evolved around two sometimes conflicting concepts competition first individual liberty free government intervention second fair competitive environment free excessive economic power since enactment sherman act enforcement competition law based various economic theories adopted government section sherman act declared illegal every contract form trust otherwise conspiracy restraint trade commerce among several states foreign nations section prohibits monopolies attempts conspiracies monopolize following enactment us court


applies principles business markets courts applied act without consistent economic analysis complemented clayton act specifically prohibited exclusive dealing agreements particularly tying agreements interlocking directorates mergers achieved purchasing stock onwards ''rule reason'' analysis frequently applied courts competition cases however period characterized lack competition law enforcement courts' application antitrust law dominated ' 'structure conduct performance'' paradigm harvard school enforcement antitrust law


based efficiency explanations chicago school became dominant legal writings judge robert bork 's book ''the antitrust paradox'' since game theory frequently used antitrust cases hart scott rodino antitrust improvements act mergers acquisitions came additional scrutiny us regulators act parties must make pre merger notification us department justice federal trade commission prior completion transaction february nd ftc reduced hart scott rodino reporting threshold million combined assets transaction european


union law competition law gained new recognition europe inter war years germany enacting first anti cartel law sweden norway adopting similar laws respectively however great depression competition law disappeared europe revived following second world war united kingdom germany following pressure united states became first european countries adopt fully fledged competition laws regional level eu competition law origins european coal steel community ecsc agreement france italy belgium


netherlands luxembourg germany following second world war agreement aimed prevent germany establishing dominance production coal steel felt dominance contributed outbreak war article agreement banned cartels article made provisions concentrations mergers abuse dominant position companies first time competition law principles included plurilateral regional agreement established trans european model competition law competition rules included


treaty rome also known ec treaty established european economic community eec treaty rome established enactment competition law one main aims eec institution system ensuring competition common market distorted two central provisions eu competition law companies established article prohibited anti competitive agreements subject exemptions article prohibiting abuse dominant position treaty also established principles competition law member states article covering public undertakings


article making provisions state aid regulations mergers included member states could establish consensus issue time today treaty lisbon prohibits anti competitive agreements article including price fixing according article agreements automatically void article establishes exemptions collusion distributional technological innovation gives consumers fair share benefit include unreasonable restraints risk eliminating competition anywhere compliant general principle european union law proportionality article prohibits abuse


dominant position price discrimination exclusive dealing article allows european council regulations govern mergers firms current regulation regulation ec general test whether concentration ie merger acquisition community dimension ie affects number eu member states might significantly impede effective competition articles provide member state 's right deliver public services may obstructed otherwise public enterprises must adhere competition principles companies article lays general rule state may


aid subsidize private parties distortion free competition provides exemptions charities regional development objectives event natural disaster leading ecj cases competition law include ''consten grundig v commission'' ''united brands v commission'' india india responded positively opening economy removing controls economic liberalisation quest increasing efficiency nation 's economy government india acknowledged liberalization privatization globalization era result indian market faces competition within outside country ref name competition warrier vs conflict competition law intellectual


property rights http lex warrierin competition law ipr citation lw lex warrier online law journal ref led need strong legislation dispense justice commercial matters competition act passed history competition law india dates back first competition law namely monopolies restrictive trade practices act mrtp enacted economic reforms legislation found obsolete many aspects result new competition law form competition act


enacted competition commission india quasi judicial body established enforcing provisions competition act ref name cci formation ref international expansion countries enacted competition laws percent countries population exceeding people countries adopted competition laws past years signaling spread competition law following collapse soviet union expansion european union currently competition authorities many states closely co operate everyday basis foreign counterparts enforcement efforts


also key area information evidence sharing many asia 's developing countries including india competition law considered tool stimulate economic growth korea japan competition law prevents certain forms conglomerates addition competition law promoted fairness china indonesia well international integration vietnam ref name papersssrncom hong kong 's competition ordinance came force year asean member states part creation asean economic community member states association south east asian nations asean pledged enact competition


laws policies end today ten member states general competition legislation place remains differences regimes example merger control notification rules leniency policies whistle blowers unlikely supranational competition authority asean akin european union clear trend towards increase infringement investigations decisions cartel enforcement enforcement wto members green whether competition law form part agreements national level competition law enforced competition authorities well private


enforcement united states supreme court explained blockquote every violation antitrust laws blow free enterprise system envisaged congress system depends strong competition health vigor strong competition depends turn compliance antitrust legislation enacting laws congress many means disposal penalize violators could example required violators compensate federal state local governments estimated damage respective economies caused violations remedy selected instead congress chose permit persons sue


recover three times actual damages every time injured business property antitrust violation blockquote european union modernisation regulation means european commission longer body capable public enforcement european union competition law done facilitate quicker resolution competition related inquiries commission issued green paper ''damages actions breach ec antitrust rules'' suggested ways making private damages claims cartels easier eu member states enforce competition laws criminal sanctions


analysed professor whelan types sanctions engender number significant theoretical legal practical challenges antitrust administration legislation seen balance guidelines clear specific courts regulators business leave little room discretion prevents application laws resulting unintended consequences guidelines broad hence allowing administrators sway improving economic outcomes versus succumbing political policies redistribute wealth chapter post war havana charter contained antitrust code never incorporated wto 's


forerunner general agreement tariffs trade office fair trading director professor richard whish wrote sceptically seems unlikely current stage development wto metamorphose global competition authority despite ongoing doha round trade talks world trade organization discussion includes prospect competition law enforcement moving global level incapable enforcement newly established international competition network icn way national authorities coordinate enforcement activities theory classical perspective


doctrine laissez faire antitrust seen unnecessary competition viewed long term dynamic process firms compete market dominance markets firm may successfully dominate superior skill innovativeness however according laissez faire theorists tries raise prices take advantage monopoly position creates profitable opportunities others compete process creative destruction begins erodes monopoly therefore government try break monopoly allow market work john stuart mill believed


restraint trade doctrine justified preserve liberty competition classical perspective competition certain agreements business practice could unreasonable restraint individual liberty tradespeople carry livelihoods restraints judged permissible courts new cases appeared light changing business circumstances hence courts found specific categories agreement specific clauses fall foul doctrine economic fairness contrive overarching conception market power earlier theorists like adam smith rejected monopoly power


basis blockquote monopoly granted either individual trading company effect secret trade manufactures monopolists keeping market constantly stocked never fully supplying effectual demand sell commodities much natural price raise emoluments whether consist wages profit greatly natural rate blockquote ''the wealth nations'' adam smith also pointed cartel problem advocate specific legal measures combat blockquote people trade seldom meet together even merriment


diversion conversation ends conspiracy public contrivance raise prices impossible indeed prevent meetings law either could executed would consistent liberty justice though law cannot hinder people trade sometimes assembling together ought nothing facilitate assemblies much less render necessary ref name book chapter smith book chapter para ref blockquote latter half th century become clear large firms


become fact market economy john stuart mill 's approach laid treatise ''on liberty'' blockquote trade social act whoever undertakes sell description goods public affects interest persons society general thus conduct principle comes within jurisdiction society cheapness good quality commodities effectually provided leaving producers sellers perfectly free sole check equal freedom buyers supplying elsewhere


able pay rational producers keep producing selling buyers keep buying last marginal unit possible output alternatively rational producers reduce output margin buyers buy amount produced waste greatest number wants greatest number people become satisfied utility perfected resources longer reallocated make anyone better without making someone else worse society achieved allocative efficiency productive efficiency simply means


society making much free markets meant reward work hard therefore put society 's resources towards frontier possible production dynamic efficiency refers idea business constantly competes must research create innovate keep share consumers traces austrian american political scientist joseph schumpeter 's notion perennial gale creative destruction ever sweeping capitalist economies driving enterprise market 's mercy led schumpeter argue monopolies need broken standard


oil next gale economic innovation would contrasting allocatively productively dynamically efficient market model monopolies oligopolies cartels one firms exist market credible threat entry competing firms prices rise competitive level either monopolistic oligopolistic equilibrium price production also decreased decreasing social welfare creating deadweight loss sources market power said include existence externalities barriers entry market free rider


problem markets may fail efficient variety reasons exception competition law 's intervention rule ''laissez faire'' justified government failure avoided orthodox economists fully acknowledge perfect competition seldom observed real world aim called workable competition follows theory one cannot achieve ideal go second best option using law tame market operation chicago school robert bork group economists lawyers largely associated


university chicago advocate approach competition law guided proposition actions originally considered anticompetitive could actually promote competition us supreme court used chicago school approach several recent cases one view chicago school approach antitrust found united states circuit court appeals judge richard posner 's books ''antitrust law'' ''economic analysis law'' robert bork highly critical court decisions united states antitrust law series law review articles book ''the antitrust paradox'' bork argued


original intention antitrust laws economic efficiency pursuit ''only'' consumer welfare protection competition rather competitors ref name bork p bork p ref furthermore acts prohibited namely cartels fix prices divide markets mergers create monopolies dominant firms pricing predatorily allowing practices vertical agreements price discrimination grounds harm consumers running different critiques us antitrust policy common theme government interference operation free markets harm good


