Characteristically nilpotent Lie algebras a survey
Whorf Hypothesis
For example, in Western culture, saying someone has an “artistic personality” implies that the person is creative, intense, and temperamental and has an unconventional lifestyle. The Chinese, however, do not have a schema or implicit personality theory for an artistic type.
Canonical Approach
42
Noncanonical Approach
42 Or … …
One-to-one Collection
42
Number Terms
• The results indicated that Japanese children were more than twice as likely as U.S. children tended to use canonical approaches on the first trial. The U.S. children tended to use one-to-one collections on the first trial. When prodded to generates a second trial. Miura also found that Japanese children used more noncanonical approaches than U.S. children. The similar results have been found using Korean and Chinese first-graders.
江苏省扬州中学2024-2025学年高三上学期8月开学考试 英语 Word版含答案
高三年级暑期英语练习2024.08第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. Where does this conversation probably take place?A. At a bus stop.B. At school.C. At home.2. What will the speakers do next?A. Order food.B. Ask for the menu.C. Leave the restaurant.3. Why does the man make the phone call?A. To cancel a visit.B. To make an appointment.C. To give some information.4. What did the speakers do last week?A. They stayed at a hotel.B. They moved their house.C. They made a special meal.5. What is probably the woman?A. A student.B. A teacher.C. A stay-at-home mother.第二节（共15题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的做答时间。
每段对话或独白读两遍。
听第6段材料，回答第6、7题。
6. What does the girl hope to do at first?A. Have a talk with the man.B. Find an actress for the school play.C. Receive an invitation from the man.7. When is the school play?A. This Monday.B. Next week.C. Next month.听第7段材料，回答第8至10题。
英语作文 墨家思想
Mozi,an ancient Chinese philosopher,founded the Mohist school of thought,which was one of the major philosophical schools during the Warring States period475221BC. His teachings,which are contained in the Mozi text,are characterized by a focus on universal love,utilitarianism,and opposition to aggression.Here is an essay on Mohist philosophy,highlighting its key principles and their relevance to modern society.Title:The Timeless Wisdom of MohismIntroductionIn the vast expanse of Chinese philosophical thought,the Mohist school stands out for its unique emphasis on universal love jian ai,utilitarianism li yi,and opposition to unjust wars.Mozi,the founder of this school,was a contemporary of Confucius and Laozi,and his teachings offer a different perspective on how society should be organized.This essay delves into the core tenets of Mohism and explores their enduring value in contemporary society.Universal Love Jian AiThe central concept of Mohism is universal love,which is the idea that one should love all people equally,without distinction of status or relationship.Mozi argued against the Confucian concept of graded love,which prioritizes family and social hierarchy.He believed that the lack of universal love was the root cause of social strife and conflict.By promoting equality in love,Mohists sought to create a harmonious society where everyones wellbeing is considered.Utilitarianism Li YiMohists were utilitarians,advocating for actions that maximize overall benefit and minimize harm.This principle was applied to all aspects of life,from personal conduct to statecraft.Mozi emphasized the importance of practicality and efficiency,arguing that actions should be judged by their outcomes rather than by adherence to traditional rites or customs.This pragmatic approach to ethics has parallels in modern utilitarian philosophy, which seeks to make decisions based on the greatest good for the greatest number. Opposition to Aggression Fei GongMozi was a staunch pacifist,opposing all forms of aggression,especially unjust wars.He believed that war was a great evil,causing unnecessary suffering and destruction.To promote peace,Mozi advocated for a defensive military strategy and the strengthening ofalliances among states.His ideas on nonaggression have influenced later thinkers and can be seen as an early form of internationalism,emphasizing cooperation and mutual respect among nations.Innovation and TechnologyAnother aspect of Mohist thought was a strong emphasis on innovation and the application of technology for the benefit of society.Mohists were known for their contributions to science and engineering,including advancements in defensive military technology.This focus on practical knowledge and its application to improve human life is a testament to the forwardthinking nature of Mohism.ConclusionThe Mohist school of thought,with its principles of universal love,utilitarianism,and opposition to aggression,offers a unique perspective on how society can be organized for the common good.While rooted in the historical context of ancient China,the teachings of Mozi resonate with modern concerns about social justice,ethical decisionmaking,and international relations.As we continue to grapple with the challenges of our time,the wisdom of Mohism reminds us of the importance of empathy,practicality,and peace in building a better world.ReflectionIn reflecting on Mohism,one cannot help but be struck by its relevance to contemporary issues.The call for universal love and the rejection of violence as a means to resolve conflicts are messages that are as pertinent today as they were in Mozis time.As we navigate the complexities of our interconnected world,the Mohist philosophy serves as a reminder of the potential for a more harmonious and equitable society.。
A review of the species of protozoan epibionts on crustaceans-11
A REVIEW OF THE SPECIES OF PROTOZOAN EPIBIONTS ONCRUSTACEANS.I.PERITRICH CILIATESBYGREGORIO FERNANDEZ-LEBORANS and MARIA LUISA TATO-PORTODepartamento de Biologia Animal I(Zoologia),Facultad de Biologia,Pnta9a,Universidad Complutense,E-28040Madrid,SpainABSTRACTAn updated inventory of the peritrich(Protozoa,Ciliophora)epibiont species on crustaceans has been carried out.Data concerning268epibiont species,their taxonomic position,and the various crustacean basibionts were considered.The overview comprised in this study may be of use in further surveys of protozoan-crustacean epibiosis.RESUMENSe ha realizado un inventario actualizado de las especies de peritricos(Protozoa,Ciliophora) epibiontes en crustáceos.Se han considerado los datos concernientes a268especies epibiontes,su posición taxonómica,y los diferentes crustáceos visión general que comprende este estudio puede ser utilizada en futuras investigaciones sobre la epibiosis protozoos-crustáceos.INTRODUCTIONEpibiosis is a facultative association of two organisms:the epibiont and the basibiont(Wahl,1989).The term“epibiont”includes organisms that,during the sessile phase of their life cycle,are attached to the surface of a living substratum, while the basibiont lodges and constitutes a support for the epibiont(Threlkeld et al.,1993).Both concepts describe ecological functions(Wahl,1989).Several crustacean groups,cladocerans,copepods,cirripedes,isopods,amphi-pods,and decapods,include forms that are hosts for macroepibiont invertebrates (Ross,1983),and for protozoan microepibionts of the phylum Ciliophora:apos-tomatids,chonotrichids,suctorians,peritrichs,and heterotrichs(Corliss,1979; Small&Lynn,1985).The study of ciliate epibionts on crustaceans began in the last century.Bütschli(1887-89)made a compilation from former publications.After-wards,other authors(Keiser,1921;Kahl,1934,1935;Precht,1935;Raabe,1947; c®Koninklijke Brill NV,Leiden,2000Crustaceana73(6):643-683644G.FERNANDEZ-LEBORANS&M.L.TATO-PORTONenninger,1948)not only described epibiont species,but proposed explanations for the processes of epibiosis.A review of the protozoan epibionts found on de-capod crustaceans was carried out by Sprague&Couch(1971).Green(1974), in a study of the epibionts living on cladocerans,pays considerable attention to protozoan species.Ho&Perkins(1985)have focused on the epibionts found on copepods.In other contemporary and also earlier works,the following aspects have been taken into account:(1)speci city between ciliates and their crustacean basi-bionts(Evans et al.,1981;Batisse,1986,1992;Clamp,1991);(2)the morpholog-ical and physiological adaptations of the epibionts(D’Eliscu,1975;Batisse,1986, 1994;Fenchel,1987;Clamp,1991;Lom&De Puytorac,1994);(3)the effects pro-duced by the epibionts on the crustaceans(Herman et al.,1971;Turner et al.,1979; Kankaala&Eloranta,1987;Nagasawa,1988);(4)the possible use of epibionts for the assessment of water quality(Antipa,1977;Henebry&Ridgeway,1979;Scott &Thune,1986);(5)the implications of protozoan epibionts on cultures of vari-ous species of crustaceans(Overstreet,1973;Johnson,1977,1978;Lightner,1977, 1988;Couch,1978;Scott&Thune,1986;V ogelbein&Thune,1988;Camacho& Chinchilla,1989);and(6)the organization of the epibiont communities on plank-tonic crustaceans(Threlkeld et al.,1993).Despite the fact that there is a considerable amount of information about the protozoan epibionts on crustaceans,since the works of Sprague&Couch(1971), Green(1974),and Ho&Perkins(1985),which relate to speci c crustacean groups, no further general reviews have appeared.Several new species of protozoan ciliate epibionts have recently been described(Dovgal,1985;Batisse,1992;Fernandez-Leborans&Gomez del Arco,1996;Zhadan&Mikrjukov,1996;Fernandez-Leborans et al.,1996,1997),and some of these are peritrich ciliates(Matthes& Guhl,1973;Bierhof&Roos,1977;Jankowski,1986;Dale&Blom,1987;Clamp, 1990,1991;Threlkeld&Willey,1993;Hudson&Lester,1994;Stoukal&Matis, 1994;Foissner,1996).The purpose of this work is to provide an up-to-date review of the peritrich ciliates living as epibionts on crustaceans:268species have been considered in this compilation,which may contribute data for studies of epibiosis in crustaceans.CRUSTACEAN PROTOZOAN EPIBIONTS,I.PERITRICH CILIATES645RESULTS1)Phylum CILIOPHORA Do ein,1901Class OLIGOHYMENOPHOREA De Puytorac,Batisse,Bohatier,Corliss, Deroux,Didier,Dragesco,Fryd-Versavel,Grain,Grolière,Hovasse,Iftode,Laval,Roque,Savoie&Tuffrau,1974Subclass P ERITRICHIA Calkins,1933Order S ESSILIDA Kahl,1933Family Epistylididae Kahl,1935Genus Rhabdostyla Kent,1880( g.1)R.bosminae Levander,1907.On the cladoceran Bosmina sp.R.conipes Kahl,1935.On the cladoceran Daphnia sp.Fresh water.On the cladocerans Daphnia magna,D.longispina and Scapholeberis mucronata (cf.Green,1957,1974).R.cyclopis Kahl,1935.On the copepod Cyclops sp.Fresh water.R.cylindrica Stiller,1935.On the cladoceran Leptodora ke Balaton (Hungary).On the cladoceran Leptodora kindtii.Denmark(Green,1974).R.hungarica Stiller,1931.On the cladoceran Leptodora ke Balaton (Hungary).R.globularis Stokes,1890.On the cladoceran Bosmina longirostris and on Diaphanosoma brachyurum.Germany(Nenninger,1948).R.invaginata Stokes,1886.On the ostracod Cypris sp.R.sessilis Penard,1922.On the copepod Cyclops sp.Fresh water.R.pyriformis Perty,1852(cf.Kahl,1935;on Entomostraca).On the clado-ceran Daphnia longispina(cf.Nenninger,1948).On the cladoceran Daph-nia hyalina(cf.Sommer,1950).On Daphnia pulex and Ceriodaphnia reticu-lata(cf.Hamman,1952).On Daphnia magna,D.pulex,D.cucullata,Simo-cephalus vetulus,Ceriodaphnia reticulata,and Leptodora kindtii(cf.Green, 1953).On Daphnia magna(cf.Green,1955).On Daphnia magna andD.longispina(cf.Green,1957).On Daphnia atkinsoni,D.hyalina,D.lon-gispina,D.curvirostris,D.obtusa,Ceriodaphnia laticaudata,and C.pulchel-la(cf.Green,1974).R.vernalis Stokes,1887.On the copepod Eucyclops agilis(cf.Henebry& Ridgeway,1979).1)For authors and dates of species of Crustacea mentioned herein,see separate section,below.646G.FERNANDEZ-LEBORANS&M.L.TATO-PORTOFigs.1-2.1,Rhabdostyla(R.pyriformis,after Green,1957);2,Epistylis(E.gammari,after Precht,1935).Rhabdostyla sp.Bierhof&Roos,1977.Between the spines at the end of the telson on Gammarus tigrinus.Germany.Rhabdostyla sp.Weissman et al.,1993.On the copepod Acartia hudsonica. Genus Epistylis Ehrenberg,1832( g.2)E.anastatica(Linnaeus,1767)(cf.Kent,1881).Syn.:Vorticella anastatica L.,1767.On Entomostraca and freshwater plants.On cyclopoid copepods and Daphnia pulex(cf.Green,1974).E.astaci Nenninger,1948.Fresh water.On the gills of the decapod Astacusastacus(as A. uviatilis)(Germany).On A.leptodactylus(cf.Stiller,1971).On the gills of Austropotamobius torrentium(cf.Matthes&Guhl,1973).E.bimarginata Nenninger,1948.Fresh water.On the appendages of Astacusastacus(as A. uviatilis).Germany.E.branchiophila Perty,1852.Syn.:E.formosa Nenninger,1948.On theparasitic copepod Lernaea cyprinacea,in freshwater environments of South Africa(Van As&Viljoen,1984).E.breviramosa Stiller,1931.On the antennal lament of the cladoceran Daph-nia ke Balaton(Hungary).On the copepod Cyclops sp.,Czechoslovakia (Srámek-Husek,1948).On the cladocerans Bosmina longirostris and Alona af nis(cf.Green,1974).E.cambari Kellicott,1885.On the gills of the decapod Cambarus sp.