components '''x''' variables determined '''c''' '''b''' given vectors math mathbf c math indicating coefficients '''c''' used single row matrix purpose forming matrix product ''a'' given matrix function whose value maximized minimized math mathbf x mapsto mathbf c mathbf x math case called objective function inequalities ''a'''''x''' nbsp nbsp '''b''' '''x''' ''' ''' constraints specify convex polytope objective function optimized context two vectors comparable dimensions


solving system linear inequalities dates back least far fourier published method solving ref name sierksmazwols ref method fourier motzkin elimination named linear programming formulation problem equivalent general linear programming problem given soviet mathematician economist leonid kantorovich also proposed method solving ref name schrijver ref way developed world war ii plan expenditures returns order reduce costs army increase losses imposed

Applied science
Transportation
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Linear programming


enemy kantorovich 's work initially neglected ussr ref name dantzig ref time kantorovich dutch american economist c koopmans formulated classical economic problems linear programs kantorovich koopmans later shared nobel prize economics ref name sierksmazwols frank lauren hitchcock also formulated transportation problems linear programs gave solution similar later simplex method ref name schrijver hitchcock died nobel prize awarded posthumously george b dantzig independently developed general linear programming formulation use planning problems


us air force ref name ref dantzig also invented simplex method first time efficiently tackled linear programming problem cases ref name dantzig arranged meeting john von neumann discuss simplex method neumann immediately conjectured theory duality realizing problem working game theory equivalent ref name dantzig provided formal proof unpublished report theorem linear inequalities january ref name dantzig dantzig 's work made available public post war years many industries applied


daily planning dantzig 's original example find best assignment people jobs computing power required test permutations select best assignment vast number possible configurations exceeds number particles observable universe however takes moment find optimum solution posing problem linear program applying simplex algorithm theory behind linear programming drastically reduces number possible solutions must checked linear programming problem first shown solvable


number algorithms types optimization problems work solving lp problems sub problems historically ideas linear programming inspired many central concepts optimization theory ' 'duality'' ' 'decomposition'' importance ''convexity'' generalizations likewise linear programming heavily used early formation microeconomics currently utilized company management planning production transportation technology issues although modern management issues ever changing companies would like maximize profits minimize costs limited resources google uses linear programming stabilize youtube videos


therefore many issues characterized linear programming problems standard form ''standard form'' usual intuitive form describing linear programming problem consists following three parts '''linear function maximized''' eg math f x x c x c x math '''problem constraints''' following form eg math begin matrix x x leq b x x leq b x x leq b end matrix math '''non negative variables''' eg math begin matrix x geq x geq


end matrix math problem usually expressed ''matrix form'' becomes math max mathbf c mathrm mathbf x mid mathbf x mathbb r n land mathbf x leq mathbf b land mathbf x geq math forms minimization problems problems constraints alternative forms well problems involving negative variables always rewritten equivalent problem standard form example suppose farmer piece farm land say ''l'' km sup sup planted either wheat barley combination two farmer limited amount fertilizer ''f'' kilograms pesticide


''p'' kilograms every square kilometer wheat requires ''f'' sub sub kilograms fertilizer ''p'' sub sub kilograms pesticide every square kilometer barley requires ''f'' sub sub kilograms fertilizer ''p'' sub sub kilograms pesticide let sub sub selling price wheat per square kilometer sub sub selling price barley denote area land planted wheat barley ''x'' sub sub ''x'' sub sub respectively profit maximized choosing optimal values ''x'' sub sub ''x'' sub sub problem expressed following linear programming problem standard form


colspan maximize math cdot x cdot x math maximize revenue total wheat sales plus total barley sales revenue objective function subject math x x leq l math limit total area math f cdot x f cdot x leq f math limit fertilizer math p cdot x p cdot x leq p math limit pesticide math x geq x geq math cannot plant negative area matrix form becomes maximize math begin bmatrix end bmatrix begin bmatrix x x end bmatrix math subject math begin bmatrix


f f p p end bmatrix begin bmatrix x x end bmatrix le begin bmatrix l f p end bmatrix begin bmatrix x x end bmatrix ge begin bmatrix end bmatrix math augmented form slack form linear programming problems converted ''augmented form'' order apply common form simplex algorithm form introduces non negative ' 'slack variables'' replace inequalities equalities constraints problems written following block matrix form maximize math z math math begin bmatrix mathbf c


mathbf mathbf end bmatrix begin bmatrix z mathbf x mathbf end bmatrix begin bmatrix mathbf b end bmatrix math math mathbf x ge mathbf ge math math mathbf math newly introduced slack variables math mathbf x math decision variables math z math variable maximized example example converted following augmented form colspan maximize math cdot x cdot x math objective function subject math x x x l math augmented constraint math f cdot x f cdot x x f math


augmented constraint math p cdot x p cdot x x p math augmented constraint math x x x x x ge math math x x x math non negative slack variables representing example unused area amount unused fertilizer amount unused pesticide matrix form becomes maximize math z math math begin bmatrix f


f p p end bmatrix begin bmatrix z x x x x x end bmatrix begin bmatrix l f p end bmatrix begin bmatrix x x x x x end bmatrix ge math duality every linear programming problem referred ''primal'' problem converted dual problem provides upper bound optimal value primal problem


matrix form express ''primal'' problem maximize '''c''' sup sup '''x''' subject ''a'''''x''' '''b''' '''x''' corresponding '' 'symmetric''' dual problem minimize '''b''' sup sup '''y''' subject ''a'' sup sup '''y''' '''c''' '''y''' alternative primal formulation maximize '''c''' sup sup '''x''' subject ''a'''''x''' '''b''' corresponding '''asymmetric''' dual problem minimize '''b''' sup sup '''y''' subject ''a'' sup sup '''y''' '''c''' '''y''' two ideas fundamental duality theory one fact symmetric dual dual dual linear program


original primal linear program additionally every feasible solution linear program gives bound optimal value objective function dual weak duality theorem states objective function value dual feasible solution always greater equal objective function value primal feasible solution strong duality theorem states primal optimal solution '''x''' sup sup dual also optimal solution '''y''' sup sup '''c''' sup sup '''x''' sup sup '''b''' sup sup '''y''' sup sup linear program also unbounded infeasible duality theory tells us


primal unbounded dual infeasible weak duality theorem likewise dual unbounded primal must infeasible however possible dual primal infeasible see dual linear program details several examples variations covering packing dualities covering lp linear program form minimize big '''b''' sup sup '''y''' big subject big ''a'' sup sup '''y''' '''c''' '''y''' big matrix ''a'' vectors '''b''' '''c''' non negative dual


covering lp packing lp linear program form maximize big '''c''' sup sup '''x''' big subject big ''a'''''x''' '''b''' '''x''' big matrix ''a'' vectors '''b''' '''c''' non negative examples covering packing lps commonly arise linear programming relaxation combinatorial problem important study approximation algorithms example lp relaxations set packing problem independent set problem matching problem packing lps lp relaxations set cover problem vertex cover problem dominating


set problem also covering lps finding fractional coloring graph another example covering lp case one constraint vertex graph one variable independent set graph complementary slackness possible obtain optimal solution dual optimal solution primal known using complementary slackness theorem theorem states suppose '''x''' nbsp nbsp '''x''' sub sub nbsp '''x''' sub sub nbsp nbsp nbsp '''x''' sub ''n'' sub primal feasible '''y''' nbsp nbsp '''y''' sub sub nbsp '''y''' sub sub nbsp nbsp nbsp '''y''' sub ''m'' sub dual feasible let '''w''' sub sub nbsp '''w''' sub sub nbsp nbsp '''w''' sub ''m'' sub denote corresponding primal slack variables let '''z''' sub sub nbsp '''z''' sub sub nbsp nbsp nbsp '''z''' sub ''n'' sub denote


corresponding dual slack variables '''x''' '''y''' optimal respective problems '''x''' sub ''j'' sub '''z''' sub ''j'' sub nbsp nbsp ''j'' nbsp nbsp nbsp nbsp nbsp nbsp ''n'' '''w''' sub ''i'' sub '''y''' sub ''i'' sub nbsp nbsp ''i'' nbsp nbsp nbsp nbsp nbsp nbsp ''m'' ''i'' th slack variable primal zero ''i'' th variable dual equal zero likewise ''j'' th slack variable dual zero ''j'' th variable primal equal zero necessary condition optimality conveys fairly simple economic principle standard form maximizing slack constrained primal resource


ie leftovers additional quantities resource must value likewise slack dual shadow price non negativity constraint requirement ie price zero must scarce supplies leftovers theory existence optimal solutions geometrically linear constraints define feasible region convex polyhedron linear function convex function implies every local minimum global minimum similarly linear function concave function implies every local maximum global maximum


optimal solution need exist two reasons first constraints inconsistent feasible solution exists instance constraints '''x''' nbsp nbsp '''x''' nbsp nbsp cannot satisfied jointly case say lp ''infeasible'' second polytope unbounded direction gradient objective function gradient objective function vector coefficients objective function optimal value attained always possible better finite value objective function optimal vertices rays


polyhedra otherwise feasible solution exists constraint set bounded optimum value always attained boundary constraint set ''maximum principle'' ''convex functions'' alternatively ''minimum'' principle ''concave functions'' since linear functions convex concave however problems distinct optimal solutions example problem finding feasible solution system linear inequalities linear programming problem objective function zero function constant function taking value zero everywhere


feasibility problem zero function objective function two distinct solutions every convex combination solutions solution vertices polytope also called ''basic feasible solutions'' reason choice name follows let ' 'd'' denote number variables fundamental theorem linear inequalities implies feasible problems every vertex '''x''' sup sup lp feasible region exists set ' 'd'' fewer inequality constraints lp treat ' 'd'' constraints equalities unique solution


