support armed forces well ref name division feminism women military roles area study receiving increasing amount attention currently women make armed forces women tended move away nursing helping roles increasing attention given brutal realities combat would affect women psychologically interesting research shows affected women tend ask help men thus avoiding many long term mental suffering male soldiers face deployment ended history psychological stress


disorders always part military life especially wartime mental health section military psychology always experienced awareness even present day much research awareness needed concerning area one first institutions created care military psychiatric patients st elizabeths hospital washington dc formerly known united states government hospital insane hospital founded united states congress currently state disrepair although operational

Social science
Psychology
Military psychology


revitalization plans scheduled begin ref name michels michels k http wwwhistoryofmilitarypsychologycom indexhtml intelligence testing united states military retrieved october ref early work james mckeen cattell coined term mental tests cattell studied wundt leipzig germany one point life strongly advocated psychology viewed science par physical life sciences ref name plucker plucker j ed ''human intelligence historical influences current controversies teaching resources'' retrieved november http wwwindianaedu intell ref promoted need standardization procedures use norms advocated


use statistical analysis study individual differences unwavering opposition america 's involvement world war nbsp ref name michels lightner witmer also spent time working wundt changed scene psychology forever position university pennsylvania coined term clinical psychology outlined program training study model clinical psychology still followed modern times eleven years later witmer founded journal ''the psychological clinic'' also routine psychological screening plan hospitalized psychiatric patients developed shepard


ivory franz civilian research psychologist st nbsp elizabeth 's hospital two years later leadership william alanson white st nbsp elizabeth 's hospital became known research training psychiatrists military medical officers hebert butts navy medical officer stationed st nbsp elizabeth 's published first protocol psychological screening navy recruits based franz 's work ref name michels intelligence testing us military lewis terman professor stanford university revised binet simon scale renaming stanford binet revision ref name plucker test beginning intelligence testing movement administered


soldiers united states army world war nbsp yerkes published results tests document became known army report ref name michels two tests initially made intelligence tests military army alpha army beta tests developed evaluate vast numbers military recruits literate army alpha tests illiterate army beta tests army beta test designed measure native intellectual capacity army beta test also helped test non english speaking service members ref name autogenerated http officialasvabcom history counhtm history military testing asvab


retrieved november ref standardized intelligence entrance tests used military branch united states transformed years finally department defense decided services use armed services vocational aptitude battery asvab screening enlistees assigning military occupations combining selection classification testing made testing process efficient also enabled services improve matching applicants available job positions allowed job guarantees qualified went fully effect ref name autogenerated yerkes war


robert yerkes president american psychological association apa worked edward b titchener group psychologists known experimentalists work resulted formulating plan apa members offer professional services world war nbsp effort even though yerkes known opposed america involved war decided psychologists could provide support developing methods selection recruits treatment war victims ref name michels spurred part america 's growing interest


work alfred binet france mental measurement well scientific management movement enhance worker productivity ref name division yerkes commissioned major us army medical service corps plan proposed surgeon general yerkes wrote council american psychological association convinced present emergency american psychology substantially serve government medical corps army navy examining recruits respect intellectual deficiency psychopathic tendencies nervous instability inadequate self control also army division psychology


medical department established medical training camp fort oglethorpe georgia train personnel provide mental testing large groups ref name michels also era condition referred shell shock first seriously studied psychologists standardized screening tests pilots administered ref name autogenerated xiao h http wwwcwuedu relation pr jan html cwu lecture outline history military psychology news headlines retrieved november ref world war ii world war ii ushered era substantial growth psychological field centering around four major areas testing individual abilities applied social


environmental factors human performance military intelligence psychological operations warfare special forces like psyop selection special duties influences personal background attitudes work group soldier motivation morals ref name division korean war korean war first war clinical psychologists served overseas positioned hospitals well combat zones particular roles vague broad fairly undefined except us air force provided detailed job descriptions air force also outlined standardized tests procedures evaluating recruits used ref


name michels vietnam war vietnam war significant challenges obstructed regular use psychologists support combat troops mental health teams small usually consisting one psychiatrist one psychologist three four enlisted corpsmen quite often medical officers including psychologists working severe conditions little field experience ref name michels despite challenges military psychiatry improved compared previous wars focused maximizing function minimizing disability preventive therapeutic measures global war terror study soldiers mental health problems


overseas contingency operation service found majority symptoms enlisted see also army alpha army beta center deployment psychology human subject research military science mkultra morale psychological warfare unit cohesion references external links http wwwdeploymentpsychorg center deployment psychology uniformed services university health sciences military life military medicine military supporting service occupations military personnel military veterans topics


beethoven ode joy flash mob sha tin hong kong alt hkfo choral orchestra performs beethoven ode joy flash mob sha tin hong kong x px '''sociomusicology''' latin ' 'socius'' companion old french ''musique'' suffix '' ology'' study old greek ''l gos'' discourse also called '''music sociology''' '' 'sociology music''' refers academic subfield sociology concerned music often combination arts well subfield musicology focuses social aspects musical behavior role music

Social science
Sociology
Sociomusicology


society sociomusicological issues work scholars sociomusicology often similar ethnomusicology terms exploration sociocultural context music however sociomusicology maintains less emphasis ethnic national identity limited ethnographic methods rather sociomusicologists use wide range research methods take strong interest observable behavior musical interactions within constraints social structure sociomusicologists likely ethnomusicologists make use surveys economic data example tend focus musical practices contemporary industrialized societies instance


proposed hypothesis biliterate trimusical hong kong sociomusicology since field musicology tended emphasize historiographic analytical critical rather sociological approaches research sociomusicology still regarded somewhat outside mainstream musicology yet increased popularity ethnomusicology recent decades field shares many similarities well development mainstreaming new musicology coinciding emergence interdisciplinary cultural studies academia sociomusicology increasingly coming fully established field values meanings associated music collectively constructed


music listeners performers listening piece reflect upon values use music make connections experiences piece perceived communicating sociology music looks specifically connections musical experiences tied person music addition act making music social production well social activity even music artist solo performer production music took level social effort instruments


theodor w adorno others included alphons silbermann charles seeger howard becker norbert elias maurice halbwachs jacques attali john mueller christopher small contemporary sociomusicologists include tia denora georgina born david hebert peter martin timothy dowd william roy joseph schloss alternative definitions entry sociomusicology ''sage international encyclopedia music culture'' david hebert argues recent use term suggests four definitions sociology music kind social scientific research music eg economic political etc specialized form ethnomusicology focused relations


sound events social structure prospective replacement term ethnomusicology see also choreomusicology music community music education music psychology references sources reading adler guido umfang methode und ziel der musikwissenschaft ''vierteljahresschrift f r musikwissenschaft'' beaud paul alfred willener ''musique et vie quotidienne essai de sociologie d'une nouvelle culture electro acoustique et musique pop improvisation'' series ''rep res'' sl ditions mame p becker howard culture careers deviant group dance musician ''outsiders studies sociology deviants'' new


boys material girls manufacturing pop dream'' poole eng blandford press honing henkjan growing role observation formalization experimental method musicology ''empirical musicology review'' https kbosuedu dspace bitstream emr honingpdf kerman joseph ''musicology'' london fontana martin peter j ''sounds society themes sociology music society '' manchester university press martin peter j ''music sociological gaze art worlds cultural production'' manchester university press mcclary susan robert walser start making sense musicology wrestles rock ''on record'' ed frith goodwin pp nbsp


middleton richard ''studying popular music'' philadelphia open university press pruett james w thomas p slavens ''research guide musicology'' chicago american library association sorce keller marcello ''musica e sociologia'' milan ricordi daniela stocks ''die disziplinierung von musik und tanz die entwicklung von musik und tanz im verh ltnis zu ordnungsprinzipien christlich abendl ndischer gesellschaft'' leske budrich opladen voyer pierre ''le rock et le r le'' ' 'sic'' montr al qu lem ac external links https webarchiveorg web http wwwniuedu popms popular music society https wwwjstororg journals html international review aesthetics sociology music http actmaydaygrouporg action criticism theory music


education http wwwams netorg american musicological society https webarchiveorg web http wwwmusicindianaedu ddm doctoral dissertations musicology online https webarchiveorg web http wwwams netorg musicology wwwhtml ams web sites interest musicologists http wwwamerican musicorg society american music http wwwams netorg gradprogphp graduate programs musicology https webarchiveorg web http www gewiuni grazat staff parncutt cimhtm conference interdisciplinary musicology http webdbiuedu sem scripts homecfm society ethnomusicology http wwwasanetorg american sociological association asa http wwwbritsoccouk british sociological association bsa https webarchiveorg web http wwwvalthelsinkifi esa european sociological association esa http wwwucmes info isa international sociological association isa https webarchiveorg web http ihbcmcharleskoinfo international hongkongers' board councils musicology musics ihbcm musicology sociology art music genres


'''housing''' generally '''living spaces''' refers construction assigned usage houses buildings collectively purpose sheltering people planning provision delivered authority related meanings ensuring members society home live whether house kind dwelling lodging shelter social issue many governments one housing authorities sometimes also called housing ministry housing department history macroeconomy housing price previous research shown housing price

