & more(2nd ed.). Berkeley: Nolo.Book: Corporate AuthorMLA Mayo Clinic Health Information.Mayo Clinic Guide to Women's Cancers. Rochester, MN: Mayo Clinic Health Information, 2005.APA Mayo Clinic Health Information. (2005).Mayo clinic guide to women's cancers. Rochester, MN: Mayo Clinic Health Information.Book: Anthology or CompilationMLA Sloane, Thomas O., ed.Encyclopedia of Rhetoric. New York: Oxford University Press, 2001. APA Sloane, T. O. (Ed.). (2001).Encyclopedia of rhetoric. New York: Oxford University Press. Chapter in Anthology or CompilationMLA Lucas, Stephen E. "Public Speaking."Encyclopedia of Rhetoric. Ed. Thomas O. Sloane. New York: Oxford University Press, 2001. 640-47.APA Lucas, S. E. (2001). Public Speaking. In T. O. Sloane (Ed.),Encyclopedia of rhetoric (pp. 640-647). New York: Oxford University Press.Signed Magazine ArticleMLA Johnson, Steven. "Your Brain on Video Games: Could They Actually be Good for You?"Discover July 2005: 38-43.APAJohnson, S. (2005, July). Your brain on video games: Could they actually be good for you?Discover, 26, 38-43.Unsigned Magazine ArticleMLA"Banking for Native Americans: On the Trail."Economist19 Feb. 2005: 70.APA Banking for native Americans: On the trail. (2005, February 19).Economist, 374, 70. Journal Article, Continuous PaginationMolinsky, Andrew L., Mary Anne Krabbenhoft, Nalini Ambady, and Y. Susan Choi. "Cracking theMLA Nonverbal Code: Intercultural Competence and Gesture Recognition Across Cultures."Journal of Cross-Cultural Psychology36 (2005): 380-395.Molinsky, A. L., Krabbenhoft, M. A., Ambady, N., & Choi, Y. S. (2005). Cracking the nonverbalAPA code: Intercultural competence and gesture recognition across cultures.Journal of Cross-Cultural Psychology, 36, 380-395.Journal Article, Noncontinuous PaginationMLA Gómez, Christina. "Latino Diversity and Political Representation."Journal of Latino-Latin American Studies 1.2 (2004): 19-32.APA Gómez, C. (2004). Latino diversity and political representation.Journal of Latino-Latin American Studies, 1(2), 19-32.Signed Newspaper ArticleMLA Elliot, Andrea. "In a Now-Suspicious America, Muslim Converts Face Discrimination."New York Times30 Apr. 2005, natl. ed.: A13.APAElliot, A. (2005, April 30). In a now-suspicious America, Muslim converts face discrimination.New York Times, p. 13A.Unsigned Newspaper ArticleMLA "Fatal Error: Seat-Belt Use Less in Pickups."Chicago Tribune16 May 2005, Midwest ed., sec.1: 6.APA Fatal error: Seat-belt use less in pickups. (2005, May 16).Chicago Tribune, section 1, p. 6. Signed Newspaper EditorialMLA Reyes, Raul A. "Cinco de Mayo and Social Security." A Today 6 May 2005, final ed.: 13A.APA Reyes, R. A. (2005, May 6). Cinco de Mayo and social security [Editorial].USA Today , p. 13A. Unsigned Newspaper EditorialMLA"Sesame Street's Private Road." Editorial.Christian Science Monitor12 May 2005: 8.APA Sesame street's private road [Editorial]. (2005, May 12).Christian Science Monitor, p. 8. Government PublicationMLA United States. U.S. Equal Employment Opportunity Commission.Indicators of Equal Employment Opportunity—Status and Trends. Washington: GPO, 2004.APAU.S. Equal Employment Opportunity Commission. (2004).Indicators of equal employment opportunity—Status and trends. Washington, DC: U.S. Government Printing Office.Signed Article in Reference WorkMLA Alvarez-Smith, Alma. "Pantoja, Antonia."Encyclopedia of Latino Popular Culture. Ed. Cordelia Ch vezáCandelaria. 2 vols. Westport, CT: Greenwood, 2004.APA Alvarez-Smith, A. (2004). Pantoja, Antonia. In C. C. Candelaria (Ed.),Encyclopedia of Latino popular culture(Vol. 2, pp. 613-614). Westport, CT: Greenwood.Unsigned Article in Reference WorkMLA "Pinchback, Pinckney Benton Stewart."African-American Political Leaders. Ed. Charles W. Carey, Jr. New York: Facts on File, 2004.APA Pinchback, Pinckney Benton Stewart. (2004). In C. W. Carey, Jr. (Ed.),African-American political leaders(pp. 212-215). New York: Facts on File.Personal InterviewMLA Velasquez, Andrew. Personal interview. 12 July 2005.APA A. Velasquez (personal communication, July 12, 2005)Letter or E-Mail CommunicationMLA Ahmed, Mohammed. E-mail interview. 11 Feb. 2005.APA M. Ahmed (personal communication, February 11, 2005)Speech or LectureHuang, Wensha. Lecture on water pollution. Geography 212: Environmental Science. University MLAof Florida. 25 Feb. 2005.Huang, W. (2005, February 25). Water pollution [Lecture]. In Geography 212: Environmental APAscience. University of Florida.Television ProgramMLA"Medical Tourists." Narr. Bob Simon. I. CBS. WCBS, New York. 24 Apr. 2005.APA Olian, C. (Producer). (2005, April 24). Medical tourists [Television broadcast]. In Sixty minutes .New York: Columbia Broadcasting System.FilmMLA The Untold Story of Emmett Louis Till. Dir. Keith A. Beauchamp. SJL Management, 2004.Beauchamp, K. A. (Director). (2004).The untold story of Emmett Louis Till[Motion picture]. APA United States. (Available from SJL Management, 400 East 58th Street, Suite 7G, New York,NY 10022)Article in Scholarly Journal Reprinted OnlineFrith, Katherine, Ping Shaw, and Hong Cheng. "The Construction of Beauty: A Cross-CulturalMLA Analysis of Women's Magazine Advertising."Journal of Communication55.1 (2005): 56-70.27 Apr. 2005 </cgi/reprint/55/1/56.pdf>.Frith, K., Shaw, P., & Cheng, H. (2005). The construction of beauty: A cross-cultural analysis ofAPA women's magazine advertising.Journal of Communication, 55, 56-70. Retrieved April 27, 2005, from /cgi/reprint/55/1/56.pdfArticle in Online Scholarly JournalKelsey, Kathleen D., and Alan D'souza. "Student Motivation for Learning at a Distance: DoesMLAOnline Journal of Distance Learning Administration7.2 (2004): 13 pp.Interaction Matter?"30 Apr. 2005 </%7Edistance/ojdla/summer72/kelsey72.html>.Kelsey, K. D., & D'souza, A. (2004). Student motivation for learning at a distance: DoesAPA interaction matter? Online Journal of Distance Learning Administration , 7(2). Retrieved April 30, 2005, from /%7Edistance/ojdla/summer72/kelsey72.htmlOnline Government PublicationUnited States. Dept. of Energy. Energy Information Administration. Office of Integrated AnalysisMLA and Forecasting.Annual Energy Outlook 2005 With Projections to 2025. Feb. 2005. 13 May 2005 </oiaf/aeo/pdf/0383(2005).pdf>.United States Department of Energy, Office of Integrated Analysis and Forecasting. (2005,APA February).Annual energy outlook 2005 with projections to 2025. Retrieved May 13, 2005, from /oiaf/aeo/pdf/0383(2005).pdfOnline Newspaper ArticleWulfhorst, Ellen. "Study: Blogs Haven't Displaced Media."Washington Post16 May 2005. 17 May MLA2005 </wp-dyn/content/article/2005/05/16/AR2005051600884.html>.APAWulfhorst, E. (2005, May 16). Study: Blogs haven't displaced media.Washington Post. Retrieved May 17, 2005, from Online EditorialKinsley, Michael. "Remember: You Can't Swat a Fly with a Computer." Editorial.Los AngelesMLA Times 8 May 2005. 11 May 2005 </news/opinion/la-oe-kinsley8may08,1,7723084.column?coll=la-util-op-ed>.Kinsley, M. (2005, May 8). Remember: You can't swat a fly with a computer [Editorial].Los APA Angeles Times. Retrieved May 11, 2005, from /news/opinion/la-oe-kinsley8may08,1,7723084.column?coll=la-util-op-edOnline Magazine ArticleMLAHerper, Matthew. "Race-Based Medicine Arrives." 10 May 2005. 11 May 2005 </business/2005/05/10/cx_mh_0509racemedicine.html>.APA Herper, M. (2005, May 10). Race-based medicine . Retrieved May 11, 2005, from /business/2005/05/10/cx_mh_0509racemedicine.htmlDocument Accessed from Online ServiceMcCartney, Anthony. "Online Thieves Are Fishing For Suckers."Tampa Tribune9 Feb. 2005: 9. MLA Academic Universe: News. Lexis-Nexis. Memorial Library, Madison, WI. 4 June 2005</universe/>.APA McCartney, A. (2005, February 9). Online thieves are fishing for suckers.Tampa Tribune .Retrieved April 29, 2005, from Lexis/Nexis Academic Universe database.Online Document from BroadcastMLA "Paleontologist Disputes Altering Discovery.". 2005. Cable News Network. 13 May 2005 </2005/TECH/science/05/13/paleontologist.movies.ap/index.html>.Paleontologist disputes altering discovery. (2005, May 13).Cable News Network. Retrieved MayAPA13, 2005, from /2005/TECH/science/05/13/paleontologist.movies.ap /index.html。