consumers paying excessive prices since threat new entrants market restrain high market share firm 's price increases competition law make merely monopoly illegal rather abusing power monopoly may confer instance exclusionary practices first necessary determine whether firm dominant whether behaves appreciable extent independently competitors customers ultimately consumer eu law large market shares raise presumption firm dominant may rebuttable firm dominant


position special responsibility allow conduct impair competition common market similarly collusive conduct market shares determined reference particular market firm product question sold although lists seldom closed certain categories abusive conduct usually prohibited country 's legislation instance limiting production shipping port refusing raise expenditure update technology could abusive tying one product sale another considered abuse restrictive consumer choice


depriving competitors outlets alleged case ''microsoft v commission'' leading eventual fine million including windows media player microsoft windows platform refusal supply facility essential businesses attempting compete use constitute abuse one example case involving medical company named ''commercial solvents'' set rival tuberculosis drugs market commercial solvents forced continue supplying company named zoja raw materials drug zoja


market competitor without court forcing supply competition would eliminated forms abuse relating directly pricing include price exploitation difficult prove point dominant firm 's prices become exploitative category abuse rarely found one case however french funeral service found demanded exploitative prices justified basis prices funeral services outside region could compared tricky issue predatory pricing practice dropping prices product much one 's


smaller competitors cannot cover costs fall business chicago school considers predatory pricing unlikely however ''france telecom sa v commission'' broadband internet company forced pay million dropping prices production costs interest applying prices except eliminating competitors cross subsidized capture lion 's share booming market one last category pricing abuse price discrimination example could company offering rebates industrial customers export sugar


customers selling goods market example according world bank 's republic armenia accumulation competition connectivity global competition report published global competitiveness index suggests armenia ranks lowest among eca europe central asia countries effectiveness anti monopoly policy intensity competition low ranking somehow explains low employment low incomes armenia mergers acquisitions merger acquisition involves competition law perspective concentration economic power hands fewer usually


means one firm buys shares another reasons oversight economic concentrations state reasons restrict firms abuse position dominance regulation mergers acquisitions attempts deal problem arises ''ex ante'' prevention market dominance united states merger regulation began clayton act european union merger regulation known ecmr competition law requires firms proposing merge gain authorization relevant government authority theory behind


mergers transaction costs reduced compared operating open market bilateral contracts concentrations increase economies scale scope however often firms take advantage increase market power increased market share decreased number competitors adversely affect deal consumers get merger control predicting market might like knowing making judgment hence central provision eu law asks whether concentration ''would'' went ahead significantly impede effective competition particular result creation


strengthening dominant position corresponding provision us antitrust states similarly blockquote person shall acquire directly indirectly whole part stock share capital assets one persons engaged commerce activity affecting commerce effect acquisition stocks assets use stock voting granting proxies otherwise may substantially lessen competition tend create monopoly blockquote amounts substantial lessening significant


impediment competition usually answered empirical study market shares merging companies assessed added although kind analysis gives rise presumptions conclusions herfindahl hirschman index used calculate density market concentration exists aside maths important consider product question rate technical innovation market problem collective dominance oligopoly economic links arise whereby new market becomes conducive collusion relevant transparent market


concentrated structure could mean firms coordinate behavior easily whether firms deploy deterrents whether firms safe reaction competitors consumers entry new firms market barriers might encounter considered firms shown creating uncompetitive concentration us still argue create efficiencies enough outweigh detriment similar reference technical economic progress mentioned art ecmr another defense might firm


taken fail go insolvent taking leaves less competitive state would happen anyway mergers vertically market rarely concern although ''aol time warner'' european commission required joint venture competitor bertelsmann ceased beforehand eu authorities also focused lately effect conglomerate mergers companies acquire large portfolio related products though without necessarily dominant shares individual market intellectual property innovation competition competition law become increasingly intertwined intellectual property


intellectual properties collaboratively designed consequence violating antitrust laws intentionally otherwise effects competition properties accepted industry standards cross licensing intellectual property bundling intellectual property rights long term business transactions agreements extend market exclusiveness intellectual property rights beyond statutory duration trade secrets remain secret eternal length life scholars suggest prize instead patent would solve problem deadweight loss innovators got reward prize provided government non profit


organization rather directly selling market see millennium prize problems however innovators may accept prize least much much earn patent question difficult determine see also consumer protection european union competition law ''the history standard oil company'' book institute consumer antitrust studies irish competition law list competition regulators list countries' copyright length relevant market resale price maintenance sherman antitrust act ssnip united states antitrust law megacorporation notes references bork robert h ''the antitrust paradox'' new york free press


nature causes wealth nations'' online https webarchiveorg web http wwwadamsmithorg smith indexhtm adam smith institute wilberforce richard alan campbell neil elles ''the law restrictive practices monopolies'' nd edition london sweet maxwell whish richard ''competition law'' th ed lexis nexis butterworths reading ''competition policy international'' available https webarchiveorg web http wwwglobalcompetitionpolicyorg elhauge einer geradin damien ''global competition law economics'' faull jonathan nikpay ali eds faull nikpay ec law competition georg erber georg kooths stefan ' windows vista securing competition' ''diw weekly report'' vol


'''military operation''' coordinated military actions state non state actor response developing situation actions designed military plan resolve situation state actor 's favor operations may combat non combat nature may referred code name purpose national security military operations often known generally accepted common usage names actual operational objectives types military operations military operations classified scale scope force employment

Applied science
Military sciences
Military operation


impact wider conflict scope military operations theater describes operation large often continental area operation represents strategic national commitment conflict operation barbarossa general goals encompass areas consideration outside military economic political impact campaign describes either subset theatre operation limited geographic operational strategic commitment battle britain need represent total national commitment conflict broader goals outside military


impact battle describes subset campaign specific military goals geographic objectives well clearly defined use forces battle gallipoli operationally combined arms operation originally known dardanelles landings part dardanelles campaign allied troops took part engagement describes tactical combat event contest specific area objective actions distinct units example battle kursk also known german designation operation citadel included many separate engagements several


combined battle prokhorovka battle kursk addition describing initial german offensive operation also included two soviet counter offensive operations operation kutuzov operation polkovodets rumyantsev strike describes single attack upon specified target often forms part broader engagement strikes explicit goal rendering facilities airports inoperable assassinating enemy leaders limiting delivery supplies enemy troops definition operational level war operational level war occupies roughly middle ground campaign 's strategic focus tactics


'' 'surgical strike''' military attack intended damage legitimate military target minimal collateral damage surrounding structures vehicles buildings general public infrastructure utilities description swift targeted attack aim minimum collateral damage nearby areas civilians surgical strike neutralization targets surgical strikes also prevents escalation full blown war surgical strike attacks carried via air strike airdropping special ops teams swift ground operation sending special troops precision bombing another

Applied science
Military sciences
Tactics
Surgical strike


example surgical strike carried aircraft contrasted carpet bombing latter results high collateral damage wide range destruction affected area may may include high civilian casualties bombing baghdad initial stages invasion iraq us forces known shock awe example coordinated surgical strike government buildings military targets systematically attacked us aircraft attempt cripple ba'athist controlled iraqi government saddam hussein examples


israel israel 's bombing iraqi nuclear reactor osirak considered prime example surgical strike ref name weeks ref commando operation entebbe uganda israeli passengers freed hijacked plane also mentioned successful surgical strike even though involve taking targets striking deep inside foreign territory covering miles start finish without engagement forces qualified 'surgical' ref name sandler ref united states united states carried numerous surgical strikes al qaeda targets afghanistan using cruise missiles


also used technology purported chemical weapons facility sudan ref name cilluffocardash ref azerbaijan october azerbaijan carried surgical strikes armenian forces destroyed three r elbrus tactical ballistic missile launchers kalbajar district ' 'de jure'' part azerbaijan ' 'de facto'' independent artsakh 's control according azerbaijan missile launchers targeting ganja mingachevir strike retaliation october ganja ballistic missile attack resulted ten civilians getting killed ref name attackcasualities ref getting injured women children among


equivalent linear ode see example riccati equation odes solved explicitly terms known functions integrals possible equation computing taylor series solutions may useful applied problems numerical methods ordinary differential equations supply approximation solution background trajectory projectile launched cannon follows curve determined ordinary differential equation derived newton 's second law ordinary differential equations odes arise many contexts mathematics social natural sciences mathematical descriptions

