LITERARY THEORY ITALIAN 0270
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International Political Economy Politics of Trade Political Consequences of Comparative Advantage Suppose you own a vineyard in England or sheep in Ponugal International trade is bad for you The English winemaker goes out of business The Portuguese shepherd may stay in business but loses market share even though he is a lowercost producer than the English shepherd For example a winemaker has money to buy up his grassland and plant additional grapevines You ask the Portuguese King or the British Prime Minister to restrain trade If they don t you stage a revolution see R Rogowski Commerce and Coalitions How Trade Affects Domestic Political Alignments Trade Barriers Boycotts and embargoes Tariffs Nontariff barriers Subsidies Boycotts and Embargos The simplest way to restrain trade is to persuade people to refrain from purchasing cheap foreign goods or even to pass a law forbidding such purchases For example you might claim that the government of South Africa was racist or that the government of Cuba was tyrannical These claims might even be true Then it would be wrong to buy goods from South Africa or Cuba The world economy produces less but owners of relatively unproductive inputs in your country make money Tariffs You might appeal to people s desire not to see their fellow citizens go out of business Your fellow citizens can protect your business by imposing a tariff that raises the price of Portuguese wine in England or English wool in Ponugal A tariff is a tax levied at the border on goods crossing the border While import tariffs are more common export tariffs also exist Nontariff barriers You might claim that English wool was fleainfested or that Portuguese wine contained toxins These claims might even be true To prevent fleas the Portuguese king might institute a health inspection at the border and require the importer to pay a fee to cover the costs of the inspection At one time Japan by insisting that American automobile production was inferior in quality and therefore each part of an imported Eagle must be separately inspected for safety Japan then charged a fee for disassemny and reassembly of each imported American vehicle doubling the price of Jeep Eagles in Japan Advertising of health risks might decrease the demand for Portuguese wine in England and shift purchases to English wine keeping English winemakers in business Subsidies Government payments to English winemakers might enable them to sell their wine at Portuguese prices Payments might be hidden For example California is a major rice exporter Rice is a wetland crop Past government investments in irrigation enable California farmers to produce rice because they are not charged the full cost of the past investments in moving water Response of the Exporters How do the Portuguese winemaker and the English shepherd respond They pressure their king or prime minister to negotiate international agreements prohibiting boycotts tariffs nontariff barriers and subsidies Since World War II GATT and VVTO Organization have negotiated and enforced these agreements GATT General Agreement on Trade and Tariffs GATT consisted of a series of rounds The Geneva Round Kennedy Round the Tokyo Round the Uruguay Round In each round trade delegations from various states assembled and negotiated bilateral deals on reduction of barriers to trade that they then offered to the assembled delegations During the Cold War communist states generally refused to take part GATT and Levels of Analysis Each state s negotiating position at GATT was the result of a domestic deal between those who gained by trade and those who lost Consequently no state simply favored eradicating barriers to trade They made what deals they could while agreeing to ignore other barriers World Trade Organization Uruguay Round culminated in the establishment of the VVTO in 1995 VVTO continues the rounds of negotiation intended to reduce trade barriers VVTO also provided a new mechanism for enforcement of trade agreements The Doha Round Since 2001 Latin American African and Asian states generally have a comparative advantage in agricultural products US can produce farm goods more cheaply but developing countries cannot produce industrial goods US and Europe subsidize farm production in various ways Developing countries asked for an end to farm subsidies US and Europe refused Europeans blaming US and US blaming Europe Negotiations collapsed without an agreement WTO Enforcement When states make agreements how can they be enforced Each state that is a party to the agreement can assert that its laws abide by the agreement It is impossible to write an agreement specific enough to enumerate all actions that might be forbidden World Trade Organization exists to judge whether policies or laws adopted by member states conform to agreements reached in the Tounds ofnego a on WTO Dispute Resolution Panel of experts employed by VVTO rules on complaints brought by a member state concerning laws or policies of another state Only a consensus of states can overrule the panel of experts which means that the complaining state can always veto an appeal In case of an adverse ruling the losing state must Change its law or policy Negotiate a settlement with the complaining state Tolerate the adoption of an offsetting policy or law by the complaining state Strategic Trade Theory An alternative view of international trade By 1990 threequarters of all trade took place among developed countries Earlier in 1950 twothirds of trade took place between developed and underdeveloped countries Developed countries traded goods within industrial sectors eg central processing units CPU for computer chips Inconsistency with Comparative Advantage I don t see why swapping CPUs for computer chips is inconsistent with the use of comparative advantage as a theory of trade Comparative advantage exists whenever the production cost ratio for any two goods in one country differs from the production cost ratio for the same goods in any other country Whether the goods are complementary farm versus industrial is irrelevant what goods are under discussion is irrelevant Sources of Comparative Advantage Comparative advantage can have wide variety of sources Relative cost of producing industrial goods varies with the date of construction of the factory that produces them Older factories have usually been converted from producing earlier goods The layout of the older factory is not optimal for production of the newer good More recent factories can be specially designed for optimal production flow Construction Date and Comparative Advantage Unless the design of the new factory reduces the production cost of CPU by exactly the same proportion as the design of the new factory for computer chips comparative advantage will always emerge whenever a country builds new factories Then the production will specialize in each country one of the old factories will close and one of the new factories will not be built and the two countries will trade Behind Strategic Trade Theory Tuesday 15 November 2006 LA Times President Bush about to leave before trip to Vietnam for meeting on trade with Asian states Before leaving President Bush met with American automobile makers Sen Debbie Stabenow DMich US needs a comprehensive American manufacturing strategy that will keep us competitive Government Subsidies Strategic trade theory says that Honda and Toyota have taken over the US automobile market because the former Japanese Ministry of International Trade and Industry helped them raise money to build new more efficient factories Ergo President Bush should have funded GM Ford and DaimlerChrysler so that US auto makers can take back the automotive market A close election in which President Obama needs Michigan to win enables Senator Stabenow to get GM included in the bailout Ford turns down the money Theories And Interests Would the auto makers pay an economics PhD to invent strategic trade theory to explain why they have lost market share to the Japanese and deserve a handout Would some economics PhD be clever enough to invent the theory in the hope that an auto maker would hire her or him as a consultant Would a Democratic Senator from Michigan endorse this theory Strategic Trade Theory is how importers answer the exporters tactics of Ricardian comparative advantage GATT and WTO Government Intervention Of course government action can create comparative advantage Air Force bought large bombers and transports from Boeing Corporation One of the these the KC135 air tanker was also the first commercial jet airliner the 707 By lengthening production runs government purchases of the KC135 reduced the unit cost of the 707 giving Boeing a lasting advantage in the international commercial airliner and transport market But this was not a strategic goal of the US government simply a side effect of military procurement policy exploited by Boeing Are Governments Effective Japan s MITI has in fact tried to target Japanese industrial production on foreign markets MITI told Sony to stay out of consumer electronics MITI told Soichiro Honda to stay out of the automobile market These examples do not prove that MITI was ineffective but Japan s export successes do not prove MITI was effective either Shifting Trade Patterns Since 1990 trade between developed countries has outweighed trade between developed and underdeveloped countries Income effect developed countries have steadily become richer while many developing countries have hardly progressed developed countries have more to trade with each other while developing countries cannot afford to buy from developed Institutional effect end of colonialism disrupted regional trade within empires between developed metropole and undeveloped colonies Institutional effect emergence of European Union Regional Integration Most trade is regional Largest trading partners of United States are Canada and Mexico Largest trading partners of EU countries are other EU countries If transaction costs increase with distance comparative advantage will favor regional trade Transportation Finding buyers Finding sellers Justification of EU After WWII two Frenchmen Jean Monnet and Robert Schuman promoted European integration on the ground that it would prevent a fourth FrancoGerman war In fact Soviet consolidation of Eastern Europe division of Germany stationing of US troops in West and possession of nuclear weapons guaranteed postwar armed standoff Franco German conflict had become irrelevant Traumatized by the war European public was in no shape for critical evaluation of claims about benefits to peace French Motives for Integration In fact the two Frenchman were worried about comparative advantage Competition from efficient German producers putting the French coal and steel industries out of business They proposed the European Coal and Steel Community ECSC Treaty of Paris 1952 as the first step in a plan to preserve inefficient French producers German Motives for Integration Konrad Adenauer first German Chancellor supported the initiative despite costs to German industry in sharing French market with inefficient French firms The new Federal Republic of Germany founded 1949 had agreed to surrender control of foreign policy to US British and French Adenauer hoped to recover full independence by cooperating with French plans for integration that would exclude the US and British For Adenauer European integration was a divide and conquer strategy The ECSC Six From ECSC to Common Market Treaty of Rome in 1958 converted added the European Economic Community to the ECSC EEC or Common Market represented agreement to lowertariffs and remove nontariff barriers among the ECSC six Logic of the Common Market France and Italy were large agricultural producers Germany Netherlands and Luxembourg were fooddeficit countries especially because division of Germany had removed the food producing northeast under Soviet control France and Italy could swap food for German and Dutch industrial goods French and Italian industry would be protected against German and Dutch rivals by socalled competition policy really a policy allocating market share to prevent German industries from outcompeting other countries Five Enlargements 1973 Denmark Ireland and the United Kingdom 1981 Greece 1986 Spain and Portugal 1995 Austria Finland and Sweden 2004 Czech Republic Estonia Cyprus Latvia Lithuania Hungary Malta Poland Slovakia and Slovenia EU It was a unique historic enlargement which signified the re unification of Europe after decades of division by an Iron Curtain 2007 planned Romania and Bulgaria to complete the fifth enlargement Six countries negotiating admission including Turkey European Union Today Cnndidm Calm ries Mumhnr 5mm Why Enlargement Economic reasons growth of economy due to free trade demands new markets and new sources of labor Political reasons European integration began as a project of Catholic parties in all six countries to maintain employment as a means of counteracting electoral competition from left parties As left parties won in some countries members of EEC began to disagree over policy By adding more members enlargement made it unlikely that either side would reestablish political unanimity and enact the policies opposed by the other side Despite efforts to block policy change by enlargement negotiations have produced significant movement toward enactment of common policies throughout EU US Policy From the verfy beginning US policy has consistently avored European integration US officials pretend to believe that the EU has prevented resumption of FrancoGerman hostilities Economic motives may have included hope that integration would enrich Europe and open markets for US exports Political motives if union is good for America it must be good for Europe a constructivist argument Hegemonic Stability Theory Answers the question when free trade will prevail and encourage globalization Begins with observation of two periods of trade liberalization removal of barriers From 1815 to approximately 1900 From 1945 to present During these periods first Britain and then the US were hegemons or dominant world military and economic powers US in free world until 1989 Throughout the world since 1989 Roles of the Hegemon 1 Wealthy hegemon can afford to patrol the global marketplace on behalf of other states British suppression of piracy US Navy s operations against Somali pirates NATO and Russia together have sent three ships Hegemon has incentive to patrol since its economy benefits from international trade Roles of the Hegemon 2 Wealth of the hegemon enables it to buy goods produced in other countries spurring realization of comparative advantage Suppose England is too poor to buy sheep and therefore cannot realize its comparative advantage in wool production relative to Portugal Then Portugal cannot sell wine to England and cannot expand its wine production beyond domestic demand Large scale of the hegemon s economy provides opportunities for other countries to increase production thereby enabling themselves to import its products Roles of the Hegemon 3 The hegemon s currency serves as the principal medium of international trade Just as money makes domestic transactions easier international trade can and sometimes does proceed by barter but increases when parties can accept a currency British pound sterling was the currency of nineteenth century globalization US dollar continues to be the medium of world oil trade even though euro and Swiss franc compete with the dollar in some other roles Roles of the Hegemon 4 The hegemon s wealth also enables it to act as the principal banker for world trade Realizing comparative advantage can require investment in ports and transportation facilities for which the banker provides loans British loans for canal and then railroad construction in nineteenth century enforced by British fleet and army American loans primarily guided by the World Bank for infrastructure Realizing comparative advantage also involves foreign direct investment to take advantage of labor abundance Loans to build factories in the PRC using capital raised in the US credit market by Taiwaneseowned banks operating from Los Angeles Are Hegemons Necessary Realists might say yes Liberals would claim that whatever a hegemon does could also be achieved by negotiation and establishment of a world institution Identity theorists would argue that it can depend on a whether states are realists or liberals g b whether states seek their own economic interest or the interest of the global community of states The Illinois Open 2004 The Philosophy of Spite Questions by UC Berkeley Juliana Froggatt Jeff Hoppes Ray Luo with one question each from Paul Reverdy and Larry Wang Literature 55 Literature Tossup l Noting that quotdivinity must live within herselfquot different sections of this poem reference Jove with no mother to suckle him and the grave of Jesus in Palestine Asking quotwhat is divinity if it can come onl in silent shadows and dreamsquot a woman sits amidst quotcomplacencies of the peignoirquot dreaming a little and feeling quotthe dark encroachment of that old catastrophequot Although she still feels quotthe need for some imperishable blissquot she is skeptical of religion severed from the real world For ten points name this early Wallace Stevens poem taking place on a day for churchgoing Answer quotSunday Morningquot Literature Tossup 2 In 2001 Liza Dalby published a fictionalized biography of this person s life The name that comes down to us is a compound of the name of a character from a famous work and the term for a position in the Bureau of Ceremony held by this writer s father Married to Nobutaka she was given a man s education much against the customs of Heianera Japan For ten points name this lady in waiting to Empress Akiko author of a posthumously published diary and a collection of poetry and of her novel The