bibliography的英文介绍

bibliography的英文介绍Bibliography是指一个文献清单或书目，其中列出了某个学科或主题领域内的所有参考书籍、期刊、文章和其他来源。

在学术和研究领域中，Bibliography是非常重要的，因为它可以帮助读者深入了解某个领域内最新的研究成果，也可以为其他学者提供参考，促进学术交流和合作。

Bibliography通常会按照一定的格式来列出引用文献的信息。

下面是一些常见的Bibliography格式：1. MLA格式：这是一种非常常见的学术论文引用格式。

在此格式下，书目通常会以作者姓名、书名、出版信息等方式列出。

2. APA格式：这种格式经常用于心理学和社会科学领域的论文和研究。

在APA格式下，书目通常会以作者、出版年份、书名、出版商等方式列出。

3. Chicago格式：这是一种比较详细的书目格式，通常会列出对于每个书目信息的详细描述。

在此格式下，书目通常会按照作者、书名、出版商、出版年份、页码等方式详细描述。

Bibliography也可以根据不同的主题或研究领域进行分类。

下面是一些常见的Bibliography分类：1. 主题Bibliography：这种Bibliography主要针对某个特定主题或领域进行整理分类。

例如，一本关于爱因斯坦的书籍的Bibliography就是一个针对物理学领域的主题Bibliography。

2. 作者Bibliography：这种Bibliography列出一个作者的所有书籍和文章，帮助研究者全面了解该作者的研究成果。

3. 期刊Bibliography：这种Bibliography列出某个期刊上发表的所有文章，帮助读者了解该期刊上的最新研究成果。

Bibliography的作用和价值不仅仅在于提供参考和引用，还可以帮助读者进行更深入的研究和思考。

对于研究者来说，Bibliography是一个极具价值的资源，可以节约大量的时间和精力，为他们的研究工作提供帮助和支持。

bibliography格式--论文参考文献格式

Bibliography FormatsA bibliography should cite all the sources used in preparing a speech—including Internet documents, personal interviews, and television programs, as well as print materials such as books, newspaper and magazine articles, reference works, government documents, and the like. There are a number of bibliographical formats, and you should check with your instructor to see which she or he wants you to follow. Examples of the two major formats—from the American Psychological Association (APA) and the Modern Language Association (MLA)—are provided below.Book: Single AuthorMLA Ramos, Jorge. Dying to Cross: The Worst Immigrant Tragedy in American History. New York: Harper, 2005.APA Ramos, J. (2005). Dying to cross: The worst immigrant tragedy in American history. New York: HarperCollins.Book: Two or More AuthorsMLA Levitt, Steven D., and Stephen J. Dubner. Freakonomics: A Rogue Economist Explores the Hidden Side of Everything. New York: Morrow-Harper, 2005.APA Levitt, S. D., & Dubner, S. J. (2005). Freakonomics: A rogue economist explores the hidden side of everything. New York: William Morrow.Book: Second or Later EditionMLA Fishman, Stephen. The Public Domain: How to Find & Use Copyright-Free Writings, Music, Art & More. 2nd ed. Berkeley: Nolo, 2004.APA Fishman, S. (2004). The public domain: How to find & use copyright-free writings, music, art, & more (2nd ed.). Berkeley: Nolo.Book: Corporate AuthorMLA Mayo Clinic Health Information. Mayo Clinic Guide to Women's Cancers. Rochester, MN: Mayo Clinic Health Information, 2005.APA Mayo Clinic Health Information. (2005). Mayo clinic guide to women's cancers. Rochester, MN: Mayo Clinic Health Information.Book: Anthology or CompilationMLA Sloane, Thomas O., ed. Encyclopedia of Rhetoric. New York: Oxford University Press, 2001. APA Sloane, T. O. (Ed.). (2001). Encyclopedia of rhetoric. New York: Oxford University Press. Chapter in Anthology or CompilationMLA Lucas, Stephen E. "Public Speaking." Encyclopedia of Rhetoric. Ed. Thomas O. Sloane. New York: Oxford University Press, 2001. 640-47.APA Lucas, S. E. (2001). Public Speaking. In T. O. Sloane (Ed.), Encyclopedia of rhetoric (pp. 640-647). New York: Oxford University Press.Signed Magazine ArticleMLA Johnson, Steven. "Your Brain on Video Games: Could They Actually be Good for You?" Discover July 2005: 38-43.APA Johnson, S. (2005, July). Your brain on video games: Could they actually be good for you?Discover, 26, 38-43.Unsigned Magazine ArticleMLA "Banking for Native Americans: On the Trail." Economist 19 Feb. 2005: 70.APA Banking for native Americans: On the trail. (2005, February 19). Economist, 374, 70. Journal Article, Continuous PaginationMLA Molinsky, Andrew L., Mary Anne Krabbenhoft, Nalini Ambady, and Y. Susan Choi. "Cracking the Nonverbal Code: Intercultural Competence and Gesture Recognition Across Cultures."Journal of Cross-Cultural Psychology 36 (2005): 380-395.APA Molinsky, A. L., Krabbenhoft, M. A., Ambady, N., & Choi, Y. S. (2005). Cracking the nonverbal code: Intercultural competence and gesture recognition across cultures. Journal ofCross-Cultural Psychology, 36, 380-395.Journal Article, Noncontinuous PaginationMLA Gómez, Christina. "Latino Diversity and Political Representation." Journal of Latino-Latin American Studies 1.2 (2004): 19-32.APA Gómez, C. (2004). Latino diversity and political representation. Journal of Latino-Latin American Studies, 1(2), 19-32.Signed Newspaper ArticleMLA Elliot, Andrea. "In a Now-Suspicious America, Muslim Converts Face Discrimination." New York Times 30 Apr. 2005, natl. ed.: A13.APA Elliot, A. (2005, April 30). In a now-suspicious America, Muslim converts face discrimination. New York Times, p. 13A.Unsigned Newspaper ArticleMLA "Fatal Error: Seat-Belt Use Less in Pickups." Chicago Tribune 16 May 2005, Midwest ed., sec.1: 6.APA Fatal error: Seat-belt use less in pickups. (2005, May 16). Chicago Tribune, section 1, p. 6. Signed Newspaper EditorialMLA Reyes, Raul A. "Cinco de Mayo and Social Security." Editorial. USA Today 6 May 2005, final ed.: 13A.APA Reyes, R. A. (2005, May 6). Cinco de Mayo and social security [Editorial]. USA Today, p. 13A. Unsigned Newspaper EditorialMLA "Sesame Street's Private Road." Editorial. Christian Science Monitor 12 May 2005: 8.APA Sesame street's private road [Editorial]. (2005, May 12). Christian Science Monitor, p. 8. Government PublicationMLA United States. U.S. Equal Employment Opportunity Commission. Indicators of Equal Employment Opportunity—Status and Trends. Washington: GPO, 2004.APA U.S. Equal Employment Opportunity Commission. (2004). Indicators of equal employment opportunity—Status and trends. Washington, DC: U.S. Government Printing Office.Signed Article in Reference WorkMLA Alvarez-Smith, Alma. "Pantoja, Antonia." Encyclopedia of Latino Popular Culture. Ed. Cordelia Chávez Candelaria. 