Formal science
Mathematics
Pure mathematics
Analysis
Ordinary differential equations


change use differentials derivatives various differentials derivatives functions become related via equations differential equation result describes dynamically changing phenomena evolution variation often quantities defined rate change quantities example derivatives displacement respect time gradients quantities enter differential equations specific mathematical fields include geometry analytical mechanics scientific fields include much physics astronomy celestial mechanics meteorology weather modeling chemistry reaction rates biology infectious diseases genetic variation ecology population modeling population competition economics stock trends


interest rates market equilibrium price changes many mathematicians studied differential equations contributed field including newton leibniz bernoulli family riccati clairaut d'alembert euler simple example newton 's second law motion mdash relationship displacement ''x'' time ''t'' object force ''f'' given differential equation math frac mathrm x mathrm f x math constrains motion particle constant mass ''m'' general ''f'' function position ''x'' ''t'' particle time ''t'' unknown function ''x'' ''t''


appears sides differential equation indicated notation ''f'' ''x'' ''t'' definitions follows let ''y'' dependent variable ''x'' independent variable ''y'' ''f'' ''x'' unknown function ''x'' notation differentiation varies depending upon author upon notation useful task hand context leibniz 's notation useful differentiation integration whereas lagrange 's notation useful representing derivatives order compactly newton 's notation math dot ddot overset math


often used physics representing derivatives low order respect time general definition given ''f'' function ''x'' ''y'' derivatives ''y'' equation form math f left xyy' ldots n right n math called explicit ''ordinary differential equation'' ''order'' ''n'' ref name harper ref generally ''implicit'' ordinary differential equation order ''n'' takes form math f left x y' y'' ldots n right math classifications defn differential equation said ''linear'' ''f'' written linear combination derivatives ''y''


math n sum n x r x math ''x'' ''x'' continuous functions ref name harper ref name kreyszig ref function ''r'' ''x'' called ' 'source term'' leading two important classifications ref name kreyszig consequently one automatic solution trivial solution ''y'' solution linear homogeneous equation '''complementary function''' denoted ''y sub c sub '' system odes number coupled differential equations form system equations '''y''' vector whose elements functions '''y''' ''x'' ''y'' sub sub ''x'' ''y'' sub sub ''x'' ''y sub sub '' ''x'' '''f'''


vector valued function '''y''' derivatives math mathbf n mathbf f left x mathbf mathbf ' mathbf '' ldots mathbf n right math ''explicit system ordinary differential equations'' ''order'' ''n'' ' 'dimension'' ''m'' column vector form math begin pmatrix n n vdots n end pmatrix begin pmatrix f left x mathbf mathbf ' mathbf '' ldots mathbf n right f left x mathbf mathbf ' mathbf '' ldots mathbf n right vdots f left x mathbf mathbf ' mathbf '' ldots mathbf n right end pmatrix math necessarily linear ''implicit'' analogue math mathbf f left x mathbf mathbf ' mathbf '' ldots mathbf n right boldsymbol math ''' ''' zero vector matrix form math begin pmatrix f x mathbf mathbf ' mathbf '' ldots mathbf n f x mathbf mathbf ' mathbf '' ldots mathbf n


particular values often chosen fulfill set 'initial conditions boundary conditions' singular solution solution cannot obtained assigning definite values arbitrary constants general solution context linear ode terminology ''particular solution'' also refer solution ode necessarily satisfying initial conditions added ''homogeneous'' solution general solution homogeneous ode forms general solution original ode terminology used guessing method section article


frequently used discussing method undetermined coefficients variation parameters theories singular solutions theory singular solutions ordinary partial differential equations subject research time leibniz since middle nineteenth century received special attention valuable little known work subject houtain darboux leader theory geometric interpretation solutions opened field worked various writers notably casorati cayley latter due


equations admit infinitesimal transformations present comparable integration difficulties also emphasized subject transformations contact lie 's group theory differential equations certified namely unifies many ad hoc methods known solving differential equations provides powerful new ways find solutions theory applications ordinary partial differential equations general solution approach uses symmetry property differential equations continuous infinitesimal transformations solutions solutions lie theory continuous group theory lie algebras differential geometry used understand


structure linear nonlinear partial differential equations generating integrable equations find lax pairs recursion operators b cklund transform finally finding exact analytic solutions de symmetry methods applied differential equations arise mathematics physics engineering disciplines sturm liouville theory sturm liouville theory theory special type second order linear ordinary differential equation solutions based eigenvalues corresponding eigenfunctions linear operators defined via second order homogeneous linear equations problems identified sturm liouville problems slp named jcf sturm j


liouville studied mid slps infinite number eigenvalues corresponding eigenfunctions form complete orthogonal set makes orthogonal expansions possible key idea applied mathematics physics engineering slps also useful analysis certain partial differential equations existence uniqueness solutions several theorems establish existence uniqueness solutions initial value problems involving odes locally globally two main theorems class wikitable theorem assumption conclusion peano existence theorem f continuous local existence


picard lindel f theorem f lipschitz continuous local existence uniqueness basic form theorems guarantee local results though latter extended give global result example conditions gr nwall 's inequality met also uniqueness theorems like lipschitz one apply dae systems may multiple solutions stemming non linear algebraic part alone local existence uniqueness theorem simplified theorem stated simply follows ref name edebvp elementary differential equations boundary value problems th edition boyce rc diprima


wiley international john wiley sons ref equation initial value problem math y' f xy quad x math ''f'' ''f'' ''y'' continuous closed rectangle math r x ax times b math ''x y'' plane ''a'' ''b'' real symbolically ''a b'' denotes cartesian product square brackets denote closed intervals interval math x hx h subset x ax math ''h'' ''the'' solution equation initial value problem found solution unique since


restriction ''f'' linear applies non linear equations take form ''f'' ''x y'' also applied systems equations global uniqueness maximum domain solution hypotheses picard lindel f theorem satisfied local existence uniqueness extended global result precisely initial condition ''x'' sub sub ''y'' sub sub exists unique maximum possibly infinite open interval math max x x x pm r cup pm infty x max math solution satisfies initial condition restriction


solution satisfies initial condition domain math max math case math x pm neq pm infty math exactly two possibilities explosion finite time math limsup x x pm x infty math leaves domain definition math lim x x pm x partial bar omega math open set ''f'' defined math partial bar omega math boundary note maximum domain solution always interval uniqueness may smaller math r math may depend specific choice ''x'' sub sub ''y'' sub sub example math y' math means ''f'' ''x y'' ''y'' sup sup


interval side opposite initial condition would disconnected initial condition therefore uniquely determined maximum domain math r math math lim x x pm x infty math one two possible cases according theorem reduction order differential equations usually solved easily order equation reduced reduction first order system explicit differential equation order ''n'' math f left x y' y'' ldots n right n math written system


''n'' first order differential equations defining new family unknown functions math math ''i'' ''n'' ''n'' dimensional system first order coupled differential equations math begin array rcl ' ' vdots n ' n n' f xy ldotsy n end array math compactly vector notation math mathbf ' mathbf f x mathbf math math mathbf ldotsy n quad mathbf f xy ldotsy n ldotsy nf xy ldotsy n math summary exact solutions differential equations solutions written exact closed form several important classes given table ''p'' ''x'' ''q'' ''x'' ''p'' ''y'' ''q'' ''y'' ''m'' ''x''''y'' ''n'' ''x''''y'' integrable functions ''x'' ''y'' ''b'' ''c'' real given constants


''y'' general case see special cases ref name mhft mathematical handbook formulas tables rd edition lipschutz r spiegel j liu schaum 's outline series isc n ref math begin align p x q p x q frac dy dx p x q dx p x q dy end align math separation variables divide ''p'' sub sub ''q'' sub sub math int x frac p lambda p lambda lambda int frac q lambda q lambda lambda c math first order separable ''x'' ref name edebvp math begin align frac dy dx f x dy f x dx end align math direct integration math int x f lambda lambda c math first order autonomous separable ''y'' ref name edebvp


math begin align frac dy dx f dy f dx end align math separation variables divide ''f'' math x int frac lambda f lambda c math first order separable ''x'' ''y'' ref name edebvp math begin align p frac dy dx q x p dy q x dx end align math integrate throughout math int p lambda lambda int x q lambda lambda c math general first order equations class wikitable scope col differential equation scope col solution method scope col general solution first order homogeneous ref name edebvp math frac dy dx f left frac x right math set


frac partial n partial x math integrate throughout math begin align f xy int x lambday lambda int lambda lambda int n x lambda lambda int x x lambda lambda c end align math math n xy partial partial int x lambday lambda math math x x xy partial partial x int n x lambda lambda math inexact differential first order ref name edebvp math begin align xy frac dy dx n xy xy dy n xy dx end align math math frac partial partial x neq frac partial n partial math integration factor '' '' ''x y'' satisfying math frac partial mu partial frac partial mu n partial x math '' '' ''x'' ''y'' found


suitable way math begin align f xy int x mu lambday lambday lambda int lambda lambda int mu x lambda n x lambda lambda int x x lambda lambda c end align math math n xy partial partial int x mu lambday lambday lambda math math x x xy partial partial x int mu x lambda n x lambda lambda math general second order equations class wikitable scope col differential equation scope col solution method scope col general solution second order autonomous math frac dx f math multiply sides equation ' 'dy'' ' 'dx'' substitute nowrap math frac dy dx frac dx frac dx left frac dy dx right math integrate twice math x pm int frac lambda sqrt int lambda f varepsilon varepsilon


c c math linear ''n''th order equations class wikitable scope col differential equation scope col solution method scope col general solution first order linear inhomogeneous function coefficients ref name edebvp math frac dy dx p x q x math integrating factor math e int x p lambda lambda math armour formula math e int x p lambda lambda left int x e int lambda p varepsilon varepsilon q lambda lambda c right math second order linear inhomogeneous function coefficients math frac dx p x frac dy dx left p x p' x right q x math integrating factor math e int x p lambda lambda math math e int x p lambda lambda left int x left int xi e int lambda p varepsilon varepsilon q lambda lambda right xi c x c right math second order


c x c e frac bx math math c e frac bx left c sin left x frac sqrt c b right c cos left x frac sqrt c b right right math ''n''th order linear inhomogeneous constant coefficients ref name mmpe math sum j n b j frac j dx j r x math complementary function ''y sub c sub '' assume substitute solve polynomial find linearly independent functions math e alpha j x math particular integral ''y sub p sub '' general method variation parameters though simple ''r'' ''x'' inspection may work ref name edebvp math c p math since sub ''j'' sub solutions polynomial degree ''n'' math prod j n alpha alpha j math