Tale afGenji Answer Murasaki Shikibu Literature Tossup 3 The author asks parenthetically Now am I free to be poetical after what were apparently seventeen lines of digression about ice storms which he characterizes as Truth breaking in With all her matteroffact He then goes on to imagine Some boy too far from town to learn baseball Whose only play was what he found himself Summer or winter and could play alone before noting One could do worse than be a swinger of these and that the author himself would like to go by climbing for ten points which title trees of a Robert Frost poem Answer Birches Literature Tossup 4 Its popularity was ended by men like Carlo Goldoni but two centuries earlier it had arisen growing out the earlier erudite version which featured works by such authors as della Porta Ariosto Boccaccio Machiavelli and even Terence and Plautus Unlike that earlier version this form employed professional actors and used vulgar dialects comic action often aided by a battacio or slapstick and stock characters like Gianduia Brighella and Pedrolino For ten points name this 16th to 18th century Italian theatrical form which gave the world Punch Scaramouche and Harlequin Answer commedia dell arte accept comedy of art or comedy of professional artists or clear knowledge equivalents Literature Tossup 5 Captain Frederick notes that men have not hearts but do have eyes and quotthey give us torment enoughquot at a ball dancing with Isabella who had expected the protagonists brother James to have a substantial inheritance Eleanor reveals the General s gambling debts and befriends the protagonist whom the author suggests quotwould have supposed her born to be an heroinequot The reading of Ann Radcliffe39s Mysteries of Udalpha causes Cathy to assume the worst of the Tilneys but she is reconciled with Henry Tilney at the end For ten points name this Jane Austen novel about the adventures of Catherine Morland at the titular adobe Answer Northanger Abbey Literature Bonus 1 Poems by Alfred Lord Tennyson from lines for ten points each 1 quotAnd all at once they sang 39Our island home Is far beyond the wave39 we will no longer roam39quot quotIs there any peace In ever climbing up the climbing wavequot Answer quotThe LotosEatersquot 2 quotOn thy cold gray stones 0 Seaquot quotBut the tender grace of a day that is dead Will never come back to mequot Answer quotBreaka Breaka Breakquot 3 quotDeath closes all But something ere the end Some work of noble note may yet be done Not unbecoming men that strove with godsquot quotTo strive to seek to find and not to yield Answer quotUlyssesquot Literature Bonus 2 Name the author from clues on a 302010 basis 1 30 points Federico Garcia Llorca wrote in an Ode to him that Never for one moment Have I stopped seeing your beard full of butter ies Or your muscles of a virgin Apollo 2 20 points Ezra Pound offered him A Pact imagining himself as a grown child Who has had a pigheaded ather 3 10 points He himself wrote November Days and Leaves of Grass Answer Walt Whitman Literature Bonus 3 Name these novels by Jose Saramago for ten points each 1 His latest work to be translated into English this is the story of Tertuliano Maximo Afonso and Antonio Claro two men who are identical down to their fingerprints Answer The Double or O homem duplicado 2 This book is about a mysterious affliction that affects everyone in an unnamed country except the doctor s wife who is also unnamed like all the characters Answer Blindness or Ensaio sobre a cegu eira 3 This novel set in 18th Century Portugal is about a real priest Bartolomeu Lourenco de Gusmao who wants to construct a ying machine with the help of the characters who give the English translation its title a soldier and a clairvoyant Answer Baltasar and Blimunda or Memorial do Convento Literature Bonus 4 Given a Greek play name its author on a 1510 basis 1 15 points Ian 10 points The Bacchae Answer Euripides 2 15 points Trachiniae 10 points Antigone Answer Sophocles or Sophokles Literature Bonus 5 Name these characters from Shakespeare39s As You Like It for ten points each 1 She is the daughter of the exiled Duke who is banished by her uncle Frederick She takes the name of Ganymede and roams the forest of Arden with Celia Answer Rosalind 2 He is the youth who defeats the wrestler Charles then rescues his brother Oliver from snakes and a lion then marries Rosalind with concent of the exiled Duke Answer Orlando 3 He tries to woo the dull and beautiful Audrey and exclaims quotI39d rather bear with you than bear you while dead tired accompanying Rosalind and Celia in Arden swer Touchstone Science 55 Science Tossup 1 All of Hirota s conditional mutants incubated with tritium thymidine contained this enzyme whose digestion by trypsin yields 2 fragments Catalyzing the nucleophilic attack of the 339OH driven by elimination and hydrolysis of inorganic pyrophosphate it was found by John Cairns to be unnecessary until it turns out that the amber suppressor mutation in tRNA had not interfered with the 539 to 339 exonuclease portion Arthur Kornberg then purified the H and 111 versions both much more processive Needing a RNA primer and a DNA template for ten points name this enzyme of DNA replication Answer DNA polymerase 1 Science Tossup 2 Due to average symmetry of interconverting molecules gauche butane has this property but butane generally doesn39t The presence of asymmetric carbons characterizes this property which makes molecules in a pure mixture optically active All amino acids possess it except glycine Molecules with this property have no plane of symmetry and has a stereocenter designated either R or S For ten points name this property of organic molecules that have nonsuperimposable mirror images from the Greek for handedness Answer chirality Science Tossup 3 It is minus the constant volume derivative of Helmholtz energy or constant pressure derivative of Gibbs energy with respect to temperature Thus plotting molar Gibbs energy against temperature shows 3 lines with more and more negative slopes at higher T corresponding to its values for solid liquid and vapor phases Trouton39s Rule gives its value for vaporization which is enthalpy divided by temperature or H minus G divided by T Its change always greater or equal to zero by the Clausius Inequality for ten points name this thermodynamic quantity that measures disorder symbolized S Answer entropy Science Tossup 4 Independently interpreted by Debye Planck39s constant divided by the product of the rest mass with the speed of light gives its namesake wavelength Discovered by measuring the distribution of intensity at different angles when xray is incident on graphite this effect produces a shift in wavelength when photons strike the surface of a light element depending only on the scattering angle Conservation of momentum and energy govern this collision between a photon and a free electron For ten points name this effect in which short wavelength photons are scattered by electrons Answer Compton effect Science Tossup 5 The source of chloroplasts in cryptom onads they store photosynthetic products in floridean starch Producers of mucilaginous polysaccharides galactose with sulfate group attached they have no flagellated stages but often have calcium carbonate in their cell walls They have different colors at different ocean depths but are colorless as parasites Used to wrap sushi and produce carageenan and agar they are colored by the phycobilin phycoerythrin along with cyanobacteria39s phycocyanin For ten points name these members of Rhodophyta an algae found in coral reefs Answer algae39 accept Rhodophyta before it is mentioned Science Bonus 1 Answer the following about photophosphorylation the light reactions of photosynthesis for ten points each 1 Photophosphorylation takes place in the membranes of these individual units that make up the grana stacks of chloroplasts Answer thylakoids 2 After P680 photosystem II abstracts electrons from H720 turning it into 072 it reduces pheophytinI which initiates an exergonic chain involving complexes of this molecule whose c type appears at the end of the electron transport chain Answer c ochrome 3 This type of photophosphorylation produces no 072 and reduces no NADP Invoked when reduced NADP levels are too high it consists of photosystem I passing electrons to ferredoxin and the redox chain finally reducing the original P700 chlorophyll Answer cyclic photophosphorylation Science Bonus 2 In hydrogenation they undergo syn addition with an Adam s39s catalyst In electrophilic addition of halogens they undergo anti addition with a bridged 3membered ring halonium ion intermediate For ten points eac 1 Name these compounds also called olefins with a carboncarbon double bond Answer alkene 2 When electrophilic addition of halogen is conducted in water and base solvent the alkene becomes a vicinal haloalcohol which undergoes intramolecular ring closure to form one of these 3membered ring compounds the simplest cyclic ether Answer epoxide39 or oxacyclopropane or oxirane39 or ethylene oxide 3 After a halonium ion is formed the nucleophile attacks the more substituted carbon of the ring because it is more positive and resembles a carbocation This is an instance of what general rule for electrophilic additions of alkenes Answer Markovnikov rule Science Bonus 3 Answer the following about the acidbase properties of amino acids for ten points each 1 Amino acids with uncharged side chains have three in ection points in this type of curve obtained by adding hydroxides to a solution of pH zero and plotting pH against hydroxide concentration Answer titration curve 2 The first and third inflection points are the pKa s of the carboxyl and amino groups respectively while the second in ection point which lies between the other two is this quantity the point where the zwitterion form is the only form present Answer isoelectric point39 or pI 3 The isoelectric point is the average of the pKa going to the zwitterion form and the pKa of the zwitterion form which can be obtained from the pH acid concentration and base concentration via this equation named for two scientists Answer HendersonHasselbalch note it is NOT HendersonHasselbach Science Bonus 4 Name these gas laws for the stated number of points 1 5 points Volume of a given amount of gas at constant temperature is inversely proportional to its pressure Answer Boyle39s law 2 5 points Volume of a given amount of gas at constant pressue is directly proportional to the absolute temperature or alternatively pressure of a given amount of gas at constant volume is directly proportional to the absolute temperature Answer Charles law or law of Charles and GayLussac 3 10 points Equal volumes of gases at the same temperature and pressure contain the same number of molecules Answer Avogadro39s law 4 10 points The total pressure in a system containing two or more different gases equals the sum of individual pressures that each gas would exert if it were alone and occupied the same volume Answer Dalton s law of partial pressures Science Bonus 4 Identify the following decompositions from linear algebra for ten points each 1 If there are n distinct lambdasubis such that A vsubi equals lambdasubi vsubi then any xsubks of a dynamical system can be written as a linear combination of the vsubis Identify this decomposition named after the vsubis Answer Eigenvector Decomposition 2 For symmetric matrix A A equals P D Pinverse we can write A as the sum of terms involving the outer products of the eigenvectors with themselves times the corresponding eigenvalues Name this decomposition of A into pieces determined by the eigenvalues of A Answer Spectral Decomposition 3 If A is In times n with rank r then there39s a quotdiagonalquot matrix Sigma with the square roots of the eigenvalues of Atranspose A on the diagonals such that A equals U Sigma Vtranspose with U and V orthogonal The Moore Penrose pseudoinverse is based on the reduced version of this decomposition Answer Singular Value Decomposition39 or SVD History 55 History Tossup 1 The race riots in Crown Heights Brooklyn in 1991 and in Gujarat India in 2002 have been classified as this kind of event The Black Hundreds and their armed wing the Yellow Shirts actively supported them and they are believed to have been organized by Okhranka the Tsarist secret police Two million Russians moved to the US in a fortyyear period after a threeyear wave of them began in 1881 For ten points name these organized massive attacks traditionally referring to those against Jews Answer Eogroms History Tossup 2 The Peace of Rueil ended the first one with a negotiated settlement making concessions to parliamentary grievances The Grande Conde victor of the battle of Rocroi shortly instigated a second one but was forced to flee to the Spanish by Anne of Austria and Cardinal Mazarin For ten points the slingshot used on the streets of Paris gives its name to this series of seventeenth century uprisings against the French crown Answer the Fronde History Tossup 3 He opposed the Boer War calling for quothome rulequot of Britain39s colonies When an imperialist heckler shouted quothome rule for hell he replied that it was quite right for each man to speak up for his own country Under the Asquith government he solved Britain39s munitions crisis during the great war and then replaced Asquith as prime minister in December 1916 For ten points identify Britain39s representative among the quotBig Four of the Versailles peace conference Answer David Lloyd George History Tossup 4 Colonel Sellers despite his respectable appearance was implicated in Senator Abner Dilworthy39s railroad finance scandal The title of this political satire was chosen by Charles Dudley Warner and Mark Twain to suggest the insubstantial corrupt society that inspired the later progressive movement For ten points name this metallic term commonly applied to America in the 1870s Answer the Gilded Age History Tossup 5 Edward Long39s 1774 history celebrated this island39s plantation culture The less enthusiastic slaves ed to its mountainous interior where they fought two quotMaroon Warsquot against the British authorities Earlier it had served as a base for the pirate Henry Morgan and after General Venables and Admiral Penn captured it in 1655 For ten points name this West Indian nation whose capital was moved from Spanish Town to Kingston Answer Jamaica History Bonus 1 Many Rom ans shared their names with family members Name these for ten points from the clues about one person with the name five if you need clues about a betterknown person with the same name 1 10 points This man s Epistulae contains a letter to Trajan expressing disbelief at anonymous denunciations he received after condemning citizens who didn t deny Christianity 5 points This scientist and historian wrote the Naturalis Histaria and died while trying to get a better view of the erupting Mt Vesuvius Answer My 2 10 points This wife of Germanicus mother of Caligula was a favorite of her grandfather Augustus but did not get on well with his successor Tiberius 5 points She was Claudius fourth wife although she was his niece39 her son Nero succeded him Answer Agrippina 3 10 points This man willingly made enemies of Pompey and Caesar the latter of whom had an affair with his wife He killed himself after Caesar s victory at Thapsus tearing out his own intestines when simply falling on his sword didn t kill him 5 points This censor opposed the repeal of the Lex Oppia and supported the Lex Voconia both antifemale laws But he is best known for championing the destruction of Carthage Answer Marcus Portius Cato History Bonus 2 Absolute rulers enjoyed issuing edicts Name these for ten points each 1 Henry 1V s 1598 document granting precarious religious toleration to the quotpretended reformed religion of the Huguenots Answer Edict of Nantes 2 Holy Roman Emperor Ferdinand 11 attempted to restore the position of the counterReform ation church with the 1629 proclamation but succeeded only in enraging the Protestant princes of North Germany Answer Edict of Restitution 3 This most famous outcome of the battle of the Mlvian Bridge granted legal rights to the Christians of the Roman Empire Answer Edict of Milan History Bonus 3 Answer the following about a conspiracy of the 1760s for ten points each 1 A coordinated surprise attack against British outposts near the Great Lakes was planned by this leader of the Ottawa Answer Pontiac 2 Pontiac s forces were defeated by British Colonel Henry Bouquet at this battle in August 1763 Bushy Run 3 The Battle of Bushy Run ended the twomonth siege of this post formerly known as Fort Duquesne Answer Fort Pit t History Bonus 4 The Roman Empire had its great historians but they can39t compare to these historians of the Dark Ages For ten points each 1 This monk of Wearmouth and J arrow immortalized the miracles of the Northumbrian saintkings in his Ecclesiastical History of the English People Answer the Venerable M 2 This sixthcentury bishop39s Ten Books of Histories are our primary source for the gory details of Merovingian dynastic politics Answer Gregogy of Tours 3 This author39s quotGeticaquot preserves much information about Attila39s empire in addition to the origin legend of the Goths Answer Jordanes History Bonus 5 Identify these anticolonial activists from their writings for ten points each 1 quot1 Speak of Freedom A Statement of African Ideology Answer Kwame Nkrumah 2 quotThe Story of My Experiments with Truth quot Answer Mohandas Gandhi 3 quotThe Wretched of the Earth Answer Frantz Fanon Religion Mythology Philosophy 33 Religion Mythology Philosophy Tossup 1 Her nose is so long it rattles the ceiling when she snores Her own legs are bony as despite her voracious appetite she is thin as a skeleton Far more interesting legs belong to the hut in which she lives in the woods accompanied by ghostly servants and three colorfully described horsemen For ten points name this guardian of the fountain of