2 vols. Westport, CT: Greenwood, 2004.APA Alvarez-Smith, A. (2004). Pantoja, Antonia. In C. C. Candelaria (Ed.), Encyclopedia of Latino popular culture (Vol. 2, pp. 613-614). Westport, CT: Greenwood.Unsigned Article in Reference WorkMLA "Pinchback, Pinckney Benton Stewart." African-American Political Leaders. Ed. Charles W. Carey, Jr. New York: Facts on File, 2004.APA Pinchback, Pinckney Benton Stewart. (2004). In C. W. Carey, Jr. (Ed.), African-American political leaders (pp. 212-215). New York: Facts on File.Personal InterviewMLA Velasquez, Andrew. Personal interview. 12 July 2005. APA A. Velasquez (personal communication, July 12, 2005) Letter or E-Mail CommunicationMLA Ahmed, Mohammed. E-mail interview. 11 Feb. 2005. APA M. Ahmed (personal communication, February 11, 2005) Speech or LectureMLA Huang, Wensha. Lecture on water pollution. Geography 212: Environmental Science. University of Florida. 25 Feb. 2005.APA Huang, W. (2005, February 25). Water pollution [Lecture]. In Geography 212: Environmental science. University of Florida.Television ProgramMLA "Medical Tourists." Narr. Bob Simon. I. CBS. WCBS, New York. 24 Apr. 2005.APA Olian, C. (Producer). (2005, April 24). Medical tourists [Television broadcast]. In Sixty minutes. New York: Columbia Broadcasting System.FilmMLA The Untold Story of Emmett Louis Till. Dir. Keith A. Beauchamp. SJL Management, 2004.APA Beauchamp, K. A. (Director). (2004). The untold story of Emmett Louis Till [Motion picture].United States. (Available from SJL Management, 400 East 58th Street, Suite 7G, New York, NY 10022)Article in Scholarly Journal Reprinted OnlineMLA Frith, Katherine, Ping Shaw, and Hong Cheng. "The Construction of Beauty: A Cross-CulturalAnalysis of Women's Magazine Advertising." Journal of Communication 55.1 (2005): 56-70.27 Apr. 2005 </cgi/reprint/55/1/56.pdf>.APA Frith, K., Shaw, P., & Cheng, H. (2005). The construction of beauty: A cross-cultural analysis of women's magazine advertising. Journal of Communication, 55, 56-70. Retrieved April 27, 2005, from /cgi/reprint/55/1/56.pdfArticle in Online Scholarly JournalMLA Kelsey, Kathleen D., and Alan D'souza. "Student Motivation for Learning at a Distance: DoesInteraction Matter?" Online Journal of Distance Learning Administration 7.2 (2004): 13 pp.30 Apr. 2005 </%7Edistance/ojdla/summer72/kelsey72.html>.APA Kelsey, K. D., & D'souza, A. (2004). Student motivation for learning at a distance: Doesinteraction matter? Online Journal of Distance Learning Administration, 7(2). Retrieved April 30, 2005, from /%7Edistance/ojdla/summer72/kelsey72.htmlOnline Government PublicationMLA United States. Dept. of Energy. Energy Information Administration. Office of Integrated Analysis and Forecasting. Annual Energy Outlook 2005 With Projections to 2025. Feb. 2005. 13 May 2005 </oiaf/aeo/pdf/0383(2005).pdf>.APA United States Department of Energy, Office of Integrated Analysis and Forecasting. (2005,February). Annual energy outlook 2005 with projections to 2025. Retrieved May 13, 2005, from /oiaf/aeo/pdf/0383(2005).pdfOnline Newspaper ArticleMLA Wulfhorst, Ellen. "Study: Blogs Haven't Displaced Media." Washington Post 16 May 2005. 17 May 2005 </wp-dyn/content/article/2005/05/16/AR2005051600884.html>.APA Wulfhorst, E. (2005, May 16). Study: Blogs haven't displaced media. Washington Post. Retrieved May 17, 2005, from Online EditorialMLA Kinsley, Michael. "Remember: You Can't Swat a Fly with a Computer." Editorial. Los Angeles Times 8 May 2005. 11 May 2005 </news/opinion/la-oe-kinsley8may08,1,7723084.column?coll=la-util-op-ed>.APA Kinsley, M. (2005, May 8). Remember: You can't swat a fly with a computer [Editorial]. Los Angeles Times. Retrieved May 11, 2005, from /news/opinion/la-oe-kinsley8may08,1,7723084.column?coll=la-util-op-edOnline Magazine ArticleMLA Herper, Matthew. "Race-Based Medicine Arrives." 10 May 2005. 11 May 2005 </business/2005/05/10/cx_mh_0509racemedicine.html>.APA Herper, M. (2005, May 10). Race-based medicine arrives. . Retrieved May 11, 2005, from /business/2005/05/10/cx_mh_0509racemedicine.htmlDocument Accessed from Online ServiceMLA McCartney, Anthony. "Online Thieves Are Fishing For Suckers." Tampa Tribune 9 Feb. 2005: 9. Academic Universe: News. Lexis-Nexis. Memorial Library, Madison, WI. 4 June 2005</universe/>.APA McCartney, A. (2005, February 9). Online thieves are fishing for suckers. Tampa Tribune. Retrieved April 29, 2005, from Lexis/Nexis Academic Universe database.Online Document from BroadcastMLA "Paleontologist Disputes Altering Discovery." . 2005. Cable News Network. 13 May 2005 </2005/TECH/science/05/13/paleontologist.movies.ap/index.html>.APA Paleontologist disputes altering discovery. (2005, May 13). Cable News Network. Retrieved May 13, 2005, from /2005/TECH/science/05/13/paleontologist.movies.ap /index.html。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