'' '' sub ''j'' sub different math c sum j n c j e alpha j x math root sub ''j'' sub repeated ''k sub j sub '' times math c sum j n left sum ell k j c j ell x ell right e alpha j x math sub ''j'' sub complex setting sub ''j'' sub ''i '' sub ''j'' sub using euler 's formula allows terms previous results written form math c je alpha j x c j e chi j x cos gamma j x varphi j math '' '' sub ''j'' sub arbitrary constant phase shift guessing method methods solving ode fail cases intuition


solution de might look like sometimes possible solve de simply guessing solution validating correct use method simply guess solution differential equation plug solution differential equation validate satisfies equation particular solution de otherwise start try another guess instance could guess solution de form math ae alpha math since


integration analysis odes matlab technical computing application matrix laboratory gnu octave high level language primarily intended numerical computations scilab open source application numerical computation maple proprietary application symbolic calculations mathematica proprietary application primarily intended symbolic calculations sympy python package solve odes symbolically julia programming language high level language primarily intended numerical computations sagemath open source application uses python like syntax wide range capabilities spanning several branches mathematics scipy python package includes ode integration module chebfun


open source package written matlab computing functions digit accuracy gnu r open source computational environment primarily intended statistics includes packages ode solving see also boundary value problem examples differential equations laplace transform applied differential equations list dynamical systems differential equations topics matrix differential equation method undetermined coefficients recurrence relation notes references polyanin v f zaitsev ''handbook exact solutions ordinary differential equations'' nd edition chapman hall crc press boca raton bibliography w johnson http wwwhtiumichedu cgi b bib bibpermq abv ''a treatise ordinary


partial differential equations'' john wiley sons http htiumichedu u umhistmath university michigan historical math collection witold hurewicz ''lectures ordinary differential equations'' dover publications polyanin v f zaitsev moussiaux ''handbook first order partial differential equations'' taylor francis london zwillinger ''handbook differential equations rd edition '' academic press boston external links http eqworldipmnetru indexhtm eqworld world mathematical equations containing list ordinary differential equations solutions http tutorialmathlamaredu classes de deaspx online notes differential equations paul dawkins lamar university http wwwsosmathcom diffeq diffeqhtml differential equations sos mathematics http numericalmethodsengusfedu mws gen ode mws gen ode bck primerpdf primer analytical


x px '''visual communication''' use visual elements convey ideas information ref name paramount components visual communication ''infographic design team infographics design data visualization'' retrieved https wwwinfographicdesignteamcom blog components visual communication ref include limited signs typography drawing graphic design illustration industrial design advertising animation electronic resources humans used visual communication since prehistoric times within modern culture several types characteristics comes visual elements consist objects models graphs diagrams maps photographs ref name outside different types characteristics elements seven

Applied science
Architecture and design
Visual communication


important approaches using people communicate share information term 'visual presentation' used refer actual presentation information visible medium text images recent research field focused web design graphically oriented usability ref name ref important figures aldous huxley regarded one prominent explorers visual communication sight related theories becoming near blind teen years result illness set stage would make one intellectual people ever explored visual communication


work includes important novels dehumanizing aspects scientific progress famously ''brave new world'' ''the art seeing'' described seeing sum sensing selecting perceiving one famous quotes see know max wertheimer said father gestalt psychology gestalt means ''form'' ' 'shape'' german study gestalt psychology show emphasis simplicity properties group visuals similarity shape color continuity proximity additional laws include closure figure ground principles studied images


also intensively taught image analysis visual communication contains image aspects interpretation images subjective understand depth meaning multiple meanings communicated image requires image analysis images analyzed though many perspectives example six major perspectives presented paul martin lester personal historical technical ethical cultural critical ref name paul martin lester ''visual communication images messages'' belmont ca thomson wadsworth ref '''personal perspective ''' viewer opinion image based personal thoughts personal response depends viewer 's thoughts


values individually however might sometimes conflict cultural values also viewer viewed image personal perspective hard change view image viewer ref name '''historical perspective ''' image 's view arising history use media times sort images changed use different new media example result using computer edit images eg photoshop quite different comparing images made edited craft ref name '''technical perspective '''


definition perspective cultural perspective involves identity symbols uses words related image use heroes image etc symbolization image cultural perspective also seen semiotic perspective ref name '''critical perspective ''' view images critical perspective viewers criticize images critics made interests society although individual makes critics way perspective differs personal perspective ref name visual aid media simple


advanced '''chalkboard whiteboard ''' chalkboards whiteboards useful visual aids particularly advanced types media available cheap also allow much flexibility ref name roth ref use chalkboards whiteboards convenient perfect visual aid often using medium aid create confusion boredom particularly student familiar properly use visual aids attempts draw board speaking detract time attention actual speech ref name roth '''poster


board ''' poster simple easy visual aid posters display charts graphs pictures illustrations biggest drawback using poster visual aid often poster appear unprofessional since poster board paper relatively flimsy often paper bend fall best way present poster hang tape wall ref name roth '''handouts ''' handouts also display charts graphs pictures illustrations important aspect use handout


person keep handout long presentation help person better remember discussed passing handouts however extremely distracting handout given might potentially difficult bring back audience 's attention person receives handout might tempted read paper keep listening speaker saying using handout speaker distributes hand right reference ref name maui ref distributing handouts


acceptable lecture hour two short lecture five ten minutes handout used ref name roth '''video excerpts ''' video great visual aid attention grabber however video replacement actual speech several potential drawbacks playing video speech lecture first video playing includes audio speaker able talk also video exciting interesting make


speaker saying appear boring uninteresting key showing video presentation make sure transition smoothly video show short clips ref name roth '''projection equipment ''' several types projectors include slide projectors powerpoint presentations overhead projectors computer projectors slide projectors oldest form projector longer used powerpoint presentations popular used often overhead projectors still used somewhat inconvenient use order use overhead


projector transparency must made whatever projected onto screen takes time costs money computer projectors technologically advanced projectors using computer projector pictures slides easily taken right computer either online saved file blown shown large screen though computer projectors technologically advanced always completely reliable technological breakdowns uncommon computers today ref name roth '''computer assisted presentations ''' powerpoint presentations extremely useful visual aid


following components foundation communicating visually hierarchy important principle assists audience processing information allowing follow visuals piece piece focal point visual aid ie website social media poster etc serve starting point audience guide order achieve hierarchy must take account components color shape tones texture figure ground balance ref name ref colors first important component communicating visuals colors displays depth connection


shapes shapes depict natural materials include curvy lines geometric rectilinear shapes shapes created man including triangles rectangles ovals circles ref name tone refers difference color intensity meaning light dark purpose achieving certain tone put spotlight graphical presentation emphasize information similarly texture enhance viewers optics creates personal feel compared corporate feel texture refers surface object whether amplify


user 's content ref name figure ground relationship figure background words relationship shapes objects types etc space look figure positive space ground negative space comparison positive space objects hold dominance visually negative space mentioned previously background addition creating strong contrast color texture tone figure ground highlight different figures balance important symmetrical asymmetrical balance visual communication symmetrical


access due internet access requirement certain limitations number characters image size ref name roth ref despite potential drawback shift towards visual images rise youtube instagram snapchat rise platforms facebook twitter followed suit integrated visual images platform outside use written posts ref name russmann svensson ref stated visual images used two ways additional clarification spoken written text create individual meaning usually incorporating ambiguous meanings


meanings assist creating casual friendships interactions either show fabricate reality major platforms becoming focused visual images growing multimodal platform users ability edit adjust pictures videos platforms ref name russmann svensson analyzing relationship visual communication social media four themes arise '''emerging genres practices ''' sharing various visual elements allow creation genres new arrangements socially accepted visual elements ie photographs gifs based platforms emerging genres used self expression


identity feel sense belonging different sub group online community ref name adami jewitt ref '''identity construction ''' similar genres users use visuals social media express identities visual elements change meaning period time person shared means visual elements dynamic makes visuals uncontrollable since person may identify specific identity rather someone evolved ref name adami jewitt '''everyday public private vernacular practices ''' theme presents difficulty deciphering considered public private


users post privacy home however post interacting users online public ref name adami jewitt '''transmedia circulation appropriation control ''' transmedia circulation refers visual elements circulated different types media visual elements images taken one platform edited posted another platform without recognizing originally came concept appropriation ownership brought question making aware idea user appropriate another person work user 's work appropriated well ref name adami


jewitt culture members different cultures participate exchange visual imagery based idea universal understandings term visual culture allows cultures feel equal making inclusive aspect every life considering visual culture communication shaped values amongst cultures especially regarding concepts high low context cultures generally high context rely heavily visual elements implied implicit meaning however cultures low context rely visual elements direct meaning