Applied science
Family and consumer science
Housing


affected macroeconomy research indicates increase consumer price index leads increase housing prices raises property price per square foot money supply positive relationship housing prices increased one unit housing prices rose study conducted hong kong increase best lending rate housing prices drop hac model mortgage repayments lead rise discount window base rate


rise rate leads drop housing prices average selling price drop us real interest rate increases interest rates hong kong must follow increasing mortgage repayments increase us real interest rate property prices decrease saleable area drops rise overnight hong kong interbank offered rate housing prices drop price per ft drop effect health housing


named housing associations housing estate housing united kingdom housing japan informal housing informal sector list housing statutes list human habitation forms right housing subsidized housing us federal housing administration references external links


symmetries regular polygons consisting reflections rotations transform polygon '''representation theory''' branch mathematics studies abstract algebraic structures ' 'representing'' elements linear transformations vector spaces studies modules abstract algebraic structures essence representation makes abstract algebraic object concrete describing elements matrices algebraic operations example matrix addition matrix multiplication theory matrices linear operators well understood representations abstract objects terms familiar linear algebra objects helps glean properties sometimes simplify calculations

Formal science
Mathematics
Pure mathematics
Algebra
Representation theory


abstract theories algebraic objects amenable description include groups associative algebras lie algebras prominent historically first representation theory groups elements group represented invertible matrices way group operation matrix multiplication ref name ref representation theory useful method reduces problems abstract algebra problems linear algebra subject well understood ref name linalg many textbooks vector spaces linear algebra advanced treatment see ref furthermore vector space


group example represented infinite dimensional allowing instance hilbert space methods analysis applied theory groups ref name ref representation theory also important physics example describes symmetry group physical system affects solutions equations describing system ref name sternberg ref representation theory pervasive across fields mathematics two reasons first applications representation theory diverse addition impact algebra representation theory illuminates generalizes fourier analysis via harmonic analysis ref name folland ref


connected geometry via invariant theory erlangen program impact number theory via automorphic forms langlands program second diverse approaches representation theory objects studied using methods algebraic geometry module theory analytic number theory differential geometry operator theory algebraic combinatorics topology success representation theory led numerous generalizations one general category theory ref name ssa ref algebraic objects representation theory applies viewed particular kinds categories representations functors object


category category vector spaces ref name description points two obvious generalizations first algebraic objects replaced general categories second target category vector spaces replaced well understood categories definitions concepts let ''v'' vector space field '''f''' ref name linalg instance suppose ''v'' '''r''' sup ''n'' sup '''c''' sup ''n'' sup standard ''n'' dimensional space column vectors real complex numbers respectively case idea representation theory abstract algebra concretely using ''n'' times ''n'' matrices real


complex numbers three main sorts algebraic objects done groups associative algebras lie algebras ref name set ''invertible'' ''n'' times ''n'' matrices group matrix multiplication representation theory groups analyzes group describing representing elements terms invertible matrices matrix addition multiplication make set ''all'' ''n'' times ''n'' matrices associative algebra hence corresponding representation theory associative algebras replace matrix multiplication ''mn'' matrix commutator ''mn'' minus ''nm''


''n'' times ''n'' matrices become instead lie algebra leading representation theory lie algebras generalizes field '''f''' vector space ''v'' '''f''' linear maps replacing matrices composition replacing matrix multiplication group gl ''v'''''f''' automorphisms ''v'' associative algebra end sub '''f''' sub ''v'' endomorphisms ''v'' corresponding lie algebra '''gl''' ''v'''''f''' definition two ways say representation first uses idea action generalizing way matrices act column vectors matrix multiplication representation


''e'' identity element ''g'' ''g'' sub sub ''g'' sub sub product ''g'' requirement associative algebras analogous except associative algebras always identity element case equation ignored equation abstract expression associativity matrix multiplication n't hold matrix commutator also identity element commutator hence lie algebras requirement ''x'' sub sub ''x'' sub sub ''a'' ''v'' ''v'' math ' quad x cdot x cdot v x cdot x cdot v


representation associative algebra ''a'' vector space ''v'' algebra homomorphism '' '' ''a'' end sub '''f''' sub ''v'' ref name representation lie algebra vector space ''v'' lie algebra homomorphism '' '' '''gl''' ''v'''''f''' terminology vector space ''v'' called '' 'representation space''' '' '' dimension finite called '' 'dimension''' representation sometimes ' 'degree'' ref name serre ref also common practice refer ''v'' representation homomorphism '' '' clear context otherwise notation ''v'''' ''


used denote representation ''v'' finite dimension ''n'' one choose basis ''v'' identify ''v'' '''f''' sup ''n'' sup hence recover matrix representation entries field '''f''' effective faithful representation representation ''v'''' '' homomorphism '' '' injective equivariant maps isomorphisms ''v'' ''w'' vector spaces '''f''' equipped representations '' '' '' '' group ''g'' '''equivariant map''' ''v'' ''w'' linear map '' '' ''v'' ''w'' math alpha g cdot v


g cdot alpha v math ''g'' ''g'' ''v'' ''v'' terms '' '' ''g'' gl ''v'' '' '' ''g'' gl ''w'' means math alpha circ varphi g psi g circ alpha math ''g'' ''g'' following diagram commutes px equivariant maps representations associative lie algebra defined similarly '' '' invertible said isomorphism case ''v'' ''w'' precisely '' '' '' '' ''isomorphic representations'' also phrased ''equivalent representations'' equivariant map often called ''intertwining


v psi v' psi' math blockquote irreducible representations either zero map isomorphism since kernel image subrepresentations particular math v v' math shows equivariant endomorphisms math v math form associative division algebra underlying field '''f''' '''f''' algebraically closed equivariant endomorphisms irreducible representation scalar multiples identity irreducible representations building blocks representation theory many groups representation math v math irreducible built subrepresentation quotient simpler sense


instance math v math finite dimensional subrepresentation quotient smaller dimension counterexamples representation subrepresentation one non trivial irreducible component example additive group math mathbb r math two dimensional representation blockquote math phi begin bmatrix end bmatrix math blockquote group vector math begin bmatrix end bmatrix math fixed homomorphism complement subspace maps blockquote math begin bmatrix end bmatrix mapsto begin bmatrix end bmatrix math blockquote giving one irreducible subreprentation true unipotent groups sup pg sup direct sums indecomposable representations


said semisimple case suffices understand irreducible representations examples complete reducibility phenomenon occur include finite groups see maschke 's theorem compact groups semisimple lie algebras cases complete reducibility hold one must understand indecomposable representations built irreducible representations extensions quotient subrepresentation tensor products representations suppose math phi g rightarrow mathrm gl v math math phi g rightarrow mathrm gl v math representations group math g math form representation math phi otimes phi math g acting tensor product vector space math v otimes v math follows math phi otimes phi g phi g otimes phi g math


math phi math math phi math representations lie algebra correct formula use math phi otimes phi x phi x otimes otimes phi x math product recognized coproduct coalgebra general tensor product irreducible representations ''not'' irreducible process decomposing tensor product direct sum irreducible representations known clebsch gordan theory case representation theory group su equivalently complexified lie algebra math mathrm sl mathbb c math decomposition easy work irreducible representations labeled parameter math l math non negative integer


space algebraic object represented important distinction finite dimensional representations infinite dimensional ones infinite dimensional case additional structures important example whether space hilbert space banach space etc additional algebraic structures also imposed finite dimensional case representation theory depends upon type field vector space defined important cases field complex numbers field real numbers finite fields fields p adic numbers additional difficulties arise fields positive characteristic


fields algebraically closed finite groups group representations important tool study finite groups also arise applications finite group theory geometry crystallography representations finite groups exhibit many features general theory point way branches topics representation theory field characteristic zero representation finite group ''g'' number convenient properties first representations ''g'' semisimple completely reducible consequence maschke 's theorem states subrepresentation


''v'' ''g'' representation ''w'' ''g'' invariant complement one proof choose projection '' '' ''w'' ''v'' replace average '' '' sub ''g'' sub defined math pi g x frac g sum g g g cdot pi g cdot x math '' '' sub ''g'' sub equivariant kernel required complement finite dimensional ''g'' representations understood using character theory character representation '' '' ''g'' gl ''v'' class function '' '' sub '' '' sub ''g'' '''f''' defined math chi varphi g mathrm tr varphi g math math mathrm tr math trace irreducible representation ''g'' completely determined character maschke 's theorem holds generally


fields positive characteristic ''p'' finite fields long prime ''p'' coprime order ''g'' ''p'' ''g'' common factor ''g'' representations semisimple studied subbranch called modular representation theory averaging techniques also show '''f''' real complex numbers ''g'' representation preserves inner product math langle cdot cdot rangle math ''v'' sense math langle g cdot vg cdot w rangle langle vw rangle math ''g'' ''g'' ''v'' ''w'' ''w'' hence ''g'' representation unitary unitary representations


automatically semisimple since maschke 's result proven taking orthogonal complement subrepresentation studying representations groups finite unitary representations provide good generalization real complex representations finite group results maschke 's theorem unitary property rely averaging generalized general groups replacing average integral provided suitable notion integral defined done compact topological groups including compact lie groups using haar measure resulting theory