the waters of life and death the irontoothed witch of the Russian forest Answer Baba Yaga Religion Mythology Philosophy Tossup 2 A character in Neil Gaiman s American Gods claims that he committed suicide in the 1930s He saved his daughter from having to marry a dwarf by keeping him up in tests of his wisdom until the sun rose at which point he turned into a rock and pretty decisively failed the test With Jarnsaxa he fathered Modi Thrud and Magni but his wife was a goddess whose golden hair had to be replaced by lvaldi s sons after Loki cut it all off For ten points name this strongest if not brightest of the Norse gods the God of Thunder Answer Thor Religion Mythology Philosophy Tossup 3 He studied effective methods of debate for assemblies in Essay on Political Tactics and of trial for courts inRat ionale ofJudicial Evidence Son of a lawyer he schemed up the Panopticon a simplistic model prison Author of Constitutional Code and Manual of Political Economy he attracted the attention of Lord ShelbuIne after criticizing Blackstone39s Commentaries inA Fragment on Government His Introduction to the Principles ofMorals and Legislation proposed hedonic calculus and advocated the greatest good for the greatest number For ten points name this founder of Utilitarianism Answer Jeremy Bentham Religion Mythology Philosophy Bonus 1 Samuel invited Jesse and all his sons to the sacrifice at Bethlehem and seeing the youngest son to be missing because he was looking after the sheep Samuel anointed him the next king of Israel For the stated number of points 1 5 points Name this handsome lad with ruddy cheeks and bright eyes of whom King Saul was jealous of because he made havoc among tens of thousands by killing Goliath Answer David 2 10 points When Saul was determined to drive a spear into David David escaped with his harp when this first wife of David and daughter of Saul let him down through a window to slip away Answer Michal 3 10 points David escaped to this friend and son of Saul who dined with Saul with the conspicuous absence of David On the second day Saul goes into a rage and tells him that with David alive neither him nor his crown is safe But this friend of David went into the fields and told David to ee in safety to the cave of Adullam Answer Jonathan 4 5 points East of the Rocks of the Wild Goats Saul came to relieve himself in a cave in which David and his men hid Instead of killing him David cut off what in Saul39s possession Because David did not kill him Saul left swearing mutual respect swer a piece of Saul39s cloak or Ming Religion Mythology Philosophy Bonus 2 Name these antiScholastics for ten points each 1 This Doctor of the Church attacked the scholastic Gilbert de la Porree at the 1148 council of Rheims and was primarily responsible for building the Cistertian order swer St Bernard of Clairvaux 2 Although this author of the Discourse on Method was an antischolastic his terms come largely from that movement Answer Rene Descartes 3 This author of the Skeptical Chemist and member of the Royal Society put forward the law bearing his name in answering an attack by the Jesuit Franciscus Linus Answer Robert Boyle Religion Mythology Philosophy Bonus 3 Vocabulary of Edmund Husserl for ten points each 1 Because quot1 think therefore 1 am quot presupposes the method of doubt Husserl starts instead with the clearer basis that quot1 always think of som ething and therefore consciousness is always pointing towards some object Name this term that describes the directionality of consciousness an idea also associated with John Searle Answer Intentionali 39 or Intention 2 By this Husserl means detachment from any point of view regarding the objective world so that we may bracket these phenomena by looking upon them without judgment or valuation Name this term Greek for quotbracketingquot Answer Phenomenological Epoche 3 This is the prescientific mode of experience advocated by Husserl Name this German word or its English translation that describes all the experiences without presupposition in which human beings are typically involved swer Lebenswelt39 or LifeWorld Fine Arts 33 Fine Arts Tossup 1 The protagonist wakes up in the middle of the night remembering the tune quotGotta Have Me Go with You which he heard the night before and drives to the Ambassador where the Glenn Williams orchestra is done playing He eventually chases down the woman who sang the tune at the Downbeat club where she sings of quotThe Man that Got Away While her career goes uphill his goes down the toilet and he becomes an alcoholic and drowns himself to relieve himself as a burden to his wife39s Oscarwinning career Remake of a 1937 William Wellman film for ten points name this musical starring Judy Garland as Mrs Norman Maine directed by George ukor Answer A Star Is Born Fine Arts Tossup 2 Modigliani s Caryatid and Matisse s Backs series pay homage to them and they are currently housed in the first school in Europe specifically established to teach drawing painting and sculpture Previously they could be found in the Grotto of the Boboli Gardens until the end of the sixteenth century Originally intended as the decoration for a tomb their artist worked on them for 40 years but left them unfinished after his patron Pope Julius 11 died For ten points name these Michelangelo statues which line the walk to his David named because their subjects can t get out of the rock in which they re carved Answer The Four Prisoners or Quattro Prigioni Fine Arts Tossup 3 His personal crisis in 1935 caused a shift to religious music and recitals with baritone Pierre Bernac producing one of his most performed works the 1959 Gloria He was publicly known even before taking lessons with Koechlin and writing the ballet Les biches for Dyagilev Although he wrote orchestral works like the Organ Concerto and chamber works like sonatas for flute oboe and clarinet he is best known for an opera depicting a couple who trade places before the wife kills the husband urging the audience to have more children For ten points name this member of Les Six who composed music for the absurd Apollinaire piece Les mamalles de Tiresias Answer Francis Poulenc Fine Arts Bonus 1 He denied he was ever born in Lowell Massachusetts saying quot1 shall be born when and where 1 want and 1 do not choose to be born in Lowell For ten points each 1 Name this American proponent of quotart for arts sake who sued John Ruskin for accusing him of quotflinging a pot of paint in the public39s face as in 187439s Nocturne in Black and Gold The Falling Rocket Answer Jam es Abbott McNeill Whistler 2 In this 1871 painting a black curtain and a picture on the wall are positioned in front of an elderly lady with her foot on a stool We see her sitting with her left side in profile Answer Arrangement in Black and Gray The Artist s Mother or Whistler s Mother 3 This 1862 musically themed painting of Whistler s mistress Joanna Heffernan was rejected by both the Royal Academy and the Paris Salon She stands on top of a bear rug dressed in the titular color Answer Symghony in White No I39 or The White Girl Fine Arts Bonus 1 He notes that quotwhen God made cripple He mean him to be lonely Later when Bess has no place to go he gives her shelter pays for the funeral of Robbins and sings quot1 got plenty o39 nuttin For ten points 1 Name this character who goes in search of his woman in NY on a goat cart in a George Gershwin opera Answer Porgy 2 First sung by J ake39s wife Clara as a lullaby on Saturday night when quotthe livin39 is easyquot this aria is later rendered by Bess as she searches for Clara39s ba y Answer quotSummertimequot 3 This husband of Bess appears after the song to take Bess back but is stabbed by Porgy This stevedore had earlier taken refuge on Kittiwah Island after killing Robbins with his cotton hook Answer Crown Fine Arts Bonus 2 Answer these things about Stravinsky39s The Rite of Spring for ten points each 1 Part One of the ballet containing the Dances of the Young Girls and the Procession of the Oldest and Wisest among others is known by this name Answer The Adoration ot the Earth or L39Adoration de la terre 2 The ballet opens with a solo theme from this instrument playing in an unusually high register swer bassoon 3 After the introductory theme comes a theme based on this interval sometimes known as the diabolus in music for its extreme dissonance Answer tritone accept also augmented fourth or diminished fth Social Science 22 Social Science Tossup 1 Studying at Barnard and Columbia she was professor at Fordham University and curator at American Museum of Natural History in NY Married to Gregory Bateson she was once criticized by Derek Freeman and wrote the autobiography Blackberry Winter as well as the biography Ruth Benedict Her studies of nonliterate people of Oceania relied not on statistics but on the notion of cultural determinism For ten points name this author of Male and Female New Lives for Old Sex and Temperament in Three Primitive Societies and regarding adolescent sexual freedom in Coming onge in Samoa Answer Margaret Mead Social Science Tossup 2 Author of The Psychology of Wants Interests andAttitudes and An Introduction to the Theory ofMental and Social Measurements he worked with Robert S Woodworth at Columbia publishing on the lack of transference in learning different tasks A student of James McKeen Cattell and William James he noted that behaviors that lead to good results are more likely to occur in response to the same stimuli and that frequent stimulusresponse pairings lead to strongly established behaviors For ten points name this author of Animal Intelligence who postulated the laws of effect and exercise Answer Edward Lee Thorndike Social Science Bonus 1 Concepts from syntax for ten points each 1 A morpheme that is phonologically dependent and syntatically independent is known as this The quotsquot in quothe39squot the genitive and contracted quotisquot are both examples of this type of bound morpheme that attaches to a phrase Answer clitic 2 This is the number of phrases with grammatical relations to the verb ie the number of arguments of the verb For example intransitives have values of 1 transitives have 2 and ditransitives have 3 Answer valence 3 Also known as selection this is the information about a word39s complement options For example the English Package classi y April 17 2009 Type Package Title Explore classi cation models in high dimensions Version 023 Date 20070313 Depends rggobi rpart MASS nnet class e1071 reshape Suggests randomForest Author Hadley Wickham lthwickhamgmai1comgt Maintainer Hadley Wickham lthwickhamgmai1comgt Description Given p dimensiona1 training data containing d groups the design space a classi cation algorithm classi er predicts which group new data belongs to Generally the input to these algorithms is high dimensional and the boundaries between groups will be high dimensional and perhaps curvilinear or multifaceted This package implements methods for understanding the division of space between the groups See ur1httphadconzc1assi y for more details License MIT LazyData true Repository CRAN Datequblication 20070314 191008 R topics documented advantage classi y explore generateiclassi cationidata generateidata simvar variables 2 classi y Index 9 adva nt age Advantage Description Calculate the advantage the most likely class has over the next most likely Usage advantage post Arguments post matrix of posterior probabilities Details This is used to identify the boundaries between classi cation regions Points With low close to O advantage are likely to be near boundaries Auth0rs Hadley Wickham lthWickham gmailcomgt Clas 51 f 1y Classi and explore a data set Description Classi y provides a convenient method to t a classi cation function Usage classifly data model classifier nlOO O O methodquotnonalignedquot Arguments data Data set use for classi cation model Classi cation formula usually of the form response predictors cl a s s i f i e r Function to use for the classi cation eg 1 da Other arguments passed to classi cation function For example if you use svm you need to use p robab 1 1t iy retrieved TRUE so that posterior probabilities can be type in rangequot classi y 3 n Number of points to simulate To maintain the illusion of a lled solid this needs to increase With dimension 10000 points seems adequate for up to four of ve dimensions but if you have more predictors than that you Will need to increase this number method method to simulate points grid random or nonaligned default See simvar for more details on the methods used type type of scaling to apply to data Defaults to commmon range See re scaler for more details Details This is a convenient function to t a classi cation function and then explore the results using GGobi You can also do this in two separate steps using the classi cation function and then explore By default in GGobi points that are not on the boundary ie that have an advantage greater than the 5 to brush mode and choose include shadowed points from the brush menu on the plot Window You can then brush them yourself to explore how the certainty of classi cation varies throughout the space Special notes You should make sure the response variable is a factor For SVM make sure to include probability TRUE in the arguments to Classifly Au th0r s Hadley Wickham lthWickham gmailcomgt See Also explore http hadconZclassifly Examples classiflykyphosis Kyphosis N lda classiflykyphosis Kyphosis N polyAge2 polyNumber2 polyStart2 lda classiflykyphosis Kyphosis N qda classiflykyphosis Kyphosis N rparU classiflykyphosis Kyphosis N knnf k classiflykyphosis Kyphosis N glm familyquotbinomialU classiflykyphosis Kyphosis N svm probabilityTRUE classiflykyphosis Kyphosis N svm probabilityTRUE kernelquotlinearU classiflykyphosis Kyphosis N bestsvm probabilityTRUE kernelquotlinearU Also can use explore directorly bsvm lt7 bestsvmSpeciesN data iris gamma 2Aell cost 2 2 4 probabilityTRL explorebsvm irim 4 explore explore Explore default Description Default method for exploring objects Usage exploremodel data nlOOOO methodquotnonalignedquot advantageTRUE Arguments mode 1 classi cation object data data set used With classi er n number of points to generate When searching for boundaries method method to generate points see gene rateidata advantage only display boundaries Details The default method currently works for classi cation functions It generates a data set lling the design space nds class boundaries if desired and then displays in a new ggobi instance Auth0rs Hadley Wickham lthWickham gmai1comgt See Also generateiclassificationidatahttphadco nZclassifly Examples bsvm lt7 bestsvmSpecies data iris gamma 2A7ll cost 2 2 4 probabilityTRL explore bsvm iris generate classi cationidam 5 gene rateiclassificationidata Generate classi cation data Description Given a model this function generates points Within Usage generateiclassificationidatamodel data n method advantage Arguments mode 1 classi cation model dat a data set used in model n number of points to generate method method to use currently either grid an evenly spaced grid random uniform random distribution across cube or nonaligned grid some random peturba tionb advantage Details If posterior probabilities of classi cation are available then the advantage Will be calculated directly If not knn is used calculate the advantage based on the number of neighbouring points that share the same classi cation Because knn is 0nA2 this method is rather slow for large gt20000 say data sets By default the boundary points are identi ed as those below the 5thpercentile for advantage Auth0rs Hadley Wickham lthWickham gmailcomgt gene rateidata Generate data Description Generate new data from a data frame Usage generateidata data nlOOOO methodquotgridquot 6 krmf Arguments dat a data frame n desired number of new observations method method to use see simva Details This method generates new data that lls the range of the supplied datasets Au th0r s Hadley Wickham lthWickham gmailcomgt knnf knn with formula Description A wrapper function for knn to allow use Usage knnf formula data k2 Arguments f o rmu l a classi cation formula data training data set k number of neighbours to use Auth0rs Hadley Wickham lthWickham gmailcomgt Olives 7 Olives Olive oil data Description The olive oil data consists of the percentage composition of 8 fatty acids palmitic palmitoleic stearic oleic linoleic linolenic arachidic eicosenoic found in the lipid fraction of 572 Italian olive oils There are 9 collection areas 4 from southern Italy North and South Apulia Calabria Sicily two from Sardinia Inland and Coastal and 3 from northern Italy Umbria East and West Liguria Usage data olives Format A data frame With 244 rows and 7 variables References Forina M and Armanino C and Lanteri S and Tiscornia E Classi cation of olive oils from their fatty acid composition 1983 in Food Research and Data Analysis edited by Martens H and Russwurm Jr H pages 189214 s imvar Simulate variable Description Simulate observations from a vector Usage simvar X n10 methodquotgridquot Arguments X data vector n desired number of points Will not always be achieved me t ho d simulation method 8 valiables Details Given a vector of data this function Will simulate data that could have come from that vector There are three methods to choose from nonaligned default grid some random peturbation grid grid of evenly spaced observations If a factor all levels in a factor Will be used regard less of n random a random uniform sample from the range of the variable Auth0rs Hadley Wickham lthWickham gmailcomgt variables Variables Description Extract predictor and response variables for a model object Usage variables model Arguments mo de l model object Details Due to the way that most model objects are stored you also need to supply the data set you used With the original data set It currently doesn t support model tted Without using a data argument Auth0rs Hadley Wickham lthWickham gmailcomgt