(NE ofU.S.A.).On the maxillae of the cray sh Astacus leptodactylus(fresh water) (cf.Matthes&Guhl,1973).E.crassicollis Stein,1867.On freshwater Entomostraca and on the pleopodsand gills of cray sh.On the gills of Astacus astacus(as A. uviatilis),andCRUSTACEAN PROTOZOAN EPIBIONTS,I.PERITRICH CILIATES647 the maxillae,maxillipeds,and gills of A.leptodactylus,in Europe(Matthes& Guhl,1973).E.cyprinaceae Van As&Viljoen,1984.On the parasitic copepod Lernaea cyprinacea(fresh water,South Africa).E.daphniae Fauré-Fremiet,1905.On the cladoceran Daphnia sp.On Daphnia magna(cf.Nenninger,1948).On the copepod Boeckella triarticulata(New Zealand)(Xu&Burns,1990).On the cladoceran Moina macrocopa in an urban stream.E.diaptomi Fauré-Fremiet,1905.On the copepod Diaptomus sp.E.digitalis Ehrenberg,1838.On the copepod Cyclops sp.E.epibarnimiana Van As&Viljoen,1984.On the parasitic copepod Lernaea barnimiana(fresh water,South Africa).E.fugitans Kellicott,1887.On the cladoceran Sida crystallina.North America.E.gammari Precht,1935.On the antennae of the gammarid Gammarus sp. (Kiel channel).On the proximal part of the rst antenna and,less commonly, on the second antenna of Gammarus oceanicus and G.salinus.In the Baltic Sea and areas of Norway(Fenchel,1965).On the rst antenna of Gammarus tigrinus(cf.Stiller,1971).E.halophila Stiller,1942.On the cladocerans Daphnia longispina and D.pulex (Lake Cserepeser,Hungary).E.harpacticola Kahl,1933.On harpacticoid copepods in the Kiel channel. E.helenae Green,1957.On the cladocerans Daphnia pulex,D.magna,D.ob-tusa,D.longispina,D.curvirostris,Ceriodaphnia pulchella,C.reticulata, ticaudata,Moina macrocopa,M.micrura,Chydorus sphaericus,Simo-cephalus serrulatus,and S.vetulus(cf.Green,1957,1974).On Daphnia magna(cf.Nenninger,1948).On Ceriodaphnia reticulata and Simocephalus vetulus(cf.Matthes,1950).E.humilis Kellicott,1887.On the gammarid Gammarus sp.and other Ento-mostraca.custris Imhoff,1884.On the pelagic copepod Cyclops sp.On the buccal appendages of the branchiopod Lepidurus apus(freshwater areas near Vienna, Austria)(Foissner,1996).E.magna V an As&Viljoen,1984.On the parasitic copepod Lernaea cypri-nacea(fresh water,South Africa).E.niagarae Kellicott,1883.On the body surface of cray sh(Niagara River, U.S.A.).On the antennae and body of the European cray sh Astacus lep-todactylus,on Austropotamobius torrentium,and on Orconectes limosus(as Cambarus af nis)(cf.Matthes&Guhl,1973).On the surface of the copepod648G.FERNANDEZ-LEBORANS&M.L.TATO-PORTOEucyclops serrulatus,and on the cladocerans Daphnia pulex,D.rosea,Cerio-daphnia reticulata,and Scapholeberis mucronata(lakes of Colorado,U.S.A.) (Willey&Threlkeld,1993).E.nitocrae Precht,1935.On the third pereiopod of Gammarus tigrinus(cf.Bierhof&Roos,1977).E.nympharum Engelman,1862.On cladocerans(Nenninger,1948).On Cy-clops sp.(cf.Foissner&Schiffman,1974).On the branchiuran Dolops ra-narum(cf.Van As&Viljoen,1984).E.ovalis Biegel,1954.On the gnathopods of Gammarus tigrinus.On the thirdpereiopod of the gammarid Gammarus pulex,and on the spines at the end of the third uropod of Gammarus tigrinus(cf.Bierhof&Roos,1977).E.plicatilis Ehrenberg,1838.On the copepods Eucyclops agilis,Cyclopsvernalis,and C.bicuspidatus(Ashmore Lake,Illinois,U.S.A.)(Henebry& Ridgeway,1979).E.salina Stiller,1941.On the rst and second antennae,coxae,and gills of thegammarid Gammarus pulex(cf.Bierhof&Roos,1977).E.thienemanni Sommer,1951.On the gills of Gammarus tigrinus(cf.Bierhof&Roos,1977).E.zschokkei(Keiser,1921).Syn.:Opercularia zschokkei Keiser,1921.On thegnathopods of the gammarid Gammarus tigrinus and on other Entomostraca.On the cladoceran Acantholeberis curvirostris(cf.Nenninger,1948).Epistylis sp.Hutton,1964.On the decapod Penaeus duorarum(Florida,U.S.A.).Between the setae of the rst antenna of Gammarus tigrinus(cf.Bierhof& Roos,1977).Epistylis sp.Hutton,1964.On the decapod Ploeticus robustus(Daytona Beach, Florida,U.S.A.).Epistylis sp.Viljoen&Van As,1983.Two species on the thoracic appendages of a freshwater brachyuran,apparently erroneously identi ed as“Potamon sp.”(South Africa)[the genus Potamon does not occur in southern Africa].Epistylis sp.Pearse,1932.On the gills of the decapods Coenobita clypeatus, Geograpsus lividus,and Pachygrapsus transversus(Florida,U.S.A.).Epistylis sp.Hudson&Lester,1994.On the gills of the decapod Scylla serrata (Moreton Bay,Queensland,Australia).Epistylis sp.Turner et al.,1979.On the estuarine copepods Acartia tonsa andA.clausi(Escambia Bay,Florida,U.S.A.).Epistylis sp.Villarreal&Hutchings,1986.Fresh water.On the maxillipeds, pereiopods,and ventral portion of the abdomen of the decapod Cherax tenuimanus(Australia).CRUSTACEAN PROTOZOAN EPIBIONTS,I.PERITRICH CILIATES649 Family Lagenophryidae Bütschli,1889Genus Lagenophrys Stein,1852( g.3)L.aegleae Mouchet-Bennati,1932.Fresh water.On the branchial laments of the anomurans Aegla sp.,Aegla castro,and Aegla franca.Arroyo Miguelete, (Uruguay)and Parana River(Brazil).L.ampulla Stein,1851.Fresh water.On the gills of species of the genus Gammarus.L.andos(Jankowski,1986)(cf.Clamp,1991).Syn.:Circolagenophrys andos Jankowski,1986.Fresh water.On the decapod Parastacus chilensis(Chile).L.anticthos Clamp,1988.Fresh water.On the branchial laments of the decapods Parastacus pugnax,P.defossus,and P.saffordi(Chile,Brazil, Uruguay).L.aselli Plate,1886.On the branchial surface of the isopod Asellus aquaticus (Hamburg,Germany).L.awerinzewi Abonyi,1928.On the gills of the decapod Potamon uviatilis(as Telphusa uviatilis)(Africa).L.bipartita Stokes,1890.On the cladoceran Daphnia sp.(fresh water,U.S.A.).L.branchiarum Nie&Ho,1943.Fresh water.On the gills of the caridean shrimp Macrobrachium nipponense(as Palaemon nipponense)(Japan).L.callinectes Couch,1967.Marine and in estuaries.On the gills of the decapods Callinectes sapidus,C.bocourti,and C.maracaiboensis(Chesapeake Bay, Maryland,Virginia,and Gulf of Mexico).mensalis Swarczewsky,1930.Fresh water.On gammarids(Lake Baikal).L.darwini Kane,1965.On the branchial laments of the decapod Cherax quadricarinatus(stream near Darwin,Australia).L.dennisi Clamp,1987.Fresh water.On the decapods Orconectes illinoiensis, Cambarus bartonii bartonii,and C.chasmodactylus(North America).L.deserti Kane,1965.Fresh water.On the gills of the decapods Cherax tenuimanus and C.quinquecarinatus(SW rivers,Australia).L.diogenes(Jankowski,1986).Syns.:Circolagenophrys diogenes Jankowski, 1986,Lagenophrys incompta Clamp,1987.Fresh water.On the gills of the decapods Orconectes illinoiensis and Cambarus diogenes(Illinois,U.S.A.).L.discoidea Kellicott,1887(cf.Clamp,1990).Syns.:Lagenophrys labiata Wallengren,1900(a junior homonym of biata Stokes,1887(cf.Clamp, 1990));L.wallengreni Abonyi,1928;Circolagenophrys entocytheris Jankow-ski,1986.Fresh water.On ostracods.On the cray sh Cambarus sp.,C.chas-modactylus,C.bartonii bartonii,and Orconectes illinoiensis(Ontario,Canada and U.S.A.).650G.FERNANDEZ-LEBORANS&M.L.TATO-PORTOFigs.3-7.3,Lagenophrys(L.eupagurus,after Clamp,1989);4,Clistolagenophrys(C.primitiva, after Swarczewsky,1930);5,Setonophrys(munis,after Clamp,1991);6,Operculigera (O.asymmetrica,after Clamp,1991);7,Usconophrys(U.aperta,after Clamp,1991).L.dungogi Kane,1965.On the branchial laments of the decapod Euastacus sp.(stream near Dungog,Australia).L.engaei Kane,1965.On the branchial laments,basal areas of the gills, branchiostegite membrane and,more rarely,on the pleopods of the decapods Engaeus victoriensis and Austroastacus hemicirratulus(Victoria,Tasmania, and Melbourne,Australia).L.eupagurus Kellicott,1893(cf.Clamp,1989).Syns.:Lagenophrys lunatus Imamura,1940;Lagenophrys articularis Nie&Ho,1943.Marine,in estu-arine areas and fresh water.On the decapods Litopenaeus setiferus(as Pe-CRUSTACEAN PROTOZOAN EPIBIONTS,I.PERITRICH CILIATES651 naeus s.)(Penaeidea,Penaeidae),on the surface of the body,Litopenaeus van-namei(as Penaeus v.),on the surface of the body,Macrobrachium nipponense (Caridea,Palaemonidae)on antennae and pleopods,Macrobrachium ohione, on the surface of the middle of the pleura,Macrobrachium rosenbergii,on the gills,Palaemon paucidens(Caridea,Palaemonidae),Palaemonetes inter-medius(Caridea,Palaemonidae),Palaemonetes kadiakensis,Palaemonetes paludosus,Palaemonetes pugio,Palaemonetes varians,on the whole body, except on the gills,Palaemonetes vulgaris,Upogebia af nis(Thalassinidea, Upogebiidae),and Pagurus longicarpus(Anomura,Paguridae),on the gills (U.S.A.,Japan,Venezuela,Thailand).L.foxi Clamp,1987.Fresh water.On the gills of the gammarids Gammarus pseudolimnaeus,G.troglophilus,G.minus,and Gammarus sp.(Missouri, U.S.A.).L.in ata Swarczewsky,1930.On the distal areas of pleopods of the gammarid Gmelinoides fasciata(Lake Baikal).L.jacobi(Kane,1969).Syn.:Stylohedra jacobi Kane,1969.On freshwater decapods in Australia.L.johnsoni Clamp,1990.Syn.:Lagenophrys labiata Stokes,1887(partim). Fresh water.On the appendages and the surface of the carapace of the gammarids Gammarus fasciatus,G.daiberi,G.tigrinus,and Crangonyx gracilis(New Jersey,Michigan,and North Carolina,U.S.A.).biata Stokes,1887(cf.Clamp,1990).Fresh water.On the appendages and on the surface of the carapace of the gammarids Gammarus fasciatus, G.daiberi,G.tigrinus,and Cangronyx gracilis(New Jersey,Michigan,and North Carolina,U.S.A.).L.leniusculus(Jankowski,1986).Syns.:Circolagenophrys leniusculus Jan-kowski,1986;L.oregonensis Clamp,1987.Fresh water.On the carapace, gills,ventral surface of the abdomen,uropods,pereiopods,and pleopods of the decapod Pacifastacus leniusculus leniusculus,and on the gills of P.leniusculus trowbridgii and P.connectens(North America).L.lenticula(Kellicott,1885)(cf.Clamp,1991).Syns.:Stylohedra lenticula Kellicott,1885;S.lenticulata Kahl,1935;Lagenophrys lenticulata(Kahl, 1935)(cf.Thomsen,1945).Fresh water.Setae of the sixth and seventh pereiopods of the gammarids Hyalella azteca and H.curvispina(U.S.A., Canada,Mexico,and Uruguay).L.limnoria Clamp,1988.Syn.:Circolagenophrys circularis Jankowski,1986 (cf.Clamp,1991).On the isopod Limnoria lignorum.L.macrostoma Swarczewsky,1930.Fresh water.On gammarids(Lake Baikal). L.matthesi Schödel,1983.On the maxillipeds of the gammarids Gammarus pulex and Carinogammarus roeselii.652G.FERNANDEZ-LEBORANS&M.L.TATO-PORTOL.metopauliadis Corliss&Brough,1965.Fresh water.On the gills of the brachyuran Metopaulias depressus(endemic on Jamaica).L.monolistrae Stammer,1935.On the pleopods of the isopod Monolistra sp.L.nassa Stein,1852.Fresh water.On the pleopods of the gammarid Gammarus pulex.L.oblonga Swarczewsky,1930.On the antennae of the gammarid Gammarus hyacinthinus(Lake Baikal).L.orchestiae Abonyi,1928.On the amphipod Orchestia cavimana(Lake Balaton,Hungary).L.ornata Swarczewsky,1930.Fresh water.On ke Baikal.L.ovalis Swarczewsky,1930.Fresh water.On the thoracic appendages of ke Baikal.L.parva Swarczewsky,1930.On ke Baikal.L.patina Stokes,1887(cf.Clamp,1990).Syn.:Lagenophrys labiata Stokes, 1887(cf.Shomay,1955).(Corliss&Brough,1965;Clamp,1973).Fresh water.On the pereiopods and gills of the gammarids Gammarus sp.and Hyalella azteca.American continent.L.rugosa Kane,1965.Fresh water.On the gills of the decapod Geocharax falcata(Victoria,Australia).L.similis Swarczewsky,1930.On ke Baikal.L.simplex Swarczewsky,1930.On ke Baikal.L.solida Swarczewsky,1930.On ke Baikal.L.stammeri Lust,1950.On ostracods.Germany.(Lust,1950a).L.stokesi Swarczewsky,1930.On ke Baikal.L.stygia Clamp,1990.Syn.:Lagenophrys labiata Stokes,1887(cf.Jakschik, 1967).Subterranean water.On the gills of the cave-dwelling amphipod Bactrurus mucronatus(Illinois,U.S.A.).L.tattersalli Willis,1942.On European copepods.L.turneri Kane,1969.On freshwater decapods in Australia.L.vaginicola Stein,1852.Syn.:Lagenophrys obovata Stokes,1887.On the genital setae and thoracopods of the copepods Cyclops miniatus and Cantho-camptus sp.L.verecunda Felgenhauer,1982.On the decapod Palaemonetes kadiakensis (Illinois,U.S.A.).L.willisi Kane,1965.Fresh water.On the gills of the decapods Cherax destructor,C.albidus,and C.rotundus(Melbourne,New South Wales(e.g., Newcastle),and NW Australia).Genus Clistolagenophrys Clamp,1991( g.4)C.primitiva(Swarczewsky,1930)(cf.Clamp,1991).Syn.:Lagenophrys primi-tiva Swarczewsky,1930.On pereiopods and pleopods of the gammarid Pallasea cancellus(Lake Baikal).Genus Setonophrys Jankowski,1986(cf.Clamp,1991)( g.5)S.bispinosa(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys bispinosa Kane,1965.On pereiopods of the decapod Cherax rotundus setosus.Stream near Newcastle(N.S.W.,Australia).munis(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys communis Kane,1965.On the body surface(telson,pleopods,pereiopods,carapace...) of the decapod Cherax destructor.On the gills of the decapods C.rotundus,C.albidus,C.quadricarinatus,Euastacus armatus,and Engaeus marmoratus(Victoria,Melbourne,and Tasmania,Australia).S.lingulata(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys lingulata Kane,1965.On the branchial laments and branchiostegite membrane of the decapods Cherax destructor, C.albidus,and C.rotundus(Victoria, Melbourne,and coastal and central areas of Australia).S.nivalis(Kane,1969)(cf.Clamp,1991).Syn.:Lagenophrys nivalis Kane, 1969.On freshwater decapods in Australia.S.occlusa(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys occlusa Kane, 1965.On the anterior zone of the branchial cavity of the decapods Cherax destructor,C.albidus,and C.rotundus(Victoria and New South Wales, Australia).S.seticola(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys seticola Kane, 1965.On the setae of the decapods Engaeus fultoni and Geocharax falcata (Victoria,Melbourne,and Templestowe,Australia).S.spinosa(Kane,1965)(cf.Clamp,1991).Syn.:Lagenophrys spinosa Kane, 1965.On the pleopods,carapace,and telson of the decapod Cherax destructor (Victoria,Melbourne,and Heathcote,Australia).S.tricorniculata Clamp,1991.On the pleopods of the decapod Geocharax falcata(Victoria,Grampian Mountains,and Wannon River,Australia). Genus Operculigera Kane,1969( g.6)O.asymmetrica Clamp,1991.On the base of the gills of the freshwater decapods Parastacus pugnax and Samastacus spinifrons(Concepción and Talcahuano,Chile).O.insolita Clamp,1991.On the base of the gills of the freshwater decapod Parastacus pugnax(Concepción,Talcahuano,Malleco,and Puren,Chile).O.montanea Kane,1969.On the freshwater decapod Colubotelson sp.