known abstract harmonic analysis arbitrary fields another class finite groups good representation theory finite groups lie type important examples linear algebraic groups finite fields representation theory linear algebraic groups lie groups extends examples infinite dimensional groups latter intimately related lie algebra representations importance character theory finite groups analogue theory weights representations lie groups lie algebras representations finite group ''g'' also linked directly algebra representations via group


algebra '''f''' ''g'' vector space '''f''' elements ''g'' basis equipped multiplication operation defined group operation linearity requirement group operation scalar multiplication commute modular representations modular representations finite group ''g'' representations field whose characteristic coprime ''g'' maschke 's theorem longer holds ''g'' invertible '''f''' one cannot divide nevertheless richard brauer extended much character theory modular representations theory played important role


early progress towards classification finite simple groups especially simple groups whose characterization amenable purely group theoretic methods sylow subgroups small well applications group theory modular representations arise naturally branches mathematics algebraic geometry coding theory combinatorics number theory unitary representations unitary representation group ''g'' linear representation '' '' ''g'' real usually complex hilbert space ''v'' '' '' ''g'' unitary operator every ''g'' ''g'' representations widely applied


quantum mechanics since thanks particular influence hermann weyl inspired development theory notably analysis representations poincar group eugene wigner one pioneers constructing general theory unitary representations group ''g'' rather particular groups useful applications george mackey extensive theory developed harish chandra others major goal describe unitary dual space irreducible unitary representations ''g'' ref name knapp ref theory


harish chandra modules easy detect admissible representations nondegenerate invariant sesquilinear form hard determine form positive definite effective description unitary dual even relatively well behaved groups real reductive lie groups discussed remains important open problem representation theory solved many particular groups sl '''r''' lorentz group harmonic analysis duality circle group ''s'' sup sup integers '''z''' generally torus ''t'' sup ''n'' sup '''z''' sup ''n'' sup well known analysis


theory fourier series fourier transform similarly expresses fact space characters real vector space dual vector space thus unitary representation theory harmonic analysis intimately related abstract harmonic analysis exploits relationship developing analysis functions locally compact topological groups related spaces ref name folland major goal provide general form fourier transform plancherel theorem done constructing measure unitary dual isomorphism regular representation ''g'' space l sup sup ''g''


linear algebraic groups tannakian categories harmonic analysis also extended analysis functions group ''g'' functions homogeneous spaces ''g'' theory particularly well developed symmetric spaces provides theory automorphic forms discussed lie groups lie group group also smooth manifold many classical groups matrices real complex numbers lie groups ref name weyl ref many groups important physics chemistry lie groups representation theory crucial application group theory


fields ref name sternberg representation theory lie groups developed first considering compact groups results compact representation theory apply ref name knapp theory extended finite dimensional representations semisimple lie groups using weyl 's unitary trick semisimple real lie group ''g'' complexification complex lie group ''g'' sup c sup complex lie group maximal compact subgroup ''k'' finite dimensional representations ''g'' closely correspond ''k'' general lie group semidirect product solvable lie group semisimple lie group


levi decomposition ref name fulton harris ref classification representations solvable lie groups intractable general often easy practical cases representations semidirect products analysed means general results called ''mackey theory'' generalization methods used wigner 's classification representations poincar group lie algebras lie algebra field '''f''' vector space '''f''' equipped skew symmetric bilinear operation called lie bracket satisfies jacobi identity lie algebras arise particular tangent spaces lie groups identity element leading


maximal subalgebra lie bracket zero abelian representation decomposed weight spaces eigenspaces action infinitesimal analogue characters structure semisimple lie algebras reduces analysis representations easily understood combinatorics possible weights occur ref name fulton harris infinite dimensional lie algebras many classes infinite dimensional lie algebras whose representations studied among important class kac moody algebras named victor kac robert moody independently discovered


algebras form generalization finite dimensional semisimple lie algebras share many combinatorial properties means class representations understood way representations semisimple lie algebras affine lie algebras special case kac moody algebras particular importance mathematics theoretical physics especially conformal field theory theory exactly solvable models kac discovered elegant proof certain combinatorial identities macdonald identities based representation theory affine kac moody algebras lie superalgebras lie superalgebras generalizations lie algebras


underlying vector space '''z''' sub sub grading skew symmetry jacobi identity properties lie bracket modified signs representation theory similar representation theory lie algebras linear algebraic groups linear algebraic groups generally affine group schemes analogues algebraic geometry lie groups general fields '''r''' '''c''' particular finite fields give rise finite groups lie type although linear algebraic groups classification similar lie groups representation theory rather


automorphic forms viewed differential forms similar objects '' '' ''g'' ''k'' ''k'' typically maximal compact subgroup ''g'' care required however quotient typically singularities quotient semisimple lie group compact subgroup symmetric space theory automorphic forms intimately related harmonic analysis symmetric spaces development general theory many important special cases worked detail including hilbert modular forms siegel modular forms important results theory include selberg trace formula


realization robert langlands riemann roch theorem could applied calculate dimension space automorphic forms subsequent notion automorphic representation proved great technical value dealing case ''g'' algebraic group treated adelic algebraic group result entire philosophy langlands program developed around relation representation number theoretic properties automorphic forms associative algebras one sense associative algebra representations generalize representations groups lie algebras representation group induces representation


corresponding group ring group algebra representations lie algebra correspond bijectively representations universal enveloping algebra however representation theory general associative algebras nice properties representation theory groups lie algebras module theory considering representations associative algebra one forget underlying field simply regard associative algebra ring representations modules approach surprisingly fruitful many results representation theory interpreted special cases results modules ring hopf


algebras quantum groups hopf algebras provide way improve representation theory associative algebras retaining representation theory groups lie algebras special cases particular tensor product two representations representation dual vector space hopf algebras associated groups commutative algebra structure general hopf algebras known quantum groups although term often restricted certain hopf algebras arising deformations groups universal enveloping algebras representation theory quantum groups added surprising insights


representation theory lie groups lie algebras instance crystal basis kashiwara generalizations set theoretic representations ' 'set theoretic representation'' also known group action ''permutation representation'' group ''g'' set ''x'' given function '' '' ''g'' ''x'' sup ''x'' sup set functions ''x'' ''x'' ''g'' sub sub ''g'' sub sub ''g'' ''x'' ''x'' math rho x x math math rho g g x rho g rho g x math condition axioms group imply '' '' ''g'' bijection permutation ''g'' ''g'' thus may equivalently


define permutation representation group homomorphism g symmetric group sub ''x'' sub ''x'' representations categories every group ''g'' viewed category single object morphisms category elements ''g'' given arbitrary category ''c'' ' 'representation'' ''g'' ''c'' functor ''g'' ''c'' functor selects object ''x'' ''c'' group homomorphism ''g'' aut ''x'' automorphism group ''x'' case ''c'' '''vect''' sub '''f''' sub category vector spaces field


'''f''' definition equivalent linear representation likewise set theoretic representation representation ''g'' category sets another example consider category topological spaces '''top''' representations '''top''' homomorphisms ''g'' homeomorphism group topological space ''x'' two types representations closely related linear representations projective representations category projective spaces described linear representations scalar transformations affine representations category affine spaces example euclidean group acts affinely upon euclidean space corepresentations unitary


antiunitary groups category complex vector spaces morphisms linear antilinear transformations representations categories since groups categories one also consider representation categories simplest generalization monoids categories one object groups monoids every morphism invertible general monoids representations category category sets monoid actions monoid representations vector spaces objects studied generally one relax assumption category represented one object full generality


simply theory functors categories little said one special case significant impact representation theory namely representation theory quivers ref name ssa quiver simply directed graph loops multiple arrows allowed made category also algebra considering paths graph representations categories algebras illuminated several aspects representation theory instance allowing non semisimple representation theory questions group reduced cases semisimple representation theory questions quiver see


also galois representation glossary representation theory group representation 's theorem list representation theory topics list harmonic analysis topics numerical analysis philosophy cusp forms representation mathematics representation theorem universal algebra notes references yurii lyubich ''introduction theory banach representations groups'' translated russian language edition kharkov ukraine birkh user verlag nd ed rd ed external links alexander kirillov jr http wwwmathsunysbedu kirillov liegroups


introduction lie groups lie algebras textbook preliminary version pdf downloadable author 's home page kevin hartnett https wwwquantamagazineorg useless perspective transformed mathematics article representation theory quanta magazine


wave attack ilfracombe 's sea walls storm '''coastal engineering''' branch civil engineering concerned specific demands posed constructing near coast well development coast hydrodynamic impact especially waves tides storm surges tsunamis often harsh environment salt seawater typical challenges coastal engineer morphodynamic changes coastal topography caused autonomous development system man made changes areas interest coastal engineering include coasts oceans