Notes on Classical Mechanics Newtonian Lagrangian and Hamiltonian Mechanics and Classical Field Theory Andrew Forrester January 28 2009 Contents 1 Ideas and Questions 2 11 Questions 2 12 Things to Look Into 3 13 Unit Questions 3 2 The Big Picture 3 21 Historical Development 3 3 Notation 4 4 Mathematics 4 5 Terms and Quantities 5 6 Theoretical Summary 6 61 Abstract Mathematical View 6 62 Important Equations 6 63 Newtonian Formalism 7 64 Lagrangian Formalism 7 65 Hamiltonian Formalism 7 66 Advantages and Disadvantages of Variational Principle Formulation 7 67 Other Stuff 8 7 Newtonian Mechanics 8 71 Forces Newton s Laws and Conservation 8 711 Examples 9 72 Extraneous Material 9 8 Lagrangian Formalism 10 81 Fundamentals 10 82 Local Differential Formulation D Alembert s Principle and Lagrange s Equations 10 821 Freedom of Lagrangian 12 83 Comments and Elaboration 13 84 Nonconservative Forces Dissipation Functions and so forth 13 85 Method of Lagrange Multipliers 14 86 Global Integral Formulation Hamilton s Principle and the Euler Lagrange Equations 14 861 Assumptions 14 9 Hamiltonian Formalism 16 91 Legendre Transformations Variational Principles and Hamilton s Equations 16 92 Constructing the Hamiltonian via the Lagrangian Formulation 17 93 Variational Principles 18 94 Canonical Transformations 18 10 Alternative Formulations 18 11 Example Lagrangians Hamiltonians and Equations of Motion 19 12 Ch 8 19 13 Conservation Theorems and Symmetry Properties 20 131 Solving the Equations of Motion 20 14 Theorems 21 15 Central Forces Trajectories Orbits and Scattering 23 16 Open Questions and Mysteries 23 17 Class on Mechanics and Field Theory 24 171 Books to Use 24 172 Class Topics 24 173 Core Topics for Class7 from Goldstein 25 174 Investigate 25 175 Take note of 25 1 Ideas and Questions 11 Questions 0 Now that I know what dz and df are one form elds7 what is 61 in functional calculus WRT the functional derivative7 etc How do the limits of integration in the calculus of variations come into play 0 Explain the advantages disadvantages of the IT and Lagiangian fULuiali 111 over the Newtonian formalism solving certain problems7 gaining information from LagrangianHamiltonian that is not otherwise available 0 Why not a generalized potential U Uq7 q q q 725 o The Work Kinetic Energy Principle can be generalized Ch 17 prob 4 ls this a generally useful result If so7 what should we call it How should we think about it o In what circumstances7 and to what extent7 are variables such as q and q considered independent 0 Examine the Lagrangians of QFT and any other Lagrangians I nd to see if they satisfy the condition for transformation into the Hamiltonian formalism Lagrangian is concave up or concave down wrt velocities7 ie7 second derivative wrt velocities is either always positive or always negative 0 How do we come up with U for the charged particle in an e m eld 0 Why is the Hamiltonian for a nonrelativistic charged particle in electromagnetic elds not T U but is the total energy 0 When is the Hamiltonian 7 equal to the total energy of the system in question and when is it not 7 equal to the total mechanical energy of the system in question and when is it not 7 conserved and when is it not A case If the Lagrangian does not explicitly depend on time AND if the generalized coordinates appearing in the Lagrangian are unconstrained7 then the Hamiltonian is conserved If you include the constrained angular coordinate in the Lagrangian as a generalized coordinate then the theorem is no longer true You have to use Lagrange multipliers or some other technique to deal with the constrained system ie to nd equations of motion http www physicsforums comarchiveindex phpt87978 html 0 Are scientists trying to come up with the most fundamental Hamiltonian of the universe and should it be conserved Perhaps once they come up with this fundamental conserved Hamiltonian then they ll know how to break it up and to examine subsystems of the universe which may have nonconserved Hamiltonians o What is the difference between a dissipation function and a generalized potential 0 ls D Alembert s principle equivalent to Newton s second law as Wikipedia claims Article D Alembert s principle 12 Things to Look Into From Goldstein s 1 index 0 Principle of Virtual work 0 Virial of Claussius o Symplectic notation for Hamilton s equations Show principle of maximal aging implies principle of least action httpwwweftaylorcomindex html 13 Unit Questions Are they really the same If not how are they different 0 torque T r x F has the same units as energy W fF ds m x N 77 Nm o angular momentum L r x p has the same units as action S det m x kg 7 J s o volumetric ux density meters cubed of substance per second per meter squared of surface thrpugh which the substance passes has the same units as velocity meters traversed per second InTm2 77 m s 2 The Big Picture Classical mechanics includes the general theory of relativity and what else See notes on relativity for details of relativistic mechanics 21 Historical Development D Alembert s principle Hamilton Jacobi eqns 0 1772 88 The French and Italian mathematician and astronomer Joseph Louis Lagrange 1736 1813 reformulates Newtonian lHtO Lagrangian o French mathematician Adrien Marie Legendre 1752 1833 c German mathematician Carl Gustav Jacob Jacobi 1804 1851 1833 The Irish mathematician William Rowan Hamilton 1805 1865 invents a reformulation of clas sical mechanics 7 Hamiltonian mechanics 1834 Hamilton s principle 00 1867 The terms generalized coordinates generalized velocities and generalized momenta were intro duced by Sir William Thomson later Lord Kelvin and P G Tait in their famous treatise Natural Philosophy 1870 Rudolf Julius Emanuel Clausius 1822 1888 proves the scalar virial theorem Notation A set of generalized coordinates q1 q2q3 qn may be denoted quENTL or qj or q or simply q This last notation will be most common and it should be clear from the context whether q represents one coordinate or a set of coordinates lf unsure assume q represents a set of coordinates rather than one coordinate 7 The same goes for canonical momenta p1p2p3 simply p 71 may be denoted pghem or pj or p or There is an ambiguity between the polar angle component of Cartesian momentum and the canonical momentum conjugate to the polar angle both of which may be denoted p9 Similar ambiguities arise for other momenta 7 How shall I resolve this ambiguity Use p9 or 1 Dot notation Newton s uxion dq dt I m not sure but this might also sometimes be used to denote the partial time derivative q What about when we go from a particle Lagrangian to a eld Lagrangian density 8L 8E ii A 7 8q 88t a E 8gp 7 Total derivative d i t dt Change over time given an arbitrary change in all other variables if any Partial derivative 8 8t Change over time given that all other variables if any are constant at Mathematics Standard Calculus Functional Calculus Differential Geometry Lie Groups Algebras Representations Small Theorems 7 Euler s thm lf fyk is a homogeneous function of the yk that is of degree n then 2k yk nf 5 Terms and Quantities Position Time Velocity Acceleration Jerk etc Inertia Momentum Force Mass Moments of force of mass of inertia etc System Degrees of Freedom Coordinates Generalized Coordinates Equation of Motion Constraint Equation of Constraint Holonomic Constraints and Systems Monogenic Forces and Systems TV Tq Kinetic Energy The energy of motion of objects relative to each other Vr Vq Potential Energy Conservative Potential Uq q t Generalized Potential also Uqq Velocity dependent Potential 9quot Dissipation Function also Rayleigh s dissipation function or viscous dissipation function Stress Tensor Energy Momentum Stress Tensor TM is the ux of 4 momentum 19 across a surface of constant zV Or TW is the ux of 4 momentum component pp across a surface of constant my T00 the ux of p0 energy in the 0 time direction is the rest frame energy density Mechanical Stress Tensor stress strain compression pressure viscosity normal and tangential tractions or equivalently direct and shear stresses See http www bun kyotou ac jpsuchiiextrem aging html Stress Holor T as a subholor of TM Dust and perfect uid which can be completely speci ed by two quantities the rest frame energy density p and an isotropic rest frame pressure p Laue s scalar Tm Einstein and von Laue proposed that the problem might lie with the eld equation which they suggested should have the linear form FTmtter p where F is some yet unknown function of j and where Tmatter is the trace of the stress energy tensor describing the density momentum and stress of any matter present77 httpenwikipediaorgwikiNordstrm stheoryofgravitation T5111 pMNV mnuMuV puMuV Tgelifect uid p W u 1971M Scalar eld theory stress tensor 2 nrnwamam 7 W anMawam W EM stress tensor FMAFV 7 nalFAVE Energy density energy ux momentum density Given Hilbert Einstein Action SH m R 1 S SH SM 167rGN where SM is the action for matter We have another de nition of the stress tensor 1 65M xilgl lgW TW E 72 Spin tensor Warning ln solid state physics and uid mechanics the stress tensor is de ned to be the spatial components of the stress energy tensor in the comoving frame of reference In other words the stress energy tensor in engineering differs from the stress energy tensor here by a momentum convective term 6 Theoretical Summary 61 Abstract Mathematical View 0 Newtonian vectors af ne space tangent space 0 A Lagrangian is a time dependent 7 form eld on coordinate space 0 The Hamiltonian is a timedependent scalar on the cotangent bundle of phase space The total space of a cotangent bundle naturally has the structure of a symplectic manifold Wikipedia Differentiable Manifold 62 Important Equations 0 Generalized Coordinates As opposed to numbering the particles 1quot1 r1q17 q27 quNilmt o Eqns of Constraint What are the issues dealing with time dependence etc 0 Transformation Eqns or Parametrization of Coordinates a kind of Point Transformation Given N particles in 3D space and k eqns of constraint T1 T1q17q27 7q3N7k7t T2 T2q17 qz 7q3N7k7 75 TSN7k r2q1 qz 7q3N7k7 75 where the independent coordinates 63 Newtonian Formalism 0 Good for elucidating physical mechanisms 64 Lagrangian Formalism 0 Local Differential Principles 7 Newton s Laws Principles of instantaneous forces and particulate motion 7 D Alembert s principle small virtual displacements about an instantaneous state a point in con guration space and then integrate 0 Global lntegral or Variational Principles 7 Hamilton s principle small virtual variations of the entire motion through con guration space of the system between times 251 and 252 from the actual motion This seems to force one to decide what the nal and initial states should be 65 Hamiltonian Formalism 0 Local Differential Principles 0 Global lntegral or Variational Principles 7 Modi ed Hamilton s principle 66 Advantages and Disadvantages of Variational Principle Formulation From Soper 3 the principle of stationary action does not apply to systems subject to frictional forces To discuss such systems one must return to an F ma approach Likewise we will have to go beyond Hamilton s principle in Chapter 13 when we discuss eld theories that include dissipative processes like viscosity heat ow and the ow of electric current through a resistor77 c From Goldstein 7 Question How many of these advantages also apply to other formulations 7 Coordinate Invariance Formulation refers to kinetic and potential energies which are always de nable and independent of coordinate system 7 Universality of technique Lagrangian formulation can be extended easily to describe systems that are not normally considered in dynamics such as elastic elds the electromagnetic eld and eld properties of elementary particles 7 Formal similarity of phenomena Formal similarities between different kinds of systems such as electrical circuits and mechanical systems become apparent Terms normally reserved for electrical circuits such as reactance and susceptance are the accepted modes of expression in much of the theory of Vibrations of mechanical systems1 7 Structural analogy of elds of study Lagrange s and Hamilton s principles together form a copact invariant way of implying the mechanical equations of motion This works outside of mechanics also variational principles can be used to express the equations of motion77 whether they be Newton s equations Maxwell s equations or the Schrodinger equation So when a variational principle is used as the basis of formulation of all elds they will exhibit at least to some degree a structural analogy 7 The methods of quantization were rst developed for particle mechanics starting essentially from the Lagrangian formulation of classical by a Lagrangian and corresponding Hamilton s variational principle it is possible to carry over the methods of particle quantization to construct a quantum electrodynamics By describing the electi eld 0 From Marion and Thorton 7 The Newtonian approach emphasizes an outside agency acting on a body the force while the Lagrangian method deals only with quantities associated with the body the kinetic and potential energies In certain situations it may not be possible to state explicitly all the forces acting on a body as is sometimes the case for forces of constraint and as is normally the case for quantum mechanical systems where we normally know the eneries but not the forces 67 Other Stuff From Abers page 47 we have that the classical equation of motion is As A H a 7 Newtonian Mechanics 71 Forces Newtonls Laws and Conservation 0 Newton s Laws of Motion 7 N1 lnteria Statement of kinematics in absence of forces interaction Special case of N2 gtk CLM and CAM for elementary particles with no external forces Not observed not inter acting 7 N2 Force Action and Momentum How does one de ne a force and mass 1For a detailed exposition see H F Olson Solutions of Engineeiing Problems by Dynamic Analogues New York Van Nostrand 1966 711 7 N3 Coaction gtk WN3 gtk SN3 N2 Various forms of Newton s Second Law N2 depend on the Laws of Coaction forms of Newton s Third Law N3 7 Forms that are always valid Single particle Superposition of multiple particles both linear and angular forms correct WN3 Weak Law of Coaction 7 WN3 The forces that two particles exert on each other are equal and opposite 7 gt N2 for Systems of particles is valid Using total mass center of mass net force 7 ln absense of external forces Conservation of total linear momentum assumes WN3 to be true so the internal forces cancel SN3 Strong Law of Coaction 7 SN3 The forces that two particles exert on each other are equal and opposite and directed along the line joining the particles 7 gt N2 for Angular momenta and forces torque is valid 7 ln absense of external forces Conservation of total angular momentum assumes SN3 to be true so the internal forces are central and cancel N3 in either form DOES NOT hold for all forces in the Newtonian picture if you include everything such as momentum of elds etc then in some sense N3 always holds elaborate on this PLN2 Q PAN2 Q CPLM Q CPAM PLN2 WN3 Q SLN2 Q CTLM PAN2 SN3 Q SAN2 Q CTAM C conservation of P particulate T total S systemicstrong W weak L linear A angular M momentum N Newton s 2 second law 3 third law Mechanical Energy Note that in some circumstances a force may be given by the gradient of a scalar function F 7VV and the mechanical energy E T V may still be de ned but 7 W 7 AV 7 E is NOT conserved Examples F 7VV where V Vlr2 7 rll VR gt SN3 F 7VV where V Vlr2 7 r1 lVg 7 V1 52 7 51 gt WN3 only 72 Extraneous Material Center of mass 7 Center of gravity 8 Lagrangian Formalism The Lagrangian formulation of classical mechanics 0 in its usual holonomic form eliminates the constraining forces from the equations of motion 0 utilizes scalar functions L T U Which can simplify problems 81 Describe how why Fundamentals Constraints Geometric limits on the system where the forces enforcing these limits are not necessarily known apriori or something like that always geometric Generalized Coordinates Coordinates of any type that fully distinguish a state ofthe system consistent with the constraints Virtual Displacement and 6r 6g Virtual Work F 6r Q 6g Variation and 6rt 6qt First Variation 6Fq t 6q gag 6q Functional Differentiation and Functional Integration Principle of Virtual Work Virtual work less constraining forces 61quot O with equilibrium F 0 a 61quot 0 IS this a sum over particles If not then the transformation to general coordinates may need an integral o holonomic constraints systems 0 nonholonomic constraints systems 82 Local Differential Formulation DlAlembertls Principle and Lagrangels Equa tions The physical and local concept of Virtual work less constraint together with Newton s second law of mo tion generates all of the equations of the Lagrangian and Hamiltonian formulations of classical mechanics It is required in both the and In practice the restriction to Virtual work less constraints presents little handicap to the applications as most problems in which the nonholonomic formalism is used relate to rolling without slipping where the constraints are obViously workless77 I give some names to the intermediate equations for organizational and mental recall purposes and I put a star by the equations that seem to be most fundamental or important to remember ic equation D Alembert s Principle Virtual work less constraining forces 61quot 0 and N2 F 7 p 0 ZF27pi6r0 with generalized coordinate and force transformations ageiaawaiwo D Alembert s Principle D Alembert s Principle with a potential with and Potential some applied forces derivable from a generalized potential Uqj 4 t d 3L 3L 7 ZilQ Elevj Tall lqi 0 Monogenic D Alembert s Principle with monogenic forces D Alembert s Principle all applied forces derivable from a generalized potential Uqj qj t d 3L 3L 7 2456 Tail lqi 0 Holonomic D Alembert s Principle with holonomic constraints D Alembert s Principle independent qj s i 7amp7 0 dtltaqjgt aqj Qj Generalized D