BibliographyR.Abraham and J.E.Marsden.Foundations of Mechanics.Addison-Wesley,second edition,1978. (with the assistance of Tudor Ratiu and Richard Cushman).1,9R.Abraham,J.E.Marsden,and T.S.Ratiu.Manifolds,Tensor Analysis and Applications,vol-ume75of Applied Mathematical Sciences.Springer-Verlag,second edition,1988.75,89,91,94, 101,102D.H.Adams.R-torsion and linking numbers from simplicial abelian gauge theories.arXiv,hep-th/9612009,1996.76,77,88R.Almeida and P.Molino.Suites d’Atiyah et feuilletages transversalement complets.C.R.Acad. Sci.Paris S´e r.I Math.,300(1):13–15,1985.148D.N.Arnold.Diﬀerential complexes and numerical stability.In Proceedings of the International Congress of Mathematicians,Vol.I(Beijing,2002),pages137–157,Beijing,2002.Higher Ed. Press.138V.I.Arnold.Mathematical Methods of Classical Mechanics,volume60of Graduate Texts in Math-ematics.Springer-Verlag,1989.Translated from the1974Russian original by K.Vogtmann and A.Weinstein.1plex analytic connections inﬁbre bundles.Trans.Amer.Math.Soc.,85:181–207, 1957.148M.J.Baines.Moving Finite Elements.Numerical Mathematics and Scientiﬁc Computation.Oxford University Press,1995.213M.Berry.Anticipations of the geometric phase.Phys.Today,pages34–40,December1990.140 A.M.Bloch.Nonholonomic Mechanics and Control.Interdisciplinary Applied Mathematics. Springer-Verlag,2003.191A.I.Bobenko,B.Lorbeer,and Y.B.Suris.Integrable discretizations of the Euler top.J.Math. Phys.,39(12):6668–6683,1998.9A.I.Bobenko and Y.B.Suris.Discrete Lagrangian reduction,discrete Euler–Poincar´e equations, and semidirect products.Lett.Math.Phys.,49(1):79–93,1999.9,72putational Electromagnetism.Electromagnetism.Academic Press,1998.Varia-tional formulations,complementarity,edge elements.4A.Bossavit.Generalizedﬁnite diﬀerences in computational electromagnetics.Progress in Electro-magnetics Research,PIER,32:45–64,2001.77A.Bossavit.Applied diﬀerential geometry(a compendium).URL .pl/ edukacja/mat/Compendium.php.(preprint),2002a.77A.Bossavit.Extrusion,contraction:Their discretization via Whitney forms.(preprint),2002b.77, 104,105A.Bossavit.On“generalizedﬁnite diﬀerences”:Discretization of electromagnetic problems. (preprint),2002c.76,77A.Cannas da Silva and A.Weinstein.Geometric Models for Noncommutative Algebras,volume10 of Berkeley Mathematics Lecture Notes.American Mathematical Society,1999.129J.R.Cardoso and F.Silva Leite.Theoretical and numerical considerations about Pad´e approximants for the matrix logarithm.Linear Algebra Appl.,330(1-3):31–42,2001.181´E.Cartan.Geometry of Riemannian spaces.Math.Sci.Press,Brookline,CA,1983.(translated from French).188´E.Cartan.Riemannian Geometry in an Orthogonal Frame.World Scientiﬁc,2001.(translated from French).188M.Castrill´o n-L´o pez.Discrete variational problems on forms.(in preparation),2003.123,135E.Celledoni and A.Iserles.Approximating the exponential from a Lie algebra to a Lie group.Math. Comp.,69(232):1457–1480,2000.181E.Celledoni and A.Iserles.Methods for the approximation of the matrix exponential in a lie-algebraic setting.IMA J.Num.Anal.,21(2):463–488,2001.181H.Cendra,D.D.Holm,J.E.Marsden,and grangian reduction,the Euler-Poincar´e equations,and semidirect products.In Geometry of Diﬀerential Equations,volume186of Amer-ican Mathematical Society Translations Series2,pages1–25.American Mathematical Society, 1998.72H.Cendra,J.E.Marsden,and grangian reduction by stages.Mem.Amer.Math. Soc.,152(722),2001.3,9,150,168,176,186D.Chang and J.E.Marsden.Geometric derivation of the Delaunay variables and geometric phases. Nonlinearity,16(2):1257–1275,2003.57Z.Chen and T.Y.Hou.A mixed multiscaleﬁnite element method for elliptic problems with oscillating coeﬃp.,72(242):541–576(electronic),2003.197,215J.Cort´e s.Geometric,Control and Numerical Aspects of Nonholonomic Systems,volume1793of Lecture Notes in Mathematics.Springer-Verlag,2002.191M.Desbrun,A.N.Hirani,M.Leok,and J.E.Marsden.Discrete exterior calculus.(in preparation), 2003a.3,72M.Desbrun,A.N.Hirani,M.Leok,and J.E.Marsden.Discrete Poincar´e lemma.Appl.Numer. Math.,2003b.(submitted).108R.A.DeVore.Nonlinear approximation.In Acta Numerica,volume7,pages51–150.Cambridge University Press,1998.197,213A.A.Dezin.Multidimensional Analysis and Discrete Models.CRC Press,1995.77,88W.E and B.Engquist.The heterogeneous multiscale mun.Math.Sci.,1(1):87–132, 2003.229M.Eastwood.A complex from linear elasticity.In The Proceedings of the19th Winter School “Geometry and Physics”(Srn´ı,1999),number63in Rend.Circ.Mat.Palermo(2)Suppl.,pages 23–29,2000.138Y.R.Efendiev,T.Y.Hou,and X.