(Aus-tralia).O.obstipa Clamp,1991.Pleopods of the isopod Metaphreatoicus australis (New South Wales,Australia).O.parastacis Jankowski,1986.On the base of the gills of the decapod Parastacus nicoleti(Isla Teja,Valdivia,Chile).O.seticola Clamp,1991.On the setae at the base of gills of the decapod Parastacus pugnax(Concepción,Chile).O.striata Jankowski,1986.On the decapod Parastacus chilensis.Chile.O.taura Clamp,1991.On the branchial laments of the freshwater decapod Parastacus pugnax(Concepción,Malleco,and Puren,Chile).O.velata Jankowski,1986.On the gills of the anomuran Aegla laevis.Chile.O.zeenahensis Kane,1969.On freshwater decapods in Australia.Family Usconophryidae Clamp,1991Genus Usconophrys Jankowski,1985(cf.Clamp,1991)( g.7)U.aperta(Plate,1889)(cf.Clamp,1991).Syns.:Lagenophrys aperta Plate, 1889;Usconophrys dauricus Jankowski,1986.On the gills and pleopods of the isopod Asellus aquaticus(Marburg and Hessen,Germany;North Carolina, U.S.A.;Brittany,Finisterre,Plougarneau,Pont-Menou,and Douron River, France).U.rotunda(Precht,1935)(cf.Clamp,1991).Syn.:Lagenophrys rotunda Precht,1935.On ostracods.Germany.Family Operculariidae Fauré-Fremiet,1979(in Corliss,1979)Genus Opercularia Stein,1854( g.8)O.allensi Stokes,1887.Syn.:O.ramosa Stokes,1887.On several living and inert substrata.On the body of the cray sh Astacus leptodactylus(cf.Matthes &Guhl,1973).O.asellicola Kahl,1935.On the isopod Asellus sp.Germany.O.coarctata Claparède&Lachmann,1858.On crabs(Buck,1961).O.crustaceorum Biegel,1954.On the gills of the cray sh Astacus astacus(asA. uviatilis).On the maxillae,maxillipeds,and pleopods of Austropotamo-bius torrentium(cf.Matthes&Guhl,1973).O.cylindrata Wrzesniowski,1807.On the copepod Cyclops sp.O.gammari Fauré-Fremiet,1905.Pereiopods of the gammarid amphipod Gammarus sp.O.lichtensteini Stein,1868.On various crabs and molluscs.O.nutans Ehrenberg,1838.Syn.:O.microstoma Stein,1854.On Entomostraca.On the cladoceran Alona af nis(cf.Matthes,1950).On the maxillipeds of the European cray sh Astacus leptodactylus(cf.Matthes&Guhl,1973).O.protecta Penard,1922.On the setae of pereiopods of the gammarid amphi-pod Gammarus pulex.O.reichelei Matthes&Guhl,1973.Found exclusively on the maxillipeds of the cray sh Astacus leptodactylus.O.stenostoma Stein,1868.On the isopod Asellus aquaticus.Genus Orbopercularia Lust,1950(cf.Lust,1950b)( g.9)O.astacicola(Matthes,1950)(cf.Matthes&Guhl,1973).Syn.:Opercularia astacicola Matthes,1950.Maxillipeds and pleopods of the cray sh Aus-tropotamobius torrentium.Genus Propyxidium Corliss,1979( g.10)P.aselli Penard,1922.On the isopod Asellus sp.P.asymmetrica Matthes&Guhl,1973.On the European cray sh Astacus astacus(as A. uviatilis).P.bosminae Kahl,1935.On the cladoceran Bosmina sp.P.canthocampti Penard,1922.On the pereiopods of the harpacticoid copepod Canthocamptus sp.Fresh water.P.cothurnioide Kent,1880.On the ostracod Cypris sp.P.hebes Kellicott,1888.On the pereiopods of the isopod Asellus aquaticus.P.henneguyi(Fauré-Fremiet,1905)(cf.Kahl,1935).Syn.:Opercularia hen-neguyi Fauré-Fremiet,1905.On the rst abdominal segment of the copepod Cyclops sp.Genus Ballodora Dogiel&Furssenko,1921( g.11)B.dimorpha Dogiel&Furssenko,1921.On Porcellio sp.and other terrestrialisopods.Genus Nuechterleinella Matthes,1990( g.12)N.corneliae Matthes,1990.On the ostracod Cypria ophthalmica.Genus Bezedniella Stoukal&Matis,1994( g.13)B.prima Stoukal&Matis,1994.Fresh water.On the ostracod Cypria sp.(Slovakia).Figs.8-14.8,Opercularia(O.nutans,after Foissner et al.,1992);9,Orbopercularia(O.astacicola, after Matthes&Guhl,1973);10,Propyxidium(P.canthocampti,after Penard,1922);11,Ballodora (B.dimorpha,after Dogiel&Furssenko,1921);12,Nuechterleinella(N.corneliae,after Matthes, 1990);13,Bezedniella(B.prima,after Stoukal&Matis,1994);14,Rovinjella(R.spheromae,afterMatthes,1972).Family Rovinjellidae Matthes,1972Genus Rovinjella Matthes,1972( g.14)R.spheromae Matthes,1972.On the marine isopod Sphaeroma serratum. Family Scyphidiidae Kahl,1933Genus Scyphidia Dujardin,1841( g.15)Scyphidia sp.Henebry&Ridgeway,1979.On the cladocerans Scapholeberis kingi,Alona costata,and Pleuroxus denticulatus(Ashmore Lake,Illinois, U.S.A.).Family Vaginicolidae De Fromentel,1874Genus Platycola Kent,1881( g.16)P.baikalica(Swarczewsky,1930).Syn.:Vaginicola baicalica Swarczewsky, 1930.Fresh water.On the gills of the gammarids Brandtia lata,Pallasea grubei,and Echinogammarus fuscus(Lake Baikal).P.callistoma Hadzi,1940.Fresh water.On the cave-dwelling isopod Microlis-tra spinosissima(former Yugoslavia).P.circularis Dons,1940.Marine.On the uropods of the isopod Limnoria sp.P.decumbens(Ehrenberg,1830).Syns.:Vaginicola decumbens Ehrenberg, 1830;Platycola ampulla De Fromentel,1874;P.regularis De Fromentel, 1874;P.striata De Fromentel,1874;P.truncata De Fromentel,1874;P.longicollis Kent,1882;P.intermedia Kahl,1935;P.re exa Kahl,1935;P.amphora Swarcezwsky,1930;P.amphoroides Sommer,1951.Fresh water.On several vegetable and animal substrata.On the gills of the gammarid Brachiuropus sp.(Lake Baikal)(Swarczewsky,1930).geniformis Hadzi,1940.Fresh water.On the cave-dwelling isopod Micro-listra spinosissima(former Yugoslavia).P.pala Swarczewsky,1930.Syn.:Vaginicola pala Swarczewsky,1930.On the gills of the gammarid Palicarinus puzyllii(as Parapallesa pazill)(Lake Baikal).Genus Cothurnia Ehrenberg,1831(cf.Claparède&Lachmann,1858)( g.17)C.angusta Kahl,1933.Brackish or fresh water.On ostracods(Kiel,Germany).C.anomala Stiller,1951.Fresh water.On the amphipod Corophium curvispi-num(Lake Balaton,Hungary).C.antarctica(Daday,1911)(cf.Warren&Paynter,1991).Syn.:Cothurniopsisantarctica Daday,1911.Marine.Epibiont on the ostracod Philomedes lae-vipes(Antarctic areas).C.astaci Stein,1854.Fresh water.On the pleopods and gills of cray sh.On the maxillae,maxillipeds,and pleopods of the cray sh Astacus astacus。
Characteristics of synchrotron radiation of longitudinally polarized spinning particle in t
·ν
(3)
The second relation in (3) means that the parameter τ becomes a proper time of the particle, while the third relations corresponds to the fact, that the electric dipole moment of the particle qµ is equal to zero, as it should be for a point particle. The first summand in (2) corresponds to the current of the particle without a dipole moment and the second term corresponds to the contribution to the current of the dipole moment of the spinning particle. In the chosen gauge for the theory of the particle without AMM considered here pµν is given by the expression [5]: g · pµν = 2 εµνλσ W λ x σ . (4) m Here W µ denotes the pseudoclassical analog of the Pauli- Lubansky vector, which is connected with the vector of the particle spin in the particle rest frame by the relation Wµ vi (vS ) = γ ( v S ) , Si + γ 2 , m γ+1
哥德尔不完备定理英文原文
哥德尔不完备定理英文原文英文回答：Gödel's incompleteness theorems are two mathematical theorems that demonstrate inherent limitations of axiomatic systems based on first-order logic. The theorems were published by Kurt Gödel in 1931 and are widely acknowledged as foundational results in mathematical logic.Theorem 1 (Incompleteness theorem): Any effectively axiomatizable theory capable of expressing basic arithmetic is either incomplete or inconsistent. That is, there are true statements about the natural numbers that cannot be proven within the theory.Theorem 2 (Undecidability theorem): No consistent, effectively axiomatizable theory capable of expressing basic arithmetic can decide all true statements about the natural numbers. That is, there are statements about the natural numbers that can neither be proven nor disprovenwithin the theory.Implications of Gödel's theorems:Limits of formal systems: Gödel's theorems demonstrate that no formal system can be both complete and consistent if it is capable of expressing basic arithmetic. This has profound implications for the foundations of mathematics and the limits of what can be proven within a given axiomatic system.Creativity and human intelligence: The incompleteness theorems suggest that there are mathematical truths that cannot be discovered through purely mechanical or algorithmic processes. This has led to speculation that human intelligence may involve non-computational elements that allow for creativity and insight.The nature of mathematics: Gödel's theorems have led to a deeper understanding of the nature of mathematics. They have helped to establish the distinction between provability and truth, and have raised questions about therole of intuition and human understanding in mathematical reasoning.中文回答：哥德尔不完备定理。
differential algebras
Discrete Mathematics and Theoretical Computer Science1,1997,229–237On the bialgebra of functional graphs and differential algebrasMaurice GinocchioLaboratoire de Physique Th´e orique et Math´e matique,Universit´e Paris7,Tour Centrale-3`e me´e tage,2,place Jussieu, F-75251Paris Cedex05,FranceE-Mail:mag@ccr.jussieu.fr1IntroductionWe have already described the expansion of∆Σλi∂i,i.e.the powers of a Lie operator in any dimension, in order tofind the expression of theflow of formal nonlinear evolution equations[1–3].In the one-dimensional case,the explicit expansion can be foundfirst in Comtet[4],and other aspects connected to the ordinary differential equations can be found in Leroux and Viennot[5]and Bergeron and Reutenauer [6].On the other hand,Grossman and Larson[7]introduced several Hopf algebras[8–10]of forests of rooted labeled trees to express the product offinite dimensional vectorfields.In this paper we concentrate us on the bialgebra G of functional graphs,i.e.graphs representing mappings offinite sets in themselves [11–15].We give only the results without proofs.In a forthcoming paper[16],we develop Hopf algebra structures,computing the antipode and giving detailed aspects and proofs.In Sect.1we consider a bialgebra structure on G and three interesting subalgebras:T the set of labeled forests;S the set of permutation graphs;and L the set of well labeled forests,i.e.with strictly decreasing labels on the chains toward the roots.Recall that the graded bialgebra L is sufficient for the calculus of the powers of one derivation[1],and it is extendable in a Hopf algebra,the element of which is known in the computer literature as‘heap ordered trees’.This bialgebra is useful to compute products of derivations or to transform differential monomials in differential algebras[17],and it is interesting to note that the elements L n(n edges)can be coded by the words(monomials)of the expansion of Q nq0q0q1q0q1q n1,where Q0q0q1is a noncommutative alphabet.We describe in particular the bialgebra L,first in the polynomial form by the‘factorial’monoid L0L0n n0,where L0n is the set of words in the expansion of Q n,and second,we establish the bijective correspondence between 1365–8050c1997Chapman&Hall230M.Ginocchio L and L.We show that the calculus are easier with L,and that the product on L can be expressed in a very natural way.For example,q0n Q n,hence the(exponential)generating function of all the elements of L.We describe principally the formalism in the general case G,and the calculus uses thefields F201 as well as characteristic zerofields K.In Sect.2,we describe the link with the graded differential algebra K U r0K U r and the graded algebra of differential operators K U D r0K U r D r,where U u1u2uββ1uβαα0β1is a set of indeterminates,D∂0∂1and the differential indeterminates uβασ1σp∂σ1∂σpuβαgenerate K U r[17].This shows that the above Q-calculus,which is a kind of‘dissection’on functional graphs can be used as pre-calculus in differential algebras as well as in discrete dynamical systems[18].2Bialgebra Based on the Semi-group of Functional Graphs2.1T ypes of Functional GraphsIn this paper,a connected functional graph will be called excycle[13,15].In the area of discrete dynamical systems,an excycle is known as a basin of attraction.Consider several graded andfiltered sets of labeled functional graphs(i)E(resp.G)the set of excycles(resp.functional graphs)and designated by G n(resp.G n),the set offunctional graphs having(resp.having at most)n1nodes for n0(ii)R(resp.T)the set of labeled arborescences(resp.forests).