Alembert s Principle with holonomic constraints and a potential Lagrange s Eqn some applied forces derivable from a generalized potential Uqj qj t d 3L 3L 7 5 a 37 i Q Monogenic Generalized D Alembert s Principle with holonomic constraints and monogenic forces Lagrange s Eqn all applied forces derivable from a generalized potential Uqj qj t d 3L 3L 7 a 5 37 7 37 7 0 Lagrange s Eqn D Alembert s Principle with holonomic constraints and monogenic conservative forces all applied forces derivable from a conservative potential Uqj d 3L 3L7 gem Dissipative Generalized Generalized Lagrange s Equation with nonconservative forces Lagrange s Eqn derivable from a dissipation function Fd 735 so Q 737 d 3L 3L 3 7 ltaTjgtiaTjquiQ Nonholonomic Monogenic D Alembert s Principle Lagrange s Eqn with special nonholonomic eqns of constraint 7 akjdqj aktdt 0 and usage of the method of Lagrange undetermined multipliers d 3L 3L 4 ltgtZwkaw 2 JENn and Ziaqujakt0 kENm The Dissipative Generalized Lagrange s Equation is the most generalized concept packed holonomic equation so it should de nitely be memorized The Nonholonomic Lagrange s Equation is used less frequently but should be kept in mind o F FC F0 F0 Fp Fr Fr Fd F11 c for constraint 0 for other p for derivable from a generalized potential r for remaining d for derivable from a dissipation function n for not derivable are there any such things or might they be derivable from something else 0 Q QCQO QCQPQr QCQPQdQn The usual holonomic Lagrangian formalism gets rid of the constraining forces 0 Kinetic energy T 2 a i A a i T 2mivmltaqjazgt i i j M0 2Mij 21 1ijij 739 73916 To T1 T2 0 Generalized force Qj conjugate to the generalized coordinate qj 8m 7 39jS Fl 861739 of 08139 aim63 L QPA 7 dt 3 aqj How does one come up with such a potential at 84 84 8r 139quot 1 89quot 8V d d 1 z z F 7 7 7 7 o Lagrangian L Lqt7 6109775 E Tcit Uqt7q t7t The dependence of L on time may arise if the constraints are time dependent if the transformation equations connecting the rectangular and generalized coordinates explicitly contain the time or if the generalized potential is explicitly time dependent 821 Freedom of Lagrangian Gauge freedom of the Lagrangian i i dF L q7q7t Lq7 q7 75 a While L T7 V is always a suitable way to construct a Lagrangian for a conservative system it DOES NOT provide the only Lagrangian suitable for the given system you may also use L T 7 V th 83 Comments and Elaboration 0 Virtual displacements and work 7 6r is a virtual in nitessimal displacement of the coordinate ri at the instant t the coordinate could be the position of a particle 6r is taken to be consistent with the forces and constraints imposed on the system at the given instant t virtual distinguishes this from actual displacements which occur over some time interval dt during which the forces and constraints may be changing 7 F the total force on a particle is decomposed into the net constraining force and the net other forces77 We restrict ourselves to systems for which the net virtual work of the forces of constraint is zero so that we may neglect them in our analysis or 0 This is true for rigid bodies and a large number of other constraints This is true for articles constrained to move on a surface unless there are sliding friction forces What about if those sliding friction forces are considered as applied or external If the surface is moving in time the virtual work is still zero even though the actual work over dt may not be Rolling friction doesn t defy this condition 7 Equilibrium Overall equilibrium F 0 so F or 0 Our assumption 6r 0 This eqn is called the principle of Virtual work The virtual work of the applied forces vanishes In general 7 0 since the 6r are not completely independent but are connected by the constraints 0 Generalized forces 0 Lagrangian L o Lagrange density or again Lagrangian E or 3 which should I use The Lagrangian is a function on the tangent bundle Wikipedia Differentiable Manifold 84 Nonconservative Forces Dissipation Functions and so forth 0 Conservative Forces 0 Nonconservative Forces 7 Derivable from a Generalized Potential velocity dependent or otherwise 7 Derivable from a Dissipation Function Fd 73 or Fd Vv l 311239 d7 d an 7 3r 7 or 7 a Qj 7 aq Zivv aq Zivv 39a 7 37 7 What s the rest of 7em 85 Method of Lagrange Multipliers o Usable whenever the eqns of constraint are in the form Zan dqj alt dt 0 739 and we may take7 since virtual displacements dqj 6 imply that dt 07 Z alj 6 0 virtual work less constraints k 0 Includes holonomic constraints Useful when 1 it s convenient to reduce all the q s to ind coords 2 want to solve for the forces of constraint We get 71 m equations for n m unknowns the rst being Lagrange s Eqns for nonholonomic systems d 3L 3L i 7 7 7 C 0 397 4 dt 8 Ek Aka Q Q j 6 Nn Eatgawk 0 k 6N 739 86 Global Integral Formulation Hamilton7s Principle and the EulerLagrange Equa tions 861 Assumptions 0 Monogenic systems 0 Virtual work less systems Hamilton s Principle 6 E 6f dtL 0 The motion of the system from time 251 to 252 is such that the line integral I ft dt L7 where L T 7 V7 has a stationary value for the correct path of the motion le7 the motion is such that the variation of the line integral I for xed t1 and 252 is zero 6 6 fdtLq1qnq1qnt 0 Can extend this to include some nonholonomic systems7 but this formulation is most useful for holonomic systems7 wherein a La grangian of independent coordinates can be set up Euler Lagrange Eqns 3322 7 g 0 2 ne 12n 90 H 75 M H qi 1024139724 139790H Lqi7 QM Extensions Consider f fyy 3 y 7m or use several pa rameters mi yielding a multiple integral and derivatives of each yi with respect to each mi andor consider variations in which the end points are not held xed 14 0 see Goldstein pg 48 In this dress7 Hamilton s principle says 6f dtT 7 12 2k 62166 dt 0 The variational principle formulation has been justly described as elegant for in the compact Hamil ton s principle is contained all of the mechanics of holonomic systems with forces derivable from poten tials The principle has the further merit that it involves only physical quantities that can be de ned without reference to a particular set of generalized coordinates7 namely7 the kinetic and potential ener gies77 o Lagrange s eqns ltgt Hamilton s principle 0 Hamilton s principle Lagrange s eqns is more important than the converse why since Hamilton s principle yields more Like what 9 Hamiltonian Formalism 91 Legendre Transformations Variational Principles and Hamilton7s Equations Original Function Legendre Transform yz 1MP A collection of points in the zy plane As a description of the original function a collection of tangent lines of slope p and y intercept 1 As a description of the Legendre trans A collection of points in the pip plane form a collection of tangent lines of slope 7m and w intercept y 0 Original Function 7 Domain R 7 Codomain R for convenience7 imagine each value as a different color 0 Original Function Level Subspaces generalization of level curves 7 1D domain 1 2 points one color 7 2D domain monochromatic curves 7 3D domain monochromatic surfaces 0 Tangent Objects 7 1D domain line hyperpoint of constant color velocity 7 2D domain conepyramid hyper closed curve with continuous distribution of color velocity that is constant in time possibly also hyper curve segment 7 3D domain hyperbubble hyper closed surface possibly also hyper bubble segment 0 Osculating Subspace for Orignal Function and Tangent Object 7 1D domain 1 point one color 7 2D domain polychromatic curves 7 3D domain polychromatic surfaces Energy function In no q t 7 Z 4amp7 7 Mn q 2 o The energy function h is identical in value with the Hamiltonian H but is a function of n 1 independent variables the q s plus 25 and the is which depend on the q s While H is a function of 271 1 independent variables 0 h is not necessarily the mechanical energy and it is not necessarily conserved 0 Whereas the Lagrangian is uniquely xed for each system by the prescription L T 7 U in dependent of the choice of generalized coordinates the energy function h depends in magnitude and functional form on the speci c set of generalized coordinates For one and the same system various energy functions h of different physical content can be generated depending on how the generalized coordinates are chosen o If frictional forces are present and derivable from a dissipation function 9quot then 9quot is related to the decay of h lnitial De nition of Canonical Momentum p 3 Also called constitutive relations from Lagrange s monogenic nonrel Equation 15 3 Initial De nition of the Hamiltonian Hqp t qipi 7 Lq q t with summation over i and q qqp 25 Modi ed Hamilton s Principle 6 fit dt qipi 7 Hqp 25 0 Hamilton s Canonical Equations q g 7p 375 7 7 7 39 3t 7 3t Hamilton s Equations in MatrixSymplectic Notation 1 J o 1 is the canonical variable vector m qr mm Pi 2 S n 0 IgtWhere0andIarenxn Jlt71 0 7 Properties of the matrix J here 3H 377 i About the symplectic notation Considerable ingenuity has been exercised in devising nomenclature schemes that result in entirely symmetric equations or combine the two sets into one Most ofthese schemes have only oddity value but one the symplectic notation has proved to be an elegant and powerful tool for manipulating the canonical equations and allied expressions 92 Constructing the Hamiltonian Via the Lagrangian Formulation 1 With a chosen set of generalized coordinates qi the Lagrangian Lq q t is constructed 2 The conjugate momenta are de ned as functions of qi q and t by the initial de nition of pi 8L8q i 03 The Hamiltonian is formed using Hqp t qipi 7 Lq q 25 At this stage one has h instead of H or rather some mixed function of qi q i pi and t q The equations pi 8L3q i are then inverted to obtain q as functions of qp 25 Possible difficulties in the inversion SHOULD BE ADDRESSED SOMEWHERE U The results of the previous step are then applied to eliminate q from H so as to express it solely as a function of qp t 93 Variational Principles 0 action abbreviated action Maupertuis action 0 Variational Principles of Mechanics A host of similar variational principles for classical mechanics can be derived in bewildering variety The variational principles in themselves contain no new physical content with respect to Newton s Laws or Lagrange s equations and they rarely simplify the practical solution of a given mechanical problem Their value lies chie y as starting points for new formulations of the theoretical structure of classical mechanics For this purpose Hamilton s principle is especially fruitful and to a lesser extent so also is the principle of least action The others have proved to be of little use except as they have led to fruitless teleological speculations on nal cause or purpose and design77 7 Principle of Stationary Action Least Action 7 Jacobi s for of the least action principle 7 Hertz s principle of least curvature 7 Fermat s principle in geometrical optics of least time for light 7 Principle of maximal proper time in general relativity 94 Canonical Transformations 0 Passive 0 Active 10 Alternative Formulations Routhian N Routh s is most useful in engineering applications But the Routhian is a sterile hybrid of the Lagrangian and Hamiltonian pictures for developing various formalisms of classical mechanics the complete Hamiltonian formulation is more fruitful77 Various others Example Lagrangians Hamiltonians and Equations of Motion 1 1 Nonrelativistic charged particle in electromagnetic elds mass m charge q U qltIgt7AV Urrt q ltIgtrt7Art r L mvz 41 qu Lrrt mr2 7qltIgtrt qArtr H p 7 qA2 qltIgt Hrp t p 7 qAr 252 qltIgtrt o The Hamiltonian is not T U but it is the total energy WHY Some other situation When a Hamiltonian Equals Total Energy 0 The Lagrangian is the sum of functions each homogeneous in the generalized velocities of degree 0 1 and 2 respectively So H L2 7 L0 cf Eq 2 57 in Goldstein o The equations de ning the generalized coordinates don t depend on time explicitly so L2 T o The forces are derivable from a conservative potential V so L0 7V and T V E H T V E Hamiltonian when Lagrangian has Simple Form 0 L L0 L1 L2 1 Lqq tgt 7 L0q7t kTq quTq 7 T is a symmetric matrix and what about the positive de nite property of the kinetic energy see below 0 p Tq k 7 q 7 T 1p 7 k 7 T 1 normally exists by virtue of the positive de nite property of the kinetic energy h qTTq 7 L0 1 Hq7p7 75 5p 7 kTT 1p 7 k 7 Loq7 75 Something else 12 Ch 8 o Legendre Transformations and the Hamilton Equations of Motion When coming up with the Hamiltonian formulation we say 8Lqi7 i7t p1 qj but when using the Hamiltonian formulation we assume pj is independent of qj Can we recover this equation If so is it different in this situation because it s an equation of motion rather than a de nition lgnorable Coordinates and Conservation Theorems Routh s Procedure and Oscillations about Steady Motion The Hamiltonian Formulation of Relativistic Mechanics Derivation of Hamilton s Equations from a Variational Principle The Principle of Least Action 13 Conservation Theorems and Symmetry Properties 131 Solving the Equations of Motion A sustem of 71 degrees of freedom will have n differential eqns that are second order in time The solution of each eqn will require two integrations reulting in 271 constants of integration 7 Could be the intial conditions the n qj s and the n q fs at the initial time ti Canonical or Conjugate M to the generalized coordinate qj 1 1 A 4 8L 861739 If qj is not Cartesian then pj will not necessarily have the dimensions of a linear momentum When qj is Cartesian if the potential is velocity dependent then the generalized momentum will not be identical with the ususal mechanical momentum 29739 If a coordinate is ignorable the Lagrangian is independent of that coordinate then its conjugate momentum is conserved or contant This is more general than the Newtonian momentum conservation laws which require WN3 or 8N3 Eg for a charged particle in an electromagnetic eld pm l qu is conserved if I and A are independent of z qu is the electromagnetic linear momentum associated with the eld of the particle energy function i i 8L hq7q7t 2611f L 7 Q dh 7 8L dt 7 8t Euler s theorem h T V in some cases but not others conserved in some cases but not others dissipation function sometimes 14 Theorems 0 Liouville7s Theorem and Equation of classical statistical and Hamiltonian mechanics The Liouville equation describes the time evolution of phase space measure aka distribution function in physics 1 dtp 7 8m Z 7 0 i1 89 p7H at P 0 where A 7 3H 3 3H 3 L 3737 3737 i1 is the Liouvillian or Liouville operator 7 Related to symplectic topology ergodic theory Hamiltonian ow conservation Noether s Thm etc 7 The equation is valid for both equilibrium and nonequilibrium systems It is a fundamental equation of nonequilibrium statistical mechanics Generalized to collisional systems it is called the Boltzmann equation 7 The equation is integral to the proof of the uctuation theorem from which the second law of thermodynamics can be derived It is also the key component of the derivation of Green Kubo relations for linear transport coefficients such as shear viscosity thermal conductivity or electrical conductivity 7 Virtually any textbook on Hamiltonian mechanics advanced statistical mechanics or symplectic geometry will derive the Liouville theorem 7 Quantum analogues Lindblad equation for the density matrix p Ehrenfest theorem each missing the last piece 1 a 77 H tp mm l 1 1 dt P lpv Hl g T hmm PIan 1 LanP 2LnPLm 1 h39c39 d A ltAHgt lt8tAgt from http enwikipedia orgwikiLiouville stheorem Hamiltonian Why are the last pieces not included The sign difference follows from the assumption that the operator is stationary and the state is timedependent Helmholtz Theorem of classical mechanics This theorem should be distinguished from Helmholtz s theorem in vector calculus the fundamental theorem of vector calculus relating to Helmholtz decomposition and Helmholtz s theorems in uid mechanics all named after Hermann von Helmholtz o Generalized Helmholtz Theorem o 1873 Bertrand7s Theorem of central force7 two body motion The only central forces that result in closed orbits for all bound particles are the inverse square law and Hooke s law General characteristics a quantitative information 7 The degenerate character of orbits in a gravitational eld xes the form of the force law Degenerate means that the periods of oscillation of the body in two variables r and 0 are commensurate7 so that the orbit is closed It is not necessary to use the elliptic character of the orbits to arrive at the gravitational force law Later on we shall encounter other formulations of the relation between degeneracy and the nature of the potential77 0 Larmor7s Theorem To rst order in B7 the effect of a constant magnetic eld on a classical system is to superimpose on its normal motion a uniform precession with angular frequency A iqBQm the Larmor frequency Noether7s Theorem Has a Lagrangian formulation and a Hamiltonian formulation Relates symmetries and conservation laws ls this what I start with See Peskin amp Schroeder pg 17 Given that the action is invariant under a transformation 6 emigir or7 equivalently7 given that the Lagrangian density is invariant up to a four divergence under the transformation we have Mm 5 1 where 6 m 604739 8M7zgt S d4xr mama 0 6S d4z 59 6 gta Wig Mama 0 8M73 ba 6 E awe 0 6 i6aj9ja eiajgj Wi i l i a wi m Maj 91M We ag m laglgjh w awe 0 but since 6017 is arbitrary7 we have ii 3 W Much ia sa Mm ma i 9 W 8 0 Now we de ne the physical conserved current and conserved charge 1 Qk 15 16 7 4 7 3k ag zsa 6 ak 436755 W W E d3z mm iid g 9ka Central Forces Trajectories Orbits and Scattering Open Questions and Mysteries 17 Class on Mechanics and Field Theory 171 Books to Use c Goldstein Classical Mechanics o Landau and Lifshitz Mechanics Davison Soper Classical Field Theory Vl Arnold A Weinstein and K Vogtmann Mathematical Methods of Classical Mechanics Flanders