Applied science
Engineering and technology
Civil Engineering
Coastal engineering


seas marginal seas estuaries big lakes besides design building maintenance '''coastal structures''' coastal engineers often interdisciplinary involved integrated coastal zone management also specific knowledge hydro morphodynamics coastal system may include providing input technology eg environmental impact assessment port development strategies coastal defense land reclamation offshore wind farms energy production facilities etc specific challenges beach nourishment dutch coast coastal environment produces challenges specific branch engineering waves storm surges tides tsunamis sea level changes sea water


marine ecosystem often coastal engineering projects need metocean conditions local wind wave climate well statistics information hydrodynamic quantities interest also bathymetry morphological changes direct interest case studies sediment transport morphological changes relevant properties sea bed sediments water ecosystem properties needed long short waves classification spectrum ocean waves according wave period walter munk occurrence wave phenomena like sea waves swell tides tsunamis require


engineering knowledge physics well models numerical models physical models practices present day coastal engineering based models verified validated experimental data apart wave transformations waves coming deep water shallow coastal waters surf zone effects waves important effects include wave loading coastal structures like breakwaters groynes jetties sea walls dikes wave induced currents like longshore current surf zone rip currents stokes drift affecting sediment transport morphodynamics wave agitation


'''systematic musicology''' umbrella term used mainly central europe several subdisciplines paradigms musicology systematic musicology traditionally conceived interdisciplinary science whose aim explore foundations music different points view acoustics physiology psychology anthropology music theory sociology aesthetics ref name schneiderleman ref important subdisciplines today music psychology sociomusicology music sociology philosophy music music philosophy music acoustics physics music cognitive neuroscience music computer sciences music including sound music computing music information retrieval computing musicology

Humanities
Performing arts
Music
Systematic musicology


subdisciplines paradigms tend address questions music general rather specific manifestations music springer handbook systematic musicology sections follow main topics field musical acoustics signal processing music psychology psychophysics psychoacoustics music ethnology also taking recent research trends consideration like embodied music cognition media applications topics like music theory philosophy music incorporated respective sections ref name hb ref european tripartite model musicology musicology regarded combination three broad subdisciplines ethnomusicology music history historical musicology systematic


musicology ethnomusicology historical musicology primarily concerned specific manifestations music performances works traditions genres people produce engage musicians composers social groups systematic musicology different tends put specific manifestations foreground although course refers instead general questions asked music questions tend answered either analysing empirical data based observation developing theory better combination th century positivist dream discovering laws music


analogy laws disciplines physics cf adler defining discipline systematic musicology terms laws slowly evaporated ideological trends stemming modernism later post structuralism fundamentally altered nature project since systematic musicology brings together several parent disciplines often regarded intrinsically interdisciplinary ref name current ref ref name schneidersystem ref system interacting subdisciplines hence alternative name systemic however systematic musicologists focus one select many subdisciplines systematic musicologists oriented toward humanities often make reference


fields aesthetics philosophy semiotics hermeneutics music criticism media studies cultural studies gender studies theoretic sociology oriented toward science tend regard discipline empirical data oriented borrow methods ways thinking psychology acoustics psychoacoustics physiology cognitive science empirical sociology ref name current recently emerged areas research least partially scope systematic musicology comprise cognitive musicology neuromusicology biomusicology music cognition including embodied music cognition academic discipline systematic musicology closely related practically oriented disciplines music technology


music information retrieval musical robotics ref name current systematic musicology less unified sister disciplines historical musicology ethnomusicology contents methods diverse tend closely related parent disciplines academic practical outside musicology diversity systematic musicology extent compensated interdisciplinary interactions within system subdisciplines make origins systematic musicology europe traced ancient greece philosophers pythagoras aristotle plato aristoxenus asked general questions music historical musicology ethnomusicology much


younger disciplines relative importance three fluctuated considerably past centuries today musicology 's three broad subdisciplines approximately equal size terms volume research activity reading rolf bader ed springer handbook systematic musicology berlin heidelberg springer doi https wwwspringercom de book mauricio toro carlos agon camilo rueda gerard assayag gelisp framework represent musical constraint satisfaction problems search strategies journal theoretical applied information technology http wwwjatitorg volumes vol vol pdf clarke eric cook nicholas eds empirical musicology aims methods prospects oxford oxford


university press dahlhaus carl musikwissenschaft und systematische musikwissenschaft c dahlhaus h de la motte haber eds systematische musikwissenschaft laaber germany laaber verlag elschek oskar systematische musikwissenschaft und pers nlichkeitsgeschichte systematische musikwissenschaft fricke jobst peter systemische musikwissenschaft k w niem ller b g tjen eds perspektiven und methoden einer systemischen musikwissenschaft pp nbsp frankfurt lang honing henkjan comeback systematic musicology new empiricism cognitive revolution tijdschrift voor muziektheorie dutch journal music theory http wwwnicikunnl mmm papers honing fpdf honing henkjan growing role observation formalization experimental method musicology ''empirical musicology review''


musikwissenschaft c dahlhaus h de la motte haber eds systematische musikwissenschaft pp nbsp laaber germany laaber verlag parncutt r systematic musicology history future western musical scholarship journal interdisciplinary music studies http wwwmusicstudiesorg first issue full systematic musicology parncutt pdf schneider albrecht systematische musikwissenschaft traditionen ans tze aufgaben systematische musikwissenschaft schumacher r systematische musikwissenschaft eine stellungnahme aus der perspektive der musikethnologie k w niem ller b g tjen eds perspektiven und methoden einer systemischen musikwissenschaft pp nbsp frankfurt lang references musicology


taipei taiwan jiaotse restaurant th avenue owner preparing famous handmade jiaozi '''sociology food''' study food relates history progression future development society includes production preparation consumption distribution conflict medical application ritual spiritual ethical cultural applications environmental labor issues aspect food distribution society examined analysis changes food supply chain globalization particular significant effects food supply chain enabling scale effect food distribution industry food

Social science
Sociology
Sociology of food


distribution impact scale effects scale effects resulting centralized acquisition purchase centres food supply chain favor large players big retailers distributors food distribution market due fact utilize strong market power financial advantage smaller players strong market power greater access financial credit market meant impose barriers entry cement position food distribution market would result food distribution chain characterized large players


one end small players choosing niche markets operate end existence smaller players specialized food distribution markets could attributed shrinking market share inability compete larger players due scale effects mechanism globalization displaced smaller role players another mechanism troubling specialized food distribution markets ability distribution chains possess brand stores brand able combat price wars competitors lowering price brand thus making consumers


likely purchase goods early history culture since beginning mankind food important simply purpose nourishment primates walked earth solely consumed food source energy hunt forage food easily hand early humans fending figured needed high energy diet keep going daily basis survive developments eventually lead agriculture also goes labor food economic part sociology


food years went food become way bring cultures people together many cultures food brings people together carried centuries homo sapiens hunting gathering colonists new world sharing feast native americans revived tradition named thanksgiving popularization restaurants eating last several decades togetherness comes eating developments show communication connectivity relating food according sociologists different groups food


divided purpose meaning cultural super foods staples culture prestige foods reflect economic status body image food mainly consumed betterment body sympathetic foods eaten acclaimed desirable property like superstition lastly physiological foods consumed specific health reason like pregnant woman eats healthy pregnancy different categories help researchers sociologists study culture perspective food often shows food grows molds


changes society example someone believes homeopathy would fall sympathetic foods physiologic foods consumed properties beliefs could another example one categories foods would caviar oysters prestige foods often expensive consume purchase show socioeconomic status ses sociological perspectives lens symbolic interactionist many symbols sociology


definitely goes along family theories sociology conflict theory also pertains sociology food mentioned food first foremost used nourishment means survival due fall conflict theory roles hunter gather meant early humans fight forage survive conflict could also display survival fittest conflict getting food nourishment ones best prevail provide nourishment families


evolved today people jobs make living goes food nourishment psychology disorders eating disorders symbolic sociology food represent much forced control lack thereof someone something essential survival eating disorders limit anorexia disorders include bulimia binge eating disorder binge eating well people disorders often use food reward cases see food something avoid even though


need survival relationship people share food always varied complex topic sociological standpoint media lot sociology food media represents society whole men women majorly women see targeted inaccurate representations perfect body leading want body like one considered normal disorders like anorexia nervosa bulimia nervosa bulimia patients


intense fear gaining weight consuming calories disorders go represent damaged relationship people share food weight always attached negativity popular media inaccurate representation leads people focus external appearance opposed taking consideration absolute need nourishment false image shown publicly perfect body looks like affected consuming many calories person normally might led anorexia nervosa mental health disorder


models like twiggy made headlines thin many women strived like body type carried dieting like south beach diet weight watchers grew popularity along popularization working work videos start mainstream dieting fads among others like atkins diet jenny craig paleo began take popularity early mid diets became mainstream included vegetarianism dairy free veganism raw diets gluten free many reasons someone would choose


certain type diet moral reasons digestive issues outside influence religious influence obesity obesity epidemic spread across america also great example food shapes society way people live along evolution type food americans consume due busy manic lives many americans fast food prepackaged foods higher calories gained popularity become mainstream american consumption environment people certain socioeconomic backgrounds live also heavily affect type food consume high calorie


low nutritional food tend less expensive easier access thus shopping food many lean towards cheaper options lack physical fitness also crucial aspect adding obesity epidemic studies found direct correlation walkability neighborhoods exercise also one 's neighborhood ready access recreation activities risk becoming weight obesity going along subject eating disorders obesity could feeling lack control comes


eating progress combating america 's obesity problem programs put place help promote healthy eating fitness restaurants putting amount calories meals also many food companies coca cola promoting making healthy choices drinks products also putting calories making nutrition facts readily available effects obesity references beardsworth alan keil teresa sociology menu invitation study food society london us routledge