'''x''' sup sup thereby study vertices means looking certain subsets set constraints discrete set rather continuum lp solutions principle underlies simplex algorithm solving linear programs algorithms convex feasible region possible values variables two variable case region shape convex simple polygon basis exchange algorithms simplex algorithm dantzig simplex algorithm developed george dantzig solves lp problems constructing feasible solution vertex


polytope walking along path edges polytope vertices non decreasing values objective function optimum reached sure many practical problems stalling occurs many pivots made increase objective function ref name dt ref ref name padberg ref rare practical problems usual versions simplex algorithm may actually cycle ref name padberg avoid cycles researchers developed new pivoting rules ref name bland ref ref name murty ref ref name dt ref name padberg ref name ps ref ref name fukudaterlaky practice simplex algorithm quite efficient guaranteed find global


optimum certain precautions ''cycling'' taken simplex algorithm proved solve random problems efficiently ie cubic number steps similar behavior practical problems ref name dt ref name todd ref however simplex algorithm poor worst case behavior klee minty constructed family linear programming problems simplex method takes number steps exponential problem size ref name dt ref name murty ref name ps fact time known whether linear programming problem solvable polynomial time ie complexity


class p criss cross algorithm like simplex algorithm dantzig criss cross algorithm basis exchange algorithm pivots bases however criss cross algorithm need maintain feasibility pivot rather feasible basis infeasible basis criss cross algorithm polynomial time complexity linear programming algorithms visit nbsp sup ''d'' sup corners perturbed cube dimension nbsp ''d'' klee minty cube worst case ref name fukudaterlaky ref ref name roos ref interior point contrast simplex algorithm finds optimal solution traversing edges vertices polyhedral set interior point


methods move interior feasible region ellipsoid algorithm following khachiyan first worst case polynomial time algorithm ever found linear programming solve problem ''n'' variables encoded ''l'' input bits algorithm runs math n l math time ref name khachiyan leonid khachiyan solved long standing complexity issue introduction ellipsoid method convergence analysis real number predecessors notably iterative methods developed naum z shor approximation algorithms arkadi nemirovski yudin projective


sidford showed solved math tilde nnz sqrt l math time math nnz math represents number non zero elements remains taking math n l math worst case current matrix multiplication time algorithm cohen lee song improved running time math tilde n omega n alpha n l math time math omega math exponent matrix multiplication math alpha math dual exponent matrix multiplication math alpha math roughly defined largest number one multiply math n times


n math matrix math n times n alpha math matrix math n math time followup work lee song zhang reproduce result via different method two algorithms remain math tilde n l math math omega math math alpha math result due jiang song weinstein zhang improved math tilde n l math math tilde n l math comparison interior point methods simplex algorithms current opinion efficiencies good implementations


simplex based methods interior point methods similar routine applications linear programming however specific types lp problems may one type solver better another sometimes much better structure solutions generated interior point methods versus simplex based methods significantly different support set active variables typically smaller latter one open problems recent work several open problems theory linear programming solution would represent fundamental breakthroughs mathematics potentially major


advances ability solve large scale linear programs lp admit strongly polynomial time algorithm lp admit strongly polynomial time algorithm find strictly complementary solution lp admit polynomial time algorithm real number unit cost model computation closely related set problems cited stephen smale among greatest unsolved problems st century smale 's words third version problem main unsolved problem linear programming theory algorithms exist solve linear programming weakly polynomial time


ellipsoid methods interior point techniques algorithms yet found allow strongly polynomial time performance number constraints number variables development algorithms would great theoretical interest perhaps allow practical gains solving large lps well although hirsch conjecture recently disproved higher dimensions still leaves following questions open pivot rules lead polynomial time simplex variants polytopal graphs polynomially bounded diameter questions relate performance analysis development simplex like methods immense


efficiency simplex algorithm practice despite exponential time theoretical performance hints may variations simplex run polynomial even strongly polynomial time would great practical theoretical significance know whether variants exist particularly approach deciding lp solved strongly polynomial time simplex algorithm variants fall family edge following algorithms named solve linear programming problems moving vertex vertex along edges polytope means theoretical performance


limited maximum number edges two vertices lp polytope result interested knowing maximum graph theoretical diameter polytopal graphs proved polytopes subexponential diameter recent disproof hirsch conjecture first step prove whether polytope superpolynomial diameter polytopes exist edge following variant run polynomial time questions polytope diameter independent mathematical interest simplex pivot methods preserve primal dual feasibility hand criss cross pivot


methods preserve primal dual feasibilitythey may visit primal feasible dual feasible primal dual infeasible bases order pivot methods type studied since essentially methods attempt find shortest pivot path arrangement polytope linear programming problem contrast polytopal graphs graphs arrangement polytopes known small diameter allowing possibility strongly polynomial time criss cross pivot algorithm without resolving questions diameter general polytopes ref name fukudaterlaky integer unknowns unknown variables


required integers problem called integer programming ip '''integer linear programming''' ilp problem contrast linear programming solved efficiently worst case integer programming problems many practical situations bounded variables np hard ''' integer programming''' '''binary integer programming''' bip special case integer programming variables required rather arbitrary integers problem also classified np hard fact decision version one karp 's np complete problems


unknown variables required integers problem called '''mixed integer programming''' mip problem generally also np hard even general ilp programs however important subclasses ip mip problems efficiently solvable notably problems constraint matrix totally unimodular right hand sides constraints integers general system total dual integrality tdi property advanced algorithms solving integer linear programs include cutting plane method branch bound branch cut branch


price problem extra structure may possible apply delayed column generation integer programming algorithms discussed padberg beasley integral linear programs linear program real variables said '''integral''' least one optimal solution integral likewise polyhedron math p x mid ax ge math said '''integral''' bounded feasible objective functions ''c'' linear program math max cx mid x p math optimum math x math integer coordinates observed edmonds giles


one equivalently say polyhedron math p math integral every bounded feasible integral objective function ''c'' optimal ''value'' linear program math max cx mid x p math integer integral linear programs central importance polyhedral aspect combinatorial optimization since provide alternate characterization problem specifically problem convex hull solutions integral polyhedron polyhedron nice compact description efficiently find optimal feasible solution linear objective conversely prove


linear programming relaxation integral desired description convex hull feasible integral solutions terminology consistent throughout literature one careful distinguish following two concepts ''integer linear program'' described previous section variables forcibly constrained integers problem np hard general ''integral linear program'' described section variables constrained integers rather one proven somehow continuous problem always integral optimal value assuming ''c'' integral optimal


value may found efficiently since polynomial size linear programs solved polynomial time one common way proving polyhedron integral show totally unimodular general methods including integer decomposition property total dual integrality specific well known integral lps include matching polytope lattice polyhedra submodular flow polyhedra intersection two generalized polymatroids ''g'' polymatroids eg see schrijver solvers scripting programming languages '''permissive licenses ''' class wikitable name license brief info glop apache v google 's open source linear programming solver


pyomo bsd open source modeling language large scale linear mixed integer nonlinear optimization suanshu apache v open source suite optimization algorithms solve lp qp socp sdp sqp java '''copyleft reciprocal licenses ''' class wikitable name license brief info cassowary constraint solver lgpl incremental constraint solving toolkit efficiently solves systems linear equalities inequalities clp cpl lp solver coin glpk gpl gnu linear programming kit lp milp solver native c api numerous third party wrappers languages specialist support flow networks bundles ampl like gnu mathprog


modelling language translator qoca gpl library incrementally solving systems linear equations various goal functions r project gpl programming language software environment statistical computing graphics minto mixed integer optimizer integer programming solver uses branch bound algorithm publicly available source code open source '''proprietary licenses ''' class wikitable name brief info aimms modeling language allows model linear mixed integer nonlinear optimization models also offers tool constraint programming algorithm forms heuristics exact methods branch cut


column generation also implemented tool calls appropriate solver cplex similar solve optimization problem hand academic licenses free charge ampl popular modeling language large scale linear mixed integer nonlinear optimisation free student limited version available variables constraints apmonitor api matlab python solve example linear programming lp problems matlab python web interface cplex popular solver api several programming languages also modelling language works aimms ampl gams mpl openopt


opl development studio tomlab free academic use excel solver function nonlinear solver adjusted spreadsheets function evaluations based recalculating cells basic version available standard add excel fortmp gams imsl numerical libraries collections math statistical algorithms available c c fortran java c net optimization routines imsl libraries include unconstrained linearly nonlinearly constrained minimizations linear programming algorithms lindo solver api large scale optimization linear integer quadratic conic general nonlinear programs stochastic programming extensions


offers global optimization procedure finding guaranteed globally optimal solution general nonlinear programs continuous discrete variables also statistical sampling api integrate monte carlo simulations optimization framework algebraic modeling language lingo allows modeling within spreadsheet 'sbest maple general purpose programming language symbolic numerical computing matlab general purpose matrix oriented programming language numerical computing linear programming matlab requires optimization toolbox addition base matlab product available routines include intlinprog linprog mathcad wysiwyg math editor functions


solving linear nonlinear optimization problems mathematica general purpose programming language mathematics including symbolic numerical capabilities mosek solver large scale optimization api several languages c javanet matlab python nag numerical library collection mathematical statistical routines developed numerical algorithms group multiple programming languages c c fortran visual basic java c packages matlab excel r labview optimization chapter nag library includes routines linear programming problems sparse non sparse linear constraint matrices together routines optimization


quadratic nonlinear sums squares linear nonlinear functions nonlinear bounded constraints nag library routines local global optimization continuous integer problems optimj java based modeling language optimization free version available sas suite solvers linear integer nonlinear derivative free network combinatorial constraint optimization algebraic modeling language optmodel variety vertical solutions aimed specific problems markets fully integrated sas system scip general purpose constraint integer programming solver emphasis mip


compatible zimpl modelling language free academic use available source code xpress solver large scale linear programs quadratic programs general nonlinear mixed integer programs api several programming languages also modelling language mosel works ampl gams free academic use vissim visual block diagram language simulation dynamical systems see also convex programming dynamic programming input output model job shop scheduling linear algebra linear production game linear fractional programming lfp lp type problem mathematical programming nonlinear programming oriented matroid quadratic programming superset linear programming semidefinite programming shadow


york geometry external links http peoplebrunelacuk mastjjb jeb lphtml guidance formulating lp problems http glossarycomputingsocietyinformsorg mathematical programming glossary http lpsolvesourceforgenet linearprogrammingfaqhtm linear programming faq http platoasuedu benchhtml benchmarks optimisation software convex optimization geometric algorithms p complete problems


thermohaline circulation '''oceanography''' ancient greek ocean write also known '''oceanology''' scientific study ocean important earth science covers wide range topics including ecosystem dynamics ocean currents waves geophysical fluid dynamics plate tectonics geology sea floor fluxes various chemical substances physical properties within ocean across boundaries diverse topics reflect multiple disciplines oceanographers utilize glean knowledge world ocean including astronomy biology chemistry climatology geography geology hydrology meteorology physics