-H.Wu.Convergence of a nonconforming multiscaleﬁnite element method.SIAM J.Numer.Anal.,37(3):888–910(electronic),2000.197,215R.Forman.Discrete Morse theory and the cohomology ring.Trans.Amer.Math.Soc.,354(12): 5063–5085(electronic),2002.76P.Goldreich and A.Toomre.Some remarks on polar wandering.J.Geophys.Res.,10:2555–2567, 1969.143E.Grinspun,P.Krysl,and P.Schr¨o der.CHARMS:A simple framework for adaptive simulation. ACM Transactions on Graphics(SIGGRAPH),21(21):281–290,July2002.229P.W.Gross and P.R.Kotiuga.Data structures for geometric and topological aspects ofﬁnite element algorithms.Progress in Electromagnetics Research,PIER,32:151–169,2001.77E.Hairer,C.Lubich,and G.Wanner.Geometric Numerical Integration,volume31of Springer Series in Computational Mathematics.Springer-Verlag,2002.Structure-preserving algorithms for ordinary diﬀerential equations.1E.Hairer,S.P.Nørsett,and G.Wanner.Solving Ordinary Diﬀerential Equations I:Nonstiﬀproblems,volume8of Springer Series in Computational Mathematics.Springer-Verlag,second edition,1993.36E.Hairer and G.Wanner.Solving Ordinary Diﬀerential Equations II:Stiﬀand diﬀerential-algebraic problems,volume14of Springer Series in Computational Mathematics.Springer-Verlag,second edition,1996.36A.Hatcher.Algebraic Topology.Cambridge University Press,2001.94,97N.J.Higham.Evaluating Pad´e approximants of the matrix logarithm.SIAM J.Matrix Anal.Appl., 22(4):1126–1135(electronic),2001.181R.Hiptmair.Canonical construction ofﬁnite p.,68(228):1325–1346,1999.4, 77,88R.Hiptmair.Discrete Hodge-operators:An algebraic perspective.Progress in Electromagnetics Research,PIER,32:247–269,2001a.77R.Hiptmair.Higher order Whitney forms.Progress in Electromagnetics Research,PIER,32:271–299,2001b.77R.Hiptmair.Finite elements in computational electromagnetism.In Acta Numerica,volume11, pages237–339.Cambridge University Press,2002.77,92A.N.Hirani.Discrete Exterior Calculus.PhD thesis,California Institute of Technology,2003.94, 105D.D.Holm,J.E.Marsden,and T.S.Ratiu.Euler–Poincar´e models of idealﬂuids with nonlinear dispersion.Phys.Rev.Lett.,349:4173–4177,1998.9,72T.Y.Hou and X.-H.Wu.A multiscaleﬁnite element method for PDEs with oscillatory coeﬃcients. In Numerical treatment of multi-scale problems(Kiel,1997),volume70of Notes Numer.Fluid Mech.,pages58–69.Vieweg,1999.197,215,229T.W.Hungerford.Algebra,volume73of Graduate Texts in Mathematics.Springer-Verlag,1974. 232,233,234C.L.Hwang and L.T.Fan.A discrete version of Pontryagin’s maximum principle.Operations Res., 15:139–146,1967.8J.M.Hyman and M.Shashkov.Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids.Appl.Numer.Math.,25(4):413–442,1997a.4J.M.Hyman and M.Shashkov.Natural discretizations for the divergence,gradient,and curl on logically rectangular put.Math.Appl.,33(4):81–104,1997b.4A.Iserles.On the numerical quadrature of highly-oscillating integrals I:Fourier transforms.Tech-nical Report2003/NA05,DAMTP,Cambridge,2003a.(to appear in IMA J.Num.Anal.).220A.Iserles.On the numerical quadrature of highly-oscillating integrals II:Irregular oscillators.Tech-nical Report2003/NA09,DAMTP,Cambridge,2003b.220A.Iserles.On the method of Neumann series for highly oscillatory equations.Technical Report 2004/NA02,DAMTP,Cambridge,2004.220A.Iserles,H.Munthe-Kaas,S.P.Nørsett,and A.Zanna.Lie-group methods.In Acta Numerica, volume9,pages215–365.Cambridge University Press,2000.203A.Iserles and S.P.Nørsett.Eﬃcient quadrature of highly oscillatory integrals using derivatives. Technical Report2004/NA03,DAMTP,Cambridge,2004.220J.D.Jackson.Classical Electrodynamics.Wiley,third edition,1998.125S.M.Jalnapurkar,M.Leok,J.E.Marsden,and M.West.Discrete Routh reduction.J.FoCM, 2003.(submitted).2S.M.Jalnapurkar and J.E.Marsden.Reduction of Hamilton’s variational principle.Dynam.Stabil. Syst.,15(3):287–318,2000.9,20,22,46,72S.M.Jalnapurkar and J.E.Marsden.Variational discretization of Hamiltonian systems.(in prepa-ration),2003.8B.W.Jordan and E.Polak.Theory of a class of discrete optimal control systems.J.Electron. Control,17:697–711,1964.8J.V.Jos´e and E.J.Saletan.Classical Dynamics:A Contemporary Approach.Cambridge University Press,1998.222T.Kaczynski,K.Mischaikow,and putational homology,volume157of Applied Mathematical Sciences.Springer-Verlag,2004.76C.Kane,J.E.Marsden,and M.Ortiz.Symplectic-energy-momentum preserving variational inte-grators.J.Math.Phys.,40(7):3353–3371,1999.1,194,202,210,212,213C.Kane,J.E.Marsden,M.Ortiz,and M.West.Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems.Int.J.Numer.Meth.Eng.,49(10):1295–1325, 2000.1,8,51S.Kobayashi and K.Nomizu.Foundations of Diﬀerential Geometry,volume1.Wiley,1963.145, 148,149P.Krysl,A.Trivedi,and B.Zhu.Object-oriented hierarchical mesh reﬁnement with CHARMS. Int.J.Numer.Meth.Eng.,2003.(to appear).229ll and M.West.Discrete variational mechanics and duality.(in preparation),2003.201B.Leimkuhler and S.Reich.Simulating Hamiltonian Dynamics,volume14of Cambridge Monographs on Applied and Computational Mathematics.Cambridge University Press,2004.1M.Leok.A mathematical model of true polar wander.Caltech SURF Report,1998.143M.Leok.Discrete Routh reduction and discrete exterior calculus.Caltech Control and Dynamical Systems,Ph.D.Candidacy Report,2002.3M.Leok.Generalized Galerkin variational integrators:Lie group,multiscale,and pseudospectral methods.(in preparation),2004.3M.Leok,J.E.Marsden,and A.Weinstein.A discrete theory of connections on principal bundles. (in preparation),2003.3,72,86A.Lew,J.E.Marsden,M.Ortiz,and M.West.Asynchronous variational integrators.Arch.Ration. Mech.An.,167(2):85–146,2003.1,74,194A.Lew,J.E.Marsden,M.Ortiz,and M.West.Variational time integrators.Int.J.Numer.Meth. Eng.,2004.