(iii)C(resp.S)the set of cycles(resp.permutation graphs).(iv)A(resp.L)the set of well labeled arborescences(resp.forests),i.e.with strictly decreasing labels on the chains toward the root(s).As in(i),we consider for(ii)–(iv)graduations andfiltrations.2.2Free Representation by Q-polynomialsLet G n be the semigroup of mappings of12n in itself(‘Semigroup of endofunctions’), Card G n n n and the subsemigroups,T n f;f G n f n f n1(i.e.f acyclic and Card T n n1n1,S n the symmetric group and Card S n n!L n f;f G n f i i(i.e.f subdiagonal and Card L n n!.We have the well known bijections F F:G n G n T n T n S n S n L n L n.Let Q q0q1be a noncommutative alphabet,Q0q0Q with q0noncommuting with the q i’s,Q n q1q2q n Q0n q0Q n and Q(resp.Q0),the corresponding free monoids.Taking F201as thefield,consider(i)the G n module F2Q n by the F2linear incidence matrix action of f G n as l f q i q f i hence l f l gl f g.On the bialgebra of functional graphs231 (ii)the generating monomial associated with f.By morphism extension,denoted again by l f,we defineQ f q f1q f2q f n l f Qιn1where Qιn q1q2q n is associated with the identityιn of G n and Qι01One again has l f l g l f g.For the following we consider(iii)The graded subsets of Q as G G n n0T T n n0S S n n0L L n n0respectively associated with G,T,S and L,with G0T0S0L01(iv)The corresponding graded F2-modules:F2G F2T F2S F2L admit components of degree n which are,respectively,G n T n S n L n modules,withdimF2G n n n dimF2T n n1n1dimF2S n dimF2L n n!(v)We will denote by R n one of the above subsemi-groups of G n(or of another category). Similarly,let R R n n0resp F2R n0F2R n be the corresponding graded subsets of Q(resp. graded F2-modules ofF2G n0F2G n.2.3Virtual Root and External ProductLet f G n I0be the set offixed points of f and H0a subset of I0,and set p q r;p r q if p q and/0otherwise.Define f0:1n0n such that f0i f i if i H0and f0i0if i H0The‘0’is the label of a virtual root added to the graph representation of f,and we will say that H0is‘confined in0’,which is a fixed point of f0We call‘extended endofunctions’such functions f0,denote by G0n0n1n their set, and we consider G n as a subset of G0n Similarly,we will have T0n T n S0n S n L0n L n Consequently, adding q0,we get the extended graded sets G0G0n n0the extended graded F2-module F2G0 n0F2G0n and their substructures F2T0F2S0F2L0Now letφG0mχ0be the characteristic function of H0φ10,and writeQφlφQιm qφ1qφ2qφmm ∏i1qφi(cf.Figures1and2).WithψG0n,consider the F2-bilinear product in F2G0defined byQφQψQψm∏i1qφi nχ0i q0q1q n12On the right-hand side we have a sum of concatened monomials,and on the right factor the substitutions q0q0q1q n and q h q h n when h0232M.Ginocchio On the other hand,the product belongs to F2G0m n This external product is associated with unit1and F2G0is‘.’graded.To see this consider i j k being0three homogeneous polynomials,A A q0;q i F2G0mB B q0;q j F2G0nC C q0;q k F2G0pthen by(2)A B B q0;q j A q0q1q n;q i n3 and so,using deg B C n p,A q0;q iB q0;q jC B q0;q j A q0q1q n;q i n CCB q0q1q p;q j p A q0q1q p q1p q n p;q i n pA q0;q i CB q0q1q p;q j pA q0;q iB q0;q j CMoreover,because T n S n L n are subsemi-groups of G n one can see that F2R0F2T0F2S0F2L0are‘.’graded subalgebras of F2G0HenceProposition1Let the sequence G0m m1of the sets of the extended endofunctions in12m and Q0q0q1be a noncommutative alphabet.ForφG0m let Qφ∏m i1qφi be the generating monomial ofφand the graded module F2-module F2G0n0F2G0n on F201generated by all the φsThen F2G0is a graded algebra for the associative product with unit1QφQψQψm∏i1qφi nχ0i q0q1q n1whereψG0n andχ0is the characteristic function ofφ10Moreover,if R0m m1is a sequence of subsets associated with subsemi-groups of the sequence G0m m1, then F2R0n0F2R0n is a graded subalgebra of F2G02.4Splitting Operatorδn F2G0This operator substitutes the n-coproduct∆n of the Leibniz–Lie type.Associate to A Q0the left linear operatorτn A acting on B Q0,such that,if A G0m B G0n,then Bτn A BA if degB n,and0 otherwise,where BA is the concatenation of B and A.(i)Now let f G m and H0as in Sect.3,and notefirst that ifτn is viewed as acting on f,then for i1m one hasτn f i n f i n,and by f0i ¯χ0i f i one hasτn f0i n¯χ0i f0i n,where¯χ01χ0According to(2),define forφG0mδn Qφτnm∏i1qφi nχ0i q0q1q n14If d0Card H0the expansion(4)gives a sum of n1d0generating monomials of functionsψκof n1n m into0n1n m,and the corresponding functional graphs factorized in commutative excycles.On the bialgebra of functional graphs233 The operatorδn A is left linear on F2G0,and(2)can be writtenQφQψQψδn Qφ5 (ii)Moreover,δp is a graded antimorphism for‘’δp A Bδp Bδp n A6 where n degB and p N.For this to compute with(5)and A B C as in Sect.3,Cδp A B A B C A B C B Cδp n A Cδp Bδp n A.If p0we recover A B Bδn A and Bδk A0if k degB(iii)Also,δn is a powerδnδnδδ1δ017 For this to compute,δpδn A q0;q iδpτn A q0q1q n;q i nτn p A q0q1q p q1pq n p;q i n pδn p A q0;q i.(iv)Define the left linear operatorµin F2G0by the expansionµ∑n0δn8By left linear action ofµA on F2G0,we get A B BµA for A B F2G0with the antimorphism propertyµA BµBµA9 which express the associativity of‘’.Proposition2Let A F2G0m B F2G0n Then the splitting linear operatorδp defined left linearly by Bδp A A B if p=n,and0otherwise,verifiesδpδp withδδ1δ01andδp A Bδp Bδp n A Moreover,µ∑n0δn is an antimorphism in F2G0such that A B BµA2.5Exponential Generating Function of the Monomials of L0All the words of L0n(i.e.subdiagonals)are obtained from the expansion of Q n q0q0q1q0q1 q n1F2L0and Q01By equation(3),one has Q m Q n Q m n,and if A F2L0m B F2L0n we have A B F2L0m n,and then we recover that F2L0is stable for the product‘’.Because Q1q0,the associativity givesQ n q0n10 With the Q[[t]]-modules on L0,one has the exponential generating functionexp tq0∑n0t nn!Q n11exp sq0exp tq0exp s t q0234M.Ginocchio2.6ExamplesConsider equations (4)and (5)for Q ψq n 0.2.6.1Rooted T rees with n=1δq 20q 1τq 0q 12q 2τq 0q 0q 2τq 0q 1q 2τq 1q 0q 2τq 1q 1q 2(Figure 3)q 20q 1q 0q 0q 0q 12q 2q 30q 2q 20q 1q 2q 0q 1q 0q 2q 0q 1q 1q 2(Figure 4)2.6.2Excycles with n=2δ2q 23q 1q 0τ2q 25q 3q 0q 1q 2τ2q 25q 3q 0τ2q 25q 3q 1τ2q 25q 3q 2(Figure 5)q 23q 1q 0q 20q 20q 25q 3q 0q 1q 2q 20q 25q 3q 0q 20q 25q 3q 1q 20q 25q 3q 2(Figure 6)3Differential Algebra3.1Differential indeterminatesLet D ∂0∂1where ∂α∂∂ξαthe αth canonical derivation in S K ξthe algebra of formal power series in ξξ0ξ1,where K is a characteristic zero field.If S N N is the set U u 1u 2u ββ1u αβα0β1with u αβS consider U as a set of indeterminates,u αβσ1σp ∂σ1∂σp u αβasdifferential indeterminates,replace S N N by KU ,and consider the graded differential algebra K Ur 0K U r and the graded algebra of differential operators K U D r 0K U r D r.To each W F 2R 0we associate the differential operator W U U D ;for example,with W r U K U r one hasW UW 0UW 1Uα∂αW 2Uαβ∂α∂βW 0U∑r 1W r U D r12We will use now the summation convention.3.2Brackets in K UDefine for u v wU the multilinear operations valued in K U .3.2.1Arborescent Brackets (Valued in K U 1)u v uv w u vβu αv βα,henceu v Du αv βα∂β(1fixed point sent to ‘0’)uv wγu αv βw γαβ,henceu v Du αv βw γαβ∂γ13Also,for AK UrBK UsA Bβ1βsA α1αr B β1βsα1αr3.2.2Circular Brackets (Valued in K U 0)uu αα(1fixed point),u vu ααv ββ(2fixed points)u vu αβv βα2cycleu v wu αγv βαw γβ3cycle14On the bialgebra of functional graphs 2353.2.3Mixed Brackets (Valued in K U 0)Let E be a proper excycle (i.e.with no fixed point);we can write it EA i 1A i 2A i p ,where the A i k ’s are arborescences with root i k If in each arborescence A i k is reduced to its root i k ,we recover simply acycle Ei 1i 2i p Now let F k be the forest under i k ,i.e.obtained by cutting the root of A i k ,and defined with F i k U F i k u j ;j N i k ,where N i k is the set of nodes of F i k :E Uu F i 1i 1u F i 2i 2u F i pi pF i 1U u i 1α1αp F i 2U u i 2α2α1F i p U u i p αp αp13.3Action of F 2R 0Moreover,F 2R 0operates K -linearly in K U with values in K U D .For this let φG 0m H 0φ1for j 0m I 1m ,and H u β1u β2u βm U ,a word on U of length m .Then the action isQ φ∏i Iq φiQ φH∏j I∏i H j∂αiu αj βj∏k H 0∂αk15The differential monomial Q φH is such that u βj is associated with j in the domain I of φIf d j is the degree in q j (in-degree of the node labeled by ‘j ’),then u αj βj is derived d j times and the indices of derivation are related to the places of the q j ’s in the word.Similarly,the differential operator D r is characterized by the number r (degree of the root)of the q 0’s and their places.So we can summarize:In a word A R 0where q j is at the place (i),then in A H the j th letter of H is derived according to i,i.e.∂αi acts.One has,in particular,taking H u 1u 2:Arborescent brackets 1U 1q 0U u 1α1∂α1u 1Dq 0q 0U u 1α1u 2α2∂α1∂α2u 1u 2D 2q 0q 1U u 1α1α2u 2α2∂α1u 2u 1D q 3q 3q 0U u 1α1u 2α2u 3α3α1α2∂α3u 1u 2u 3Dq 0q 0q 2q 2U u 1α1u 2α2α3α4u α33u α44∂α1∂α2u 1u 3u 4u 2D 2Circular brackets q 1U u 1α1α1u 1q 1q 2U u 1α1α1u 2α2α2u 1u 2q 2q 1U u 1α1α2u 2α2α1u 1u 2q 3q 1q 2U u 1α1α3u 2α2α1u 3α3α2u 1u 2u 33.4Product of Differential OperatorsThe product (2)on words with correspondence (15)gives the product of differential operators.We state,without proof,Proposition 3Let the graded differential algebra K U r 0K U r and the graded algebra of differ-ential operators K U D r 0K U r D r Let φG 0m I 1m H j φ1j for j 0m and H u β1u β2u βm a word on U of length m.Then the mapping of F 2G 0into K U D which associates to the generating monomial Q φ∏i I q φi of φthe differential operator Q φH ∏j I ∏i H j ∂αi u αj βj ∏k H 0∂αk236M.Ginocchio is a morphism,such that ifψG0n and K is a word on U of length n,one has QφH QψK QφQψKH, where KH is the concatenation of K and H.ExampleA q0B q2q1q0H u4K u1u2u3A B q2q1q0q0q1q2q3q2q1q0q0q2q1q0q1q2q1q0q2q2q1q0q3(Figure7)A H u1DB K u1u2u3DA HB K u1u2u3u4D2u4u1u2u3D u1u2u4u3DObserve that:u4u1u2u3D u1α1α2α4u2α2α1u3α3u4α4∂α3u1α1α2u2α2α1α4u3α3u4α4∂α3which corresponds to q2q1q0q1q2,i.e.the second and third terms in the graph expansion. AppendixTo view Figures1–7,click here.To return to the main paper,click on the red box.References[1]Ginocchio,M.(1995).Universal expansion of the powers of a derivation,Letters in Math.Phys.34(4),343–364.[2]Ginocchio,M.and Irac-Astaud,M.(1985).A recursive linearization process for evolution equations.Reports on Math.Phys.21,245–265.[3]Steeb,W.H.and Euler,N.(1988).Nonlinear Evolution Equations and Painlev´e Test.World Scien-tific.[4]Comtet,L.(1973).Une formule explicite pour les puissances successives de l’op´e rateur de d´e rivationde m.Roy.Acad.Sci.276A,165–168.[5]Leroux,P.and Viennot,G.(1986).Combinatorial resolution of systems of differential equations I:ordinary differential equations.Actes du colloque de combinatoire´e num´e rative,Montr´e al.Lecture Notes in Mathematics1234,pp.210–245.Springer-V erlag.[6]Bergeron, F.and Reutenauer, C.(1987).Une interpr´e tation combinatoire des puissances d’unop´e rateur diff´e rentiel lin´e aire.Ann.Sci.Math.Quebec11,269–278.[7]Grossman,R.and Larson,R.G.(1989).Hopf-algebraic structures of families of trees.J.Algebra126,184–210.[8]Joni,A.A.and Rota,G.C.(1979).Coalgebras and bialgebras in combinatorics.Studies.in Appl.Math.61,93–139.On the bialgebra of functional graphs237 [9]Nichols,W.and Sweedler,M.E.(1980).Hopf algebras and combinatorics,in‘Umbral calculus andHopf algebras’.Contemp.Math.6.[10]Sweedler,M.E.(1969).Hopf Algebras.Benjamin.[11]Berge,C.(1983).Graphes.Gauthier-Villars.[12]Comtet,L.(1974).Advanced Combinatorics.Reidel.[13]Denes,J.(1968).On transformations,transformation-semigroups and graphs.In Erd¨o s-Katona,ed-itor,Theory of Graphs.Academic Press,pp.65–75.[14]Foata,D.and Fuchs,A.(1970).R´e arrangements de fonctions et d´e b.Theory8,361–375.[15]Harary,F.(1959).The number of functional digraphs.Math.Annalen138,203–210.[16]Ginocchio,M.On the Hopf algebra of functional graphs and differential algebras.Discr.Math.Toappear.[17]Kaplansky,I.(1976).Introduction to Differential Algebras.Springer-V erlag.[18]Robert,F.(1995).Les syst`e mes Dynamiques Discrets.Springer-V erlag.。
帕金森病(英文)-PPT课件
Clinical findings
A. Tremor
4~6Hz tremor of Parkinsonism is characteristically most conspicuous at rest, it increases at times of emotional stress and often improves during voluntary activity.