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Geography
Physical geography
Oceanography


paleoceanography studies history oceans geologic past '''oceanographer''' person studies many matters concerned oceans including marine geology physics chemistry biology history map gulf stream benjamin franklin courtesy noaa photo library early history humans first acquired knowledge waves currents seas oceans pre historic times observations tides recorded aristotle strabo bc early exploration oceans primarily cartography mainly limited surfaces animals fishermen brought


nets though depth soundings lead line taken portuguese campaign atlantic navigation earliest example systematic scientific large project sustained many decades studying currents winds atlantic work pedro nunes one great mathematicians remembered navigation context determination loxodromic curve shortest course two points surface sphere represented onto two dimensional map ref name mathshistoryst andrewsacuk https mathshistoryst andrewsacuk biographies nunes retrieved ref published treatise sphere mostly commentated translation earlier work others


included treatise geometrical astronomic methods navigation states clearly portuguese navigations adventurous endeavour '' nam se fezeram indo acertar mas partiam os nossos mareantes muy ensinados e prouidos de estromentos e regras de astrologia e geometria que sam cousas que os cosmographos ham dadar apercebidas e leuaua cartas muy particularmente rumadas e na ja de que os antigos vsauam '' done chance seafarers departed well taught provided instruments rules astrology astronomy geometry matters cosmographers would provide


took charts exact routes longer used ancient credibility rests personally involved instruction pilots senior seafarers onwards royal appointment along recognised competence mathematician astronomer ref name mathshistoryst andrewsacuk main problem navigating back south canary islands south boujdour sail alone due change regime winds currents north atlantic gyre equatorial counter current push south along northwest bulge africa


uncertain winds northeast trades meet southeast trades doldrums leave sailing ship mercy currents together prevalent current wind make northwards progress difficult impossible overcome problem clear passage india around africa viable maritime trade route systematic plan exploration devised portuguese return route regions south canaries became 'volta largo' 'volta mar' 'rediscovery' azores islands merely reflection heightened strategic


importance islands sitting return route western coast africa sequentially called 'volta de guin ' 'volta da mina' references sargasso sea also called time 'mar da baga' west azores reveals western extent return route ref name referencea carlos calinas correia arte de navegar na poca dos descobrimentos colibri lisboa ref necessary sail make use southeasterly northeasterly winds away western coast africa northern latitudes westerly


winds bring seafarers towards western coasts europe secrecy involving portuguese navigations death penalty leaking maps routes concentrated sensitive records royal archives completely destroyed lisbon earthquake however systematic nature portuguese campaign mapping currents winds atlantic demonstrated understanding seasonal variations expeditions setting sail different times year taking different routes take account seasonal predominate winds happens early late th century early


th bartolomeu dias followed african coast way south august vasco da gama would take open sea route latitude sierra leone spending months open sea south atlantic profit southwards deflection southwesterly brazilian side brazilian current going southward gama departed july pedro alvares cabral departing march took even larger arch west latitude cape verde thus avoiding summer monsoon would blocked route taken


gama time set sail furthermore systematic expeditions pushing western northern atlantic teive vogado teles ulmo documents relating supplying ships ordering sun declination tables southern atlantic early suggest well planned systematic activity happening decade long period bartolomeu dias finding southern tip africa gama 's departure additionally indications travels bartolomeu dias area ref name referencea significant consequence systematised knowledge


negotiation treaty tordesillas moving line demarcation leagues west leagues west azores bringing brazil portuguese area domination knowledge gathered open sea exploration allowed well documented extended periods sail without sight land accident pre determined planned route example days bartolomeu dias culminating mossel bay months gama spend southern atlantic use brazil current southward days cabral took


cape verde landing monte pascoal brazil danish expedition arabia said world 's first oceanographic expedition ship gr nland board group scientists including naturalist peter forssk l assigned explicit task king frederik v study describe marine life open sea including finding cause mareel milky seas purpose expedition equipped nets scrapers specifically designed collect samples open waters bottom great depth although juan ponce


de le n first identified gulf stream current well known mariners benjamin franklin made first scientific study gave name franklin measured water temperatures several atlantic crossings correctly explained gulf stream 's cause franklin timothy folger printed first map gulf stream ref name noaa franklin ref atlantic indian oceans james rennell information currents pacific ocean gathered explorers late th century including james cook louis antoine de bougainville james rennell wrote first scientific textbooks


oceanography detailing current flows atlantic indian oceans voyage around cape good hope mapped '' banks currents lagullas '' also first understand nature intermittent current near isles scilly known rennell 's current sir james clark ross took first modern sounding deep sea charles darwin published paper reefs formation atolls result second voyage hms ''beagle'' robert fitzroy published four volume report


''beagle' 's three voyages edward forbes undertook dredging aegean sea founded marine ecology first superintendent united states naval observatory matthew fontaine maury devoted time study marine meteorology navigation charting prevailing winds currents textbook ''physical geography sea'' one first comprehensive oceanography studies many nations sent oceanographic observations maury naval observatory colleagues evaluated information distributed results worldwide modern oceanography knowledge oceans remained confined topmost


fathoms water small amount bottom mainly shallow areas almost nothing known ocean depths british royal navy 's efforts chart world 's coastlines mid th century reinforced vague idea ocean deep although little known exploration ignited popular scientific interest polar regions africa mysteries unexplored oceans undertook first global marine research expedition seminal event founding modern science


oceanography '' challenger'' expedition first true oceanographic cruise expedition laid groundwork entire academic research discipline ref name noaa http oceanexplorernoaagov explorations mountains background challenger challengerhtml hms challenger expedition 'mountains sea' expedition ocean explorer website noaa accessed january ref response recommendation royal society british government announced expedition explore world 's oceans conduct appropriate scientific investigation charles wyville thompson sir john murray launched ''challenger'' expedition leased royal navy modified scientific work equipped


separate laboratories natural history chemistry ref name rice ref scientific supervision thomson ''challenger'' travelled nearly surveying exploring journey circumnavigating globe ref name rice nbsp deep sea soundings nbsp bottom dredges nbsp open water trawls nbsp serial water temperature observations taken around nbsp new species marine life discovered result ''report scientific results exploring voyage hms challenger years '' murray supervised publication described report greatest advance knowledge planet since celebrated discoveries fifteenth sixteenth centuries


went found academic discipline oceanography university edinburgh remained centre oceanographic research well th century murray first study marine trenches particular mid atlantic ridge map sedimentary deposits oceans tried map world 's ocean currents based salinity temperature observations first correctly understand nature coral reef development late th century western nations also sent scientific expeditions private individuals institutions first purpose built oceanographic


johan hjort ambitious research oceanographic marine zoological project ever mounted led classic book ''the depths ocean'' first acoustic measurement sea depth made meteor expedition gathered ocean depth measurements using echo sounder surveying mid atlantic ridge easter ellen cupp first woman earned phd scripps united states completed major work diatoms remained standard taxonomy field well death


cupp let go position scripps sverdrup specifically commended cupp conscientious industrious worker commented decision reflection ability scientist sverdrup used instructor billet vacated cupp employ marston sargenta biologist studying marine algae new research program scripps financial pressures prevent sverdrup retaining services two young post doctoral students walter munk roger revelle cupp 's partner dorothy rosenbury found position teaching high school remained rest career


russell sverdrup johnson fleming published ''the oceans'' major landmark ''the sea'' three volumes covering physical oceanography seawater geology edited mn hill published rhodes fairbridge 's ''encyclopedia oceanography'' published great global rift running along mid atlantic ridge discovered maurice ewing bruce heezen mapped heezen marie tharp using bathymetric data mountain range arctic ocean found arctic institute ussr theory seafloor spreading


developed harry hammond hess ocean drilling program started deep sea vents discovered jack corliss robert ballard submersible auguste piccard invented bathyscaphe used bathyscaphe investigate ocean 's depths united states nuclear submarine made first journey ice north pole flip floating instrument platform spar buoy first deployed tanya atwater led first woman oceanographic expedition time gender policies restricted women oceanographers


participating voyages significant extent much emphasis application large scale computers oceanography allow numerical predictions ocean conditions part overall environmental change prediction early techniques included analog computers ishiguro storm surge computer generally replaced numerical methods eg slosh oceanographic buoy array established pacific allow prediction el ni events saw start world ocean circulation experiment woce continued geosat seafloor mapping data became available