(to appear).1,212K.C.H.Mackenzie.Lie algebroids and Lie pseudoalgebras.Bull.London Math.Soc.,27(2):97–147, 1995.148grangian formulation of discrete systems and concept of diﬀerence space.Math. Japonica,27(3):345–356,1981.8E.L.Mansﬁeld and P.E.Hydon.On a variational complex for diﬀerence equations.In The Geo-metrical Study of Diﬀerential Equations(Washington,DC,2000),volume285of Contemporary Mathematics,pages121–129.American Mathematical Society,2001.77J.E.Marsden.Lectures on Mechanics,volume174of London Mathematical Society Lecture Note Series.Cambridge University Press,1992.9,11,12,13,59,66J.E.Marsden.Geometric mechanics,stability,and control.In L.Sirovich,editor,Applied Mathe-matical Sciences,volume100,pages265–291.Springer-Verlag,1994.140,143J.E.Marsden.Geometric foundations of motion and control.In Motion,Control and Geometry, pages3–19.National Academy Press,1997.140,143J.E.Marsden,R.Montgomery,and T.S.Ratiu.Reduction,symmetry,and phases in mechanics. Mem.Amer.Math.Soc.,88(436):1–110,1990.13,59,143J.E.Marsden,G.W.Patrick,and S.Shkoller.Multisymplectic geometry,variational integrators, and nonlinear mun.Math.Phys.,199(2):351–395,1998.8,193,195J.E.Marsden,S.Pekarsky,and S.Shkoller.Discrete Euler–Poincar´e and Lie–Poisson equations. Nonlinearity,12(6):1647–1662,1999.2,9,129,205,207,209J.E.Marsden,S.Pekarsky,and S.Shkoller.Symmetry reduction of discrete Lagrangian mechanics on Lie groups.J.Geom.Phys.,36(1-2):140–151,2000a.2,9,129J.E.Marsden,S.Pekarsky,S.Shkoller,and M.West.Variational methods,multisymplectic geometry and continuum mechanics.J.Geom.Phys.,38(3-4):253–284,2001.193,195J.E.Marsden and T.S.Ratiu.Introduction to Mechanics and Symmetry,volume17of Texts in Applied Mathematics.Springer-Verlag,second edition,1999.1,17,44,140J.E.Marsden,T.S.Ratiu,and J.Scheurle.Reduction theory and the Lagrange–Routh equations. J.Math.Phys.,41(6):3379–3429,2000b.9,11,13,22,46,59,72J.E.Marsden and grangian reduction and the double spherical pendulum.Z.Angew. Math.Phys.,44(1):17–43,1993a.9,46J.E.Marsden and J.Scheurle.The reduced Euler-Lagrange equations.In Dynamics and Control of Mechanical Systems(Waterloo,ON,1992),volume1of Fields Institute Communications,pages 139–164.American Mathematical Society,1993b.9,46J.E.Marsden and J.M.Wendlandt.Mechanical systems with symmetry,variational principles and integration algorithms.In M.Alber,B.Hu,and J.Rosenthal,editors,Current and Future Directions in Applied Mathematics,pages219–261.Birkh¨a user,1997.8J.E.Marsden and M.West.Discrete mechanics and variational integrators.In Acta Numerica, volume10,pages317–514.Cambridge University Press,2001.1,8,14,37,38,194,203C.Mattiussi.An analysis ofﬁnite volume,ﬁnite element,andﬁnite diﬀerence methods using some concepts from algebraic put.Phys.,133(2):289–309,1997.77C.Mattiussi.Theﬁnite volume,ﬁnite diﬀerence,andﬁnite element methods as numerical methods for physicalﬁeld problems.Adv.Imag.Elect.Phys.,113:1–146,2000.74,77R.McLachlan and M.Perlmutter.Integrators for nonholonomic mechanical systems.(preprint), 2003.191M.Meyer,M.Desbrun,P.Schr¨o der,and A.H.Barr.Discrete diﬀerential-geometry operators for triangulated2-manifolds.VisMath,2002.92,103R.Montgomery.How much does a rigid body rotate?A Berry’s phase from the eighteenth century. Amer.J.Phys.,59:394–398,1991.143B.Moritz.Vector Diﬀerence Calculus.PhD thesis,University of North Dakota,2000.77B.Moritz and W.A.Schwalm.Triangle lattice green functions for vectorﬁelds.J.Phys.A.,34(3): 589–602,2001.77J.Moser and A.P.Veselov.Discrete versions of some classical integrable systems and factorization of matrix mun.Math.Phys.,139(2):217–243,1991.8S.M¨u ller and M.Ortiz.On theΓ-convergence of discrete dynamics and variational integrators.J. Nonlinear Sci.,2004.(to appear).1J.R.Munkres.Elements of Algebraic Topology.Addison-Wesley,1984.78,87,88R.M.Murray,Z.Li,and S.S.Sastry.A Mathematical Introduction to Robotic Manipulation.CRC Press,1994.235R.A.Nicolaides and D.-Q.Wang.Convergence analysis of a covolume scheme for Maxwell’s equations in three p.,67(223):947–963,1998.77J.Nocedal and S.J.Wright.Numerical Optimization.Springer Series in Operations Research. Springer-Verlag,1999.197S.P.Novikov.Discrete connections on the triangulated manifolds and diﬀerence linear equations. arXiv,math-ph/0303035,2003.188M.Oliver,M.West,and C.Wulﬀ.Approximate momentum conservation for spatial semidiscretiza-tions of nonlinear wave equations.Numer.Math.,2004.(to appear).213P.J.Olver.Geometric foundations of numerical algorithms and symmetry.Appl.Algebra Engrg. put.,11(5):417–436,2001.Special issue“Computational geometry for diﬀerential equations”.177J.-P.Ortega and T.S.Ratiu.Hamiltonian Singular Reduction.Progress in Mathematics.Birkh¨a user, 2001.(to appear).65G.W.Patrick.Two Axially Symmetric Coupled Rigid Bodies:Relative Equilibria,Stability Bifur-cations,and a Momentum Preserving Symplectic Integrator.PhD thesis,University of California at Berkeley,1991.71S.Pekarsky and M.West.Discrete diﬀeomorphism groupoids and circulation conservingﬂuid inte-grators.(in preparation),2003.131J.E.Prussing and B.A.Conway.Orbital Mechanics.Oxford University Press,1993.57E.J.Routh.Stability of a Given State of Motion.Macmillian,1877.Reprinted in Stability of Motion,A.T.Fuller(ed.),Halsted Press,1975.9,43E.J.Routh.Advanced Rigid Dynamics.Macmillian,1884.9A.Sanyal,J.Shen,and N.H.McClamroch.Variational integrators for mechanical systems with cyclic generalized coordinates.