A. Anticholinergic drugs
trihexyphenidyl (antan)
common side effects: dryness of the mouth, constipation, urinary retention, confusion .
started with a small dose, then gradually increased until benefit occurs or side effects limit further increments.
Parkinsonism, but many patients fail to respond for its benefit is short-lived
C. Levodopa
Levodopa is converted in the body to dopamine, help all the major clinical features of Parkinsonism, and is often particularly helpful against hypokinesia.
Pathogenesis
Dopamine and acetylcholine are present in the corpus striatum, where they act as neurotransmitters.
Cosmological perturbations on a magnetised Bianchi I background
Abstract Motivated by the isotropy of the CMB spectrum, all existing studies of magnetised cosmological perturbations employ FRW backgrounds. However, it is important, to know the limits of this approximation and the effects one loses by neglecting the anisotropy of the background magnetic field. We develop a new treatment, which fully incorporates the anisotropic magnetic effects by allowing for a Bianchi I background universe. The anisotropy of the unperturbed model facilitates the closer study of the coupling between magnetism and geometry. The latter leads to a curvature stress, which accelerates positively curved perturbed regions and balances the effect of magnetic pressure gradients on matter condensations. We argue that the tension carried along the magnetic force-lines is the reason behind these magneto-curvature effects. For a relatively weak field, we also compare to the results of the almost-FRW approach. We find that some of the effects identified by the FRW treatment are in fact direction dependent, where the key direction is that of the background magnetic field vector. Nevertheless, the FRW-based approach to magnetised cosmological perturbations remains an accurate approximation, particularly on large scales, when one looks at the lowest order magnetic impact on gravitational collapse. On small scales however, the accuracy of the perturbed Friedmann framework may be compromised by extra shear effects. PACS numbers: 9880H, 0440N, 4775, 9530Q, 9862E, 0420
Probability & incompressible Navier-Stokes equations An overview of some recent development
3 j =1
u(x, 0+ ) = u0 (x),
(1)
∂ 2 /∂x2 j ; the latter two are applied component-wise to vector-valued functions. The term p(x, t) is the (scalar) pressure, g(x, t) represents external forcing, and ν > 0 is the kinematic viscosity. Probabilists might want to write the term ν ∆ as 1 2 2ν ∆ in anticipation of the heat kernel in the form k (x, t) =
1. Navier-Stokes Equations: Background The present paper is an attempt to provide a brief orientation to Navier-Stokes equations from a probabilistic perspective developed in the course of working with a focussed research group in this area during the past few years at Oregon State University (OSU). An effort is made to furnish a bit more background for the uninitiated on some of the basics of these equations along with a summary description of the probabilistic methods and results. The approach is in somewhat “broad strokes”. The reader should be able to follow and/or supply most basic calculations, but the more technical proofs of some of the main results are
A New Algebraization of the Lame Equation
ψ ′′ (x) + E − m ℓ(ℓ + 1) sn2 x ψ (x) = 0 , (1.1)
The Lam´ e equation,
where ℓ is a real parameter1 , and sn x ≡ sn(x|m) is the usual Jacobian elliptic function of modulus m, occupies a central position in the theory of differential equations with periodic coefficients. The study of its properties has attracted the attention of many illustrious mathematicians over the last century; classical references are [1–4]. Basic properties of the Lam´ e equation are as follows. First, it arises by separation of variables in the Laplace equation in ellipsoidal coordinates. Secondly, it possesses two linearly independent 2K (k ) or 4K (k )-periodic solutions (for characteristic √ values of E ) if and only if ℓ is a nonnegative integer. Here k = m, and K (k ) (denoted by K from now on) is the complete elliptic integral of the first kind with parameter k :
形态鉴别特征 英语
形态鉴别特征英语When it comes to distinguishing between two similar objects, the first thing you'll notice is often their size. One might be noticeably larger or smaller than the other, giving an instant visual cue. The shape, too, can be a giveaway. One object might be round and smooth, while the other could be angular and jagged.Colors are another vital aspect to consider. Some creatures or plants have distinctive color patterns that set them apart from others. Maybe one has a bright red hue, while the other is a muted green. These color differences can be striking and easy to identify.Texture is another distinguishing factor. Some materials feel smooth and silky to the touch, while others might be rough and bumpy. You can often tell a lot about an object just by feeling its surface.For more intricate objects, details like patterns ormarkings can be key. A particular bird might havedistinctive stripes or spots on its feathers, while a leaf might have a unique vein pattern. These tiny butsignificant differences can help you identify one object from another.Lastly, the behavior or movement of an object can also be a telltale sign. Animals, for instance, have unique ways of moving and interacting with their environment. By observing these behaviors, you can often distinguish between similar species. So, whether it's size, shape, color, texture, details, or behavior, there are always ways to distinguish between objects and creatures in the natural world.。
贝尔曼——翻译的12种变形倾向
思考题
• 如何理解 “扩充法加剧了作品原来的无定 形性，使它从无形的丰富变成无形的空洞” ？
翅膀
大门
牢笼
巨人
小路/小巷
门/入口
9. 对语言模式的破坏 (the destruction of linguistic patternings)
• 文本系统的本质超越能指、隐喻等层面，延伸至文本使用 的句子类型及句型结构。这样的模式也可能包括一种语音 对时间的使用，对某种从句的依赖。
• 合理化、明晰化、扩充等翻译策略都会引入一些原文本质 系统排斥的元素，以致文本的系统性受到损害。
5. 质量受损 (qualititive impoverishment)
• 译文的质量受损是指用新的术语、表达法、人物形象来代 替原文，而这些术语、表达法、人物形象缺少原文语言中 醒人耳目的丰富性，相应地，它们的指示(signifying)或“形 象(iconic)的丰富性也会受损。
6. 数量缺失(quantitative impoverishment)
东西。翻译凭借自己的活动来激活文中的这些因素。 → 二是明晰化法把原文不希望清晰的部分变得清晰。
3. 扩充 (expansion)
• 斯坦纳(George Stainer)：翻译就是“通货膨胀”。
• 扩充，在一定程度上是前两种倾向的结果。合理化、明晰 化都要扩充，将原文“折叠”的部分“展开”。
• 扩充，并没有扩充任何实质性的内容，只是徒增文本的臃 肿；把原文自身清晰的语言变得模糊；拖沓松散，打乱原 文行文节奏。(过 度翻译overtranslate)
安托瓦纳·贝尔曼——翻译 的12种变形倾向
l安托瓦纳·贝尔曼(Antoine Berman)
• 贝尔曼（1942-1991）是当代法国著名的理论家，拉美文 学及德国哲学的翻译家，以其一贯的哲学立场而闻名译学 界。
生药学和植物疗法的基本原理英文版_部分10
ARALIACEAEImportant medicinal plants from the familyl Hedera helix L.[(common)ivy],used as a cough remedyl Panax ginseng C.A.Meyer(ginseng),used as an adaptogene(a very ill-defined category)and to combat mental and physical stress[and sometimes replaced by Eleutherococcus(Acanthopanax)senticosus(Rupr.and Maxim) Maxim from the same family].Morphological characteristics of the family This family consists mostly of woody species,charac-terized by hermaphrodite flowers in a simple umbel (see the closely related Apiaceae with a double umbel).The leaf lobes are hand-shaped,and the flow-ers relatively inconspicuous with two pistils,an infer-ior gynaecium,a small calyx and generally a white to greenish corolla,with free petals and sepals. DistributionThis family of>700species is widely dispersed in tropical and subtropical Asia and in the Americas. Hedera helix is the only species native to Europe.Chemical characteristics of the familyOf particular importance from a pharmacognostical perspective are the saponins,triterpenoids and some acetylenic compounds.The triterpenoids(gin-sengosides)are implicated in the pharmacological effects of Panax ginseng,while saponins(hederasa-ponins)are of relevance for the secretolytic effect of Hedera helix.ASPHODELACEAE(‘MONOCOTYLEDONEAE’)This family is often included in the Liliaceae(lily family).Important medicinal plants from the familyl Aloe vera(L.)Burman f.(syn.Aloe barbadensis, Barbardos aloe)and A.ferox Miller(Cape aloe), both strong purgatives(see p206and208).Aloe leaves contain a gel which is also applied topically for skin conditions;for botanical description.(see p.286,Chapter22).Morphological characteristics of the family Members of this family are generally perennials,and,in the case of Aloe,usually woody,with a basal rosette and the typical radial hermaphrodite flower structure of the Liliales.The petals and sepals are identical in form and colour,and composed of 3þ3free or fused,3þ3free stamens and three fused superior carpels.DistributionThis family,with about600species,is widely dis-tributed in South Africa(a characteristic element of the Cape flora);some species occur naturally in the Mediterranean(Asphodelus).Chemical characteristics of the family Typical for the genus Aloe are anthranoids and anthraglycosides(aloe-emodin),which are respon-sible for the species’laxative effects,as well as poly-saccharides accumulating in the leaves.Contrary to other related families,the Asphodelaceae do not accumulate steroidal saponins.ASTERACEAE–THE‘DAISY’FAMILY(ALSO KNOWN AS COMPOSITAE)This large family has kept botanists busy for many centuries and still no universally accepted classifica-tion exists.All members of the family have a complex inflorescence(the capitula),which gave rise to the older nameofthefamily:Compositae(¼inflorescence composed of many flowers).In other features,the family is rather diverse,especially with respect to its chemistry.Important medicinal plants from the familyl Arnica montana L.(arnica),used topically, especially for bruisesl Artemisia absinthum L.(wormwood or absinthium),used as a bitter tonic and choleretic l Calendula officinalis L.(marigold),used topically, especially for some skin afflictionsl Cnicus benedictus L.(cnicus),used as a cholagogue (a bitter aromatic stimulant)l Cynara scolymus L.(artichoke),used in the treatment of liver and gallbladder complaints and several other conditionsl Echinacea angustifolia DC.,E.pallida Nuttall andE.purpurea(L.)Moench(Cone flower),now commonly used as an immunostimulantl Matricaria recutita L.(chamomille/camomille; several botanical synonyms are also commonly used,including Chamomilla recutita andMatricaria chamomilla)(see Chapter14,p.208). l Tussilago farfara L.(coltsfoot),a now little used expectorant and demulcent.Morphological characteristics of the family (Fig.4.3)The family is largely composed of herbaceous and shrubby species,but some very conspicuous trees are also known.The most important morphological trait is the complex flower head,a flower-like struc-ture,which may in fact be composed of a few or many flowers(capitulum or pseudanthium).In some sections of the family(e.g.the subfamilyRay floretFlowerheadDisk floret Stigma(a)FruitM. maritima ssp inodora L.Scentless chamomile Matricaria chamomilla L.Wild ChamomileFig.4.3(a)Two members of the genus Matricaria.(Left)Matricaria chamomilla L.is aromatic and used medicinally.(Right) Matricaria maritima L.subsp.inodora Schultz[¼Tripleurospermum perforatum(Me´rat)Wagenitz],also known as Matricaria inodora,is not aromatic and is not used medicinally.The illustration shows typical morphological differences in these two species, such as the form of the flower heads and the fruit,but it also shows how similar the two species are in many other characteristics. From Fitch(1924).