recent years studies advanced particular knowledge ocean acidification ocean heat content ocean currents el ni phenomenon mapping methane hydrate deposits carbon cycle coastal erosion weathering climate feedbacks regards climate change interactions study oceans linked understanding global climate changes potential global warming related biosphere concerns atmosphere ocean linked evaporation precipitation well thermal flux solar insolation wind stress major driver ocean currents ocean sink atmospheric carbon dioxide factors relate


changes ocean chemistry focuses primarily geochemical cycles following central topic investigated chemical oceanography ocean acidification ocean acidification describes decrease ocean ph caused anthropogenic carbon dioxide emissions atmosphere ref name cald ref seawater slightly alkaline preindustrial ph recently anthropogenic activities steadily increased carbon dioxide content atmosphere added co sub sub absorbed oceans forming carbonic acid lowering ph ref name epa ocean acidity ref ocean acidification ref name feely ref ref name zeebe ref ref name gattusohansson ref ph


expected reach year ref name aboutantarctica important element skeletons marine animals calcium calcium carbonate becomes soluble pressure carbonate shells skeletons dissolve carbonate compensation depth ref name pinet ref calcium carbonate becomes soluble lower ph ocean acidification likely affect marine organisms calcareous shells oysters clams sea urchins corals ref name pmel ref ref name orr ref carbonate compensation depth rise closer sea surface affected planktonic organisms include pteropods coccolithophorids foraminifera important food chain tropical


ocean floor including plate tectonics paleoceanography physical oceanography physical oceanography studies ocean 's physical attributes including temperature salinity structure mixing surface waves internal waves surface tides internal tides currents following central topics investigated physical oceanography seismic oceanography ocean currents since early ocean expeditions oceanography major interest study ocean currents temperature measurements tides coriolis effect changes direction strength wind salinity temperature main factors determining ocean currents thermohaline circulation thc ''thermo '' referring temperature '' haline'' referring salt


content connects ocean basins primarily dependent density sea water becoming common refer system 'meridional overturning circulation' accurately accounts driving factors beyond temperature salinity examples sustained currents gulf stream kuroshio current wind driven western boundary currents ocean heat content https climatenasagov climate reel oceansclimatechange oceans climate change nasa oceanic heat content ohc refers heat stored ocean changes ocean heat play important role sea level rise thermal expansion


international council exploration sea scripps institution oceanography founded followed woods hole oceanographic institution virginia institute marine science later lamont doherty earth observatory columbia university school oceanography university washington britain national oceanography centre institute natural environment research council successor uk 's institute oceanographic sciences australia csiro marine atmospheric research cmar leading centre international hydrographic bureau ihb formed monaco related


disciplines see also list seas ocean optics ocean color ocean chemistry references sources hamblin jacob darwin https booksgooglecom booksid jruk ergc dq hamblin oceanographers cold war pg pp ots us ku jpm sig bck mb et ih rmdrris nwzzg hl en sa x oi book result resnum ct result ''oceanographers cold war disciples marine science'' university washington press steele j k turekian thorpe ''encyclopedia ocean sciences'' san diego academic press vols sverdrup keith duxbury alyn c duxbury alison b ''fundamentals oceanography'' mcgraw hill lang michael ian g macintyre klaus r tzler eds http wwwsilsiedu smithsoniancontributions marinesciences sc recordsinglecfmfilename scms ''proceedings smithsonian marine science symposium'' smithsonian contributions marine sciences washington dc smithsonian institution scholarly press boling guo daiwen


huang http wwwworldscientificcom worldscibooks ''infinite dimensional dynamical systems atmospheric oceanic science'' world scientific publishing http wwwworldscientificcom doi suppl suppl file chap pdf sample chapter russell joellen louise https libraryucsdedu dc object bb pdf regents university california external links http podaacjplnasagov nasa jet propulsion laboratory physical oceanography distributed active archive center podaac data centre responsible archiving distributing data physical state ocean http wwwscrippsucsdedu scripps institution oceanography one world 's oldest largest important centres ocean earth science research education public service http wwwwhoiedu woods hole oceanographic institution whoi one world 's largest private non profit ocean research


engineering education organizations http wwwbodcacuk british oceanographic data centre source oceanographic data information https webarchiveorg web http dapperpmelnoaagov dchart noaa ocean weather data navigator plot download ocean data http wwwvegaorguk video programme freeview video 'voyage bottom deep deep sea' oceanography programme vega science trust bbc open university http atlasinvestigadhoccom atlas spanish oceanography https webarchiveorg web http investigadhoccom investigadhoc https webarchiveorg web http stommeltamuedu baum paleo ocean glossary physical oceanography related disciplines steven k baum department oceanography texas university http barcelona oceancom barcelona oceancom inspiring education marine sciences https webarchiveorg web http cfoocoza seaatlas indexphp cfoo sea atlas source oceanographic live data buoy monitoring education


x rays start nm extend across electromagnetic spectrum nm earth 's atmosphere opaque '''x ray astronomy''' observational branch astronomy deals study x ray observation detection astronomical objects x radiation absorbed earth 's atmosphere instruments detect x rays must taken high altitude balloons sounding rockets satellites x ray astronomy uses type space telescope see x ray radiation standard optical telescopes mauna kea observatories cannot x ray emission expected astronomical objects

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contain extremely hot gases temperatures million kelvin k hundreds millions kelvin mk moreover maintenance e layer ionized gas high earth 's thermosphere also suggested strong extraterrestrial source x rays although theory predicted sun stars would prominent x ray sources way verify earth 's atmosphere blocks extraterrestrial x rays ways sending instrument packages high altitude developed x ray sources could studied existence solar x rays confirmed early


mid twentieth century v converted sounding rocket purpose detection extra terrestrial x rays primary secondary mission multiple satellites since ref name sp ref first cosmic beyond solar system x ray source discovered sounding rocket called scorpius x sco x first x ray source found constellation scorpius x ray emission scorpius x times greater visual emission whereas sun million times less addition energy output x rays times greater total emission


sun wavelengths many thousands x ray sources since discovered addition intergalactic space galaxy clusters filled hot dilute gas temperature megakelvins mk total amount hot gas five ten times total mass visible galaxies sounding rocket flights first sounding rocket flights x ray research accomplished white sands missile range new mexico v rocket january detector placed nose cone section


rocket launched suborbital flight altitude atmosphere x rays sun detected us naval research laboratory blossom experiment board ref name rockooni ref aerobee rocket launched june utc detected first x rays emitted source outside solar system ref name giacconi ref ref name sp ref scorpius x ref name giacconi ref known x ray sources sco x compact stars neutron stars black holes material falling black hole may emit x rays black hole energy source


x ray emission gravity infalling gas dust heated strong gravitational fields celestial objects ref name britannica ref based discoveries new field x ray astronomy starting scorpius x riccardo giacconi received nobel prize physics ref name giacconibio ref largest drawback rocket flights short duration minutes atmosphere rocket falls back earth limited field view rocket launched united states able see sources southern sky rocket launched


australia able see sources northern sky x ray quantum calorimeter xqc project launch black brant microcalorimeter xqc turn century part joint undertaking university wisconsin madison nasa 's goddard space flight center known x ray quantum calorimeter xqc project astronomy interstellar medium '''ism''' gas cosmic dust pervade interstellar space matter exists star systems within galaxy fills interstellar space blends smoothly surrounding intergalactic medium


interstellar medium consists extremely dilute terrestrial standards mixture ions atoms molecules larger dust grains cosmic rays galactic magnetic fields ref name spitzer ref energy occupies volume form electromagnetic radiation '''interstellar radiation field''' interest hot ionized medium consisting coronal cloud ejection star surfaces sup sup sup sup k emits x rays ism turbulent full structure spatial scales stars born deep inside large complexes molecular clouds typically parsecs size lives deaths stars


interact physically ism stellar winds young clusters stars often giant supergiant hii regions surrounding shock waves created supernovae inject enormous amounts energy surroundings leads hypersonic turbulence resultant structures stellar wind bubbles superbubbles hot gas sun currently traveling local interstellar cloud denser region low density local bubble measure spectrum diffuse x ray emission interstellar medium energy range kev nasa launched black brant white sands


astrophysical sources hard x ray kev band ref name harrison ref maiden flight took place may fort sumner new mexico usa angular resolution heft c ' rather using grazing angle x ray telescope heft makes use novel tungsten silicon multilayer coatings extend reflectivity nested grazing incidence mirrors beyond kev heft energy resolution kev full width half maximum kev heft launched hour balloon flight may instrument performed within specification observed tau x crab nebula high resolution gamma ray


hard x ray spectrometer hiregs balloon borne experiment called high resolution gamma ray hard x ray spectrometer hiregs observed x ray gamma rays emissions sun astronomical objects ref name hiregs ref launched mcmurdo station antarctica december steady winds carried balloon circumpolar flight lasting two weeks time rockoons navy deacon rockoon photographed shipboard launch july rockoon blend ''rocket'' ''balloon'' solid fuel rocket rather immediately lit ground first carried upper atmosphere


gas filled balloon separated balloon maximum height rocket automatically ignited achieved higher altitude since rocket move lower thicker air layers would required much chemical fuel original concept rockoons developed cmdr lee lewis cmdr g halvorson f singer james van allen aerobee rocket firing cruise march ref name rockooni july july naval research laboratory nrl shipboard launched eight deacon rockoons


solar ultraviolet x ray observations n w southwest san clemente island apogee nbsp km ref name nrl ref x ray astronomy satellite x ray astronomy satellites study x ray emissions celestial objects satellites detect transmit data x ray emissions deployed part branch space science known x ray astronomy satellites needed x radiation absorbed earth 's atmosphere instruments detect x rays must taken high altitude balloons sounding rockets satellites x ray telescopes mirrors focusing x rays glancing reflection swift gamma ray burst mission contains grazing incidence