(preprint),2003.45J.M.Sanz-Serna and M.P.Calvo.Numerical Hamiltonian Problems,volume7of Applied Mathe-matics and Mathematical Computation.Chapman&Hall,1994.1J.R.Schewchuck.What is a good linearﬁnite element?Interpolation,conditioning,anisotropy and quality measures.URL /~jrs/papers/elemj.ps.(preprint), 2002.79W.A.Schwalm,B.Moritz,M.Giona,and M.K.Schwalm.Vector diﬀerence calculus for physical lattice models.Phys.Rev.E.,59(1,part B):1217–1233,1999.77S.Sen,S.Sen,J.C.Sexton,and D.H.Adams.Geometric discretization scheme applied to the abelian Chern–Simons theory.Phys.Rev.E,61(3):3174–3185,2000.76,77,88,91A.Shapere and F.Wilczek.Geometric Phases in Physics,volume5of Advanced Series in Mathe-matical Physics.World Scientiﬁc,1989.140M.Shashkov.Conservativeﬁnite-diﬀerence methods on general grids.Symbolic and Numeric Com-putation Series.CRC Press,1996.4N.Steenrod.The Topology of Fibre Bundles.Princeton University Press,1951.145Y.Suris.Hamiltonian methods of Runge–Kutta type and their variational interpretation.Mat. Model.,2(4):78–87,1990.36,37F.L.Teixeira.Geometric aspects of the simplicial discretization of Maxwell’s equations.Progress in Electromagnetics Research,PIER,32:171–188,2001.77K.Theodoropoulos,Y.-H.Qian,and I.G.Kevrekidis.“Coarse”stability and bifurcation analysis using timesteppers:a reaction diﬀusion example.Proc.Natl.Acad.Sci.,97(18):9840–9843,2000. 229P.Thoutireddy and M.Ortiz.A variational r-adaptation and shape-optimization method forﬁnite-deformation elasticity.Int.J.Numer.Meth.Eng.,2003.(to appear).213Y.Y.Tong,S.Lombeyda,A.N.Hirani,and M.Desbrun.Discrete multiscale vectorﬁeld decompo-sition.ACM Transactions on Graphics(SIGGRAPH),July2003.75,101E.Tonti.Finite formulation of electromagneticﬁeld.IEEE Trans.Mag.,38:333–336,2002.77L.N.Trefethen.Spectral methods in MATLAB.Software,Environments,and Tools.Society for Industrial and Applied Mathematics(SIAM),2000.222V.Vedral.Geometric phases and topological quantum computation.Int.J.Quantum Inform.,1 (1):1–23,2003.140A.P.Veselov.Integrable discrete-time systems and diﬀerence operators.Funct.Anal.Appl.,22(2): 83–93,1988.8A.P.Veselov.Integrable Lagrangian correspondences and the factorization of matrix polynomials. Funct.Anal.Appl.,25(2):112–122,1991.8G.Walsh and S.Sastry.On reorienting linked rigid bodies using internal motions.IEEE Trans. Robotic Autom.,11:139–146,1993.143grangian mechanics and groupoids.In Mechanics Day(Waterloo,ON,1992), volume7of Fields Institute Communications,pages207–231.American Mathematical Society, 1996.129A.Weinstein.Groupoids:unifying internal and external symmetry.A tour through some examples. In Groupoids in Analysis,Geometry,and Physics(Boulder,CO,1999),volume282of Contem-porary Mathematics,pages1–19.American Mathematical Society,2001.129J.M.Wendlandt and J.E.Marsden.Mechanical integrators derived from a discrete variational principle.Physica D,106(3-4):223–246,1997.8H.Whitney.Geometric Integration Theory.Princeton University Press,1957.76J.Wisdom,S.J.Peale,and F.Mignard.The chaotic rotation of Hyperion.Icarus,58(2):137–152, 1984.71putational Topology Algorithms for Discrete2-Manifolds.PhD thesis,California Institute of Technology,2003.76A.Zanna and H.Z.Munthe-Kaas.Generalized polar decompositions for the approximation of the matrix exponential.SIAM J.Matrix Anal.Appl.,23(3):840–862(electronic),2001/02.181IndexSymbolsF L,see Legendre transformF L d,see Legendre transform,discrete J,see momentum mapJ L,see momentum map,LagrangianJ d,see momentum map,discreteL d,see Lagrangian,discreteˆRµ,see RouthianX d(K),see vectorﬁeld,primalX d( K),see vectorﬁeld,dual∆,see Laplace–Beltramidiv,see divergenceΩkd(K),see form,primalΩkd( K),see form,dual∗,see Hodge starδ,see codiﬀerential,seeﬂatκ,see causality sign,see sharp,see circumcentric,duality operator ∧,see wedge productd,see exterior derivativei X,see contractionAactiondiscrete,14Atiyah sequence,148discrete,see discrete Atiyah sequence augmentationexample,114,117one-ring cone,114B boundary,89dual,91example,90bundleG-bundle,145adjoint,148base space,145bundle space,145ﬁber,145ﬁber bundle,145principal bundle,145projection,145structure group,145C causality sign,127example,127cellcomplex,84example,84,85 chain,87complex,90example,87change of variables,135circumcenter,79circumcentricsubdivision,79dual,79duality operator,79 coboundary,90cochain,88complex,90cocone,109codiﬀerential,92complexcell,see cell,complexchain,see chain,complexcochain,see cochain,complexprismal,126simplicial,see simplicial,complex sub,see subcomplexcone,109example,112,115generalized,113geometric,109logical,112connection,1471-form,148discrete,see discrete connectionfrom discrete connection,176mechanical,11principal,10to discrete connection,181 constraintsstructured,74contractionalgebraic,105extrusion,105curvatureLevi-Civita connection,see connection,Levi-Civita,curvatureDdiﬀeomorphism,131groupoid,133interpolatory methods,133non-degenerate,132one-parameter family,132discrete Atiyah sequence,154splitting,165,167from discrete connection1-form,166from discrete horizontal