Differential Forms with Applications to the Physical Sciences 0 MTW Gravitation has interesting things to say about EampM and perhaps Mechanics Interesting references 7 From Goldstein F Klein and A Sommerfeld Theorie des Krez39sels a monumental work on the theory of the top In Volume H many pages are given to a thorough demolishing of the popular or elementary derivations of gyroscopic precession The authors remark that it was the unsatisfactory nature of these derivations that led them to write the treatise 172 Class Topics Advanced Classical Mechanics and Classical Field Theory and their relation to all subtopics of physics from physical and mathematical perspectives o Lagrangian and Hamiltonian formalism 7 Lagrangian generalized coords and momenta 7 Hamiltonian canonical coords and momenta 7 Legendre transformations generating functions physics versus math generating functions 7 Canonical transformations 7 contact transformations symplectomorphisms Hamilton Jacobi eqns conserved quantities 7 Poisson Brackets Symplectic Manifolds Hamiltonian ow 7 and the relation to the many quantization schemes 0 Theorems in classical mechanics 7 Noether s Thm 7 Liouville s Thm the uctuation thm and proof for the second law of thermodynamics Ehrenfest thm Lindblad eqn 7 Helmholtz Thm 7 Stone von Neumann thm Speci c Problems 7 the Runge Lenz vector and its quantum counterpart 7 Small distance cuts off in classical theories eg viscosity speed of sound magnetic susceptibility and their relationship to cuts off in QFT 7 at atomic scales where continuum description no longer applies 7 see Peskin and Schroeder pg 266 o Continuum and uid mechanics o Dynamical systems differential equations bifurcation theory and Hamiltonian systems differential dynamics including hyperbolic theory and quasiperiodic dynamics ergodic theory low dimensional dynamics 7 Chaos and Ergodicity o Asymptotic methods Asymptotic Fundamental mathematics of asymptotic analysis asymptotic ex pansions of Fourier integrals method of stationary phase Watson lemma method of steepest descent uniform asymptotic expansions elementary perturbation problems 173 Core Topics for Class from Goldstein Ch 1 Elementary Principles Ch 2 Variational Principles and Lagrange s Eqns Ch 6 Small Oscillations Ch 8 Hamilton Eqns of Motion Ch 9 Canonical Transformations Ch 12 Lagrangians Hamiltonians for Fields Continuous Systems 174 Investigate Ch 10 Ch 11 o Landau and Lifshitz Mechanics 175 Take note of 0 pg ix 7 Manipulation of tensors in non Euclidean spaces in Chs 6 and 7 7 Complex Minkowski space 0 pg xi xii 7 the technique of action angle variables is needed for the older quantum mechanics 7 the Hamilton Jacobi eqn and the principle of least action provide the transition to wave mechanics 7 Poisson brackets and canonical transformations are invaluable in formulating the newer quantum mechanics 7 classical mechanics affords the student an opportunity to master many of the mathematical tech niques necessary for quantum mechanics While still working in terms of the familiar concepts of classical physics the discussion of central force motion includes the kinematics of scattering and the clasical solution of scattering problems by the technique of a uni ed mathematical treatment of rotations in terms of the eigen value problem for an orthogonal matrix it becomes possible to include at an early stage the difficult concepts of re ection operations and pseudotensor quantities and spinors can be introduced in connection with the properties of Cayley Klein parameters The Democratic Peace and Mass Slaughter Alternative Means of Establishing Political Power The Democratic Peace Stylized Facts Democracies seldom or never make war on one another Whether seldom or never is accurate depends on how one defines democracy Democracies often make war on dictatorships whether monarchic or authoritarian Dictatorships often go to war with each other and with democracies Mass Slaughter Stylized Facts Democracies seldom or never commit mass slaughter of populations living within the boundaries of their state They sometimes slaughter foreign populations during wars They sometimes also follow policies that lead to mass deaths among foreign populations even in time of peace Democracies sometimes commit a certain amount of political killing Eg lynchings Again both facts depend on how one defines democracy Dictatorships often commit mass slaughter Dictatorships invariably commit political killings Definitional Problems Mass Slaughter In 1838 the United States Army forced some fifteen thousand Cherokee to move from their homes in Georgia to what is now Oklahoma Fourthousand died en route on the Trail of Tears Resembles Armenian genocide conducted by Turks in 1915 who forced Armenians to relocate to a desert Whether US soldiers killed any of the Cherokee who died en route is not known to me Was this mass slaughter by a democracy Some men nominally of European descent were entitled to elect the House of Representatives state legislators who chose Senators and electors who chose the President and Vice President Men deemed of nonEuropean ancestry men lacking property and all women could not vote In 1838 the United States was a democracy only if democracy is defined as some people have the right to vote for some holders of ultimate political authority lf democracy is defined as all adults have the right to vote and all those exercising ultimate political authority are elected the Trail of Tears is mass slaughter not committed by a democracy Today the President continues to be elected by the states not the voters The Electoral College today usually makes no practical difference Definitional Problems Democratic Peace Georgia and Russia made war in August 2008 Both states are governed by presidents and legislatures elected by universal adult suffrage Is this war between democracies Russia denies freedoms of communication and association often thought necessary to make elections effective Nau labels Russia partially democratic in the map pp 542543 Even if this is war between democracies such wars remain unusual Asymmetry While definitional problems are serious the asymmetry between dictatorships and democracies both in whom they fight and whom they slaughter remain evident What accounts for this asymmetry Realism liberalism and the identity perspective can each generate accounts of the democratic peace Realism and Democratic Peace 1 Some realists including me think the democratic peace is just another name for American hegemony Full democracies before about 1960 were all too small to make war eg Scandinavian states Britain and France were democracies within Europe but exercised dictatorship over huge colonial populations in Asia and Africa Since 1949 all the states that became democracies after 1960 have belonged to the US alliance network either formally or tacitly Israel Sweden This view fails to answer two questions Why did democracies ally with each other in opposition to the Soviet dictatorship Why did the Soviet Union conquer Eastern Europe while the US merely pressured Western Europe to surrender its colonies Realism and Democratic Peace 2 David Lake at UCSD thinks that voters in democracy can reject taxes that dictators use to buy armed forces Since they must all disarm in peacetime democracies cannot fight each other Disarmament also compels democracies to ally with each other for protection against dictators By weakening democracies military forces disarmament makes them tempting targets for dictators to attack By letting their economies grow disarmament enables them to defeat the dictators in the resulting wars Liberals and Democratic Peace 1 Liberals think trade strengthens interest groups that can pressure democracies not to make war on each other But what about cartelized interests in undemocratic states like Wilhelmine Germany that pressure states to engage in policies that promote international antagonism Liberals and Democratic Peace 2 Democracy within the state requires negotiations and mutual respect for rights of adversaries Ifthese norms export to international negotiations democracies should be more able to negotiate in institutions that promote peace Failure of democracies to observe norms toward dictatorships does not bear on the question of export since observing norms is like disarming liberalism says each state should not if the other doesnt Identity and Democratic Peace Democracy sets an example that is a threat to dictatorships where the ruled might be inspired to demand democracy The example of democracy does not threaten other democracies Dictatorships do threaten other dictatorships Each dictatorship conquers a population inhabiting the territory controlled by that dictatorship Each dictatorship might want to conquer the population inhabiting territories that its forces can reach Consequently warfare will pit dictatorships against other dictatorships and against democracies but will not pit democracies against other democracies War might arise between democracies in special cases like Russia against Georgia where control of a disputed territory has implications for the ability of each incumbent to retain office Neither state will try to conquer the other Mass Slaughter Mass slaughter is often called genocide Definition of genocide Choices about humanitarian intervention Rwanda Kosovo Darfur Mass slaughter as a pattern why dictators do it Definition of Genocide In the present Convention genocide means any of the following acts committed with intent to destroy in whole or in part a national ethnical racial or religious group as such a Killing members ofthe group b Causing serious bodily or mental harm to members of the group c Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part d Imposing measures intended to prevent births within the group e Forcibly transferring children of the group to another group Article llConvention on the Prevention and Punishment of the Crime of GenOCIde adopted by UN GA Dec1948 Security Council Resolution 1674 Reaf rms the responsibility to protect populations from genocide war crimes ethnic cleansing and crimes against humanity Adopted 28 April 2006 Responsibility to protect R2P Trivialization Note mass slaughters that are not genocide are also covered under SC Res 1674 Enforcement of the Prohibition against Genocide Any Contracting Party may call upon the competent organs of the United Nations to take such action under the Charter of the United Nations as they consider appropriate for the prevention and suppression of acts of genocide or any of the other acts enumerated in Article Article 8 of the Genocide Convention Competent organ is the Security Council Because the Security Council does the enforcing the enforcement Will be vetoed if the state committing genOCIde is a permanent member of the Security Council has the support of a permanent member of the SC has the support of eight nonpermanent members Inaction in Rwanda Battles won by forces of the Rwandan Patriotic Front invading from neighboring Uganda compelled Rwandan President Habyarimana to accept a UNbrokered peace settlement in 1993 He ordered weapons to be distributed to Rwandan Hutu in preparation for an attack on Tutsi When Habyarimana was assassinated in 1994 by unknown assailants perhaps own followers Hutu recipients of arms began slaughtering Tutsi as well as Hutu described as disloyal They killed approximately one out of nine Rwandans French Belgian and Italian troops rescued Europeans who were not threatened and then stood aside while the slaughter continued Meanings Precolonial rulers in the region now called Rwanda called themselves watutSI Wa is the local pronunciation of a common Bantu prefixual particle meaning kind of person Ruled were called wahutu Watutsi and wahutu are political subdivisions synonymous With rulers and ruled not ethnic groups They speak the same language KinyanNanda the local variant of the Bantu language continuum that prevails from west to south Africa Impact of Colonialism Belgian colonialists seeking policemen taught French to both Tutsi and Hutu 1959 Frencheducated Hutus led an uprising that overthrew the Tutsi king slaughtered thousands of his supporters and drove Tutsi aristocrats into exile Tutsi exiles and Hutu opponents of the rebels formed the Rwandan Patriotic Front In 1990 RPF counterattacked Is This Tribal Warfare Are there any tribes in Africa at all Tribe is a way of calling people uncivilized Both civilization and tribe originate in ancient Rome Civilization derives from civiz as which Rome s rulers coined to translate a Greek word that has given us politics and meant the organization of a city Tribus was the word for each of the three subdivisions of the original Roman kingdom it is a contraction of compound of words meaning three and be a threebe Europeans arriving by ship in west and central Africa found cities that were not organized according to the Greek model with which Europeans were familiar Since African cities did not correspond to the European model the Europeans considered Africa uncivilized Since tribus was the only available alternative to civitas Africans not possessed of civilization must therefore belong to tribes People in Africa speak languages and form communities but these communities are not tribes Political Strategy Habyarimana and his supporters were losing to the RPF because their plunder of the country had alienated today s descendants of both historical Hutu and historical Tutsi They tried to win back young Hutu by frightening them with threat of renewed Tutsi domination Awareness of precolonial conditions was strong enough that many young people began to think of themselves both as Hutu and as endangered by the Tutsi Tutsi predominance in RPF made this danger seem real to Hutu Kosovo Yugoslavia formed in 1919 under the rule of the King of Serbia Communist takeover in 1945 was led by a Croat named Tito heading an organization mainly composed of Serbs from Bosnia Death of Tito led to assertion of autonomy by communists ruling territories with mainly Slavicspeaking populations A fragile unity was maintained by common fear of a Soviet takeover Disappearance of Soviet threat as USSR began to disintegrate in summer 1991 enabled local authorities to declare independence in Slovenia and Croatia declarations soon followed in Bosnia and Macedonia Yugoslavia WW Language Difference Most people in the former Yugoslavia speak languages belonging to a South Slavic continuum that also includes Bulgarian The languages spoken in Slovenia and Macedonia at the northwestern and southeastern ends of the former Yugoslavia are sufficiently distinctive to count as separate languages The same form of South Slavic is spoken in Serbia Croatia and Bosnia of course with regional variation Officially Serbian is written in a Cyrillic alphabet and Croatian in a Latin alphabet This difference corresponds to the historical Orthodoxy of Serbia and Catholicism of Croatia Croatian separatists have gone to great lengths to separate Croatian from Serbian usage Kruh compare circle meaning round became Croatian for bread because both Serbs and Croats bake bread in round loaves Kheb meaning loaf Old English haf became Serbian for bread because the round thing that both bake is a loaf Responsetolndependence Serbian commanders of the Yugoslav Army tried but failed to intimidate the Slovenes and Croats They armed members of Serbian majority of Krajina who drove out Croats while creating the Republic of Serbian Krajina They armed Bosnian Serbs who drove Bosniaks out of certain Bosnian cities while creating the Serbian Republic Bosniak and Serb Bosnians are divided into three groups Serbs descended from families that were Orthodox Christians Croats descended from families that were Catholics Bosniaks descended from Slavic families that converted to Islam during Ottoman rule ie descendants of the ruling group in Ottoman Bosnia All three speak SerboCroatian Under communism both kinds of Christianity and Islam were officially discouraged Christianity has revived some since 1991 Serbian Politics When Yugoslavia was rejected by local nationalists in the other regions the Yugoslav Communist leader Milosevic feared that Serbian nationalists would overthrow him Wanting to seem less like a Communist Milosevic took two steps a he introduced elections that b he won by trying to seem like a Serbian nationalist ie anti Communist presenting himself as the defender of Serbs in Krajina and Bosnia Armed by order of Milosevic Krajina Serbs began ethnic cleansing in Krajina as did Bosnian Serbs in Bosnia Srebenica 1995 Srebenica was a largely Bosniak town surrounded by Serbheld territory Bosniaks whose ancestors were rulers inhabited cities Serbs whose ancestors were peasants inhabited surrounding vmages UN declared Srebenica a safe haven for Bosniaks and sent 400 Dutch paratroopers to guard them In July 1995 Serbs entered the town expelled the women children and aged and killed 8312 youngish men They also machinegunned the convoys of women 1children and aged leaving the city although killing many ewer US Response US had sent military officers to train the army of newly independent Croatia Now the US ambassador approved the Croatian plan to use the army for an offensive to recapture Krajina US aircraft probably provided air support to the offensive Croatian soldiers killed many Serb civilians to encourage the other 200000 Krajina Serbs to heed warnings from Serbia to flee US officers stood by helplessly although they could have sacrificed themselves beside the Serb victims R2P Effects on Milosevic Milosevic now agreed to negotiate a settlement in Bosnia Deprived of his opportunity to stand up for Serbs in Krajina and Bosnia he now needed a new focus of attention for his defense of Serbs Kosovo became the locale where he could do that Kosovo Kosovo is located south of the Serbian capital Beograd Belgrade in English Inhabitants are almost all Albanian speakers whose forebears converted to