(b)Schematic of typical flower heads(a capitulum)of the Asteraceae(compositae).df,disk flowers;tf,tubular flowers;in,involucre,from Brimble(1942).Lactucoideae,which includes lettuce and dande-lion),only ligulate(tongue-shaped)or disk(ray) florets are present in the dense heads.In the other major segment(subfamily Asteroideae),both ligu-late and radiate/discoid flowers are present on the same flower head,the former generally forming an outer,showy ring with the inner often containing large amounts of pollen.The flowers are epigynous, bisexual or sometimes female,sterile or functionally male.The(outer)calyx has five fused sepals and in many instances later develops into a pappus(feath-erlike in dandelions,in other instances more bristly),which is used as a means for dispersingthe fruit;it is lacking in many other taxa.The fused petals(generally five)form a tubus or a ligula.The two gynaecia are epigynous and develop into tiny, nut-like fruits(achene or cypsela).The leaves are generally spirally arranged,simple,dissect or more or less compound.DistributionMore than21,000species are known from practi-cally all parts of the world,with the exception of Antarctica,and the family has found niches in a large variety of ecosystems.The family is particu-larly well-represented in Central America and southern North America(Mexico).Chemical characteristics of the familyA typical chemical trait of this family is the presence of polyfructanes(especially inulin)as storage carbo-hydrates(instead of polysaccharides)in perennial taxa.Inulin-containing drugs are used for preparing malted coffee(e.g.from the rootstocks of Cichorium intybus,chicory).In many taxa,some segments of the family accumulate sesquiterpene lactones(typi-cally with15-carbon atoms such as parthenolide; Fig.4.4),which are important natural products responsible for the pharmacological effects of many botanical drugs such as Chrysanthemum parthenium(feverfew)and Arnica montana(arnica). Polyacetylenic compounds(polyenes),and essential oil,are also widely distributed.Some taxa accumu-late pyrrolizidine alkaloids,which,for example,are present in Tussilago farfara(coltsfoot)in very small amounts.Many of these alkaloids are known for their hepatotoxic effects.Other taxa accumulate unusual diterpenoids;the diterpene glycoside stevioside(Fig.4.4),for example,is of interest because of its intensely sweet taste.CAESALPINIACEAEThis family was formerly part of the Leguminosae(or Fabaceae)and is closely related to two other families: the Fabaceae(seebelow)andtheMimosaceae(not dis-cussed).Many contain nitrogen-fixing bacteria in root nodules.This symbiotic relationship is beneficial to both partners(for the plant,increased availability of physiologically usable nitrogen;for the bacterium, protection and optimal conditions for growth).Important medicinal plants from the familyl Cassia senna L.and C.angustifolia Vahl(Senna), used as a cathartic.Morphological characteristics of the family (Fig.4.5)Nearly all of the taxa are shrubs and trees.Typically the leaves are pinnate.The free or fused calyx is composed of five sepals,the corolla of five generally free petals,the androecium of ten stamens,with many taxa showing a reduction in the number of stamens(five)or the development of staminodes instead of stamens.The flowers are zygomorphic and have a very characteristic shape,if seen from above,resembling a shallow cup.DistributionThe2000species of this family are mostly native to tropical and subtropical regions,with some species common in the Mediterranean region.The family includes the ornamental Cercis siliquastrum L.(the Judas tree),native to the western Mediterranean, which according to(very doubtful)legend was the tree on which Judas Iscariot hangedhimself. Parthenolide SteviosideCH2OHO OOHOHOOHOHOOHHOH2CFig.4.4Chemical characteristics of the familyFrom a pharmaceutical perspective the presence of anthranoides with strong laxative effects is of parti-cular interest.Other taxa accumulate alkaloids,such as the diterpene alkaloids of the toxic Erythrophleum.FABACEAEThis family is also classified together with the Mimosaceae and the Caesalpiniaceae as the Legu-minosae(or Fabaceae,s.l.;see note under Caesalpi-niaceae).One of its most well-known characteristics is that many of its taxa are able to bind atmospheric nitrogen.Important medicinal plants from the familyl Cytisus scoparius(L.)Link(common or Scotch broom),which yields sparteine(formerly used in cardiac arrhythmias,as an oxytoxic,and in hypotonia to raise blood pressure)l Glycyrrhiza glabra L.(liquorice),used as an expectorant and for many other purposesl Melilotus officinalis L.(melilot or sweet clover);the anticoagulant drug warfarin was developed from dicoumarol,first isolated from spoiled hay of sweet clover l Physostigma venenosum Balfour(Calabar bean),a traditional West African arrow poison,which contains the cholinesterase inhibitor physostigmine,used as a myotic in glaucoma,in postoperative paralysis of the intestine and to counteract atropine poisoning.Morphological characteristics of the family This family is characterized by a large number of derived traits.Most of the taxa of this family are her-baceous,sometimes shrubby and only very rarely trees.Typically,the leaves are pinnate and some-times the terminal one is modified to form a tendril, used for climbing.Bipinnate leaves are not found in this family.The five sepals are at least basally uni-ted.The corolla is formed of five petals and has a very characteristic butterfly-like shape(papilionac-eous),with the two lower petals fused and forming a keel-shaped structure,the two lateral ones pro-truding on both sides of the flower and the largest petal protruding above the flower,being particu-larly showy.The androecium of ten stamens gener-ally forms a characteristic tubular structure with at least nine out of ten of the stamens forming a sheath. Normally,the fruit are pods,containing beans(tech-nically called legumes)with two sutures,which open during the drying of the fruit(Fig.4.6).(a)(c)(d)(b)Fig.4.6Flower of Pisum sativum(common pea,Fabaceae, sensu stricto):(a)entire flower showing the various elements of the corolla(co;b,banner;w,wing(two);k,keel;ca calyx);(b) calyx;(c)stamens(nine fused and one free);(d)gynaecium;(e) the four petals of the corolla.Modified after Frohne&Jensen(1998).(c)(a)(b)Fig.4.5Cassia angustifolia,a typical Caesalpiniaceae:(a) typical zygomorphic flower(yellow in its natural state);(b) fruit(one of the botanical drugs obtained from the species);(c) flowering branch showing the leaves composed of leaflets,and the inflorescence.Modified after Frohne&Jensen(1998).DistributionThis is a cosmopolitan family with about 11,000species,and is one of the most important families.It includes many plants used as food:for example,numerous species of beans (Phaseolus and Vigna spp.,Vicia faba L.),peas (Pisum sativum L.),soy [Gly-cine max (L.)Merrill],fodder plants (Lupinus spp.)and medicines (see above).Chemical characteristics of the familyThis large family is characterized by an impressive phytochemical diversity.Polyphenols (especially flavonoids and tannins)are common,but from a phar-maceutical perspective various types of alkaloids are probably the most interesting and pharmaceutically relevant groups of compounds.In the genera Genista and Cytisus (both commonly called broom)as well as Laburnum ,quinolizidine alkaloids,including cytisine and sparteine (Fig.4.7),are common.The hepatotoxic pyrrolizidine alkaloids are found in this family (e.g.in members of the genus Crotolaria ).Other important groups of natural products are the isoflavonoids,known for their oestrogenic activ-ity,and the coumarins used as anticoagulants (see Melilotus officinalis above).Glycyrrhiza glabra L.(licor-ice)is used because of its high content of the triterpe-noid glycyrrhic acid,which,if joined to a sugar,is called glycyrrhizin (a saponin)and is used in confec-tionery as well as in the treatment of gastric ulcers (controversial).Last but not least,the lectins must be mentioned.These large (MW 40,000–150,000),sugar-binding proteins agglutinate red blood cells and they are a common element of the seeds of many species.Some are toxic to mammals,for example phasin from the common bean (Phaseolus spp.),which is the cause of the toxicity of uncooked beans.HYPERICACEAEThis small family was formerly part of the Gutti-ferae and is of pharmaceutical importance becauseof St John’s wort,which in the last decade of the 20th century became one of the most important medicinal plants in Western medicine.Important medicinal plants from the familyl Hypericum perforatum L.(St John’s wort)hasclinically well-established effects in mild forms of depression.It has also been employed topically for inflammatory conditions of the skin.Morphological characteristics of the familyThe leaves are opposite,often dotted with glands.A characteristic feature of this family is a secondary increase in the number of stamens (polyandrous flowers).The fruit are usually capsules,but berries may occur in some species.DistributionThis family,with about 900species,has its main area of distribution in the tropics and in temperate regions.Chemical characteristics of the familyThe former name Guttiferae is an important indicator of a characteristic chemical feature:the presence of resins,balsam and other glands containing excretory products.For example,the hypericin glands,with a characteristic red colour,are present especially in the flowers and contain naphthodianthrones,includ-ing hypericin (Fig.4.8)and pseudohypericin,which are characteristic for some sections of the genus.Typi-cal for the family in general are also xanthones (found nearly exclusively in this family and in the Gentiana-ceae).The genus is known to accumulate flavonoids and their glycosides (rutoside,hyperoside),as well as hyperforin (Fig.4.8)and its derivatives,which are derived from the terpenoidpathway.QuinolizidineCytisineSparteineNNN HHHO Fig.4.7。
The primes contain arbitrarily long polynomial progressions
Contents 1. Introduction 2. Notation and initial preparation 3. Three pillars of the proof 4. Overview of proof of transference principle 5. Proof of generalized von Neumann theorem 6. Polynomial dual functions 7. Proof of structure theorem 8. A pseudorandom measure which majorizes the primes 9. Local estimates 10. Initial correlation estimate 2 7 15 20 25 35 41 48 52 54
60 62 66 69 71 73 77 80
1. Introduction In 1975, Szemer´ edi [31] proved that any subset A of integers of positive upper ∩[N ]| density lim supN →∞ |A |[N ]| > 0 contains arbitrarily long arithmetic progressions. Throughout this paper [N ] denotes the discrete interval [N ] := {1, . . . , N }, and |X | denotes the cardinality of a finite set X . Shortly afterwards, Furstenberg [10] gave an ergodic-theory proof of Szemer´ edi’s theorem. Furstenberg observed that questions about configurations in subsets of positive density in the integers correspond to recurrence questions for sets of positive measure in a probability measure preserving system. This observation is now known as the Furstenberg correspondence principle. In 1978, S´ ark¨ ozy [29]1 (using the Hardy-Littlewood circle method) and Furstenberg [11] (using the correspondence principle, and ergodic theoretic methods) proved independently that for any polynomial2 P ∈ Z[m] with P (0) = 0, any set A ⊂ Z of positive density contains a pair of points x, y with difference y − x = P (m) for some positive integer m ≥ 1. In 1996 Bergelson and Leibman [6] proved, by purely ergodic theoretic means3, a vast generalization of the Fustenberg-S´ ark¨ ozy theorem - establishing the existence of arbitrarily long polynomial progressions in sets of positive density in the integers.