lift,167to discrete connection1-form,166to discrete horizontal lift,168discrete connection1-form,see discrete connection1-formcomputation,178derived geometric structures,172exact,178extended groupoid composition,173from continuous connection,181from discrete connection1-form,158from discrete horizontal lift,162geometric control,186higher-order tangent bundle,176horizontal component,171isomorphism,168Lagrangian reduction,185Levi-Civita,188curvature,189mechanical,161,179from discrete Lagrangian,182order of approximation,180relating the representations,156to continuous connection,176to discrete connection1-form,156to discrete horizontal lift,161vertical component,171discrete connection1-formfrom discrete connection,156from discrete horizontal lift,165from splitting of Atiyah sequence,166 local representation,160properties,157to discrete connection,158to discrete horizontal lift,163to splitting of Atiyah sequence,166 discrete generator,152discrete horizontal lift,161from discrete connection,161from discrete connection1-form,163from splitting of Atiyah sequence,168 to discrete connection,162to discrete connection1-form,165to splitting of Atiyah sequence,167 discrete mechanics,14,121,194groupoid,129with symmetry,17discrete Riemannian manifold,188 divergence,101dual cellcircumcentric,see circumcentric,dual orientation,see orientation,dual cell dynamic problems,129EEuler–Lagrangediscrete operator,185equations,9discrete,15reduceddiscrete,186exterior derivative,90extrusion,104contraction,see contraction,extrusionexample,104Lie derivative,see Lie derivative,extru-sionFface,78ﬁber product,146Filon quadrature,220ﬂat,93ﬂow,104example,107formdual,91primal,88Ggenerating function,16geometric phaserigid-body,143groupoidcomposition,130extended,see discrete connection,extendedgroupoid compositiondiﬀeomorphism,see groupoid,diﬀeomor-phismdiscrete mechanics,see discrete mechan-ics,groupoidinverse,131source,130target,130visualizing,131HHamiltonian,10vectorﬁeld,10Harmonic functions,123harmonic functionsaction functional,123Euler–Lagrange,123highly-oscillatory integral,220Hodge star,91Lorentizan space,127holonomy,140horizontalcomponent,153discrete,see discrete connection,horizon-tal componentdirections,147lift,149discrete,see discrete horizontal liftspace,11discrete,153Iinner product,122integrator,17LLagrange1-formsdiscrete,15Lagrange2-formdiscrete,15Lagrange mapdiscrete,15push-forward,16Lagrange–Poincar´ediscrete operator,185 Lagrangian,9discrete,14,194approximate,17exact,16,194group-regular,20polynomials and quadrature,37symplectic Runge–Kutta,36double spherical pendulum,64satellite,57Laplace–Beltrami,102Laplace–deRham,103lattice theory,74Legendre transform,9discrete,16reduced Routh,13Lie derivativealgebraic,108extrusion,107Mmanifoldsﬂat,89non-ﬂat,85,89,137Maxwell equations,124action functional,125Euler–Lagrange,125metriclocal,86,190momentum map,10discrete,17Lagrangian,10momentum shift,12,13 multigrid,136multiscaleshape function,215,218variational integrator,see variational in-tegrator,multiscalemultisymplecticconﬁguration bundle,195ﬁrst jet bundle,195ﬁrst jet extension,195geometry,195variational integrator,see variational in-tegrator,multisymplecticNnatural charts,205Noether’s theorem,10discrete,18norm,123Lorentzian,127Oorientationdual cell,81dual of dual,81example,81,82Ppairingnatural,89phase spacediscrete,14Poincar´e lemma,108counterexample,120polytope,78pull-backform,135vectorﬁeld,134push-forwardform,135vectorﬁeld,134Rreductioncontangent bundle,42continuous,9cotangent bundle,12,42discrete,14,22Euler–Poincar´e,207Hamiltonian,12Lagrange–Poincar´e,185Lagrangian,11reconstruction,13discrete,19relating discrete and continuous,34relating Lagrangian and Hamiltonian,12 Routh,11,42symplectic Runge–Kutta,see symplecticRunge–Kutta,reduction remeshing,136Routh equations,12discrete,26computational considerations,69constrained,46,47,56forced,46,51,52,56preservation of symplectic form,27double spherical pendulum,63satellite,57Routhian,12double spherical pendulum,67satellite,59SSchr¨o dinger equation,222action functional,222discrete action,225Euler–Lagrange,226 shape space,10sharp,93simplex,78example,84,85examples,78simplicialcomplex,78triangulation,78 skeleton,78star-shapedgeneralized,114logically,112trivially,109Stokes’theoremgeneralized,90 subcomplex,78support volume,83example,84,85 symplectic Runge–Kutta,35 reduction,38,42 symplectic structurecanonical,10reduced,12discrete,27Ttrajectorydiscrete,14V variational integratordiscrete action,202Euler–Poincar´e,207function space,197Galerkin,203generalized,197higher-order,198Lie group,202multiscale,215planar pendulum with a stiﬀspring,216multisymplectic,196,199numerical quadrature,197pseudospectral,222Schr¨o dinger equation,223spatio-temporally adaptive,212symplectic-energy-momentum,200 variational principlediscrete,194Hamilton’s,11Lagrange–d’Alembert,51reduced,11variational problems,74harmonic functions,see harmonic functions Maxwell equations,see Maxwell equationsSchr¨o dinger equation,see Schr¨o dinger equa-tionvectorﬁelddual,92primal,92velocitymaterial,132spatial,133vertex,78verticalcomponent,154discrete,see discrete connection,verticalcomponentdirections,147space,11。