wolter telescope xrt focus x rays onto state art ccd x ray telescopes xrts varying directionality imaging ability based glancing angle reflection rather refraction large deviation reflection ref name swift ref ref name chandra ref limits much narrower fields view visible uv telescopes mirrors made ceramic metal foil ref name xrayoptics ref first x ray telescope astronomy used observe sun first x ray picture taken grazing incidence telescope sun taken rocket borne telescope april first x ray


image sun taken using pinhole camera aerobee hi rocket ref name blake ref utilization x ray mirrors extrasolar x ray astronomy simultaneously requires ability determine location arrival x ray photon two dimensions reasonable detection efficiency x ray astronomy detectors proportional counter array rossi x ray timing explorer rxte satellite x ray astronomy detectors designed configured primarily energy occasionally wavelength detection using variety techniques usually limited technology time x ray detectors collect individual x rays photons x ray electromagnetic radiation


count number photons collected intensity energy kev photons collected wavelength c nbsp nm fast photons detected counts per hour tell us object emitting astrophysical sources x rays andromeda galaxy high energy x ray ultraviolet light released january light curve x shows long term medium term variability pair vertical lines delineate eclipse compact object behind companion star case companion two solar mass star radius


nearly four times sun eclipse shows us orbital period system days several types astrophysical objects emit fluoresce reflect x rays galaxy clusters black holes active galactic nuclei agn galactic objects supernova remnants stars binary stars containing white dwarf cataclysmic variable stars super soft x ray sources neutron star black hole x ray binaries solar system bodies emit x rays notable moon although x ray brightness moon arises reflected solar x rays combination


many unresolved x ray sources thought produce observed x ray background x ray continuum arise bremsstrahlung black body radiation synchrotron radiation called inverse compton scattering lower energy photons relativistic electrons knock collisions fast protons atomic electrons atomic recombination without additional electron transitions ref name morrison ref intermediate mass x ray binary imxb binary star system one components neutron star black hole component intermediate mass star ref name podsiadlowski ref hercules x composed neutron star accreting matter normal star


hz herculis probably due roche lobe overflow x prototype massive x ray binaries although falls borderline high low mass x ray binaries ref name priedhorsky ref july astronomers reported observation hard tidal disruption event candidate associated asassn hx located near nucleus galaxy ngc noted observation represented one tidal disruption events hard powerlaw x ray spectra ref name ref ref name ref celestial x ray sources celestial sphere divided constellations international astronomical union iau constellations areas sky


celestial x ray sources x ray astrophysics tends focus physical reason x ray brightness whereas x ray astronomy tends focus classification order discovery variability resolvability relationship nearby sources constellations rosat pspc false color image portion nearby stellar wind superbubble orion eridanus superbubble stretching across eridanus orion within constellations orion eridanus stretching across soft x ray hot spot known orion eridanus superbubble '''eridanus soft x ray enhancement''' simply '''eridanus bubble''' area interlocking arcs h


emitting filaments soft x rays emitted hot gas mk interior superbubble bright object forms background shadow filament gas dust filament shown overlaid contours represent micrometre emission dust temperature k measured iras filament absorbs soft x rays ev indicating hot gas located behind filament filament may part shell neutral gas surrounds hot bubble interior


energized ultraviolet uv light stellar winds hot stars orion ob association stars energize superbubble lys across observed visual h x ray portions spectrum proposed future x ray observatory satellites several projects proposed x ray observatory satellites see main article link explorational x ray astronomy ulysses' second orbit arrived jupiter february swing maneuver increased inclination ecliptic degrees usually observational astronomy considered occur earth 's surface beneath


neutrino astronomy idea limiting observation earth includes orbiting earth soon observer leaves cozy confines earth observer becomes deep space explorer ref name kawakatsu ref except explorer explorer earlier satellites series ref name smith ref usually probe going deep space explorer leaves earth orbit around earth satellite space probe qualify deep space x ray astronomer explorer astronobot explorer needs carry aboard xrt x ray detector


leave earth 's orbit ''ulysses'' launched october reached jupiter gravitational slingshot february passed south solar pole june crossed ecliptic equator february solar x ray cosmic gamma ray burst experiment grb main objectives study monitor solar flares detect localize cosmic gamma ray bursts situ detection jovian aurorae ''ulysses'' first satellite carrying gamma burst detector went outside orbit mars hard x ray detectors operated range kev detectors consisted mm thick


mm diameter csi tl crystals mounted via plastic light tubes photomultipliers hard detector changed operating mode depending measured count rate ground command change spacecraft telemetry mode trigger level generally set sigma background sensitivity sup sup erg cm sup sup nj sup sup burst trigger recorded instrument switches record high resolution data recording kbit memory slow telemetry read burst data consist either ms resolution count rates ms count rates sum


detectors also channel energy spectra sum detectors taken either second integrations 'wait' mode data taken either integrations energy channels shortest integration time outputs detectors summed ''ulysses'' soft x ray detectors consisted mm thick nbsp cm sup sup area si surface barrier detectors nbsp mg cm sup sup beryllium foil front window rejected low energy x rays defined conical fov half angle detectors


passively cooled operate temperature range nbsp c detector energy channels covering range kev x rays pluto theoretical x ray astronomy theoretical x ray astronomy branch theoretical astronomy deals theoretical astrophysics theoretical astrochemistry x ray generation emission detection applied astronomical objects like theoretical astrophysics theoretical x ray astronomy uses wide variety tools include analytical models approximate behavior possible x ray source computational numerical simulations approximate observational data potential observational consequences available


compared experimental observations observers look data refutes model helps choosing several alternate conflicting models theorists also try generate modify models take account new data case inconsistency general tendency try make minimal modifications model fit data cases large amount inconsistent data time may lead total abandonment model topics astrophysics astrochemistry astrometry fields branches astronomy studied theoreticians involve


spectral emission results wavelength ranges astronomical model addressing likely source x ray emission constructed example scorpius x x ray spectrum steeply drops x ray energy increases kev likely thermal plasma mechanism ref name morrison addition radio emission visible continuum roughly would expected hot plasma fitting observed x ray flux ref name morrison plasma could coronal cloud central object transient plasma energy source unknown could related


idea close binary ref name morrison crab nebula x ray spectrum three features differ greatly scorpius x spectrum much harder source diameter light years ly astronomical units au radio optical synchrotron emission strong ref name morrison overall x ray luminosity rivals optical emission could nonthermal plasma however crab nebula appears x ray source central freely expanding ball dilute plasma energy content times total energy content large visible


character leading disappearance stellar fields leaving small scale turbulence generated fields among red giants ref name kashyap analytical x ray astronomy high mass x ray binaries hmxbs composed ob supergiant companion stars compact objects usually neutron stars ns black holes bh supergiant x ray binaries sgxbs hmxbs compact objects orbit massive companions orbital periods days circular slightly eccentric orbits sgxbs show typical hard x ray spectra accreting pulsars show strong absorption obscured hmxbs x ray luminosity ''l'' sub x sub increases sup sup erg sup sup sup sup watts


mechanism triggering different temporal behavior observed classical sgxbs recently discovered supergiant fast x ray transients sfxt still debated ref name zuritaheras ref stellar x ray astronomy stellar x ray astronomy said started april detection x rays capella ref name catura ref rocket flight date briefly calibrated attitude control system star sensor pointed payload axis capella aur period x rays range kev detected x ray reflector system co aligned star sensor ref name catura x ray luminosity ''l'' sub x sub


sup sup erg sup sup sup sup w four orders magnitude sun 's x ray luminosity ref name catura stellar coronae coronal stars stars within coronal cloud ubiquitous among stars cool half hertzsprung russell diagram ref name gudel ref experiments instruments aboard skylab copernicus used search soft x ray emission energy range kev stellar coronae ref name mewe ref experiments aboard ans succeeded finding x ray signals capella sirius cma x ray emission enhanced solar like corona proposed first time ref name mewe high temperature capella 's corona


obtained first coronal x ray spectrum capella using heao required magnetic confinement unless free flowing coronal wind ref name gudel proxima centauri discovered emitting high energy radiation xuv cen identified low activity coronal source ref name telleschi ref operation einstein observatory x ray emission recognized characteristic feature common wide range stars covering essentially whole hertzsprung russell diagram ref name telleschi einstein initial survey led significant insights x ray sources abound among types stars across hertzsprung russell diagram


across stages evolution x ray luminosities distribution along main sequence agreement long favored acoustic heating theories interpreted effect magnetic coronal heating stars otherwise similar reveal large differences x ray output rotation period different ref name gudel fit medium resolution spectrum ux ari subsolar abundances required ref name gudel stellar x ray astronomy contributing toward deeper understanding magnetic fields magnetohydrodynamic dynamos release energy tenuous astrophysical plasmas various plasma physical processes interactions


emission pre main sequence stars discovered einstein observatory ref name feigelson ref ref name montmerle ref x ray emission primarily produced magnetic reconnection flares stellar coronae many small flares contributing quiescent x ray emission stars ref name feigelson ref pre main sequence stars large convection zones turn drive strong dynamos producing strong surface magnetic fields leads high x ray emission stars lie saturated x ray regime unlike main sequence stars show rotational modulation x ray emission sources x ray emission include accretion hotspots ref name kastner ref collimated outflows ref name pravdo ref x ray emission


indicator stellar youth important studies star forming regions star forming regions milky way galaxy projected galactic plane fields numerous unrelated field stars often impossible distinguish members young stellar cluster field star contaminants using optical infrared images alone x ray emission easily penetrate moderate absorption molecular clouds used identify candidate cluster members ref name feigelson ref unstable winds given lack significant outer convection zone theory predicts absence magnetic dynamo earlier stars ref name gudel early stars