rely textual explanations politics visual communication politics become primary sense communication dialogue text become secondary sense due fact people turn towards televisions become dependent visuals sound bite become popular perfected art among political figures despite favored mode showcasing political figure 's agenda shown news coverage displayed image bites instead voices images short videos visuals deemed essential


function political communication behind visuals functions political figures use functions include ref name schill ref '''argument function ''' although images indicate words said function conveys idea images association objects ideas visuals politics make arguments different aspects political figure 's character intentions introducing visual imagery sound targeted audience clarify ambiguous messages political figure said interviews news stories ref name schill '''agenda setting function ''' function important political


figures produce newsworthy pictures allow message gain coverage reason due agenda setting theory importance public agenda taken consideration media determines importance certain story issue ref name schill said politicians provide interesting attention grabbing picture likely news coverage way politician gain news coverage provide exclusivity media capture certain event despite ability control whether receive coverage


create image appearing family oriented religiously involved showing commonality disadvantaged community ref name schill '''identification function ''' identification function visuals create identification political figures audiences words audience may perceive type similarity political figure voter finds similarity candidate likely vote voter notices candidate perceived similarities less likely vote ref name schill '''documentation function ''' similar stamp


passport indicated certain country photographs political figure document event happened documenting event occurred evidence proof argumentative claims political figure claims one thing evidence either back disprove ref name schill '''societal symbol function ''' function used visuals political figures use iconic symbols draw emotional power instance political figures stand american flags photographed military personnel even attending


sport three areas societal symbols hold strong sense patriotism comparison congressional candidates may pictured former current presidents gain implied endorsement many places like statue liberty mount rushmore tomb unknown soldier seen iconic societal symbols hold sense emotional power ref name schill '''transportation function ''' transportation function using visuals transporter viewer different time place visuals figuratively bring viewers past idealized future political figures use tactic


science medicine shown need visual communication assist explaining non scientific readers bohr 's atomic model nasa 's photographs earth visual elements served tools furthering understand science medicine ref name bordley specifically elements like graphs slides portray data scientific concepts patterns revealed graphs used association data determine meaningful correlation photographs useful physicians rely figuring visible signs diseases illnesses ref name poland ref however using visual


elements negative effect understanding information two major obstacles non scientific readers lack integration visual elements every day scientific language incorrectly identifying targeted audience adjusting level understanding ref name bordley tackle obstacles one solution science communicators must place user center design called user centered design design focuses strictly user interact visual element minimum stress maximum level efficiency ref name poland another solution could


implemented source university based programs programs universities need introduce visual literacy science communication helping producing graduates accurately interpret analyze evaluate design visual elements understanding science medicine ref name poland see also advertising art director graphic design illustration models communication optical communication photography sign industry telepresence typography videoconference ''visual communication'' journal visual culture visual design visual language visual rhetoric visual sociology references design communication design communication studies academic disciplines graphic design optical communications


molecular structure rotating diamond '''molecular physics''' study physical properties molecules chemical bonds atoms well molecular dynamics important experimental techniques various types spectroscopy scattering also used field closely related atomic physics overlaps greatly theoretical chemistry physical chemistry chemical physics addition electronic excitation states known atoms molecules exhibit rotational vibrational modes whose energy levels quantized smallest energy differences exist different rotational states pure rotational spectra

Natural science
Physics
Molecular physics


'''method experimental physics vol molecular physics''' ''l marton'' '' claire marton'' '''atomic molecular optical physics new research''' ''lt chen'' nova science publishers inc new york references atomic molecular optical physics


uses computing internet cdc cyber range mainframe computers cyberbullying bullying harassment using electronic means cyber party political party created john mcafee us presidential election cybercaf internet caf business provides internet access cyberculture emergent cultures based use computer networks cybergoth sub culture cybersex colloquially cyberstalking use internet electronic means stalk harass individual group organization cyberspace global technology environment arts entertainment media cy er five person edm idol group cyber marvel comics marvel comics supervillain cyber

Applied science
Military sciences
Military weapons
Cyber


russian soviet sci fi character see strugatsky 's works doctor cyber dc comics supervillain cyberpunk science fiction genre see also centre integrative bee research ciber cybernetics disambiguation cybernetic organism cyborg organic biomechatronic body parts cyberneticist one studies cybernetics cyber city disambiguation cyberspace disambiguation cyborg disambiguation


'''systematic theology''' discipline christian theology formulates orderly rational coherent account doctrines christian faith addresses issues bible teaches certain topics true god universe ref name ref also builds biblical disciplines church history well biblical historical theology systematic theology shares systematic tasks disciplines constructive theology dogmatics ethics apologetics philosophy religion method methodological tradition differs somewhat biblical theology systematic theology draws


core sacred texts christianity simultaneously investigating development christian doctrine course history particularly philosophy ethics social sciences natural sciences using biblical texts attempts compare relate scripture led creation systematized statement whole bible says particular issues within christianity different traditions intellectual ecclesial approach systematic theology different ways impacting method employed develop system b understanding theology 's task c doctrines included system order doctrines


appear even diversity generally case works one describe systematic theologies begin revelation conclude eschatology since focused truth systematic theology also framed interact address contemporary world numerous authors explored area case charles gore john walvoord lindsay dewar charles moule among others framework developed theologians involved review postbiblical history doctrine first treating biblical materials process concludes applications contemporary issues categories


since systemic approach systematic theology organizes truth different headings ref name ten basic areas categories although exact list may vary slightly theology proper study character god angelology study angels biblical theology study bible christology study christ ecclesiology study church eschatology study end times ref name grace institute ref hamartiology study sin pneumatology study holy spirit soteriology study salvation


theological anthropology study nature humanity history establishment integration varied christian ideas christianity related notions including diverse topics themes bible single coherent well ordered presentation relatively late development eastern orthodoxy early example provided john damascus 's th century ''exposition orthodox faith'' attempts set order demonstrate coherence theology classic texts eastern theological tradition west peter lombard 's th century ''sentences'' wherein thematically collected great series quotations


church fathers became basis medieval scholastic tradition thematic commentary explanation thomas aquinas 's ''summa theologiae'' best exemplifies scholastic tradition lutheran scholastic tradition thematic ordered exposition christian theology emerged th century philipp melanchthon 's ''loci communes'' countered calvinist scholasticism exemplified john calvin 's ''institutes christian religion'' th century primarily protestant groups new kind systematic theology arose attempted demonstrate christian doctrine formed coherent system premised one fundamental axioms


circles used refer ''topical'' collection exploration content bible different perspective provided bible 's message garnered simply reading biblical narratives poems proverbs letters story redemption manual live godly life one advantage approach allows one see bible says regarding subject eg attributes god one danger tendency assign technical definitions terms based


passages read meaning everywhere term used bible eg justification paul uses letter romans proposed evangelical theologians used different sense james uses letter view systematic theology complementary biblical theology biblical theology traces themes chronologically bible systematic theology examines themes topically biblical theology reflects diversity bible systematic theology reflects unity however contemporary systematic theologians evangelical


persuasion would question configuration discipline systematic theology concerns twofold first instead systematic exploration theological truth systematic theology defined way described synonymous biblical theology instead contemporary systematic theologians seek use available resources ascertain nature god god 's relationship world including philosophy history culture etc sum theologians argue systematic biblical theology two separate though related disciplines second systematic theologians claim evangelicalism far diverse


''systematic theology'' zondervan hodge charles https archiveorg details systematictheol hodggoog ''systematic theology'' grand rapids wm b eerdmans publishing co jenson robert w ''systematic theology'' oxford oxford university press melanchthon philipp ''loci communes'' st louis concordia publishing house miley john ''systematic theology'' newlands george ''god christian perspective'' edinburgh clark oden thomas c ''systematic theology'' volumes peabody prince press pannenberg wolfhart ''systematic theology'' grand rapids wm b eerdmans publishing co pieper francis ''christian dogmatics'' st louis concordia publishing


house reymond robert l ''a new systematic theology christian faith'' nd ed word publishing schleiermacher friedrich ''the christian faith'' edinburgh clark thielicke helmut ''the evangelical faith'' edinburgh clark thiessen henry c ''systematic theology'' grand rapids william b erdsmans publishing co tillich paul ''systematic theology'' volumes turretin francis parts ''institutes elenctic theology'' van til cornelius ''an introduction systematic theology'' p r press watson richard ''theological institutes'' weber otto ''foundations dogmatics'' grand rapids eerdmans christian theology christian terminology


'''experimental physics''' category disciplines sub disciplines field physics concerned observation physical phenomena experiments methods vary discipline discipline simple experiments observations cavendish experiment complicated ones large hadron collider overview sir ernest rutherfords laboratory early th century experimental physics regroups disciplines physics concerned data acquisition data acquisition methods detailed conceptualization beyond simple thought experiments realization laboratory experiments often put contrast theoretical physics