proquest ebrary web november caplan pat ed food health identity london us routledge proquest ebrary web december halkier bente consumption challenged food medialised everyday lives farnham gb routledge proquest ebrary web december institute medicine hunger obesity understanding food insecurity paradigm workshop summary washington us national academies press proquest ebrary web december lupton deborah food body self london gb sage publications ltd proquest ebrary web november marsden terry cavalcanti josefa salete barbosa eds research


rural sociology development labor relations globalized food bingley gb emerald group publishing limited proquest ebrary web november ritzer george explorations sociology consumption fast food credit cards casinos london gb sage publications ltd proquest ebrary web november see also food studies food industry index sociology food articles reading ''carolan ''the sociology food agriculture'' routledge new york london '' beardsworth alan ''sociology menu invitation study food society'' routledge germov john ''a sociology


food nutrition social appetite'' oxford university press kingsolver barbara ''animal vegetable miracle year food life'' harpercollins levenstein harvey ''revolution table transformation american diet'' oxford university press nestle marion ''food politics food industry influences nutrition health'' univ california press mennell stephen ''the sociology food eating diet culture'' sage publications ritzer george ''the mcdonaldization society'' sage publications schlosser eric ''fast food nation dark side american meal'' harpercollins references external links https webarchiveorg web http wwwartsadelaideeduau centrefooddrink research center


history food drink http wwwfoodtimelineorg food timeline https archivetoday http wwwworldfoodscienceorg cms world food science food science sociology


'''history political thought''' dates back antiquity history world thus history political thinking humans stretches european medieval period renaissance age enlightenment political entities expanded basic systems self governance monarchy complex democratic communist systems exist industrialized modern era parallel political systems expanded vaguely defined frontier type boundaries definite boundaries existing today history political thought often overlapped history philosophy ancient political thought

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around bce china began experience time peace prosperity allowed rise called hundred schools thought influential confucius ref name ref thinking firmly based traditional chinese worldview saw values loyalty duty respect paramount ref name ref believed people society improved reciprocal treatment moral example set leader embodying virtues society would respond good leaders emulating ref name encapsulated saying ref name


work however society ordered hierarchically modeled patriarchal family headed absolute sovereign ref name however confucius also believed state employ meritocratic class administrators advisers recruited civil service exams among later chinese thinkers mozi agreed ideas meritocracy leading example opposed family model governance belief would nepotistic ref name ref mencius however championed ideas later ref name alternative chinese philosophy called legalism argued instead virtue authoritarian discipline crucial


thought existing political arrangements monarchy oligarchy democracy promoted interests people power ignorant virtues instead would pursue honour wealth leading conflict injustice correct plato proposed ''republic'' philosopher kings would know achieve good life power instead india chanakya c th century bce offered ''arthashastra'' practical advice run government also believed virtue leader merit advisers important furthermore also


argued end justifies means using best means available defeat enemies rulers substitute virtues defeated enemy 's vices enemy good shall twice good prior manu wrote similar topics manusmriti post classical political thought europe early christian philosophy augustine hippo large rewrite plato christian context main change christianity wrought moderate stoicism theory justice roman world emphasize role


state applying mercy moral example augustine also preached one member city either citizen city god civitas dei city man civitas terrena augustine 's ''city god'' influential work period refuted thesis first sack rome christian view could realized earth view many christian romans held medieval period political philosophy europe heavily influenced christian thinking much


islam based qur'an muhammad strongly altered power balances perceptions origin power mediterranean region early islamic philosophy emphasized inexorable link science religion process ijtihad find truth effect ''all'' philosophy political real implications governance view challenged mutazilite philosophers held greek view supported secular aristocracy sought freedom action independent caliphate late medieval period however asharite view islam general triumphed


islamic political philosophy indeed rooted sources islam ie qur'an sunnah words practices muhammad however western thought generally supposed specific area peculiar merely great philosophers islam al kindi alkindus al farabi abunaser bn sina avicenna ibn bajjah avempace ibn rushd averroes ibn khaldun political conceptions islam kudrah sultan ummah simaa even core terms qur'an ie ibada din rab ilah taken basis analysis hence


ideas muslim political philosophers also many jurists ulama posed political ideas theories example ideas khawarij early years islamic history khilafa ummah shia islam concept imamah considered proofs political thought clashes ehl sunna shia th th centuries genuine political character th century arab scholar ibn khaldun considered one greatest political theorists british philosopher anthropologist ernest gellner considered ibn khaldun 's definition government institution


prevents injustice commits best history political theory modern political thought renaissance renaissance secular political philosophy began emerge century theological political thought europe one influential works burgeoning period niccol machiavelli 's ''the prince'' written published machiavelli 's death work well ''the discourses'' rigorous analysis classical period much influence modern political thought west minority including jean jacques rousseau would interpret ''the


prince'' satire meant imply medici recapture florence subsequent expulsion machiavelli florence though work written medici family order perhaps influence free exile machiavelli supported republic florence rather oligarchy medici family rate machiavelli presents pragmatic somewhat consequentialist view politics whereby good evil mere means used bring end ie maintenance political authority thomas hobbes well known theory social contract goes


expand view start th century english renaissance john locke particular exemplified new age political theory work ''two treatises government'' locke proposes state nature theory directly complements conception political development occurs founded contractual obligation locke stood refute sir robert filmer 's paternally founded political theory favor natural system based nature particular given system age enlightenment eug ne delacroix 's ''liberty leading people'' louvre painting created


time old modern political philosophies came violent conflictduring enlightenment period new theories human definition reality way perceived along discovery societies americas changing needs political societies especially wake english civil war american revolution french revolution led new questions insights thinkers jean jacques rousseau montesquieu john locke theorists driven two basic questions one right need


people form states two best form state take fundamental questions involved distinction concepts state government decided state would refer set enduring institutions power would distributed use justified term government would refer specific group people occupied state given time created laws ordinances people government included would bound conceptual distinction continues operate political science although political


eastern bloc cold war line thought would result maoism ho chi minh thought hoxhaism titoism industrialisation enabled rise colonialism accompanied ideology imperialism later anti imperialist ideologies would counter gandhism nasserism see also divine right kings history economic thought history feminism history political science intellectual history references references reading fiala andrew ed '' https booksgooglecom booksid xxapbgaaqbaj printsec frontcover dq bloomsbury companion political philosophy hl en sa x ved ahukewje njxumnjahvnh akhf sbgyq aeikjaa bloomsbury companion political philosophy '' klosko george ed ''oxford handbook history political philosophy'' korab karpowicz w julian '' https booksgooglecom booksid f cocgaaqbaj printsec frontcover dq history political philosophy great political thinkers thucydides locke hl en sa x ved ahukewim fucnjahvejt khdrmdmmq aeikjaa v onepage q history political philosophy great political thinkers thucydides locke f false


'''''history political thought''''' quarterly peer reviewed academic journal established dedicated history political philosophy political science journal published imprint academic exeter england co founded historians iain hampsher monk janet coleman ranked journal australian political studies association abstracting indexing journal abstracted indexed scopus ibz online philosopher 's index arts humanities citation index worldwide political science abstracts sociological abstracts historical abstracts l'ann e philologique international bibliography social sciences external links political science


'''catholic theology''' understanding catholic doctrine teachings results studies theologians based canonical scripture sacred tradition interpreted authoritatively magisterium catholic church article serves introduction various topics catholic theology links fuller coverage found major teachings catholic church discussed early councils church summarized various creeds especially nicene nicene constantinopolitan creed apostles' creed since th century church produced catechisms summarize teachings recently

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catholic church understands living tradition church contain essentials doctrine faith morals protected error times infallibly defined teaching church believes revelation guided holy spirit sacred scripture developed sacred tradition entirely rooted original ' 'deposit faith'' developed deposit faith protected magisterium college bishops ecumenical councils overseen pope beginning council jerusalem recent second vatican council


twice history pope defined dogma consultation bishops without calling council formal catholic worship ordered means liturgy regulated church authority celebration eucharist one seven sacraments center catholic worship church exercises control additional forms personal prayer devotion including rosary stations cross eucharistic adoration declaring somehow derive eucharist lead back church community consists ordained clergy consisting episcopate priesthood


diaconate laity like monks nuns living consecrated life constitutions according ''catechism'' christ instituted seven sacraments entrusted church ref name ccc ref baptism confirmation chrismation eucharist penance anointing sick holy orders matrimony profession faith human capacity god catholic church teaches desire god written human heart man created god god god never ceases draw man man may turn away god


god never stops calling man back man created image likeness god man know certainty god 's existence human reason man 's faculties make capable coming knowledge existence personal god order man able enter real intimacy god willed reveal man give grace able welcome revelation faith summary church teaches man nature vocation


religious coming god going toward god man lives fully human life freely lives bond god god comes meet humanity church teaches god revealed gradually beginning old testament completing revelation sending son jesus christ earth man revelation started adam eve broken original sin rather god promised send redeemer god revealed covenants noah abraham god delivered law moses mount sinai


spoke old testament prophets fullness god 's revelation made manifest coming son god jesus christ creeds creeds latin ''credo'' meaning believe concise doctrinal statements confessions usually religious beliefs began baptismal formulas later expanded christological controversies th th centuries become statements faith apostles creed ''symbolum apostolorum'' developed nd th centuries popular creed used worship western christians central doctrines