spectral type b shocks developing unstable winds likely source x rays ref name gudel coolest dwarfs beyond spectral type classical dynamo longer operate internal structure dwarf stars changes significantly become fully convective ref name gudel distributed sup sup dynamo may become relevant magnetic flux surface topology magnetic fields corona systematically change across transition perhaps resulting discontinuities x ray characteristics around spectral class dm ref name gudel however observations seem support


picture long time lowest mass x ray detection vb e v shown steady emission levels x ray luminosity ''l'' sub x sub nbsp sup sup erg sup sup sup sup w flares order magnitude higher ref name gudel comparison late dwarfs shows rather continuous trend ref name gudel strong x ray emission herbig ae stars herbig ae stars pre main sequence stars x ray emission properties reminiscent hot stars others point coronal activity cool stars particular presence flares high temperatures ref name gudel nature strong emissions remained controversial


models including unstable stellar winds colliding winds magnetic coronae disk coronae wind fed magnetospheres accretion shocks operation shear dynamo presence unknown late type companions ref name gudel k giants fk com stars giants spectral type k unusually rapid rotation signs extreme activity x ray coronae among luminous ''l'' sub x sub sup sup erg sup sup sup sup w hottest known dominant temperatures mk ref name gudel however current popular hypothesis involves merger close binary system orbital angular momentum companion


transferred primary ref name gudel pollux brightest star constellation gemini despite beta designation th brightest sky pollux giant orange k star makes interesting color contrast white twin castor evidence found hot outer magnetically supported corona around pollux star known x ray emitter ref name hatzes ref eta carinae classified peculiar star eta carinae exhibits superstar center seen image chandra x ray observatory credit chandra science center nasa new x ray


central regions mk horseshoe shaped outer structure chandra image contains puzzles existing ideas star produce hot intense x rays says prof kris davidson university minnesota ref name horack ref davidson principal investigator eta carina observations hubble space telescope popular theory x rays made colliding gas streams two stars close together 'd look like point source us happens gas streams escape farther distances extended hot stuff middle


new image gives demanding new conditions theory meet ref name horack amateur x ray astronomy collectively amateur astronomers observe variety celestial objects phenomena sometimes equipment build united states air force academy usafa home us 's undergraduate satellite program continues develop falconlaunch sounding rockets ref name helms ref addition direct amateur efforts put x ray astronomy payloads space opportunities allow student developed experimental payloads put board commercial sounding rockets free charge ride ref name blaylock ref major


limitations amateurs observing reporting experiments x ray astronomy cost building amateur rocket balloon place detector high enough cost appropriate parts build suitable x ray detector history x ray astronomy nrl scientists j purcell c johnson dr f johnson among recovering instruments v used upper atmospheric research new mexico desert v number launched january photo dr richard tousey nrl eo hulburt us naval research laboratory associates gregory


breit merle tuve carnegie institution washington explored possibility equipping robert h goddard 's rockets explore upper atmosphere two years later proposed experimental program rocket might instrumented explore upper atmosphere including detection ultraviolet radiation x rays high altitudes ref name spacelab ref late presence hot tenuous gas surrounding sun inferred indirectly optical coronal lines highly ionized species ref name gudel sun known surrounded hot tenuous corona ref name grottian ref mid


radio observations revealed radio corona around sun ref name gudel beginning search x ray sources earth 's atmosphere august gmt us army formerly german v rocket part project hermes launched white sands proving grounds first solar x rays recorded burnight ref name keller ref sensitivity detectors increased greatly years x ray astronomy addition ability focus x rays developed enormously allowing production high quality images many fascinating celestial objects major


questions x ray astronomy x ray astronomy uses major spectral probe peer source valuable tool efforts understand many puzzles stellar magnetic fields magnetic fields ubiquitous among stars yet understand precisely fully understood bewildering variety plasma physical mechanisms act stellar environments ref name gudel stars example seem magnetic fields fossil stellar magnetic fields left period formation others seem generate field anew frequently extrasolar x ray source astrometry initial detection


extrasolar x ray source first question usually asked source extensive search often made wavelengths visible radio possible coincident objects many verified x ray locations still readily discernible sources x ray astrometry becomes serious concern results ever greater demands finer angular resolution spectral radiance inherent difficulties making x ray optical x ray radio x ray x ray identifications based solely positional coincidents especially handicaps making identifications large uncertainties positional determinants made balloons rockets poor


name russell ref thought energy necessary heat corona provided turbulent motion convection zone photosphere two main mechanisms proposed explain coronal heating ref name erdelyi first wave heating sound gravitational magnetohydrodynamic waves produced turbulence convection zone ref name erdelyi waves travel upward dissipate corona depositing energy ambient gas form heat ref name alfven ref magnetic heating magnetic energy continuously built photospheric motion released magnetic reconnection


form large solar flares myriad similar smaller events nanoflares ref name parker ref currently unclear whether waves efficient heating mechanism waves except alfv n waves found dissipate refract reaching corona ref name sturrock ref addition alfv n waves easily dissipate corona current research focus therefore shifted towards flare heating mechanisms ref name erdelyi coronal mass ejection coronal mass ejection cme ejected plasma consisting primarily electrons protons addition small quantities heavier elements helium oxygen iron plus entraining coronal


closed magnetic field regions evolution closed magnetic structures response various photospheric motions different time scales convection differential rotation meridional circulation somehow leads cme ref name gopalswamy ref small scale energetic signatures plasma heating observed compact soft x ray brightening may indicative impending cmes soft x ray sigmoid shaped intensity soft x rays observational manifestation connection coronal structure cme production ref name gopalswamy relating sigmoids x ray wavelengths magnetic structures current systems solar atmosphere key understanding relationship


cmes ref name gopalswamy first detection coronal mass ejection cme made december r tousey us naval research laboratory using oso ref name howard ref earlier observations '''coronal transients''' even phenomena observed visually solar eclipses understood essentially thing largest geomagnetic perturbation resulting presumably prehistoric cme coincided first observed solar flare flare observed visually richard christopher carrington geomagnetic storm observed recording magnetograph kew gardens instrument recorded '''crotchet'''


instantaneous perturbation earth 's ionosphere ionizing soft x rays could easily understood time predated discovery x rays roentgen recognition ionosphere kennelly heaviside exotic x ray sources div align center ss possible ulx ray source div microquasar smaller cousin quasar radio emitting x ray binary often resolvable pair radio jets lsi periodic radio emitting binary system also gamma ray source cg observations revealing growing number recurrent x ray transients characterized short


ten years' worth yohkoh sxt images demonstrating variation solar activity sunspot cycle august peak cycle september peak cycle credit yohkoh mission institute space astronautical science isas japan nasa us solar cycle shown sequence images right times sun almost x ray dark almost x ray variable betelgeuse hand appears always x ray dark hardly x rays emitted red giants


rather abrupt onset x ray emission around spectral type f large range luminosities developing across spectral class f altair spectral type v vega v altair 's total x ray luminosity least order magnitude larger x ray luminosity vega outer convection zone early f stars expected shallow absent type dwarfs yet acoustic flux interior reaches maximum late early f stars provoking investigations magnetic activity type stars along three principal lines chemically peculiar stars


parent star transit methods particularly promising low mass stars jupiter like planet could eclipse rather significant coronal area ref name gudel x ray detectors become sensitive observed planets normally x ray non luminescent celestial objects certain conditions emit fluoresce reflect x rays comet lulin ''swift'' data swift 's ultraviolet optical telescope shown blue green x ray telescope red nasa 's swift gamma ray burst mission satellite monitoring comet lulin closed gm earth first time astronomers see


simultaneous uv x ray images comet solar wind fast moving stream particles sun interacts comet 's broader cloud atoms causes solar wind light x rays 's swift 's xrt sees said stefan immler goddard space flight center interaction called charge exchange results x rays comets pass within three times earth 's distance sun lulin active atomic cloud especially dense result x ray emitting region extends far sunward comet ref name reddy ref see also balloons


x ray astronomy crab unit gamma ray astronomy history x ray astronomy iras list x ray space telescopes solar x ray astronomy stellar x ray astronomy ultraviolet astronomy x ray telescope references sources ''the content article adapted expanded http imaginegsfcnasagov public domain '' external links http heasarcgsfcnasagov docs heasarc headates many xrayhtml many known x ray sources http heasarcgsfcnasagov cgi bin tools high energy source high energy sourcepl favorite object x ray gamma ray euv source http wwwwikiskyorg x ray sky survey wikisky audio cain gay http wwwastronomycastcom astronomy ep x ray astronomy astronomy cast x ray astronomy plasma physics astronomical imaging astronomical x ray sources observational astronomy astronomical sub disciplines x rays


linguistics related fields '''pragmatics''' study context contributes meaning field study evaluates human language utilized social interactions well relationship interpreter interpreted pragmatics encompasses phenomena including implicature speech acts relevance conversation ref name mey mey jacob l ''pragmatics introduction'' oxford blackwell nd ed ref well nonverbal communicationtheories pragmatics go hand hand theories semantics studies aspects meaning syntax examines sentence structures principles relationships ability understand another speaker 's intended meaning called