Natural science
Physics
Experimental physics


concerned predicting explaining physical behaviour nature acquisition knowledge although experimental theoretical physics concerned different aspects nature share goal understanding symbiotic relation former provides data universe analyzed order understood latter provides explanations data thus offers insight better acquire data set experiments theoretical physics also offer insight data needed order


gain better understanding universe experiments devise order obtain history distinct field experimental physics established early modern europe known scientific revolution physicists galileo galilei christiaan huygens johannes kepler blaise pascal sir isaac newton early th century galileo made extensive use experimentation validate physical theories key idea modern scientific method galileo formulated successfully tested several results dynamics particular law inertia later became first


well mechanical energy ludwig boltzmann nineteenth century responsible modern form statistical mechanics besides classical mechanics thermodynamics another great field experimental inquiry within physics nature electricity observations th eighteenth century scientists robert boyle stephen gray benjamin franklin created foundation later work observations also established basic understanding electrical charge current john dalton discovered atoms different elements different weights proposed modern theory atom hans christian


rsted first proposed connection electricity magnetism observing deflection compass needle nearby electric current early michael faraday demonstrated magnetic fields electricity could generate james clerk maxwell presented royal society set equations described relationship electricity magnetism maxwell 's equations also predicted correctly light electromagnetic wave starting astronomy principles natural philosophy crystallized fundamental laws physics enunciated improved succeeding centuries th century


sciences segmented multiple fields specialized researchers field physics although logically pre eminent longer could claim sole ownership entire field scientific research current experiments cms detector experimental endeavour lhc cern examples prominent experimental physics projects relativistic heavy ion collider collides heavy ions gold ions first heavy ion collider protons located brookhaven national laboratory long island usa hera collides electrons positrons protons part desy located hamburg germany


lhc large hadron collider completed construction suffered series setbacks lhc began operations shut maintenance summer world 's energetic collider upon completion located cern french swiss border near geneva collider became fully operational march year half later originally planned ligo laser interferometer gravitational wave observatory large scale physics experiment observatory detect cosmic gravitational waves develop gravitational wave observations astronomical tool currently two


ligo observatories exist ligo livingston observatory livingston louisiana ligo hanford observatory near richland washington jwst james webb space telescope planned launch successor hubble space telescope survey sky infrared region main goals jwst order understand initial stages universe galaxy formation well formations stars planets origins life method experimental physics uses two main methods experimental research controlled experiments natural experiments controlled experiments


often used laboratories laboratories offer controlled environment natural experiments used example astrophysics observing celestial objects control variables effect impossible famous experiments famous experiments include degree field galaxy redshift survey micron sky survey mass bell test experiments boomerang experiment camera obscura experiments cavendish experiment cosmic background explorer cowan reines neutrino experiment davisson germer experiment double slit experiment foucault pendulum franck hertz experiment geiger marsden experiment gravity probe gravity probe b hafele keating experiment homestake experiment ligo oil drop experiment michelson morley experiment sloan digital sky survey stern gerlach experiment wilkinson microwave anisotropy probe wu experiment experimental


techniques well known experimental techniques include crystallography ellipsometry faraday cage interferometry nmr laser cooling laser spectroscopy raman spectroscopy signal processing spectroscopy stm vacuum technique x ray spectroscopy inelastic neutron scattering prominent experimental physicists famous experimental physicists include alhazen al biruni al khazini fl galileo galilei isaac newton laura bassi michael faraday ernst mach john william strutt rd baron rayleigh wilhelm r ntgen karl ferdinand braun henri becquerel albert abraham michelson heike kamerlingh onnes j j thomson jagadish chandra bose pierre curie william henry bragg marie curie


robert andrews millikan ernest rutherford lise meitner max von laue clinton davisson c v raman william lawrence bragg james chadwick pyotr kapitsa charles drummond ellis john cockcroft patrick blackett baron blackett ukichiro nakaya enrico fermi ernest lawrence walter houser brattain pavel cherenkov carl david anderson ernst ruska john bardeen william shockley chien shiung wu charles hard townes rosalind franklin owen chamberlain nicolaas bloembergen vera rubin mildred dresselhaus samar mubarakmand gerd binnig


steven chu wolfgang ketterle andre geim lene hau rainer weiss timelines see timelines listings physics experiments timeline atomic subatomic physics timeline classical mechanics timeline electromagnetism classical optics timeline gravitational physics relativity timeline nuclear fusion timeline particle discoveries timeline particle physics technology timeline states matter phase transitions timeline thermodynamics see also physics engineering experimental science measuring instrument references reading external links physics


materiel movements exercise cobra gold '''materiel''' '''mat riel''' refers supplies equipment weapons military supply chain management typically supplies equipment commercial supply chain context military context term ''materiel'' refers either specific needs excluding manpower force complete specific mission general sense needs excluding manpower functioning army materiel management consists continuing actions relating planning organizing directing coordinating controlling evaluating application resources ensure effective economical support military

Applied science
Military sciences
Logistics
Materiel


forces includes provisioning cataloging requirements determination acquisition distribution maintenance disposal terms materiel management materiel control inventory control inventory management supply management synonymous military materiel often shipped used severe climates without controlled warehouses fixed material handling equipment packaging labeling often need meet stringent technical specifications help ensure proper delivery final use military procurement allows commercial packaging rather stringent military grades materiel commercial distribution context refers products business distinct involved operating


business see also anti materiel rifle inventory mat riel french army military acquisition military logistics military supply chain management supply chain united states army materiel command air force materiel command united states army medical research materiel command references external links freight transport military logistics


recent past definition description near eastern branch archaeology highly eurocentric americocentric reflecting origins growth field western academic traditions however absence better solutions continued heavy involvement western academics term taken hold remains frequent use definition near east usually based fertile crescent region nile valley modern egypt mesopotamia modern iraq also usually included iran arabian peninsula islands anatolia modern day turkey cyprus north africa west egypt

Social science
Archaeology
Near Eastern Archaeology


history archaeological investigation region grew th century discipline biblical archaeology efforts mostly europeans uncover evidence biblical old new testaments narratives much archaeological work region still influenced discipline although within last three decades marked tendency archaeologists dissociate work biblical frameworks near eastern archaeology term wide often generalised application frequently divided regional sub branches archaeology modern states region along broad thematic lines regions


loosely defined often based recognizable entities evidence cultural cohesion coincide topographical zones scholars may differ way region divided regional divisions also may change period period common fields study biblical archaeology dealing region history bible assyriology dealing mesopotamia egyptology dealing ancient history today egypt parts sudan prehistoric archaeology tied region instead deals origins culture invention writing


geographic subdivisions egypt egyptology one example specialized branch deals nile valley cultures egypt associated regions sub saharan africa sinai peninsula east parts north africa includes language studies history archaeology related disciplines nowadays much work also done prehistoric archaeological record practitioners best described prehistorians southern levant syria palestine name levant syria palestine used refer area adjacent east coast mediterranean southern region included term encompasses israel


west bank gaza strip part jordan palestine ancient roman byzantine name also use crusades period ottoman rule british mandate region also called holy land land israel canaan biblical associations foregoing names perceived political overtones meaning neutral geographically based term southern levant become popular archaeologists wish refer area without prejudice political orientation many contexts sinai peninsula


also considered part southern levant although part modern state egypt archaeologically distinguished heartland egypt nile valley delta northern levant term northern levant used refer lebanon syrian littoral portions mediterranean coast turkey province hatay usually regions included greater syria name used refer whole area anatolia mesopotamia arabia mediterranean coast lebanon syrian arab republic parts northern


israel also known phoenicia ancient kingdom however term suffers problems canaan equivalents generally used strict historical sense anatolia landmass anatolia modern turkey bordered several seas includes parts northern mesopotamia tigris euphrates rise turkey flow south iraq cyprus cyprus ancient alashiya large island eastern mediterranean separate cultural entity periods human occupation however proximity anatolia northern southern levant


responsible influences regions especially case cyprus important source copper much region mesopotamia mesopotamia land two rivers considered begin less near modern border iraq refers flat valley southern tigris euphrates rivers tributaries rivers empty shatt al arab waterway separates iraq iran sumerology specialized discipline deals history language archaeology ancient sumer southern mesopotamia mostly th


rd millennium bce assyriology deals assyrians succeeded sumerians covers much region language still use iran persia iran sometimes known persia includes large plateau periphery including zagros mountains sub disciplines region deal mostly languages history archaeology regions within large area arabian peninsula arabian peninsula offshore islands separate geographical zone contacts sinai well watered regions north sea far east organisations group western iranian archaeologists


conference held susa khuzestan iran henry wright william sumner elizabeth carter genevieve dolfus greg johnson saeid ganjavi yousef majidzadehvanden berghe due historic interest archaeology near east especially due biblical links area large number organisations dedicated archaeological investigation region include american schools oriental research publishes journal ''near eastern archaeology magazine'' council british research levant publishes journal http wwwartmanacuk arthist levanthtm levant netherlands institute near east


publishes journal http wwwnino leidennl publication bibliotheca orientalis bibliotheca orientalis see also levantine archaeology genetic history middle east ''near eastern archaeology'' near eastern bioarchaeology icaane international congress archaeology ancient near east external links https webarchiveorg web http wwwancientneareastnet ancient near east net http wwwetanaorg etana https webarchiveorg web http wwweblaforumorg library bcah introduction biblical archaeology https webarchiveorg web http wwwbiblicalarcheologynet resources biblical archaeology http wwwcenturyoneorg potteryhtml pottery types levant http wwwcenturyonecom jerusalemwallshtml jerusalem circuit walls http wwwanthropologyuwedupl bioarchaeology near east archaeological sub disciplines ancient near east