trinity god creator doctrines found creed traced statements current apostolic period creed apparently used summary christian doctrine baptismal candidates churches rome nicene creed largely response arianism formulated councils nicaea constantinople respectively ratified universal creed christendom council ephesus ref name ephesus ''catholic encyclopedia'' http wwwnewadventorg cathen ahtm council ephesus ref sets main principles catholic christian belief ref name schaff


creed recited sunday masses core statement belief many christian churches well ref name schaff schaff ''creeds christendom history critical notes'' pp ref ref name richardson richardson ''the westminster dictionary christian theology'' p ref chalcedonian creed developed council chalcedon though accepted oriental orthodox churches taught christ acknowledged two natures inconfusedly unchangeably indivisibly inseparably one divine one human natures perfect nevertheless perfectly united one person athanasian creed received


concept known sola scriptura books considered canonical vary depending upon denomination using defining variations reflection range traditions councils convened subject bible always includes books jewish scriptures tanakh includes additional books reorganizes two parts books old testament primarily sourced tanakh variations books new testament containing books originally written primarily greek catholic orthodox canons include books septuagint


greek jewish canon catholics call deuterocanonical protestants consider books apocryphal versions bible separate apocrypha section books considered canonical publisher catholic theology distinguishes two senses scripture literal spiritual ''literal'' sense understanding scripture meaning conveyed words scripture discovered exegesis following rules sound interpretation ' 'spiritual'' sense three subdivisions allegorical moral anagogical meaning mystical spiritual senses ''allegorical'' sense includes typology example would parting red sea


understood type sign baptism ''moral'' sense understands scripture contain ethical teaching ''anagogical'' interpretation includes eschatology applies eternity consummation world catholic theology adds rules interpretation include injunction senses sacred scripture based ''literal'' historical character four gospels faithfully hand jesus taught salvation scripture must read within living tradition whole church task authentic interpretation entrusted bishops communion


pope celebration christian mystery sacraments seven sacraments church source summit eucharist ref name ccc ref according ''catechism'' sacraments instituted christ entrusted church ref name ccc vehicles god 's grace flows person receives proper disposition ref name ccc order obtain proper disposition people encouraged cases required undergo sufficient preparation permitted receive certain sacraments ref name mongoven ref receiving sacraments ''catechism'' advises


attribute efficacy prayers sacramental signs mere external performance apart interior dispositions demand fall superstition ref name ccc ref participation sacraments offered church way catholics obtain grace forgiveness sins formally ask holy spirit ref name ccc sacraments baptism confirmation chrismation eucharist penance reconciliation anointing sick holy orders matrimony eastern catholic churches often called ''holy mysteries'' rather ' 'sacraments'' liturgy pope benedict xvi celebrates


eucharist canonization frei galv paulo brazil may sunday holy day obligation catholics required attend mass mass catholics believe respond jesus' command last supper remembrance council trent pope pius v codified standard book celebration mass roman rite ref name trent ref ref name cath update ref everything decree pertained priest celebrant action altar ref name cath update participation people devotional rather


liturgical ref name cath update mass text latin universal language church ref name trent liturgy called tridentine mass endured universally second vatican council approved mass paul vi also known new order mass may celebrated either vernacular latin ref name cath update catholic mass separated two parts first part called liturgy word readings old new testaments read prior gospel reading priest 's homily


second part called liturgy eucharist actual sacrament eucharist celebrated catholics regard eucharist source summit christian life ref name ccc believe bread wine brought altar changed transubstantiated power holy spirit true body blood soul divinity christ since sacrifice cross eucharist ''one single sacrifice'' ref name ccc ref church purport ' 're sacrifice'' jesus mass rather ' 're present'' ie make present


sacrifice unbloody manner ref name ccc eastern catholic eastern catholic churches term ''divine liturgy'' used place ''mass'' various eastern rites used place roman rite rites remained constant roman rite going back early church times eastern catholic orthodox liturgies generally quite similar liturgical action seen transcending time uniting participants already heavenly kingdom elements liturgy meant symbolize eternal realities go back early christian traditions


evolved jewish christian traditions early church first part liturgy liturgy catechumens scripture readings times homily second part derives last supper celebrated early christians belief partaking communion bread wine body blood christ together become body christ earth church liturgical calendar latin church annual calendar begins advent time hope filled preparation celebration jesus' birth second


works theophilus antioch wrote trinity god father word son wisdom holy spirit term may use time afterwards appears tertullian following century word general use found many passages origen according doctrine god divided sense person third whole rather person considered fully god see perichoresis distinction lies relations father unbegotten son


eternal yet begotten father holy spirit 'proceeding' father western theology son regardless apparent difference origins three 'persons' eternal omnipotent thought trinitarian christians revelation regarding god 's nature jesus christ came deliver world foundation belief system according prominent catholic theologian th century god self communication creation grace incarnation god really gives really appears


would lead conclusion come knowledge immanent trinity study god 's work economy creation salvation god father depiction god father offering right hand throne christ pieter de grebber utrecht museum catharijneconvent orb globe world almost exclusively associated father depictions trinity central statement catholic faith nicene creed begins believe one god father almighty maker heaven earth things visible


invisible thus catholics believe god part nature god created nature exists god viewed loving caring god active world people 's lives desires humankind love one another god son christ depicted creator world byzantine mosaic monreale sicily catholics believe jesus god incarnate true god true man fully divine fully human jesus become fully human suffered pain finally succumbed injuries gave


spirit said finished suffered temptations sin true god defeated death rose life according new testament god raised dead ascended heaven seated right hand father return fulfil rest messianic prophecy including resurrection dead last judgment final establishment kingdom god according gospels matthew luke jesus conceived holy spirit born virgin mary


little jesus' childhood recorded canonical gospels although infancy gospels popular antiquity comparison adulthood especially week death well documented gospels contained within new testament biblical accounts jesus' ministry include baptism healings teaching going good god holy spirit holy spirit depicted corrado giaquinto jesus told apostles death resurrection would send advocate holy spirit teach everything remind


told ref name onefaith barry ''one faith one lord'' p ref gospel luke jesus tells disciples evil know give good gifts children much heavenly father give holy spirit ask ref name schreck schreck ''the essential catholic catechism'' pp ref nicene creed states holy spirit one god father god son jesus thus catholics receiving holy spirit receiving god source good ref name kreeft kreeft ''catholic christianity''


p ref catholics formally ask receive holy spirit sacrament confirmation chrismation sometimes called sacrament christian maturity confirmation believed bring increase deepening grace received baptism ref name schreck cojoined early church spiritual graces gifts holy spirit include wisdom see follow god 's plan right judgment love others boldness witnessing faith rejoicing presence god ref name schreck corresponding fruits holy spirit love joy peace patience kindness goodness


faithfulness gentleness self control ref name schreck schreck ''the essential catholic catechism'' p ref validly confirmed person must state grace means cannot conscious committed mortal sin must also prepared spiritually sacrament chosen sponsor godparent spiritual support selected saint special patron ref name schreck soteriology sin salvation soteriology branch doctrinal theology deals salvation christ eternal life divine life nowiki cannot merited free gift


god crucifixion jesus explained atoning sacrifice words gospel john takes away sins world one 's reception salvation related justification fall man according church teaching event known fall angels number angels chose rebel god reign ref name ccc ref ref name ccc ref leader rebellion given many names including lucifer meaning light bearer latin satan devil sin pride considered one seven deadly sins


attributed satan desiring god 's equal ref name schreck schreck ''the essential catholic catechism'' p ref according genesis fallen angel tempted first humans adam eve sinned bringing suffering death world ''catechism'' states sin christians classify certain behaviors acts sinful means certain acts violation conscience divine law catholics make distinction two types sin mortal sin grave violation god 's law turns man away god redeemed


repentance cause exclusion christ 's kingdom eternal death hell contrast venial sin meaning forgivable sin set us direct opposition friendship god ref name ccc ref although still constituting moral disorder deprive sinner friendship god consequently eternal happiness heaven ref name ccc jesus christ savior depiction jesus mary theotokos vladimir th century old testament god promised send people savior ref name kreeft kreeft ''catholic christianity'' pp ref church believes


savior jesus john baptist called lamb god takes away sin world nicene creed refers jesus begotten son god begotten made consubstantial father things made supernatural event called incarnation catholics believe god came heaven salvation became man power holy spirit born virgin jewish girl named mary believe jesus' mission earth included giving people word example follow


recorded four gospels ref name mcgrath mcgrath ''christianity introduction'' pp ref church teaches following example jesus helps believers grow like therefore true love freedom fullness life ref name schreck schreck ''the essential catholic catechism'' p ref focus christian 's life firm belief jesus son god messiah christ title messiah comes hebrew word ''m '' meaning ''anointed one'' greek translation ''christos'' source english word christ christians believe


messiah jesus anointed god ruler savior humanity hold jesus' coming fulfillment messianic prophecies old testament christian concept messiah differs significantly contemporary jewish concept core christian belief death resurrection jesus sinful humans reconciled god thereby offered salvation promise eternal life heaven catholics believe resurrection jesus according new testament jesus central figure christianity crucified died buried within tomb resurrected