Humanities
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Pragmatics


''pragmatic competence'' pragmatics emerged subfield pioneering work jl austin paul grice origin field pragmatics reaction structuralist linguistics outlined ferdinand de saussure many cases expanded upon idea language analyzable structure composed parts defined relation others pragmatics first engaged synchronic study opposed examining historical development language however rejected notion meaning comes signs existing purely abstract space ''langue'' meanwhile historical


pragmatics also come field gain linguists' attention two different schools emerged anglo american pragmatic thought european continental pragmatic thought also called perspective view areas interest study speaker 's meaning focusing phonetic grammatical form utterance speaker 's intentions beliefs study meaning context influence given context message requires knowledge speaker 's identities place time utterance


study implicatures things communicated even though explicitly expressed study relative distance social physical speakers order understand determines choice said said study meant opposed intended meaning unsaid unintended unintentional information structure study utterances marked order efficiently manage common ground referred entities speaker hearer ref name ref formal pragmatics study aspects meaning use


driving permitted proceed non driving context body cast greenish glow possess light source radiates green possess light green surface another example ambiguous sentence went bank example lexical ambiguity word bank either reference place money kept edge river understand speaker truly saying matter context pragmatically ambiguous well similarly


sentence sherlock saw man binoculars could mean sherlock observed man using binoculars could mean sherlock observed man holding binoculars ' 'syntactic ambiguity'' meaning sentence depends understanding context speaker 's intent defined linguistics sentence abstract entity string words divorced non linguistic context opposed utterance concrete example speech act specific context closely conscious subjects stick common words idioms phrasings topics


easily others surmise meaning stray common expressions topics wider variations interpretations suggests sentences intrinsic meaning meaning associated sentence word either represent idea symbolically ''the cat sat mat'' sentence english someone say someone else cat sat mat act utterance implies sentence term expression word cannot symbolically represent single true meaning meaning


underspecified cat sat mat potentially ambiguous contrast meaning utterance inferred knowledge linguistic non linguistic contexts may may sufficient resolve ambiguity mathematics berry 's paradox arises similar systematic ambiguity word definable referential uses language referential uses language signs used refer certain items sign link relationship signified signifier defined de saussure huguenin signified entity concept


world signifier represents signified example would ''signified concept cat ''signifier word cat relationship two gives sign meaning relationship explained considering mean meaning pragmatics two different types meaning consider '' 'semantic referential meaning''' '''indexical meaning''' semantic referential meaning refers aspect meaning describes events world independent circumstance uttered example would propositions '' santa claus eats cookies '' case proposition


describing santa claus eats cookies meaning proposition rely whether santa claus eating cookies time utterance santa claus could eating cookies time meaning proposition would remain meaning simply describing something case world contrast proposition santa claus eating cookie right describes events happening time proposition uttered semantic referential meaning also present meta semantical statements ''tiger carnivorous mammal''


signified signifier arbitrarily linked signified cat signifier word cat ref name relationships allow us use signs convey want say two people room one wanted refer characteristic chair room would say chair four legs instead chair four legs former relies context indexical referential meaning referring chair specifically room moment latter independent context semantico referential meaning meaning


individuals involved topic conversation hand repeated one would think necessary four factors widely accepted use referent language including competition possible referent ii salience referent context discussion iii effort unity parties involved finally iv blatant presence distance last referent ref name referential expressions form anaphora ref name also means connecting past present thoughts together create context information hand analyzing


context sentence determining whether use referent expression necessary highly reliant upon author speaker 's digression correlated strongly use pragmatic competency ref name ref name nonreferential uses language silverstein 's pure indexes michael silverstein argued nonreferential pure indices contribute utterance 's referential meaning instead signal particular value one contextual variables although nonreferential indexes devoid semantico referential meaning encode pragmatic meaning sorts contexts indexes mark varied examples include


'''sex indexes''' affixes inflections index sex speaker eg verb forms female koasati speakers take suffix '''deference indexes''' words signal social differences usually related status age speaker addressee common example deference index v form language v distinction widespread phenomenon multiple second person pronouns correspond addressee 's relative status familiarity speaker honorifics another common form deference index demonstrate speaker 's respect


meaning utterances unchanged possible often impermissible forms pragmatic meaning vastly different performative jl austin introduced concept performative contrasted writing constative ie descriptive utterances according austin 's original formulation performative type utterance characterized two distinctive features truth evaluable ie neither true false uttering ''performs'' action rather simply describing one examples hereby pronounce man wife accept apology meeting adjourned performative


factors speech event represents privileging corresponding function one referential corresponds '''context''' speech event six constitutive factors corresponding functions diagrammed '''the six constitutive factors speech event''' context message addresser addressee contact code br '''the six functions language''' referential poetic emotive conative phatic metalingual referential function corresponds factor context describes situation object mental state descriptive statements referential function consist definite descriptions deictic


slogans phatic function language sake interaction therefore associated contact factor phatic function observed greetings casual discussions weather particularly strangers metalingual alternatively called metalinguistic reflexive function use language jakobson calls code discuss describe related fields considerable overlap pragmatics sociolinguistics since share interest linguistic meaning determined usage speech community however sociolinguists tend interested variations language within communities influences


philosophy politics also present field pragmatics dynamics societies oppression expressed language pragmatics helps anthropologists relate elements language broader social phenomena thus pervades field linguistic anthropology pragmatics describes generally forces play given utterance includes study power gender race identity interactions individual speech acts example study code switching directly relates pragmatics since switch code effects shift pragmatic force ref name duranti according charles w morris pragmatics


tries understand relationship signs users semantics tends focus actual objects ideas word refers syntax syntactics examines relationships among signs symbols semantics literal meaning idea whereas pragmatics implied meaning given idea speech act theory pioneered jl austin developed john searle centers around idea performative type utterance performs action describes speech act theory 's examination illocutionary acts many goals pragmatics


outlined computational pragmatics defined victoria fromkin concerns humans communicate intentions computers little ambiguity possible process integral science natural language processing seen sub discipline artificial intelligence involves providing computer system database knowledge related topic series algorithms control system responds incoming data using contextual knowledge accurately approximate natural human language information processing abilities reference resolution computer determines two objects different one


important tasks computational pragmatics formalization great amount discussion boundary semantics pragmatics many different formalizations aspects pragmatics linked context dependence particularly interesting cases discussions semantics indexicals problem referential descriptions topic developed theories keith donnellan proper logical theory formal pragmatics developed carlo dalla pozza according possible connect classical semantics treating propositional contents true false intuitionistic semantics dealing


second hand act every aspect language semantics syntactics even phonematics functionally interacts pragmatics distinction language speech last conclusion attempts refute saussure 's division ''langue'' ''parole'' chomsky 's distinction deep structure surface structure simultaneously significant works concepts j l austin 's ''how things words'' paul grice 's cooperative principle conversational maxims brown levinson 's politeness theory geoffrey leech 's politeness maxims levinson 's presumptive meanings j rgen habermas 's universal pragmatics dan sperber deirdre wilson 's relevance theory dallin oaks 's ''structural ambiguity


http wwwericedgov pdfs ed pdf moumni hassan politeness parliamentary discourse comparative pragmatic study british moroccan mps speech acts question time unpub phd thesis mohammed v university rabat morocco mey jacob l ''pragmatics introduction'' oxford blackwell nd ed kepa korta john perry http platostanfordedu entries pragmatics ''pragmatics'' stanford encyclopedia philosophy potts christopher ''the logic conventional implicatures'' oxford studies theoretical linguistics oxford oxford university press robinson douglas ''performative linguistics speaking translating things words'' london new york routledge robinson douglas ''introducing performative pragmatics'' london


new york routledge sperber dan wilson deirdre http wwwdansperbercom pragmaticshtm pragmatics f jackson smith eds oxford handbook contemporary philosophy oup oxford also available https webarchiveorg web http wwwphonuclacuk home deirdre papers pragmatics doc thomas jenny ''meaning interaction introduction pragmatics'' longman verschueren jef https wwwuantwerpenbe en rg ipra research publications books ''understanding pragmatics'' london new york arnold publishers verschueren jef jan ola stman jan blommaert eds ''handbook pragmatics'' amsterdam benjamins watzlawick paul janet helmick beavin jackson ''pragmatics human communication study interactional patterns pathologies paradoxes'' new york norton wierzbicka anna ''cross cultural pragmatics semantics human interaction''


berlin new york mouton de gruyter yule george ''pragmatics'' oxford introductions language study oxford university press silverstein michael shifters linguistic categories cultural description meaning anthropology basso selby eds new york harper row wardhaugh ronald introduction sociolinguistics blackwell duranti alessandro linguistic anthropology cambridge university press carbaugh donal cultural communication intercultural contact lea external links https platostanfordedu entries pragmatics pragmatics ''stanford encyclopedia philosophy'' http wwwieputmedu mean c meaning context sensitivity ''internet encyclopedia philosophy'' http wwwelseviercom wps find journaldescriptioncws home description description journal pragmatics semiotics linguistics terminology


'''systems analysis''' process studying procedure business identify goal purposes create systems procedures efficiently achieve another view sees system analysis problem solving technique breaks system component pieces well parts work interact accomplish purpose field system analysis relates closely requirements analysis operations research also explicit formal inquiry carried help decision maker identify better course action make better decision