'''atmospheric chemistry''' branch atmospheric science chemistry earth 's atmosphere planets studied multidisciplinary approach research draws environmental chemistry physics meteorology computer modeling oceanography geology volcanology disciplines research increasingly connected areas study climatology composition chemistry earth 's atmosphere importance several reasons primarily interactions atmosphere living organisms composition earth 's atmosphere changes result natural processes volcano

Natural science
Chemistry
Atmospheric chemistry


emissions lightning bombardment solar particles corona also changed human activity changes harmful human health crops ecosystems examples problems addressed atmospheric chemistry include acid rain ozone depletion photochemical smog greenhouse gases global warming atmospheric chemists seek understand causes problems obtaining theoretical understanding allow possible solutions tested effects changes government policy evaluated atmospheric composition visualisation composition volume earth 's atmosphere water vapour


name nyt ref colspan '''minor constituents mole fractions ppm ''' argon ar carbon dioxide sup sup co sub sub sup b sup neon ne helium methane sup sup ch sub sub krypton kr hydrogen h sub sub nitrous oxide n sub sub xenon xe nitrogen dioxide sub sub


ch sub sub vary season location sup b sup co sub sub increasing ppm annually see carbon dioxide earth 's atmosphere trace gas composition besides major components listed earth 's atmosphere also many trace gas species vary significantly depending nearby sources sinks trace gases include compounds cfcs hcfcs particularly damaging ozone layer characteristic foul odor rotten eggs smelt concentrations low ppb ''approximate'' amounts near


benzene c sub sub h sub sub methanol ch sub sub oh ethanol c sub sub h sub sub oh trichlorofluoromethane ccl sub sub f sup p sup dichlorodifluoromethane ccl sub sub f sub sub sup p sup chloromethane ch sub sub cl bromomethane ch sub sub br sup p sup iodomethane ch sub sub carbonyl sulfide ocs sup p sup sulfur dioxide sub sub sup p sup hydrogen sulfide h sub sub sup p sup carbon disulfide cs sub sub sup p sup


explanation sydney chapman gordon dobson ozone layer created maintained explanation photochemical smog arie jan haagen smit studies ozone issues led nobel prize chemistry award shared paul crutzen mario molina frank sherwood rowland ref name nobelprize ref st century focus shifting atmospheric chemistry increasingly studied one part earth system instead concentrating atmospheric chemistry isolation focus seeing one part single system


rest atmosphere biosphere geosphere especially important driver links chemistry climate effects changing climate recovery ozone hole vice versa also interaction composition atmosphere oceans terrestrial ecosystems ref ref name ap ref ''not'' absorbed br nasa simulation november width image earth globalairquality nitrogendioxidelevels jpg caption nitrogen dioxide global air quality levels br released december ref name nasa ref width methodology observations lab measurements modeling three central elements atmospheric chemistry progress atmospheric chemistry often driven


interactions components form integrated whole example observations may tell us chemical compound exists previously thought possible stimulate new modelling laboratory studies increase scientific understanding point observations explained observation observations atmospheric chemistry essential understanding routine observations chemical composition tell us changes atmospheric composition time one important example keeling curve series measurements today show steady


rise concentration carbon dioxide see also ongoing measurements atmospheric co sub sub observations atmospheric chemistry made observatories mauna loa mobile platforms aircraft eg uk 's facility airborne atmospheric measurements ships balloons observations atmospheric composition increasingly made satellites important instruments gome mopitt giving global picture air pollution chemistry surface observations advantage provide long term records high time resolution limited vertical horizontal space provide observations


surface based instruments eg lidar provide concentration profiles chemical compounds aerosol still restricted horizontal region cover many observations available line atmospheric chemistry observational databases laboratory studies measurements made laboratory essential understanding sources sinks pollutants naturally occurring compounds experiments performed controlled environments allow individual evaluation specific chemical reactions assessment properties particular atmospheric constituent types analysis interest includes


gas phase reactions well heterogeneous reactions relevant formation growth aerosols also high importance study atmospheric photochemistry quantifies rate molecules split apart sunlight resulting products addition thermodynamic data henry 's law coefficients also obtained modeling order synthesise test theoretical understanding atmospheric chemistry computer models chemical transport models used numerical models solve differential equations governing concentrations chemicals atmosphere


simple complicated one common trade numerical models number chemical compounds chemical reactions modeled versus representation transport mixing atmosphere example box model might include hundreds even thousands chemical reactions crude representation mixing atmosphere contrast models represent many physical processes atmosphere due constraints computer resources far fewer chemical reactions compounds models used interpret observations test understanding chemical reactions


predict future concentrations chemical compounds atmosphere one important current trend atmospheric chemistry modules become one part earth system models links climate atmospheric composition biosphere studied models constructed automatic code generators eg autochem kinetic preprocessor approach set constituents chosen automatic code generator select reactions involving constituents set reaction databases reactions chosen ordinary differential equations describe time evolution automatically constructed


see also oxygen cycle ozone oxygen cycle paleoclimatology scientific assessment ozone depletion tropospheric ozone depletion events references reading brasseur guy p orlando john j tyndall geoffrey ''atmospheric chemistry global change'' oxford university press finlayson pitts barbara j pitts james n jr ''chemistry upper lower atmosphere'' academic press seinfeld john h pandis spyros n ''atmospheric chemistry physics air pollution climate change'' nd ed john wiley sons inc warneck peter ''chemistry natural atmosphere'' nd ed academic press wayne richard


p ''chemistry atmospheres'' rd ed oxford university press j v iribarne h r cho ''atmospheric physics'' reidel publishing company external links https webarchiveorg web http wwwwmoch web arep reports ozone ozone asst reporthtml wmo scientific assessment ozone depletion http igacjisaowashingtonedu igac international global atmospheric chemistry project http wwwvegaorguk video programme paul crutzen interview freeview video paul crutzen nobel laureate work decomposition ozone talking nobel laureate harry kroto vega science trust https webarchiveorg web http wwwautocheminfo constituentobservationaldatabasehtml cambridge atmospheric chemistry database large constituent observational database common format https webarchiveorg web http wwwatmospherempgde enid c e b bab e ff c service home html environmental science published everybody round earth http jpldataevaljplnasagov indexhtml nasa jpl


chemical kinetics photochemical data use atmospheric studies http wwwiupac kineticchcamacuk kinetic photochemical data evaluated iupac subcommittee gas kinetic data evaluation http wwwshsuedu chm tgc glossary gloshtml atmospheric chemistry glossary sam houston state university http wwwatmospphysicsutorontoca people loic chemistryhtml tropospheric chemistry http wwwesfedu chemistry dibble atmoschemcalchtm calculators use atmospheric chemistry http wwwchemistrylandcom chm airwebreathe comp aircompositionhtml illustrated elementary assessment composition air atmospheric chemistry environmental chemistry chemistry


'''mechanochemistry''' '''mechanical chemistry''' coupling mechanical chemical phenomena molecular scale includes mechanical breakage chemical behaviour mechanically stressed solids eg stress corrosion cracking enhanced oxidation tribology polymer degradation shear cavitation related phenomena eg sonochemistry sonoluminescence shock wave chemistry physics even burgeoning field molecular machines mechanochemistry seen interface chemistry mechanical engineering possible synthesize chemical products using mechanical action mechanisms mechanochemical transformations often complex different usual thermal photochemical mechanisms ref name hickenboth ref method

Natural science
Chemistry
Mechanochemistry


ball milling widely used process mechanical force used achieve chemical processing transformations special issue chemical society review vol issue dedicated theme mechanochemistry fundamentals applications ranging nano materials technology reviewed mechanochemical approach used synthesize metallic nanoparticles catalysts magnets graphyne metal iodates nickel vanadium carbide molybdenum vanadium carbide nanocomposite powders mechanochemistry radically different traditional way dissolving heating stirring chemicals solution eliminates need many solvents mechanochemistry could


help make many chemical processes used industry environmentally friendly example mechanochemical process used environmentally preferable way synthesize pharmaceutically attractive phenol hydrazones term mechanochemistry sometimes confused mechanosynthesis refers specifically machine controlled construction complex molecular products ref name nanosystems ref ref name roadmap ref mechanochemical phenomena utilized since time immemorial example making fire oldest method making fire rub pieces wood creating friction hence heat allowing wood undergo combustion high temperature another method involves


use flint steel spark small particle pyrophoric metal spontaneously combusts air starting fire instantaneously see also embryonic differentiation waves mechanoluminescence tribology references reading lenhardt j ong choe r evenhuis c r martinez j craig l trapping diradical transition state mechanochemical polymer extension science chemistry


include chinese arabic sanskrit blockquote realize educated japanese hardly frame single literary sentence without use chinese resources day siamese burmese cambodgian bear unmistakable imprint sanskrit pali came hindu buddhism centuries ago whether argue teaching latin greek schools argument sure studded words come us rome athens get indication early chinese culture buddhism classical mediterranean civilization