preaching useless trust god useless death resurrection jesus important events christian theology form point scripture jesus gives ultimate demonstration power life death thus ability give people eternal life generally christian churches accept teach new testament account resurrection jesus modern scholars use belief jesus' followers resurrection point departure establishing continuity historical jesus proclamation


early church liberal christians accept literal bodily resurrection hold convincing interior experience jesus' spirit members early church church teaches signified passion jesus crucifixion people opportunity forgiveness freedom sin reconciled god ref name kreeft sinning according greek word scripture ''amartia'' falling short mark succumbing imperfection always remain road perfection life ref name ccc people sin failing obey


ten commandments failing love god failing love people sins serious others ranging lesser venial sins grave mortal sins sever person 's relationship god ref name ccc ref name ccc ref ref name onefaith barry ''one faith one lord'' p ref penance conversion grace free operation effects grace understood differently different traditions catholicism eastern orthodoxy teach necessity free cooperate grace mean come god cooperate grace


semipelagianism early church heresy postulates human nature evil since god creates evil thing continue inclined sin concupiscence need grace god able repent believe gospel reformed theology contrast teaches people completely incapable self redemption point human nature evil grace god overcomes even unwilling heart arminianism takes synergistic approach lutheran doctrine teaches justification grace alone faith alone though common understanding doctrine justification


reached lutheran theologians forgiveness sins according catholicism forgiveness sins purification occur life example sacraments baptism reconciliation however purification achieved life venial sins still purified death sacrament anointing sick performed priest since involves elements forgiveness sin priest anoints oil head hands ill person saying prayers church ref name kreeft kreeft ''catholic christianity'' p ref baptism second


conversion st augustine'' benozzo gozzoli people cleansed personal sins baptism ref name kreeft kreeft ''catholic christianity'' p ref sacramental act cleansing admits one full member church conferred person 's lifetime ref name kreeft catholic church considers baptism important parents obliged see infants baptised within first weeks infant danger death baptised without delay declares practice infant baptism immemorial tradition


church explicit testimony practice second century quite possible beginning apostolic preaching whole 'households' received baptism infants may also baptized council trent november necessity second conversion baptism delineated ref david macdonald catholic apologist written regard paragraph endeavor conversion human work movement contrite heart drawn moved grace respond merciful


love god loved us first ref name macdonald ref penance reconciliation since baptism received sacrament penance reconciliation principal means catholics obtain forgiveness subsequent sin receive god 's grace assistance sin based jesus' words disciples ''gospel john'' ref name kreeft kreeft ''catholic christianity'' p ref penitent confesses sins priest may offer advice impose particular penance performed penitent prays act contrition


priest administers absolution formally forgiving person 's sins ref name kreeft kreeft ''catholic christianity'' p ref priest forbidden penalty excommunication reveal matter heard seal confessional penance helps prepare catholics validly receive holy spirit sacraments confirmation chrismation eucharist afterlife ''eschaton'' nicene creed ends look resurrection dead life world come accordingly church teaches person appear judgment seat christ immediately death receive


clothed ill cared prison visited amen say whatever one least brothers mine ref ref name matthew ref final judgment bring end human history also mark beginning new heaven earth righteousness dwells god reign forever ref name schreck schreck ''the essential catholic catechism'' p ref three states afterlife catholic belief heaven time glorious union god life unspeakable


joy lasts forever ref name schreck purgatory temporary state purification although saved free enough sin enter directly heaven state requiring purgation sin god 's mercy aided prayers others ref name schreck finally freely chose life sin selfishness sorry sins intention changing ways go hell everlasting separation god church teaches one condemned hell without freely deciding reject god 's love ref name schreck god


predestines one hell one determine whether anyone else condemned ref name schreck catholicism teaches god 's mercy person repent even point death saved like good thief crucified next jesus ref name schreck ref name luke ref second coming christ end time died resurrected bodily dead last judgment whereupon jesus fully establish kingdom god fulfillment scriptural prophecies ref name res thomas aquinas http wwwnewadventorg summa htm ''summa theologicum supplementum tertiae partis''


questions ref prayer dead indulgences pope depicted antichrist signing selling indulgences martin luther 's ''passional christi und antichristi'' lucas cranach elder catholic church teaches fate purgatory affected actions living context mention practice indulgences indulgence remission god temporal punishment due sins whose guilt already forgiven indulgences may obtained oneself behalf christians


died prayers dead indulgences envisioned decreasing duration time dead would spend purgatory traditionally indulgences measured term days quarantines ie day periods lent years meaning equivalent length canonical penance part living christian ref name autogenerated ref imposition canonical penances determinate duration fell desuetude expressions sometimes popularly misinterpreted reduction much time person 's stay purgatory ref name autogenerated concept time like


space doubtful applicability purgatory pope paul vi 's revision rules concerning indulgences expressions dropped replaced expression partial indulgence indicating person gained indulgence pious action granted addition remission temporal punishment acquired action equal remission punishment intervention church historically practice granting indulgences widespread associated abuses led seen increasingly bound money criticisms directed sale indulgences


source controversy immediate occasion protestant reformation germany switzerland salvation outside catholic church catholic church teaches one holy catholic apostolic church founded jesus concerning non catholics ''catechism catholic church'' drawing document ''lumen gentium'' vatican ii explains statement outside church salvation blockquote reformulated positively statement means salvation comes christ head church body basing scripture tradition council teaches church


pilgrim earth necessary salvation one christ mediator way salvation present us body church explicitly asserted necessity faith baptism thereby affirmed time necessity church men enter baptism door hence could saved knowing catholic church founded necessary god christ would refuse either enter remain affirmation aimed


fault know christ church nevertheless seek god sincere heart moved grace try actions know dictates conscience may achieve eternal salvation although ways known god lead fault ignorant gospel faith without impossible please church still obligation also sacred right evangelize


men blockquote ecclesiology church mystical body christ catholics believe catholic church continuing presence jesus earth ref name schreck schreck ''the essential catholic catechism'' p ref jesus told disciples abide vine branches thus catholics term church refers merely building exclusively ecclesiastical hierarchy first foremost people god abide jesus form different parts spiritual body ref name norman norman ''the roman catholic church


illustrated history'' p ref together composes worldwide christian community catholics believe church exists simultaneously earth church militant purgatory church suffering heaven church triumphant thus mary mother jesus saints alive part living church ref name kreeft kreeft ''catholic christianity'' pp ref unity church heaven earth called communion saints ref name kreeft kreeft ''catholic christianity'' p ref ref name ccc ref one holy catholic apostolic section second vatican council 's dogmatic constitution church ''lumen gentium'' states


church constituted organized world society subsists catholic church governed successor peter bishops communion although many elements sanctification truth found outside visible structure elements gifts belonging church christ forces impelling toward catholic unity faith church faith church latin ''fides ecclesiae'' basic concept catholic theology implies faithful individual catholic church whole considered


primary carrier christian faith refers act believing ''fides qua creditur'' well matters doctrine ''fides quae creditur'' according catholic teaching church received complete faith jesus christ apostles ' 'depositum fidei'' led holy spirit promised christ john church progressively times unpacks displays germ creed keeping actual alive may reductions unbalances single ages regions church whole however trusted sustained


truth maturate towards complete understanding equally concept act believing personal devotion holy inconceivable god individual participation devotion church means devotion christ father holy spirit single faithful consequence invited acquire faith church assiduously possible personal possession nevertheless aware insufficiency isolated cogitation listening common voice church devotion virgin mary saints


holy family catholics believe church community christians exists earth heaven simultaneously thus virgin mary saints alive part living church prayers devotions mary saints common practices catholic life devotions worship since god worshiped church teaches saints cease intercede father us fraternal concern weakness greatly helped ref name ccc catholics venerate mary many titles blessed virgin mother god


help christians mother faithful given special honor devotion saints honor devotion differs essentially adoration given god catholics worship mary honor mother god mother church spiritual mother believer christ called greatest saints first disciple queen heaven rev catholic belief encourages following example holiness prayers devotions asking intercession rosary hail mary memorare


common catholic practice church devotes several liturgical feasts mary mainly immaculate conception mary mother god visitation assumption nativity blessed virgin mary americas feast lady guadalupe pilgrimages marian shrines like lourdes france f tima portugal also common form devotion prayer ordained ministry bishops priests deacons roman catholic deacon wearing dalmatic men become bishops priests deacons sacrament holy orders candidates priesthood must college degree addition another four


years theological training including pastoral theology catholic church following example christ apostolic tradition ordains males church teaches apart ministry reserved priests women participate aspects church 's life leadership ref name nazareth ref bishops believed possess fullness catholic priesthood priests deacons participate ministry bishop body college bishops considered successors apostles pope cardinals patriarchs primates archbishops metropolitans bishops members catholic church episcopate college


prayer witness marriages conduct wake funeral services candidates diaconate go diaconate formation program must meet minimum standards set bishops' conference home country upon completion formation program acceptance local bishop candidates receive sacrament holy orders august pope francis established study commission women 's diaconate determine whether ordaining women deacons revived would include deacon 's role preaching eucharist deacons may married celibate men ordained priests