Genomics and the origin of species
Major insights into the genetics of speciation have come from various approaches (BOX 1), which range from the mapping of individual genes that cause reproductive isolation to the characterization of genome-wide dif-ferentiation patterns, and from quantitative genetic approaches to admixture analyses that associate pheno-types with reduced gene flow between populations 1–3. These empirical approaches have a long history that started with the work of Dobzhansky 4 and Muller 5. The theoretical understanding of the genetics of specia-tion has advanced markedly 6–10. However, the deluge of empirical data from next-generation sequencing (NGS), along with the emergence of new analytical approaches, necessitates the integration of this theoretical work to strengthen the conceptual foundations of the nascent field of speciation genomics . Such integration will help to elucidate the relationships between evolutionary processes and genomic divergence patterns on the one hand, and between genomic properties and speciation processes on the other hand, and it will help to unify research on both the ecological and non-ecological causes of speciation.In this Review, we first discuss areas in which genomic approaches have begun to make important contributions to speciation research (BOX 1), which include elucidating patterns and rates of genome-wide divergence, improving our understanding of both the genomic basis and the evo-lution of intrinsic and extrinsic reproductive barriers, and identifying mechanisms by which different barriers become genomically coupled. We also highlight areas that would benefit from further attention, such as the distributions of locus effect sizes , pleiotropy and genomic constraint. We conclude by discussing how NGS dataand innovative population genomic analyses — which use genome-wide data to make inferences about evo-lutionary processes in natural populations — could contribute to further progress in integrating these study areas into a more comprehensive and coherent understanding of speciation genomics.Speciation: theory and classical evidenceIn line with others 1,3, we define speciation as the origin of reproductive barriers among populations that permit the maintenance of genetic and phenotypic distinctive-ness of these populations in geographical proximity. These reproductive barriers can be initiated either by divergent selection (that is, ‘ecological’ or sexual selec-tion that creates extrinsic reproductive isolation ) or by the evolution — through genetic drift, as an indirect con-sequence of selection, or through genomic conflict — of genetic incompatibilities that cause intrinsic reproductive isolation (BOX 2). The study of the accumulation of intrinsic isolation has a strong tradition in evolutionary biology 1,11. However, most recent population genomic studies of divergence across the genomes of incipient and sister species have investigated cases of putative ecological speciation and have focused on divergent adaptation and extrinsic isolation (but see REF . 12, discussed below, for an important role for genomic conflict in generating reproductive incompatibilities).Extrinsic postzygotic isolation arises as a consequence of either divergent or disruptive selection when the via-bility or the fertility of migrants or of individuals with intermediate genotypes is reduced 2. Prezygotic sexual isolation and also extrinsic postzygotic isolation (when hybrids have reduced mating success 13) may evolve as*Department of Fish Ecology and Evolution, Eawag: Swiss Federal Institute of Aquatic Science and T echnology,Center for Ecology, Evolution and Biogeochemistry, 6047 Kastanienbaum, Switzerland; and Division of Aquatic Ecology and Evolution, Institute of Ecology and Evolution, University of Bern, 3012 Bern, Switzerland.Correspondence to O.S. e‑mail: ole.seehausen@eawag.chdoi:10.1038/nrg3644Reproductive isolationThe absence or restriction of gene flow between populations beyond that caused by spatial separation.Gene flowThe movement of allelesbetween populations. For gene flow to occur, individuals must disperse between populations and successfully reproduce with local individuals.Therefore, gene flow can be reduced not only by dispersal barriers but also by either intrinsic or extrinsic reproductive isolation.Genomics and the origin of speciesOle Seehausen*, Roger K. Butlin, Irene Keller, Catherine E. Wagner, Janette W. Boughman, Paul A. Hohenlohe, Catherine L. Peichel and Glenn‑Peter Saetre et al.Abstract | Speciation is a fundamental evolutionary process, the knowledge of which is crucial for understanding the origins of biodiversity. Genomic approaches are anincreasingly important aspect of this research field. We review current understanding of genome-wide effects of accumulating reproductive isolation and of genomic properties that influence the process of speciation. Building on this work, we identify emergent trends and gaps in our understanding, propose new approaches to more fully integrate genomics into speciation research, translate speciation theory into hypotheses that are testable using genomic tools and provide an integrative definition of the field of speciation genomics.when they are not transmitted by the same rules (for example, biparental versus uniparentalinheritance) or when a gene causes its own transmission to the detriment of the rest of the genome. The presenceof elements that bias transmission (that is, distorter loci) is expected to lead to the evolution of loci that restore Mendelian segregation (that is, restorer loci).Intrinsic reproductive isolationFitness reduction in hybrids that is independent of the environment.a consequence of divergent sexual selection3,14 that isoften, but not always, mediated by differences in envi-ronments15,16. Prezygotic sexual isolation and extrin-sic postzygotic isolation are therefore dependent ongenotype–environment interactions in the wider sense,in which mating partners are part of the external envi-ronment. By contrast, intrinsic postzygotic isolation isindependent of the external environment. Consequently,different types of genes and gene networks, and differentevolutionary processes may be involved in generatingthese classes of isolation. Extrinsic postzygotic isola-tion and sexual isolation can rapidly evolve17, and theyoften interact with each other16 and with the evolution ofintrinsic postzygotic isolating barriers18(BOX 2). Selectioncan initiate speciation in situations both with and with-out gene flow between populations, whereas intrinsicincompatibilities are less likely to accumulate whengene flow is present6. However, adaptive divergenceand ecological speciation are not the same. Divergentadaptation alone rarely causes sufficient reproductiveisolation to allow the accumulation or the persistenceof species differences in geographical proximity: thistypically requires the evolution of prezygotic isolation1,3(BOX 2), although it is possible that this varies betweenmajor taxonomic groups such as insects compared withvertebrates or plants.Ecological speciationThe evolution of reproductive isolation as a consequence of divergent or disruptive natural selection between populations that inhabit different environments or exploit different resources.Postzygotic isolationEffects of barriers that act after fertilization, such as hybrid sterility and hybrid inviability. It can be either extrinsic (that is, mediated by the environment) or intrinsic.Disruptive selectionSelection within a single population that favours extreme phenotypes over intermediate phenotypes.Sexual isolationReproductive isolation due to reduced mating between members of divergent populations, includingbehavioural assortative mate choice and assortative fertilization in animals, as well as pollinator-mediated assortative mating in plants. It is most often thought of as prezygotic but can also be postzygotic if there isdisruptive sexual selection.F ST -outlier analysesThe comparison of thedistribution of F ST values across loci with the distribution expected in the absence of divergent selection for the same average differentiation. A locus with an F ST value that exceeds expectation is likely to be influenced by divergent selection, either on the locus itself or on a linked locus.Prezygotic isolationEffect of barriers that act before or after mating but before fertilization, including the isolating effects ofdivergent mate choice, habitat preference, reproductive timing and gametic incompatibility.Bateson–Dobzhansky–Muller incompatibilities(BDMI). Intrinsic postmating barriers that are the result of epistatic interactions between alleles at two or more loci that reduce fitness in hybrids but not in the parental populations.The available evidence suggests that negative epistatic interactions — Bateson–Dobzhansky–Muller incompatibilities (BDMIs; although hereafter we use the more common abbreviation, DMIs) — are the most frequent cause of intrinsic postzygotic isolation 1,19–21. However, other mechanisms, including underdominance 22 and gene duplication, transposition and gene loss 23–25, may also cause intrinsic postzygotic isolation. The time course of the accumulation of DMIs is not well understood 19,26–28, and accumulation rates may vary among taxa and among mechanisms that underlie DMI evolution 19. DMIs were long thought to arise as a consequence of genetic drift, as a result of stochastic deactivation of gene duplicates 29 or as a by-product of ecological selection 30. However, theo-retical considerations, such as the slow pace of neutral accumulation of barriers 31, and early empirical evidence for positive selection on loci that contribute to incom-patibilities 32, suggested that genetic drift was unlikely to be a common source of incompatibilities. Instead, recent observations indicate that genomic conflict may be a common mechanism that drives DMI evolution 20,33–35 (BOX 3), as originally proposed in 1991 (REFS 34,35). Genomic conflict may arise from competing interests of males and females 36; from meiotic drivers 37,38, mobile elements 39,40 or other ‘selfish’ genetic elements and their suppressors; and from competing interests between genomes of organelles and the nucleus 41,42. Sexual conflict is thought to drive the evolution of new sex chromo-somes 43,44, and empirical observations suggest that the turnover of sex chromosomes has a role in the evolution of reproductive isolation 45,46.The different evolutionary mechanisms that underlie the build-up of both extrinsic and intrinsic postzygotic isolation and of prezygotic isolation suggest that their genomic signatures will also be distinct. The genomic architecture of extrinsic isolation is likely to resemble that of adaptive population divergence and is likely to be diverse and scattered across multiple regions in the genome (see below). However, there are theoretical arguments and empirical evidence that sites under selection in the genome will spatially cluster when adaptive evolution proceeds under prolonged bouts of divergent selec-tion with either migration or recurrent hybridization 47. For intrinsic isolation, incompatibility factors that are driven by genomic conflict are expected to accumulate in genomic regions of reduced recombination where linkage disequilibria between distorter loci and responder loci can become established 48,49. Sex chromosomes are partic-ularly susceptible to the accumulation of incompatibility factors that are derived from genomic conflict because these chromosomes are constantly in a ‘battle’ over seg-regation, whereas only small and tightly linked autoso-mal regions are in conflict with their homologues 34. At the same time, there will be particularly strong selection for suppression of sex-linked distorter loci because they tend to bias sex ratios 50,51. The genomic architecture of certain types of prezygotic isolation may also be influ-enced by regions of reduced recombination around sex-determining loci 52 or sex chromosomes 53, particularly when sex linkage resolves sexually antagonistic effects of sexual selection 54. Alternatively, prezygotic isolationloci may accumulate near extrinsic ecological isola-tion loci (see the section below on genomic coupling of reproductive barriers). All of these signatures must be distinguished from background patterns of genetic diversity and divergence that depend on the populations’ history of genetic drift, gene flow, background selection and episodes of positive selection that are unrelated to reproductive isolation.The search for signatures in the genetic architecture of reproductive isolation has a long ‘pre-genomic’ his-tory 55,56. However, there has been a historical disconnec-tion between research programmes that were focused on intrinsic isolation, which have typically concentrated on later stages of speciation 20,57, and those focused on extrinsic postzygotic isolation and prezygotic sexual isolation at early stages of speciation 2,30,15,16. As a result of this disconnection, it is currently a challenge to com-pare the evolutionary rates of different components of reproductive isolation and their relevance to specia-tion. Such rates have been compared in the same taxon using pre-genomic methods 11,58–60, and the data suggest that prezygotic and extrinsic postzygotic isolation often evolve faster than intrinsic postzygotic isolation, which is consistent with expectations from classical theory 61. The availability of genome-wide data will now permit testing of this pattern with a considerable increase in resolution.Genomics and the ‘speciation continuum’After speciation is complete, populations accumulate dif-ferences as a result of mutation, genetic drift and ongo-ing selection. Therefore, reproductively isolated species often differ in traits that evolved under ecological selec-tion and in others that evolved under sexual selection, and these species may also have intrinsic incompatibili-ties. A central task of speciation genetics is to reconstruct the sequence in which these different barriers originated in order to distinguish between causes and consequences of speciation. To achieve this, one would ideally take an unbiased view of the entire genome at all stages of the same speciation process. However, speciation can rarely be studied in real time in natural populations of sexually reproducing multicellular organisms. Estimates of varia-tion among loci in the timing and the magnitude of gene flow could help to determine the order in which repro-ductive barriers emerged, but it is challenging to make such inferences, and current methods are not accurate enough for this purpose 62. However, by integrating case studies of closely related taxa that vary in their extent of divergence (that is, the ‘speciation continuum ’), infer-ences can often be made about the chronology and the importance of different factors and processes involved.Investigations of this speciation continuum have made important contributions to speciation research 63,64, and this approach is being adopted in NGS-based genome scan and transcriptome scan studies of specia-tion. The major questions being addressed are: to what extent is divergence at different stages of speciation localized in the genome (that is, the island view) and to what extent is it widespread? To what extent can hetero-geneity in divergence be attributed to selective processes compared with genetic drift? What are the sources ofUnderdominance Heterozygotic inferiority; that is, the phenotype expressed in heterozygotes has lower fitness than that of either homozygote. This can cause disruptive selection.Meiotic driversFactors that distort Mendelian segregation. At a heterozygous site, the driving variant will be found in more than half of the gametes.Sexual conflictThe evolution of phenotypic characteristics by sexual selection when the trait confers a fitness benefit on one sex but a fitness cost on the other. HybridizationMating between individuals that belong to distinct species or populations. If postmating isolation is incomplete, hybridization leads to the introgression of genes from one population to another. Linkage disequilibriumThe statistical association of the alleles at two loci within gametes in a population. Although linkage disequilibrium tends to be greater between linked loci, it can also arise between physically unlinked loci (for example, because of selection, nonrandom mating or gene flow).Distorter lociLoci that underlie meiotic drive, which is the non-Mendelian segregation of alleles in meiosis. Distorter loci mayact on other loci, so-called responder loci.Responder lociLoci that show deviations from Mendelian segregation (that is, meiotic drive) owing to the effect of distorter loci. Speciation continuum Variation of the strength of reproductive isolation between two incipient species eitherin different locations or in different species pairs that belong to the same evolutionary lineage andthat diverge in similar ways.selection? Does genomic divergence tend to follow acommon trajectory as it proceeds along the speciationcontinuum? And how are all of these affected by theextent of geographical isolation? A recently much citedscenario for speciation without strong geographical iso-lation, which is derived from earlier models65,66, involvesan early stage of divergence at which differentiation islimited to a small number of loci (that is, islands) thatare under strong divergent selection. The size of theseregions would gradually increase through the processof divergence hitchhiking, and the effective migration ratewould eventually decrease globally across the genome,which gives rise to genome-wide divergence (that is,genomic hitchhiking)67,68.Genome scans of ecological speciation. Several NGS-based genome scans of the speciation continuum havefound surprisingly variable patterns of genomic diver-gence. It seems that incipient species can quickly accu-mulate substantial divergence even in the presence ofgene flow (FIG. 1). However, in some cases — such as thoseof Heliconius spp. butterflies69, Helianthus spp. sunflow-ers70 and poplar trees71 — divergence between parapatricecotype populations is limited to a few large genomicregions, whereas it is widespread across the genome inother cases72–75. NGS-based genome scans of sympatricsister species have generally reported genomically wide-spread and highly heterogeneous divergence that varieson a very local scale75–81. Few studies have looked forGenome scanComparison of genome-wide patterns of diversity within populations and/or divergence between populations at hundreds or thousands of markers. Until recently, most studies usedamplified fragment length polymorphisms (AFLPs) but this has recently changed, and single-nucleotide polymorphisms (SNPs)generated by next-generation sequencing or SNP chips are being used.evidence of divergence hitchhiking, and the available results are inconsistent 69,76,82. Genome-wide average F ST often increases as phenotypic divergence increases 80,83, but divergence seems to remain heterogeneous across the genome for a long time, which is potentially due to repeated episodes of interspecific gene flow even after reproductive isolation has become strong 84,85. The first generation of NGS-based population genomic studies of ecological speciation has therefore shown that ecologi-cal selection can cause strong isolation of small genomic regions between diverging populations and that, when reproductive isolation is strong enough to permit per-sistence of incipient species in sympatry, many unlinked regions typically experience significant isolation.So where does the heterogeneity in genomic diver-gence come from? It is commonly inferred to resultFigure 1 | Genomic patterns of divergence along the ‘speciation continuum’ of Heliconius spp. butterflies. Thepatterns of differentiation between hybridizing parapatric races (part Aa ) and sympatric species (part Ac ), as well as those between geographically isolated (that is, allopatric) races (part Ab ) and species (part Ad ), are shown along the genome; the x axes represent chromosome positions. Divergence is highly heterogeneous even between allopatric populations of the same species (part Ab ). The shapes of the frequency distributions of locus-specific F ST values (part B ) clearly differ both between the different stages in the continuum and between geographical scenarios. For example, the greater variance is consistent with gene flow between species in sympatry (part Bc ). However, the challenge is to distinguishbetween speciation with gene flow (parts Ba , Bc ) and that without gene flow (parts Bb , Bd ). All species shown are from the genus Heliconius , and all subspecies shown are from the species Heliconius melpomene. FG, French Guiana; Pan, Panama; Per, Peru. Figure is modified, with permission, from REF . 