Islam under the Ottoman called Kosovars Albanian is lndoEuropean but not Slavic To prove they were not Serbs Serbian Communists had opened schools that taught in Albanian and had encouraged Albanian literature and broadcasting To prove they were not Communists the Serbian Communist Milosevic and his followers cutback or closed schools publishers and broadcasts A few Kosovars formed the Kosovo Liberation Army and killed some local Serbs Refugee Crisis In summer 1998 as opponents in Serbia demonstrated against Milosevic to protest his ineffectiveness in protecting Serbs in Krajina and Bosnia he ordered the Yugoslav Army to crack down on the KLA by driving its supporters from their homes This move quieted the demonstrations in Beograd and Milosevic negotiated an agreement with NATO allowing the refugees to go home In January 1999 Serbian forces not necessarily the Army slaughtered Kosovars in one village NATO officers visited the village and reported the atrocity NATO responded by beginning to bomb Serbian targets on March 24 1999 Expulsion of Kosovars NATO s bombing proved it would retaliate against but not prevent ethnic cleansing in Kosovo Milosevic therefore felt free to order the expulsion of Kosovars From a population numbering about 16 million 800000 were counted in neighboring countries Albania Macedonia Bosnia and autonomous Yugoslav Montenegro Up to 500000 more were refugees inside Kosovo although this number is not well documented In other words more than three quarters of Kosovars were driven from their homes in April and May when Europe is still cold and rainy causing many to die of exhaustion and disease US Response Pressed by British Prime Minister Tony Blair President 1Ellinton finally agreed to invade Kosovo with ground orces Threat of invasion was communicated to Milosevic by the former Russian chair of government and the former Finnish President speaking for the EU Facing a ground campaign that would destroy the Yugoslav Army which had suffered little damage in the air campaign Yugoslav military commanders forced Milosevic to agree that a NATO force would enter Kosovo unopposed to supervise the return of the Kosovars to their homes All Serbian forces were withdrawn both military and irregular Darfur Darfur is in western Sudan a country strung out along the Nile river in northeast Africa south of Egypt Darfur population consists almost entirely of Muslims Sudan is ruled from Khartoum by President Omar alBashir a nominal Muslim South Sudan Insurgency AlBashir was a soldier who commanded the fight against an insurgency in south Sudan that nominally ended in 1996 in a negotiated settlement The opponents in south Sudan were animists or Christians Unable to defeat the rebels AlBashir staged a military coup in Khartoum in 1989 and organized an election approving him as President Nominal Islam Having failed to defeat the Christian and animist insurgents despite extensive massacres of civilians aIBashir needed to restore his prestige He sought an alliance with a radical Islamist supposed to have connections with Osama bin Laden AIBashir imposed Islamic law in Sudan Darfuri Insurgency In 2003 oppression associated with introduction of Islamic law caused Muslims in Darfur to begin raiding posts of the Sudanese Army Failure of alBashir s campaign in south Sudan together with dramatic successes of Darfuri rebel raids apparently convinced him to change tactics Janjaweed Rather than trying to use the army to defeat the rebels alBashir formed a local militia or drew upon an existing one Called thejanjaweed this militia engaged in attacks on villagers said to support the rebels Janjaweed is recruited primarily among Darfuri Muslims who make their living by herding cattle and camels The villagers who have been attacked are mainly sedentary farmers raising grain Farmers and Herders Farm populations occupy land that varies in fertility Location near streams encourages fertility Local variation in rainfall varies fertility Farmers located on fertile land grow crops increase their population and gradually push into less fertile areas Farmers living in the least fertile areas cannot grow crops sufficient to feed their families and must turn to other activities These farmers become herders In Darfur near the farming areas herders of cattle In Darfur far from the farming areas herders of camels 1lcletrflters are farmers unlucky enough to occupy land of marginal e I I y Since all of Darfur is an area of marginal fertility often the local cattle herders are descendants of lucky farmers Skills Herders develop different skills than farmers Herders learn to ride horses which to farmers are either draft animals or replaced by oxen Herders learn to use knives in cutting up hides and in gelding Herders learn to slaughter cattle Conflict Farmers remain in the same place and must prevent movement of animals that will eat or trample their crops Herders must move in a seasonal cycle as their herds exhaust vegetation in a particular area and as rainfall that supports grasses shifts As farming areas expand herders migration routes are blocked Consequently herdsmen and farmers are invariably in conflict eg range wars in American West Ethnicity Since herders are farmers who tried to farm marginal land there are no physiological differences between farmers and herders in Darfur However differences in ways of life cause herders and farmers to infer different identities Families are economic units Herder parents prefer their children to find spouses with herding skills Farmer parents prefer their children to find spouses with farming skills From parental expressions of preference the children infer identities stressing the difference between herder and farmer group labels or ethnicity Acquisition of group labels produces linguistic differentiation Darfuri nomads tend to speak Arabic especially among the cattleherding Baqqara of the south Darfuri farmers tend to speak Fur a NiloSaharan language but being Muslim often have Arabic names Darfur is Arabic home of the Fur Physiologically they are indistinguishable Language preference distinguishes Arabs from Fur Connection to alBashir AlBashir provokes conflict in Darfur because of his political vulnerability Having failed in south Sudan to defeat Christians and animists alBashir needs political support He musters political support by trading on his reputation for fighting Christians and animists Since the enemy of my enemy is my friend as an antiChristian and antianimist alBashir seems like a friend to Muslims Stereotypes Stereotypically a Muslim is an Arab This stereotype is false Islam specifically rejects racial identity as a basis for religious faith and is open to all However Qur an is written in Arabic the language of Arabs Stereotypical Arab is a herder on horseback AlBashir s allies in Darfur are the Muslim herders who conform more closely to the Arab stereotype than do the Muslim farmers Discrimination AlBashir s favoritism toward the herders was said by the rebels to motivate their attacks on the army Rebels engage in recruiting among the farmers This claim simply means that the rebels share alBashir s view that his false self representation as an Arab means that his natural allies are the herders Herders come to view themselves as potential victims of rebel success Climate Change Increasing desertification in Sudan sharpens conflict over land usage between herders and farmers As land turns to desert herders can survive only by encroaching on land previously used in farming As climate dries land increasingly becomes marginal for farming and herder populations grow Desertification may be attributable in part to pollution from Europe Genocidal Consequences Given the rebel attacks alBashir responded by arming the janjaweed and ordering them to attack not the armed and dangerous rebels but the defenseless farmers Herder killing skills knifework skills and horseback mobility make the janjaweed efficient agents of mass slaughter Perhaps 200000 to 500000 people have been killed Neither religious difference which doesn t exist nor ethnic difference which doesn t exist has any bearing Religious and ethnic difference are our categories for misconceiving the violence done by people who do not fit ourways of conceiving the world What has happened in Darfur has been mass slaughter not genocide Roots of Mass Slaughter In each case mass slaughter is a dictator s gamble to win loyalties against domestic rivals by imagining a greater threat The dictator exploits awareness of suffering by past generations blamed on contemporaries who have nothing to do with the past It involves sharpening ethnic divides that have previously been blurred or insignificant Even genocide is not the obliteration of a people It is the slaughter of numerous persons International Response Why act in Kosovo but not in Rwanda Darfur or Krajina Definitional issues International issues Matters of Definition Genocide is defined to fit European conceptions of ethnicity that are irrelevant to Rwanda or Darfur Tribalism and Islam are categories used to describe human beings as other and therefore not deserving of efforts to protect them Definition of genocide as done by a whole people who are a collective perpetrator is another means to deny that victims need protection A perpetrator is another kind of other If Krajina Serbs are a collective perpetrator their need for protection can be ignored they do not need to be defended from Croatians Rather than worrying about whether the definition of genocide fits one could worry about people under attack International Considerations Having negotiated an intergovernmental agreement to develop Sudanese oil reserves China has protected alBashir against accusations of genocide in the Security Council China has also supplied light weapons used to kill farmers in Darfur Recently China has tried to persuade alBashir to show restraint in Darfur Troops from African countries under the auspices of the African Union have been sent to police a truce between the rebels and the government African Union opposes European or American intervention in Africa Europeans and Americans promise financial aid to African states providing troops but fail to perform on the promises The troops lack any mandate to protect civilians against the janjaweed against government troops or against the rebels Since October 2007 the African troops in Darfur have been resubordinated to a delegation combining a representative of the African Union with a representative of the United Nations The African troops include Rwandans operating under orders of Paul Kagame the Tutsi leader accused by France of having arranged the assassination ofthe Hutu leader Habariyamana whose supporters then staged the Rwandan slaughter Effective military intervention would require US transport aircraft and probably troops but US ground capabilities are fully committed in Iraq and Afghanistan The Iraq Connection If one supports military action to rescue people threatened with mass slaughter why oppose the war in Haq Despite his secular regime Saddam Hussein ruled with support from Arab families of Sunni Muslim heritage They accepted Saddam s rule because he ordered mass slaughters of Shi a Muslims and Kurds Kurds are speakers of an lndoEuropean language related to Persian in contrast to the Arabic spoken by Iraqi Arabs Isn t this genocide 227EI6 eatne NonCovalent Molecular Forces How does tnts reactton occur H20 ttqutd gt H20 gas 7 BONDS u0 0 0 I Add energy 9 H H H10 gas tnbteeutes ate veryfarapan H10 ttqute bundtng between tnbteeutes Use heat to add energy t e bott Water to turn H20 to gas BOHH VQ Qotrtt o How rnucn energy do you need to cnange a substance trorn ttqutd to gas state 0 Water s botttng potnt ts ngn for a rnotecute wetgntng onty18amu Nhy Data Bothrtg Potrtt Nact 1413 C BrCt 5 7C H20 100 C Ar 7186K I Ionic NaCl tstt Na Cl or Nacl397 Covatertt torttc AEN cnange tn etectrortegattvtty1 6 39 AEN 3 0 CH O e9 0 9 Sodtum 21 9 ionic tontc gt strong bond 0 Tne negattve ton otcntortne ts etectrorstattcatty attracted to tne postttve cnarge on sodturn o 188 kcatmot to breakthe bond Huge number but typtcat tortontc corn ounds 0 Therefore NaCI s oiling point is high 14 3 no because tt takes a tot ofertergy tn tne torrn otneat tn tnts case to break tne bonds and turn tne rnotecute tnto tts gas state DipoleDipole BrCl u ts tt Br Cl or Brcl39 39 AEN 3 0 CH O e9 2 8 Bromme 0 2 9 covalent 39 9 Shartt tg of etectt orts not CompeIey even and covatent 50 BrCt t5 best descrtbed as golar covalent EJ EGTRGSTATIG Electrostatic Attraction opposite cnarges tnat attract ponds and nave perrnanent dipoies dipoieadipoie ponding BRcl quotmareCL Strengtn of attraction foHovvs Couiornp s Lavv force of eiectrostatic V V V attraction is proportionai to magnitude ofme difference between cnarges L Puiai Cavaient tnan bromine Tnis causes a snirt in eiectron densitv towards chiorine resuiting in a siignt negative dipoie densitv o attracti gt Dipoledipole attraction accounts for Bros 5 ac poiiing point in ionic case force of attraction is stronger and ponds are narder to break cornpared to dipoiea dipoie L23 attraction Bond dipoie depends on gt AEN gt pond iengtn Exampies Brici AEN o 2 HaciHAEN 04 bond is sndrier I Hydrogen Bonding H20 0 ionicMEN35ovvgene2invdrogenizi o gt Borderiine vaiue but rnore cuvaennhan ionic 5 5 quotG39 mdrogeri bonding between tne negative dipoie of oxygen andtne H H Ill 0 positive dipoie ofme nvdrogen of a differeri rnoiecuie Tnis reaction is very important and very Widespread 13 I 39 Witn attacned to a very eiectronegative atorn and anotner acceptor atorn Witn a verv negative dipoie e a negativeiv cnarged atorn or a neutrai oxygen or nitrogen Witn ione pairs Van der Waals Argon Ar has a ppTTTng puTnL there mus L be same tpree aetTng between rndTeedTes Ionic NUT There Ts nu thterenee Tn ETectrunEgatTthy between Wu arguns d 39 ole dipole NET NET punds nu dTppTes d nded drpgenT Hbo 7 Nu y Then what P quotll What tpree Ts thdTng these atdrns at aTT7 There s a ppTTTng peTTnt abuve absuTutE zerd sd there must be same tpree P ETeetrdns ean resppnd ddTe y and Tnqu tasterthan ndeTeT TWp uquot argun atdrns nurmaHy dun We eaeh pther peeadse they pdth have thT sheTTs e ETeetrdns ean shTtt td pne sTde Nuvvthey We eaeh ptherT Amamve I forceTsprEsEnL Weak and ternpdrary Tt Ts TTtTeetTng and 2 a cuntact fume TWEI alums must be ETDSE tugether Tn urder El dTStDn theTr eTeetrpn drum and resth Tn thTs attraEITvE tpree 7 The attractTvE tpree Ts eaTTed Lundun depersTeTn a k a Van derWaalsquot tdrees d What dd yer need turthTstpree td pe present7 ETeetrdns an eTeetrpn erdd That sALL yer needT Theretpre EverymuTecuTE Ts TntTdeneed bythTsfurce The Extenttu theh the tpree Ts present depends dn hdweasy Tt Ts td Tnqu detprt the eTeetrpn Tuuds Te polariza ility Van der WaaTs strength d EasTTy deteTrted Tuuds are eaTTed soft thtTethtd detprt Tuuds are eaTTed hard Atprn EpTTTng RdTnt ac Trends He r 268 Harder SmaHes L alum wa atprnTe weTght NE 7 24B T Ar V THE T Kr r T52 T X2 7 Tm v Rn r B2 sptter Largest alum thhest atprnTe weTght Why Ts Tt easTertu deturt Radun Rn Tt s Targer d Tn Rm Tts vaTEnce eTeetrdns are turther apart peeadse Tt Ts a wager atprn Theretpre the ndeTeds has Tess epntrpT uverthe eTeetrdns and Rn Ts so er Tren atomic weight d GeneraT prdad ruTET but weTght Ts nut Examy a true trend m Boiling point 36 C Sausageshaped more surface area Boiling point 30 0C Boiling point 95 0C Sphere shape less surface area Trend boiling point decreases with more branches and less surface area This means that Van derWaals forces are strongerwhen the molecule has greater surface area Van der Waals is dependent on o Polarizability hardsofi 0 Surface area the more SA stronger Van der Waals force P PP N Ionic strength hundreds of kcallmol Covalent bonds 30160 kcallmol Dipoledipole tens of kcallmol b nd39n 5 kcalmol Van derWaals 01 kcallmol other noncovalent force l A Ion dipole A bond dipole interacts with an ion i A negative ion anion is attracted to a positive dipole ofanother molecule ii A positive ion cation attracts the negative dipole ofanother molecule Examprer ANIGNC39MIIIIIH 83 5 GL IIIIIIIH 0H 5 639 Exam H cATIaNCOIIIIIIII NAG quotIquot D H I B Ion pl r e the name band m benzene pruduce pr ahath uuds tnat attract atmns ex ELEcWoN amen HGGH 9 121 I C Pi stacking mstuned We rnvan uervvaars rurces and resurt m a Weak attractmn re Wu benzene nngs I Wnen tne pr erectrun crew at une benzene nng becumEs attracted tutnat er anuther rts erectruns snrrt awayfrum tne utnerrnurecure negauve cnarges reper eacn utner wnrcn subsequenuy attracts the erectruns urtne secund benzene wnrcn snrrttuwarus tne pusmve mpcne ans resurts m aposmve mpge un une srue urtne pr erectmn uud Ex two benzenes Tne erectmns urtne nrstnenzene snrrt awayfrum tne s ans creates a new mpu e wnrcn attracts tne erectrun 6 Stand benzene ctuuu 9r 0 r 2 939 we Discussion Problems Practice with Features 1 What feature or features differentiates the sound in each of the following pairs State Which member of the pair has the value Symbols are IPA Example p b bis V0iced a w A i h q x x b d D j p t r K 1 c j q k Em s k kw d u y 1 kj k t W 9 e i y m u w f i 1 n TeE g 6 Z 0 V 5 h l 1 p m b a high shared syllabic back r0und b round shared sy11abic low back c round shared syllabic c0ns0nantal bac1dfr0nt d back shared syllabic high r0und e round shared syllabic high ibackJrfront f tense shared syllabic high bac1dfr0nt g strident shared CORONAL anteri0r c0ntinuant h consonantaL lateral shared CORONAL s0n0rant nasal spr7g1 constrigl shared LABIAL CORONAL DORSAL LABIALCORONAL shared DORSAL c0ntinuant V0ice anteri0r distributed shared CORONAL c0ntinuant delire1 V0ice front shared DORSAL high c0ntinuant V0ice syllabic shared c0ns0nantal back high r0und strident shared CORONAL anteri0r c0ntinuant de17rel V0ice labiodentalstrident shared LABIAL s0n0rant c0ntinuant voice nasal shared LABIAL c0ntinuant V0ice high shared DORSAL fr0nt s0n0rant c0ntinuant 