belief pope catholic bishops spiritual successors original twelve apostles historically unbroken chain consecration see holy orders pope spiritual head leader catholic church makes use roman curia assist governing elected college cardinals may choose male member church must ordained bishop taking office since th century current cardinal always elected new testament contains warnings teachings considered


truth guide truth clerical celibacy regarding clerical celibacy ''catechism catholic church'' states called consecrate undivided heart lord affairs lord give entirely god men celibacy sign new life service church 's minister consecrated accepted joyous heart celibacy radiantly proclaims reign god br eastern churches different discipline force many centuries bishops chosen solely


among celibates married men ordained deacons priests practice long considered legitimate priests exercise fruitful ministry within communities moreover priestly celibacy held great honor eastern churches many priests freely chosen sake kingdom god east west man already received sacrament holy orders longer marry catholic church 's discipline mandatory celibacy priests within latin church allowing limited individual exceptions criticized


following either protestant reformation practice rejects mandatory celibacy eastern catholic churches 's eastern orthodox churches 's practice requires celibacy bishops priestmonks excludes marriage priests ordination allow married men ordained priesthood july bishop emmanuel milingo created organization married priests responding milingo 's november consecration bishops vatican stated value choice priestly celibacy reaffirmed conversely young men united states increasingly entering formation priesthood long held traditional teaching


comfort suffer patience forgive hurt give advice correction need pray living dead ref name onefaith creation evolution today church 's official position remains focus controversy non specific stating faith scientific findings regarding human evolution conflict specifically church allows possibility human body developed previous biological forms god 's special providence immortal soul given humankind view falls spectrum


viewpoints grouped concept ''theistic evolution'' opposed several significant points view see creation evolution controversy discussion comparison traditions latin eastern catholicism eastern catholic churches theological spiritual liturgical patrimony traditions eastern christianity thus differences emphasis tone articulation various aspects catholic theology eastern latin churches mariology likewise medieval western scholasticism thomas aquinas particular little reception east eastern catholics respect papal authority


title orthodox protestant beliefs christian denominations differ catholics varying degrees eastern orthodox belief differs mainly regard papal infallibility filioque clause doctrine immaculate conception otherwise quite similar protestant churches vary beliefs generally differ catholics regarding authority pope church tradition well role mary saints role priesthood issues pertaining grace good works salvation ref name mcmanners mcmanners ''oxford illustrated history christianity'' pp ref five solas


one attempt express differences see also catholic catholic reformation eastern orthodox roman catholic theological differences eastern orthodox roman catholic ecclesiastical differences catholicism criticism roman catholic church catholic ecclesiology general roman calendar indult catholic list canonizations lists roman catholics philosophy theology fundamental theory catholic canon law scholasticism ten commandments catholic theology traditionalist catholic references notes '''''nota bene''''' cic stands ''code canon law'' latin name ''codex iuris canonici'' canons cited thus cic c works cited


'''irregular warfare''' '''iw''' defined united states joint doctrine violent struggle among state non state actors legitimacy influence relevant populations concepts associated irregular warfare older term ref name gates gates john us army irregular warfare college wooster ref one earliest known uses term ''irregular warfare'' english edition modern irregular warfare defense policy military phenomenon former nazi officer friedrich august freiherr von der heydte original german edition book

Applied science
Military sciences
Tactics
Irregular warfare


september attacks united states key proponent iw within us dod michael g vickers former paramilitary officer cia cia 's special activities division sad premiere unit unconventional warfare creating combating irregular warfare units example sad paramilitary officers created led successful irregular units hmong tribe war laos northern alliance taliban war afghanistan kurdish peshmerga ansar al islam forces saddam


hussein war iraq irregular warfare favors indirect warfare asymmetric warfare approaches though may employ full range military capabilities order erode adversary 's power influence inherently protracted struggle test resolve state strategic partners ref name dodd irregular warfare iw dod directive united states department defense december http wwwdticmil whs directives corres pdf ppdf ref distinction regular irregular forces unrelated term irregular warfare term irregular warfare settled upon distinction traditional warfare unconventional


goal undermining supporting authority iw favors indirect approaches though may employ full range military capabilities seek asymmetric approaches order erode adversary 's power influence iw defined violent struggle among state non state actors legitimacy influence relevant population iw involves conflicts enemy combatants regular military forces nation states iw war among people opposed industrial war ie regular war examples nearly modern wars include least element irregular warfare


since time napoleon approximately conflict irregular nature however following conflicts may considered exemplified irregular warfare ref name gates ref name white afghan civil war algerian war american indian wars american revolutionary war ref group nb according definition regular forces came much american revolutionary war arw american forces meet following criteria times arw fixed distinctive emblem recognizable distance carrying arms openly conducting operations accordance laws customs war br notwithstanding


terms modern international humanitarian law also developed much later arw american forces formed part armed forces party armed conflict belonging party 's regular forces since united states america exist hence could regular forces american forces insurgency least operating outside territory even territory occupation american forces become regular forces cannot considered regular forces entire period


arw example american flag got established years arw started also great disparities american british forces france started assist american forces disparity started narrowed conflict disparity surely counts asymmetric warfare also boston tea party viewed guerrilla tactics least good portion arw counted iw although entire arw counted iw controversial however since arw


fought arw thought safe classify iw even though american forces acted respects regular forces towards end conflict ref arab revolt chinese civil war cuban revolution first chechen war first sudanese civil war iraq war kosovo war lebanese civil war portuguese colonial war rwanda civil war second boer war second chechen war second sudanese civil war somali civil war philippine american war vietnam war libyan civil war syrian civil war iraqi civil war second libyan civil war yemeni civil war present activities


activities types conflict included iw asymmetric warfare civil military operations cmo colonial war foreign internal defense fid guerrilla warfare gw insurgency counter insurgency coin law enforcement activities focused countering irregular adversaries military intelligence counter intelligence activities stabilization security transition reconstruction operations sstro terrorism counter terrorism transnational criminal activities support sustain iw narco trafficking illicit arms trafficking illegal financial transactions unconventional warfare uw according dod five core activities iw counter insurgency coin counter terrorism ct unconventional warfare uw foreign internal defense fid stabilization operations modeling simulation result dod


directive ref name dodd united states armed forces studying irregular warfare concepts using modeling simulation wargames exercises several military wargames military exercises associated iw including unified action unified quest january tri service maritime workshop ref name ref joint irregular warrior series war games ref name expeditionary warrior war game series ref name december naval war college maritime stability operations game focused specifically stability operations maritime domain conducted naval service ref name see also arms trafficking asymmetric warfare center irregular warfare armed


groups civil military operations civilian casualty ratio counter insurgency counter intelligence counter terrorism endemic warfare foreign internal defense fourth generation warfare guerrilla warfare hague conventions illegal drug trade information warfare insurgency irregular military improvised fighting vehicle law enforcement low intensity conflict military intelligence political warfare psychological operations small wars journal strategic communication stabilization security transition reconstruction operations third geneva convention troubles unconventional warfare war terror war drugs '''individuals ''' che guevara clarence ransom edwards fran ois g r friedrich august freiherr von der heydte john r taylor e lawrence michael g vickers robert rogers' rules ranging


notes references group nb references external links military art science major irregular warfare specialty track http wwwusmaedu dmi irregular warfarehtm pincus walter irregular warfare future present washington post april https wwwwashingtonpostcom wp dyn content article ar html phillips joan fairchild muir irregular warfare maxwell air force base march http wwwauafmil au aul bibs irregularhtm gustafson michael modern irregular warfare counterinsurgency swedish national defence college http wwwkkrvase artiklar kkrvaht pdf coons kenneth c jr harned glenn irregular warfare warfare joint force quarterly national defense university http wwwnduedu inss press jfq pages editions pdf naval postgraduate school nps center terrorism irregular warfare ctiw http wwwnpsedu academics centers ctiw united states joint forces command usjfcom joint


irregular warfare center jiwc http wwwjfcommil abt jiwchtml ''armed groups irregular warfare adapting professional military education'' richard h shultz jr roy godson querine hanlon washington dc national strategy information center https webarchiveorg web http wwwstrategycenterorg publications armedgroups tomkins paul https purlfdlpgov gpo gpo irregular warfare annotated bibliography fort bragg nc united states army special operations command warfare type military science military doctrines guerrilla warfare tactics


'''gaelic literature''' literature vernacular gaelic languages ireland scotland isle man gaelic literature recognised third oldest literature tradition europe behind latin literature greek literature literature written gaelic languages st centuries ad present day latin used extensively gaelic lands advent christianity however gaels vanguard regards using language write literary works merit history old gaelic ce ce oldest surviving literature gaelic

Humanities
Languages and literature
Gaelic Literature


piece dedicated colm cille iona ad arrival christianity ireland gaels limited level literacy primitive irish manifested ogham inscriptions wood stone typically memorials dead boundary markers traditional stories people circulated form oral culture rather written works christian nature first appear ''sean ghaeilge'' old irish earliest form written latin script would appear gaelic speaking monks wanted


impart religion flocks native tongue thought likely first church hymns prayers composed old irish early th century work ''amra choluim chille'' earliest extant literary work nature left us written early form ''sean ghaeilge'' meter old fashioned appearance rest literature period experts think composed dall n forgaill towards end th century colm cille died