87 ©(2013) Cold Spring Harbor Laboratory Press.| Genetics0.012345678910111213141516170.20.40.60.8 1.00.00.20.40.60.8 1.0F STFST1.00.50F ST1.00.50F S T 1.00.50F S T1F ST 0F ST 0.00.20.40.60.8 1.00.00.20.40.60.8 1.0F ST Bb Early stage withgeographical isolationBc Late stage withoutgeographical isolationBa Early stage without geographical isolation Ad Allopatric species: H. cydno (Pan) versus H. m. melpomene (FG)Ac Sympatric species: H. cydno (Pan) versus H. m. rosina (Pan)Ab Allopatric races: H. m. rosina (Pan) versus H. m. melpomene (FG)H. m. aglaope (Per)Divergence hitchhikingWhen divergent selection on a locus reduces the effective migration rate for physically linked regions, which increases the opportunity for divergence at loci under weaker selection in the surrounding regions. Regions of divergencehitchhiking may remain much larger than those of traditional hitchhiking after a selective sweep within populations because of the persistent reduction in the ability of flanking regions to recombine away from a divergently selected gene.ParapatricPertaining to organisms, populations or species that inhabit either adjacent geographical regions orspatially distinct but adjacent habitats and that may exchange genes.SympatricPertaining to organisms, populations or species that share the same geographical region and that overlap in their use of space with no spatial barriers to gene exchange.F ST(Also known as Wright’s fixation index). A measure of population subdivision that compares the correlationbetween two gene copies that are randomly drawn from the same population to thatbetween two gene copies that are drawn from two different populations. An F ST of 1indicates that two populations are fixed for alternative alleles.AllopatricPertaining to organisms, populations or species that inhabit distinct geographical regions and are therefore not exchanging genes.CoalescenceThe merging of two genetic lineages in a common ancestor.Incomplete lineage sortingThe situation in which some alleles share a more recent common ancestor with alleles in another species than with other alleles in the same species.from locus-specific differences in the effects of diver-gent selection and gene flow. Indeed, genome scans have shown strong isolation at genomic loci that were known to be under divergent selection 64,69,70,72,74. However, caution is warranted because different evolutionary processes can leave similar signatures in the genome. Heterogeneous genomic divergence is sometimes also observed between allopatric populations of the same species in the absence of any current gene flow 76,86,87 (FIG. 1). Indeed, many studies assume ongoing gene flow between species, even though stochastic variation due to recent coalescence times and incomplete lineage sorting can lead to low divergence and high heterogeneity in a similar way, particularly when they are combined with selection 88,89. Statistical methods are available to distinguish divergence in isolation from that with gene flow, and these methods are increasingly being applied to genome-scale data sets (BOX 1; reviewed in REF . 90).Even in the absence of selection, divergence is expected to vary owing to both the stochasticity of genetic drift and the complexities of population his-tory, and this variation can be enhanced by confound-ing effects of genomic heterogeneity 91. In particular, regions of low recombination and/or high gene den-sity often show reduced intraspecific diversity, which inflates relative divergence as measured by either F ST or D a (that is, relative average divergence that is cor-rected for intraspecies diversity)88. This can result from background selection against deleterious mutations 92, intraspecific selective sweeps (in allopatry)88 or even a direct influence of recombination on genetic diver-sity 93. It is challenging to disentangle these processes 94. Some have suggested correcting for recombination rate in the interpretation of F ST patterns 83. Others have sug-gested that absolute divergence measures such as D xy are more robust to diversity artefacts 95, especially when they are corrected for local mutation rate 96. It seems unlikely that any single parameter will reliably disen-tangle divergent selection and gene flow from neutral processes. Having a good knowledge of the geographi-cal context of population divergence will help, but new parameter-rich modelling approaches 90 will be fre-quently required to distinguish between hypotheses of primary divergence with gene flow, secondary contact with hybridization and incomplete lineage sorting.Adaptive divergence has been shown to accumu-late preferentially in regions of low recombination 97, including the centres of chromosomes 83, the vicinity of centromeres 98, sites of inversions 74 and often (but not always 12,71) sex chromosomes 98–100. Heterogeneity in genomic divergence that is seen in allopatry might also result from gene-flow–selection balance that has occurred in the past 47,76. Finally, the assumption that the baseline F ST reflects neutral divergence may be violated in cases in which divergent selection is pervasive and multifarious , and this would bias against the detection of theselection signature 81.There is evidence for repeated divergence of the same genes or the same genomic regions across rep-licate pairs of species or environmental contrasts, which strongly supports the idea that these regionsare indeed involved in adaptation and/or reproductive isolation 72,74,85,97,101–103. The detection of such parallel divergence may require dense sampling of genomes or transcriptomes because the highest levels of repeat-ability may be observed at the scale of genomic regions rather than that of individual genes or single-nucleotide polymorphisms (SNPs)97. In this case, the repeatability in the heterogeneity of genomic divergence may be due, at least partly, to shared genomic heterogeneity in both recombination and mutation rates rather than to parallel adaptive divergence, but the shared genomic structure may facilitate the repeated accumulation in the same genomic regions of adaptive differentiation 97. Another approach involves combining classic cline theory with genome-wide analyses, which allows measurements of the strength of selection at specific loci 79 (BOX 1). In the future, parameter-rich coalescent models of divergence with gene flow fitted to genomic data may be able to account for the heterogeneity of demographic history across the genome when seeking to identify genomic regions that have reduced gene flow 84,104. Finally, genome scans combined with manipulative selection 81, quantitative trait locus (QTL) mapping 82,105, candidate gene mapping 72,74 and admixture mapping 79,106–108 can be used to investigate whether divergent genomic regions contain loci that contribute to reproductive isolation.Several recent studies have found a contribution of ancient alleles to recent divergence, as exemplified by sticklebacks 74,109, cichlids 77,110, Rhagoletis spp. flies 111 and Heliconius spp. butterflies 112. Ancient alleles are iden-tifiable owing to the accumulation of many substitu-tions or to the sharing across wide spatial or taxonomic ranges. The sources of such ancient allelic variation can be either standing genetic variation or hybridization 113. It is difficult to distinguish between these hypoth-eses in practice because of the challenges of differen-tiating incomplete lineage sorting from hybridization 90 (BOX 1). The balance of evidence from NGS data implies introgressive hybridization rather than standing genetic variation as the source of ancient alleles in most of the above cases. Speciation in these cases might have been facilitated by hybridization that provides genetic mate-rial for both adaptation and reproductive isolation in the face of gene flow. Future research should test this hypothesis further by combining genomic and ecological approaches.Genomic divergence and intrinsic isolation. Many studies have investigated DMI genes in strongly isolated spe-cies but, in many cases, it remained unclear whether the fixation of the underlying mutations was a cause or a consequence of speciation 20,57. Regardless of whether identified DMI alleles are the first step in the origin of reproductive isolation, a striking pattern from recent work is that these alleles have evolved under strong positive selection rather than genetic drift and that genomic conflict is often implicated as the source of this selection. For example, one study identified Overdrive (Ovd ), which is an X-linked gene that underlies both hybrid male sterility and sex ratio distortion in crosses between Drosophila pseudoobscura pseudoobscura and。
Characterization of irregularly shaped bodies
Characterization of irregularlyMS 198-235Pasadena, CA 91109 described as irregular.However, for certain target opportube necessary for the purpose ofcorrespond physically to the directions the 21) projection of the object has and of inertia. An optimal mosaic size can then be rectangle, andin a flyby scenario which the spacecraft travels in a linear traje size of the asteroid can be parametrized in a parameter estimation can be by a least-squares fit using the size takenis less than the rectangular 1are likely to be irregularly shaped. Aa prior knowledge of an asteroid, it is difficult to infer itsalone,complete shape characterization may not be necessary under therectangulara mosaic pointingA bounding rectanglecan be used in determining the appropriate time t o start theIn this paper, we show how to computeit to design a for asteroidflyby. We also2RECTANGULAR BOUND] NGnear encounter of an asteroid flyby, the boundary points of the]7,a set of the1,. ...–is the center ofgravity of the boundary points,by thethey agree closely with our Letbe the straight, lines passing through the center of correspondingto the smaller respectively.can be distances to u andboundary p and the corresponding moonsubsequent of the apparent objectsize at every the simple case of an asteroid flybyspinthe size from the observations during the near encounter period.be the distanceis the object size). be object and,r fwherefocal length.are expressed in pixels:whereis the angular fieldwhere 1least-squares(2)and theis the errorcomputed fromthe singular valueas the size of the object,boundary points.a series ofsize, wc canabsoluteonly the timeand the reference bearbitrarilyable to And from the estimate wc also obtainthe closest encounterrelative to the size of object(i.e.of(a). ._—– —.7.. 12500-.l.—...—. —...-40-2002040 tosimulation. (a)solid line represents the actual size of the object in the field ofpixel resolution.)thedimension information is more accurate when the object isbefore the closest encounter, the predicted size mayadditional information on object4 MOSAIC PLANNINGAs an application of rectangle bounding and object sizehow the mosaic sequence canbe generatedSince the error of the estimated object size is large nearwe require that the entirebefore the closest encounter.xoverlapof the image width) betweenofbut also for amount of o v e r l a ppointing accuracy. Figure 3 is a of a2x3 mosaic.If thestartingremains toJa2x3 increasesthe expected time to take earl be obtained by solving for(71 – l) At.Figure 3, the rotation 2 to,w h e r e at and of view of the camera. Note that the overlapoverlap (the overlap between the first two frames). specifiesthe first and determination of bothalso helps in constructing the composite4 shows theof is shown to ‘l’hefuture work will devise of irregularly shaped objects to handlecasesFigure 4: graphic。
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J.M.ANCOCHEA AND O.R.CAMPOAMOR
an excellent work which contained much of the information known about derivation algebras of Lie algebras. Among others, he introduced special classes of algebras which were shown to be non CNLA [93]. The importance of CNLAs within the variety of nilpotent Lie algebra laws was soon recognized by the author, and he also formulated an interesting question which is nowadays not satisfactorily solved : the problem of Tˆ ogˆ o. He asked for the existence of CNLA of derivations, this is, algebras for which both the derivations and the derivations of these are nilpotent. Very little is known about the general structure of such Lie algebras, though its existence has been verified by various authors [8]. The deformations theory for algebraic structures of M. Gerstenhaber in 1964 [38], originally developed to study the rigidity of algebraic structures, has become since then a powerful tool to determine the nilpotence of derivations. M. Vergne [96] applied in 1966 the cohomology theory of Lie algebras [60] to the study of the variety of nilpotent Lie algebras, obtaining in particular interesting results about its irreducible components. In particular, she showed the existence of only two naturally graded filiform Lie algebras, Ln and Qn , the second existing only in even dimension. In particul˜ nar, the first algebras has been a central research object for the last thirty years. Studying its deformations, lots of families of CNLA have been constructed [52]. In 1970 J. L. Dyer gave a nine dimensional example of CNLA [33], which was interesting in its own as it had an unipotent automorphism group. This property is not satisfied by the original example of Dixmier and Lister, and showed than even CNLA can have quite different behaviours. By that time, it was perfectly known that such algebras could exist only from dimension 7 on, as a consequence of the classification in 1958 of the six dimensional algebras [75]. In 1972 G. Favre discovered the lowest dimensional CNLA known until then [35], which additionally was of the same nature as Dyer’s example. At the same time, G. D. Leger and E. Luks investigated the metabelian Lie algebras and proved several results about their rank, and establishing that rank one algebras were given if the existence of a characteristic ideal containing the derived subalgebra is assured. These results can be interpreted as a constructive proof that the original example of 1957 is the known CNLA with lowest characteristic sequence. The last author applied in 1976 computational methods to prove the existence of CNLA in any dimension greater or equal to seven. Four years later, S. Yamaguchi constructed families of CNLA in arbitrary dimension, constructions that have been completed and generalized in later years [52]. The topological study of the variety of Lie algebra laws led R. Carles [18] to study the topological properties of CNLA. Among other results he states that the set of CNLA is constructible for n ≥ 7. For the particular dimension 7, he also proves that CNLA do not form an open set. Recently [8] this result has been generalized to any dimension. Another interesting approach to the CNLA has been deformation theory applied to the Borel subalgebras of complex simple Lie algebras, like done by Y. B. Khakimdjanov in 1988 to prove that almost all deformations of the nilradical of Borel subalgebras of complex simple Lie algebras are characteristically nilpotent. This has shown that these algebras are in fact in abundance within the variety of nilpotent laws. M. Goze and the last cited author [40] proved, in 1994, that for any dimension n ≥ 9 an irreducible component of the filiform variety Fn contains an open set consisting of CNLA. Filiform Lie algebras, specifically the model filiform Lie algebra Ln , has been also the fundamental source for constructing families of CNLAs. In particular, its cohomology has been calculated, which has allowed to describe its deformations in
arXiv:math/0011224v1 [math.RA] 27 Nov 2000
CHARACTERISTICALLY NILPOTENT LIE ALGEBRAS : A SURVEY
´ MAR´ CAMPOAMOR
1. Introduction The theory of characteristically nilpotent Lie algebras co