Humanities
Languages and literature
Linguistics
Classical Language


literary language ancient egypt c th century bc th century ad old babylonian akkadian language c th th centuries bc imitated standard later literary works middle assyrian akkadian language c th th centuries bc vedic sanskrit form sanskrit classical standardization used vedic texts c th th centuries bc classical hebrew language tanakh particular prophetic books c th th centuries bc old persian court language achaemenid empire th th


centuries bc classical chinese based literary language zhou dynasty c th century bc classical greek attic dialect th century bc classical sanskrit described p ini 's ashtadhyayi th century bc classical tamil sangam literature c nd century bc nd century ad defined tolk ppiyam classical pali buddhist canon used language nd centuries bc classical latin literary language st century bc classical mandaic literary aramaic mandaeism st century ad classical syriac literary aramaic syriac christianity rd th centuries middle persian court language


sassanid empire rd th centuries classical coptic language egypt coptic orthodox church alexandria rd th centuries liturgical language present day middle ages ge'ez language ethiopian orthodox tewahedo church garima gospels dated th century th century various scholars classical armenian oldest attested form armenian th century literary language th century classical arabic based language qur'an th century present classical kannada court language rashtrakuta empire earliest available literary work


''kavir jam rga'' ad ref name britannicalit ''encyclop dia britannica'' kannada literature quote ''the earliest literary work ''kavir jam rga'' c ad treatise poetics based sanskrit model'' ref old saxon language saxon christian literature th th centuries old english language ''beowulf'' ''anglo saxon chronicle'' many divergent written dialects partially standardized west saxon form old french language chivalric romance th th centuries old georgian language georgia th th centuries old east slavic language kievan rus' th th centuries angkorian old khmer language khmer empire


th th centuries new persian language classical persian literature th present old nubian language nubia th th th centuries old javanese language old javanese literature used primarily hindu buddhist javanese kingdom era th th centuries ref name hcresse ref ref name ogloblin ref old bulgarian language first bulgarian empire golden age th century earliest manuscript ''freising manuscripts'' classical tibetan religious literary language tibet th century present classical japanese language heian period literature th th centuries middle korean language goryeo joseon th th centuries old


occitan language troubadours th th centuries middle high german language medieval german literature th th centuries old serbian language serbia conquest ottoman empire th th centuries classical telugu earliest available literary work telugu mahabharata ad classical malayalam earliest extant prose work ''ramacharitam'' th century ref name charitam k ramachandran nair ayyappapanicker p ref old norse language viking age th century middle bulgarian language second bulgarian empire th th centuries middle low german language hanseatic league


brazil classical mapuche language th th centuries chile chinook jargon trade language native american tribes pacific northwest th century early modern period awadhi lingua franca northern india mughal rule led use poets th th centuries renaissance italian language italian renaissance th th centuries late old portuguese language portuguese golden age th th centuries early modern spanish language spanish golden age th th centuries classical azeri lingua franca caucasus mountain region language azeri literature th th centuries


aspect influence classical language later language classical languages india classicism classics golden age metaphor lingua franca list lingua francas list languages first written accounts literary language sacred language official language standard language world language references reading ashdowne richard accidence acronyms deploying electronic assessment support classical language teaching university context ''arts humanities higher education'' beach adam r creation classical language eighteenth century standardizing english cultural imperialism future


literary canon ''texas studies literature language'' coulson michael ''sanskrit introduction classical language'' sevenoaks kent hodder stoughton crooker jill kathleen rabiteau interwoven fabric ap latin examinations sat ii latin test national standards classical language learning ''the classical outlook'' denizot camille olga spevak ''pragmatic approaches latin ancient greek'' philadelphia john benjamins publishing company eschbach szabo viktoria shelley ching yu hsieh chinese classical language botanical science semiotics transcription


''kodikas code ars semeiotica international journal semiotics'' nos gruber miller john ''when dead tongues speak teaching beginning greek latin'' oxford oxford university press hymes robert getting words right speech vernacular language classical language song neo confucian 'records words' ''journal song yuan studies'' https wwwjstororg stable koutropoulos apostolos modernizing classical language education communicative language teaching educational technology integration classical greek ''human architecture journal sociology self knowledge'' tieken herman blaming brahmins texts lost found tamil literary history ''studies


history'' watt jonathan classical language instruction window cultural diversity ''international journal diversity organisations communities nations'' whitney william dwight ''sanskrit grammar including classical language older dialects veda brahmana'' th issue nd ed cambridge harvard university press


'''regional geography''' major branch geography focuses interaction different cultural natural geofactors specific land landscape counterpart systematic geography concentrates specific geofactor global level basics attention paid unique characteristics particular region natural elements human elements regionalization covers techniques delineating space regions rooted tradition german speaking countries two pillars regional geography idiographic study ''l nder'' spatial individuals specific places countries continents typological

Social science
Geography
Regional Geography


study ''landschaften'' spatial types landscapes coastal regions mountain regions border regions etc approach diagram regional geography world regional geography also certain approach geographical study comparable quantitative geography critical geography approach prevailed second half th century first half th century period regional geography paradigm central within geographical sciences later criticised descriptiveness lack theory strong criticism leveled particular


quantitative revolution main critics g h kimble ref name kimble ght ''the inadequacy regional concept'' london essays geography edd ld stamp sw wooldridge pp ref fred k schaefer regional geography paradigm influenced many geographical sciences including economic geography geomorphology regional geography still taught universities study major regions world western hemisphere may cultural regions northern latin america corresponding geographic regions continents namely north south america whose boundaries differ significantly


cultural regions eastern hemisphere europe asia may considered cultural regions continents depending criteria used differentiate determine shared boundaries discrepancies arise aforementioned lack unifying theory behind definitions delineations continents regions addition notion city region approach study geography underlining urban rural interactions gained credence since mid geographers also attempted reintroduce certain amount regionalism since involves complex definition regions interactions


scales regional geography used basis geomorphological works david linton henri baulig ref name karna ref yet according karna lidmar bergstr regional geography since longer accepted mainstream scholarship basis geomorphological studies ref name karna notable figures notable figures regional geography alfred hettner germany concept chorology paul vidal de la blache france possibilism approach possibilism softer notion environmental determinism united states richard hartshorne concept areal differentiation


school carl sauer strongly influenced alfred hettner paul vidal de la blache also seen regional geography broadest sense see also chorography regional planning regional studies references area studies branches geography history geography


mathematics '''operator theory''' study linear operators function spaces beginning differential operators integral operators operators may presented abstractly characteristics bounded linear operators closed operators consideration may given nonlinear operators study depends heavily topology function spaces branch functional analysis collection operators forms algebra field operator algebra description operator algebras part operator theory single operator theory single operator theory deals properties

Formal science
Mathematics
Pure mathematics
Analysis
Operator theory


identifies class linear operators modelled multiplication operators simple one hope find abstract language spectral theorem statement commutative c algebras see also spectral theory historical perspective examples operators spectral theorem applies self adjoint operators generally normal operators hilbert spaces spectral theorem also provides canonical decomposition called '' 'spectral decomposition''' '''eigenvalue decomposition''' '''eigendecomposition''' underlying vector space operator acts normal operators '''normal operator''' complex hilbert space


hilbert space ''h'' ''aa'' ''bb'' exists contraction ''c'' ''a cb'' furthermore ''c'' unique ''ker'' ''b'' ''ker'' ''c'' operator ''c'' defined ''c bh '' ''ah'' extended continuity closure ''ran'' ''b'' zero orthogonal complement ''ran'' ''b'' operator ''c'' well defined since ''aa'' ''bb'' implies ''ker'' ''b'' ''ker'' ''a'' lemma follows particular ''aa'' ''bb'' ''c'' partial isometry unique ''ker'' ''b'' ''ker'' ''c'' general bounded operator ''a'' math frac


frac math ''aa'' sup sup unique positive square root ''aa'' given usual functional calculus lemma math u frac math partial isometry ''u'' unique ''ker'' ''a'' ''ker'' ''u'' note ''ker'' ''a'' ''ker'' ''aa'' ''ker'' ''b'' ''ker'' ''b'' ''b'' ''b'' ''aa'' sup sup take ''p'' ''aa'' sup sup one obtains polar decomposition ''a'' ''up'' notice analogous argument used show ''a p'u' '' ''p' '' positive ''u' '' partial isometry ''h'' finite dimensional ''u'' extended unitary operator true


general see example alternatively polar decomposition shown using operator version singular value decomposition property continuous functional calculus '' '' c algebra generated ''a'' similar weaker statement holds partial isometry polar part ''u'' von neumann algebra generated ''a'' ''a'' invertible ''u'' c algebra generated ''a'' well connection complex analysis many operators studied operators hilbert spaces holomorphic functions study operator intimately linked questions


function theory example beurling 's theorem describes invariant subspaces unilateral shift terms inner functions bounded holomorphic functions unit disk unimodular boundary values almost everywhere circle beurling interpreted unilateral shift multiplication independent variable hardy space success studying multiplication operators generally toeplitz operators multiplication followed projection onto hardy space inspired study similar questions spaces bergman space operator algebras theory operator algebras brings algebras


x overline lambda x math ''x'' ''a'' math x x x x math '''remark''' first three identities say ''a'' algebra last identity called '''c identity''' equivalent math xx x math c identity strong requirement instance together spectral radius formula implies c norm uniquely determined algebraic structure math x x x sup lambda x x lambda text invertible math see also invariant subspace functional calculus spectral theory resolvent formalism compact operator