Applied science
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might otherwise made terms analysis synthesis stems greek meaning take apart put together respectively terms used many scientific disciplines mathematics logic economics psychology denote similar investigative procedures analysis defined procedure break intellectual substantial whole parts synthesis means procedure combine separate elements components form coherent whole system analysis researchers apply methodology systems involved forming overall picture system analysis used every field


something developed analysis also series components perform organic functions together system engineering system engineering interdisciplinary field engineering focuses complex engineering projects designed managed information technology development computer based information system includes system analysis phase helps produce data model precursor creating enhancing database several different approaches system analysis computer based information system developed system analysis according waterfall model would constitute following steps development feasibility


study determining whether project economically socially technologically organizationally feasible fact finding measures designed ascertain requirements system 's end users typically involving interviews questionnaires visual observations work existing system gauging end users would operate system terms general experience using computer hardware software system would used another view outlines phased approach process approach breaks system analysis phases scope definition clearly defined objectives requirements necessary meet project 's requirements defined


stakeholders problem analysis process understanding problems needs arriving solutions meet requirements analysis determining conditions need met logical design looking logical relationship among objects decision analysis making final decision use cases widely used system analysis modeling tools identifying expressing functional requirements system use case business scenario event system must provide defined response use cases evolved object oriented analysis policy analysis discipline today known policy analysis originated


application system analysis first instituted united states secretary defense robert mcnamara practitioners practitioners system analysis often called dissect systems grown haphazardly determine current components system shown year engineering effort business manufacturing processes examined part k automation upgrades employment utilizing system analysis include system analyst business analyst manufacturing engineer systems architect enterprise architect software architect etc practitioners system analysis called upon create new systems often modify


expand document existing systems processes procedures methods researchers practitioners rely system analysis activity system analysis already applied various research practice studies including business management educational reform educational technology etc see also related topics system thinking system architecture software architecture enterprise architecture systems analyst systems design policy analysis program designer cybernetics systems theory types system analysis accident analysis business analysis cost effectiveness analysis cost benefit analysis dsrp failure analysis logico linguistic modeling morphological analysis soft systems methodology software prototyping spiral model waterfall model system thinkers donella meadows nancy leveson russell l ackoff howard


odum henry paynter jay forrester gregory bateson stewart brand buckminster fuller robert mcnamara stafford beer ludwig von bertalanffy references selected publications bentley lonnie kevin c dittman jeffrey l whitten ''system analysis design methods'' hawryszkiewycz igor ''introduction system analysis design'' prentice hall ptr whitten jeffery l lonnie bentley kevin c dittman ''fundamentals system analysis design methods'' external links http wwwcilcocouk briefing studies indexhtml useful set guides case study practical application business system analysis methods https webarchiveorg web http websimmonsedu benoit lis systemsanalysishtml comprehensive description


discipline system analysis simmons college boston usa archive original wwwsimmonsedu http wwww computingcom systemsanalysis system analysis design introductory level lessons futures techniques financial analysts


'''universal algebra''' sometimes called '''general algebra''' field mathematics studies algebraic structures examples models algebraic structures instance rather take particular groups object study universal algebra one takes class groups object study basic idea universal algebra '''algebra''' '''algebraic structure''' set ''a'' together collection operations ''a'' '''''n'' ary operation''' ''a'' function takes ''n'' elements ''a'' returns single element ''a'' thus ary operation ''nullary operation''

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Universal algebra


represented simply element ''a'' ''constant'' often denoted letter like ''a'' ary operation ''unary operation'' simply function ''a'' ''a'' often denoted symbol placed front argument like ''x'' ary operation ''binary operation'' often denoted symbol placed arguments like ''x'' nbsp nbsp ''y'' operations higher unspecified ''arity'' usually denoted function symbols arguments placed parentheses separated commas like ''f'' ''x''''y''''z'' ''f'' ''x'' sub sub ''x'' sub ''n'' sub researchers allow infinitary operations


math textstyle bigwedge alpha j x alpha math ''j'' infinite index set thus leading algebraic theory complete lattices one way talking algebra referring algebra certain type math omega math math omega math ordered sequence natural numbers representing arity operations algebra equations operations specified nature algebra defined axioms universal algebra often take form identities '''equational laws''' example associative axiom


binary operation given equation ''x'' nbsp nbsp ''y'' nbsp nbsp ''z'' nbsp ''x'' nbsp nbsp ''y'' nbsp nbsp ''z'' axiom intended hold elements ''x'' ''y'' ''z'' set ''a'' varieties collection algebraic structures defined identities called variety '''equational class''' restricting one 's study varieties rules quantification including universal quantification math forall math except equation existential quantification math exists math logical connectives conjunction relations equality particular inequalities order relations study equational classes seen special branch model theory typically


dealing structures operations ie type symbols functions relations equality language used talk structures uses equations algebraic structures wider sense fall scope example ordered groups involve ordering relation would fall within scope class fields equational class type signature field laws written equations inverses elements defined ''non zero'' elements field


inversion cannot added type one advantage restriction structures studied universal algebra defined category ''finite products'' example topological group group category topological spaces examples usual algebraic systems mathematics examples varieties always obvious way since usual definitions often involve quantification inequalities groups example consider definition group usually group defined terms single binary operation subject


axioms associativity previous section ''x'' nbsp nbsp ''y'' nbsp nbsp ''z'' nbsp nbsp nbsp ''x'' nbsp nbsp ''y'' nbsp nbsp ''z'' nbsp formally ''x''''y''''z'' ''x'' ''y'' ''z'' ''x'' ''y'' ''z'' identity element exists element ''e'' element ''x'' one ''e'' nbsp nbsp ''x'' nbsp nbsp nbsp ''x'' nbsp nbsp nbsp ''x'' nbsp nbsp ''e'' nbsp formally ''e'' ''x'' ''e'' ''x'' ''x'' ''x'' ''e'' inverse element identity element easily seen unique usually denoted ''e'' ''x'' exists element ''i'' ''x'' nbsp nbsp ''i'' nbsp nbsp nbsp ''e'' nbsp nbsp nbsp ''i'' nbsp nbsp ''x'' nbsp formally ''x'' ''i'' ''x'' ''i'' ''e'' ''i'' ''x'' authors also use closure axiom ''x'' nbsp nbsp ''y'' belongs ''a'' whenever ''x'' ''y'' already implied


calling binary operation definition group immediately fit point view universal algebra axioms identity element inversion stated purely terms equational laws hold universally elements also involve existential quantifier exists group axioms phrased universally quantified equations specifying addition binary operation nullary operation ''e'' unary operation ''x'' usually written ''x'' sup sup axioms become associativity identity element


formally ''x'' ''e'' ''x'' ''x'' ''x'' ''e'' inverse element nbsp formally ''x'' ''x'' ''x'' ''e'' ''x'' ''x'' summarize usual definition single binary operation signature equational law associativity quantified laws identity inverse universal algebra definition operations one binary one unary one nullary signature equational laws associativity identity inverse quantified laws except outermost universal quantifiers allowed varieties key point extra operations add information follow uniquely usual definition group although usual


definition uniquely specify identity element ''e'' easy exercise shows unique inverse element universal algebra point view well adapted category theory example defining group object category theory object question may set one must use equational laws make sense general categories rather quantified laws refer individual elements inverse identity specified morphisms category example topological group inverse must exist element wise must


three basic constructions universal algebra homomorphic image subalgebra product homomorphism two algebras ''a'' ''b'' function ''h'' ''a'' nbsp nbsp ''b'' set set b every operation ''f'' sub ''a'' sub corresponding ''f'' sub ''b'' sub b arity say ''n'' ''h'' ''f'' sub ''a'' sub ''x'' sub sub ''x'' sub ''n'' sub nbsp ''f'' sub ''b'' sub ''h'' ''x'' sub sub ''h'' ''x'' sub ''n'' sub sometimes subscripts ''f'' taken clear context algebra function example ''e'' constant nullary operation ''h'' ''e'' sub ''a'' sub nbsp nbsp ''e'' sub ''b'' sub unary operation ''h'' ''x'' nbsp ''h'' ''x'' binary operation


''h'' ''x'' nbsp nbsp ''y'' nbsp ''h'' ''x'' nbsp nbsp ''h'' ''y'' things done homomorphisms well definitions certain special kinds homomorphisms listed entry homomorphism particular take homomorphic image algebra ''h'' ''a'' subalgebra ''a'' subset ''a'' closed operations ''a'' product set algebraic structures cartesian product sets operations defined coordinatewise basic theorems isomorphism theorems encompass isomorphism theorems groups


rings modules etc birkhoff 's hsp theorem states class algebras variety closed homomorphic images subalgebras arbitrary direct products motivations applications addition unifying approach universal algebra also gives deep theorems important examples counterexamples provides useful framework intend start study new classes algebras enable use methods invented particular classes algebras classes algebras recasting methods terms universal algebra possible


interpreting applied classes also provided conceptual clarification jdh smith puts '' looks messy complicated particular framework may turn simple obvious proper general one '' particular universal algebra applied study monoids rings lattices universal algebra came along many theorems notably isomorphism theorems proved separately classes universal algebra proven every kind algebraic system paper higgins


referenced well followed framework range particular algebraic systems paper notable discussion algebras operations partially defined typical examples categories groupoids leads subject higher dimensional algebra defined study algebraic theories partial operations whose domains defined geometric conditions notable examples various forms higher dimensional categories groupoids constraint satisfaction problem universal algebra provides natural language constraint satisfaction problem csp csp


refers important class computational problems given relational algebra existential sentence math varphi math algebra question find whether math varphi math satisfied algebra often fixed refers problem whose instance existential sentence math varphi math proved every computational problem formulated algebra example ''n'' coloring problem stated csp algebra math big dotsn neq big math ie algebra math n math elements single relation inequality dichotomy


monad category sets finitary monad category sets arises lawvere theory however monad describes algebraic structures within one particular category example category sets algebraic theories describe structure within large class categories namely finite products recent development category theory operad theory nbsp operad set operations similar universal algebra restricted equations allowed expressions variables duplication omission variables allowed thus


partial functions certain partial functions also handled generalization lawvere theories known essentially algebraic theories another generalization universal algebra model theory sometimes described universal algebra logic history alfred north whitehead 's book ''a treatise universal algebra'' published term ''universal algebra'' essentially meaning today whitehead credits william rowan hamilton augustus de morgan originators subject matter james joseph sylvester coining term ref name gratzer ref time structures lie algebras hyperbolic


work abraham robinson alfred tarski andrzej mostowski students period papers written along lines suggested birkhoff 's papers dealing free algebras congruence subalgebra lattices homomorphism theorems although development mathematical logic made applications algebra possible came slowly results published anatoly maltsev went unnoticed war tarski 's lecture international congress mathematicians cambridge ushered new period model theoretic aspects developed mainly tarski well