10W shared DORSAL s0n0rant high c0ntinuant V0ice1 round shared DORSAL high c0ntinuant V0ice sonorant shared LABIAL r0und c0ntinuant V0ice 2 rweevpparwr 1 The shared feature DORSAL is according to the features in the Hayes text I suggest in my lecture notes that pharyngeals should not be automatically classified DORSAL because the pharynx and tongue dorsurn can be independently controlled Pharyngeal consonanm can certainly be pronounced with no raising of the tongue dorsurn and one could in principle differentiate plain vs pharyngealized velars Practice with features 2 2 For each segment if you change the value of the feature indicated what new segment will be derived Old segment Feature to be changed a j syllabic b 0 high c 5 voice d s strident e e back f 0 back g u round h X back a U syllabic i syllabic 9 syllabic shared consonantal high back round b 0 high 11 high 9 thigh shared syllab1c back low round c d5 voice E voice 9 voice shared CORONAL anterior continuant delayed release d s strident 6 strident 9 strident shared CORONAL anterior continuant voice e e back if back 9 back shared syllabic high low round f 0 back 0 back 9 back shared syllabic high low round g u round m round 9 round shared syllabic high back h x back x 3123 a shared DORSAL sonorant continuant voice The features high and back must both be changed assuming that we incorporate a distinction between neutral velars such as X and back velars such as X If there is only a distinction between velars such as X and uvulars such as x then a change of back 9 back could automatically force a change high 9 high 2 The sounds w 3quotquot also constrast in consonantaL approximant but these features automatically follow from the specification of isonorant plus the other features I would suggest that the soun s s ould also contrast in LABTAL ie w is LABTAL and 3quotquot is LABIAL The redundant association of LABIAL with round is clearly incorrect These gestures are independent A problem with the feature system however is that it gives no other way to make the clear articulatory association between LABIAL and round Practice with features 3 3 Formulate the following statements in terms of the features that we are learning in class Assume that the segments here come from a total inventory of phonemes something like that of English a u U o o are deleted in wordfinal position after p b m modeled on Telugu sy11abic LABIAL iround 9 0 continuant 41mm b i 1 e 8 2e become y Y 0 06 after w AA modeled onarule of Yana syllabic 9 LABIAL isyllabic front round round 7 C n t d become I k g before k g place assimilation found in many languages CORONAL CORONAL DORSAL continuant 9 SAL 7 continuant anterior low nasal The input consonants have to be specified by the tongue blade feature anterior to keep them distinct from alveopalatals When the active articulator is DORSAL this feature becomes irrelvant since the blade of the tongue plays no role and hence need not be mentioned In a fuller theory of features we might want to have an automatic convention that zeros out features when a higher order feature such as DORSAL or LABIAL changes 3 1 L 53 1 become s LE CE when s 2 follow later in the same word modeled on Navajo strident X anterior CORONAL 9 anterior strident distributed 7 Note The left side does not need fanterior if the rule is assumed to convert sz vacuously to s z e 9 6 become V in all contexts found in the speech ofmany small children LABIAL labiodental sonorant 7CORONAL continuant 9 0 strident amenor 0distributed 0strident The feature CORONAL is not needed on the left since the only strident fricatives are 6 6 As noted for 3 when CORONAL changes to CORONAL the tongue blade features become irrelevant and hence are zeroed out Practice with features 4 f g Pquot f 6 s j become v 6 z 3 when surrounded by vowels modeled on Italian sonorant continuant 9 V0ice Syllabic 7 Syllabicl 8 1 become e i before another vowel modeled on British English syllabic front flow 9 tense 7 syllabic As in 4 we do not need to mention tense on the left side of the arrow Presumably the tense vowels e i are unaffected by the rule We simply let the rule apply to them vacuously S Z become E after n English dialecm dance lens 8 has two possibilities a We convert a stop into an affricatethis is the first version below and the one implied in the problem by the tie over the two symbols b We insert a stop between a nasal and a following fricative implying that the result is a sequence of nts and ndz anterior 1 strident continuant CORONAL anterior strident ocvoice 9 continuant n 7 anterior ii 0 9 n7 strident ocvoice 1 1 w j become 1 g u i in word final position after a consonant modeled on Rus s ian sonorant nasal 9 syllab1c syllab1c 7 W0rd isyllabic not needed on the left side of the arrow the rule can apply harmlessly to sounds that are already syllabic Practice with features 5 j W t d become r if preceded by a vowel or 1 and followed by a vowel To make the rule simple you may assume that there are no underlying forms in which td are preceded by W AA j h actual rule of American English sonorant continuant CORONAL dela ed release continuant 9 y consonantal syllabic anterior apprommam 7 ap voice The output looks incredibly messy We could clean it up if we made use of certain implications inherent in our feature system any ap is also continuant and approximant and any approximant is sonorant delayed release and voice By specifiying ap we should thus get continuan1 approximant sonorant delayed release and voice for free p t become w r respectively between vowels but remain before a consonant or word final modeled on an alternation in Korean 39cominuam a roximant DORSAL 9 f1 syllabic isyllabic V0ice v01ce The change to approximant carries with it the features continuant sonorant and since the range of approXimant segments at a particular place of articulation will be limited probably also consonantal for the labial glide and tap for the coronal Practice with features 6 5 The sonority hierarchy Spanish word initial consonant sequences The data table below gives words illustrating every possible sequence of consonants that can come at the beginning of a word in Spanish Examples are in Spanish orthography which gives a pretty good representation of the phonetics Note the following 0 i j before a vowel as in esta fjesta festival 0 u w before a vowel as in nuevo nwe o ne 0 c k before a back vowel or consonant as in cuatro kwatro four qu k before a front vowel or glide j as in quien kjen who 0 z s as in brazo braso arrn cousin cuatro four seven dream festival fire crooked death snow new hare tuerca wheel No words in Spanish begin with the following consonant sequences a gj such as gjera b tl dl such as tlara c sonorant sonorant such as rpara mdara rsara fricative stop such as Apara ara e lr nasal such as lmara rnara f jw liquid such as jlara wrara g stop fricative e g psara kfara h sonorant nasal such as pmara dnara snara fmara i nasal liquid such as mlara nrara j s l r such as slara srara A Q v 3 This is the only example in my dictionary of ch EV plus a consonant at the beginning of a word The absence of chC clusters is not a phonological restriction per se Almost all words beginning in ch are borrowings so the types of environments where ch appears is related to the source languages not internal Spanish features Practice with features 7 ANALYSIS 1 Provide A SINGLE PHONOI OGICAI GFNFRAll ATlON that is a correct characterization of all the existing word initial clusters in Spanish With reference to the SONORITY HIERARCHY all the cluster sequences have the characteri zation LESS SONOROUS gt MORE SONOROUS This is called the SONORITY SEQUENCING PRINCIPLE whereby the world s languages prefer syllables that build in sonority toward the vowel which is the peak of the syllable 2 a Absence of gj This is due to the history of the Romance languages Latin g had turned into j or disappeared completely before vowels even before the Romance languages had split up and since the source of Spanish j in Cj clusters is usually a front vowel there was no source for gj For example Latin gamma gt Spanish yema gem Latin gelare gt Spanish helar elar to freeze 3 b Absence of tl dl Clusters like pl stop l on the one hand and tr alveolar stop liquid on the other hand suggest that the absence of tl dl is unrelated to SONORITY SEQUENCING What other explanation might there be for this gap Note that English also lacks tl dl though pl tr and even sl are fine The explanation seems to be an articulatory conflict between the tongue position required for the alveolar stop and the alveolar placement of the tongue for 1 One would think that it would be easy enough to make an alveolar closure then make a lateral release for the l which is exactly what most speakers do in a word like bottle 39batll Nonetheless the gesture seems to be avoided if a vowel follows 4 0 D Provide A SINGLE PHONOLOGICAL GENERALIZATION that is a correct characteriza tion of all the NON existing word initial clusters listed in c f With reference to the SONORITY HIERARCHY all the cluster sequences have the characteri zation MORE SONOROUS gt LESS SONOROUS that is they all run counter to the SONORITY SEQUENCING PRINCIPLE 5 g i What might be an explanation for the impermissibility of the clusters in g i In each case the two classes of consonants are contiguous to each other in the sonority hierarchy in the case of h this means taking all the obstruents stops and fricatives as a class contigous to the nasals The classes seem to be too close in sonority to comfortably adhere to the SONORITY SEQUENCING PRINCIPLE 6 j Why might the absence of sl sr clusters seem strange How might we account for this Fricativeliquid adheres to the SONORITY SEQUENCING PRINCIPLE and in fact exists in at ower and frt o cold One proposal has been that we must distinguish degrees of sonority within categories In the present case we may want to say that within the fricative category s is more sonorous than f and hence is too close to liquids in sonority as in g i It is however not clear with more sonorous means in this case Practice with features 8 5 BOLE Account for the different pronunciations of the glide in the Bole data with a rule using a variable The Bole vowel system is i e u o a Bole is atone language and also has distinctive vowel length but marking of these features is omitted here 1 qine whoever soandso 2 kod39uqi handle 3 qej i handle 4 zeqe ladder 5 wunti nose 6 bowu father 7 wosi fire 8 awo stomach 9 waji fighting 10 sawa a type of pot syllabic consonantal 9 ocfrom 7 Eyllablc roun 0L ront The rule could also have used ocback but by using front we avoid the issue of whether central vowels have to be called back Also w rather than u seems to be the elsewhere allophone Using the feature front thus makes the rule look like an assimilation of an otherwise back sound to front 6 More practice with variables Account for the following vowel altemants in suffixes using a single rule Assume that the vowels here are all the vowels in the language Assume further that the vowels i A are classified back front modeled on Turkish In suffixes only i e y o u o i A after roots whose last vowel is i e y o u o i A That is one could have words like bit ken ler gi fm ji vez del pik tAm but not bit kan lor gi fun ji voz dAl Put another way if the language were to have a plural suf x gV it would have four forms depending on the root to which it was suffixed jut g0 birds sAm gA bees tib ge boys zyz gta basketballs Discourse Dictators and Democrats Lecture 11 Russian Discursive Distinctiveness through Import of Church Slavic Topics Political institutions in Russia to 1917 Common origins of Russian and English Diversification of East and South Slavic Use of imports to distinguish discourse of rule from Russian Trade and Rule in Russia Navigable rivers owing generally either west to east or north to south could be used to transport goods cheaply by boat b twe northern Europe via the Baltic Sea and Constantinople via the Black Sea Early Russian rulers built for i cations eg the Kremlin in Moscow beside the rivers 39om which they taxed the riverine commerce 7 Moderri Kremlin was rebuilt uridertne supervision of ari taliari architect brought iri later owns conducting the river trade arose around the forti cations and were fed and clothed by con scating crops from surrounding villages Political Institutions Russian towns were ruied by a singie extended famiiy tnat rotated maie descendants as cniefs of tne fortification controiiing each town 7 The senior cousin in tnisfamiiy controiied tne town of Kyiv nowcapitai of Ukraine 7 otnercousi scended to fortifications controiiing towns of increasing size or importance astne members of tne dynasty controiiing tnose townsfaiied to produce sons Despite norninai oyeriordsnip by tne ruier of Kyiv in fact cousins frequentiy fougnt eacn other sometimes witn outsiders as aiiies e In 1198 Andrei Bogoiiupswi God s tavurite W ruier of tne compined svladirnircS uzdal ied a sack of Kyiv and instaiied nisyounger ed Kyiv tnen maybe tne iargest city in Europe 7 In 1328 ruier of Lithuania captured tne rebuilt Kyiv wnicn remained Lithuanian later Roiisn territoryfortnree centuries i a Language Russian is an eastern variety of Slavic languages Spoken to the east of Finland the Baltic states Germany Austria d 7 Hungarian Magyar and Romanian are exceptions 7 Many otnerianguages are spoken iri Russia Slavic languages derive from the same source as English Imported Political Discourse Russians used foreign words as tities for ruiers Ruler jur a city was caiied kriiaz39r prutchermanic kuriirigaz English ing 7 1547 iSIKII greatg oid Russian iEii pig kriiaz39 of Muscuvvtuuk titie tsar 7 Latin caesare signifying tnat tsar was to kriiaz39 as caesar to fex e 721 tsar Pelfadupted even more august Latin titie imoefatofr source of Engiisn ernperur 7 Highest supordinates of tne kniaz vvere caiied boiare propapiyfrom Turkish 7 Petr apoiisned ooiare in favor of Roiisn shliakhetstio Enforcers of ruie tende to bear Russian tities Words for tne ru ed were Russian 7 smerde a peasant wno couid be pougnt or sold apparentiy meant stinker cf Dutcn koop Engiisn snop e a peasant wno couid buy ms free om e nnoiope a slave pemaps originaiiy castrated N c Myth of Imported Rulers The Russian Primary Chronicle states unarnbiguously that the originai tarniiy or town rulers the Rus were Scandinavians inyited o restore peace to the territory 7 erne speeiaiists derive Rossiiarrurn rinnisn ruolsi meaning Sweden and derived rrern a Swedish word rur ruvvers e ot rs derive tnis word rrern Slavic narne ruryanuus riyers Sorne historians reiect the story or the invitation to the Scandinavians but do not know it to be raise 7 Myths serve tneir purpose regardless ertne tru For our purposes ussian rulers c ose to repeat a rnyth presenting thernselyes as bearing an identity roreign to Russia and dirrerent rrorn that or the Russians oyervvhorn the ruled e Surne pore Nurse narnes pronounced in Russian Oleg Helgi igor lngvar Discourse of Rule in 988 the Kyiyan iE likii kniaz yiadirnir converted to Christianity and demanded that the enrorcers or nis rule do iiiltewise e Peasants propapiy did not convert Bioie had been transiatedrrorn oreeiltinto South Slavic in 863 e Transiators were two Byzantine Greekrspeaking rnunks wno nad iearned South Slavic 7 They were ernpioyed bythe WestrSlayicrspeaking ruler or Moravia in Central Europe 7 He was trying We Aironso in Spain to tree nirnseir ortne influence or Frankish enore rnen e Priests and rnunks trained in transiation were tnen persecuted in Moravia and tied to Bulgaria yiadirnir i Bui aria Oid Church Slavonic distinguished Christian rulers or xyiv and other Russian rortresses rrorn pagan peasants rnported their Old Church Slavonic Bible and liturgy frorn Old Church Slavonic and Russian Unbegaun South Slavic was intelligible to speakers of West Slavic and did not require translation Example Where South Slavic has ra East Slavic has oro Modern Russian gorod city grad su ix ofa city name storona side strana country Generalization not meant to apply to every word South Slavic Cheo East Slavic lob forehead Unbegaun implies that such exceptions were rare enough that they could be easily learned Usage In contrast to Latin Old Church Slavonic never became n administrative language 7 At ieast Unbegaun and other speciaiists say so But Old Church Slavonic was the basis for an inference of identity expressed as privative opposition w39 ne ation ofsome and with elongation of reference to the bearers of identity 7 Metropolitan Hilarion ca i050 Not tor the ignorant do we Write butfor those Who have abundantly irnbibed the sWeetness of books e Cornpare Caxton i390 notrora rudeypiondyshh rnan but oniyeror a cierke amp a noble gentylrnen that reietn and ynderstondeth in raytes or arrnes in ioue amp in nooie chyuairye lntelligibility and Identity AngloNorman r intelligibleto Norman nobles e unintelligibleto AngioSaxon and oaeiic ViiSins Fran is atin e unintelligibleto Franks e unintelligibleto serw Old Churc Slavonic r intelligible to kniazi and their druzhina entourage r intelligibeto ussian smerdy n re c separate identity may correlate with intelligibility but do not depend on it Do we ever see a discourse of rule that is intelligible to the ruled but unintelligible to the rulers Continuing Modification Said to be used for religious purposes alone Old Church Slavonic forms nevertheless penetrated administrative language of Russ39a The Cheobirnaia or petition 7 By 1547 When the ruler of Russia had started to be call lsar any petition to authority necessarily began witn narne beats witn the forehead e Oid Church Slavonic oneo appeared not Russian 7 Elevation rnetapnor equivalentto mushkenum to strike the ground witn the torenead the petitioner rnust becorne horizontal Like Englishmen learning French Russians began to introduce Old Church Slavonic forms into their Russian
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