celebrated mother 's day anna reeves jarvis woman originally organized mother 's work day 's protesting lack cleanliness sanitation work place ref name slatecom ref jarvis died daughter created national mother 's day honor mother ref name slatecom mothers frequently important role raising offspring title given non biological mother fills role common stepmothers deviancy discourses many cultural contradictions diverse arrangements practices challenge intensive mothering ideology however considered deviant discourses


since conform script full time motherhood context marriage include single mothers welfare mothers minority mothers immigrant mothers lesbian mothers types motherhood categories mutually exclusive ref name investigating motherhood furthermore women cannot choose mothers deal many internal external pressures ref name motherhood mandate ref motherhood statistics united states million women mothers ages national average age first child births years births teenage girls

Social science
Sociology
Sociology of fatherhood


maurice godelier critical novelty human society compared humans' closest biological relatives chimpanzees bonobos parental role assumed males unaware father connection many cultures especially traditional western father usually husband married couple many times fathers important role raising offspring title given non biological father fills role common stepfathers males married biological mothers east asian western traditional families fathers heads families means


duties include providing financial support making critical decisions must obeyed without question rest family members cultural concepts family specifics father 's role vary according cultural folkways sociologists term bourgeois family arose typical th th century european households father 's role somewhat limited family model father acts economic support sometimes disciplinarian family mother female relative oversees child rearing structure enforced


welfare centers reacted maternal dominance infant welfare parenting interwar britain arguing fathers play crucial role upbringing children study conducted science female parenting would called mother craft words 'ma ma' 'mom' usually regarded terms endearment directed towards mother figure generally one first words child speaks 'da da' 'dad' often precede reflect stronger bond father child


mother child merely simpler pronounce 'mummy' 'mum' require greater control mouth muscles children tend remember 'daddy' according research exciting child contemporary theories number studies given american public determine men view define fatherhood specifically studies focused men choose become fathers relationship fatherhood contemporary masculinity surprisingly recent research fatherhood framed identity theory focused salience centrality importance


father identity men 's lives especially may linked men 's involvement children according identity theory salient central identity likely individuals engage behaviors associated salience refers readiness act identity particular situation centrality refers importance identity relation identities centrality father identity usually held higher level opposed brother husband etc due gendered expectation men must good fathers men view


role father central crucial person likely engage children strive participate responsible fatherhood men fail successfully become fathers unable children view lack fatherhood threat masculinity result threat masculinity serves driving force men possibly become fathers never want seen infertile effeminate ref name stryker ref men choose fatherhood studies men choose fathers often


focus role fatherhood crucial masculinity man 's central identity many men blame economic difficulties cultural differences life situations potential factors deter fatherhood ref name stryker economic difficulties see economic problem serve primary explanation men avoid fatherhood men difficult separate occupational success fatherhood financially providing one 's family central identity father united states result complex relationship formed economic struggles importance fatherhood men


employed low earnings often feel failed fathers men hand men low socioeconomic status find fatherhood appealing gives measure accomplishment denied occupational world terms cultural importance fatherhood white men men color differing views fatherhood affect many men participate fatherhood lastly men blame life situations primary factor decision pursue fatherhood life situations defined


individual 's relationship status single married age studies shown men older married tend likely pursue fatherhood proposed men continue view marriage work fatherhood package deal meaning lacking one components like work marriage may result decision children also proposed married men feel expected pursue fatherhood part marriage though personally may want children


society single parent families canada one parent families become popular since percent children raised single parent ref name macionis percent children raised single parent ref name macionis number single parent families continue rise four times likely mother parent raising child high percentage mothers becoming sole parent sometimes due result divorce unplanned pregnancy inability find befitting partner children raised


single parent commonly disadvantage due characteristics parenting mother father make significant contributions development child therefore one parent 's ability raise child may hindered cohabitation residence containing unmarried couple called cohabitation type family style becoming increasingly accepted canada increased ref name macionis last decades living significant become normalized society cohabitation drastically increased united states


within last years increasing nearly percent data census showed million couples living together without first getting married compared million two thirds couples married shared home together two years marriage gay lesbian couples gay lesbian couples categorized sex relationships denmark first nation allow sex couples get married provide equal rights citizens ref name macionis many nations began allow sex marriages


occur canada spain ref name macionis united states supreme court ruling mandated sex marriage constitutional therefore allowed states united states child rearing sex couples children sex couples either come past relationships opportunities like adoption artificial insemination data collected us census suggested children united states raised lesbian gay couples us census reported lesbian gay couple


partnership households raising children sex households trend child rearing amongst gay lesbian couples partnerships rise also support general public gay lesbian couples partnerships raising children time high since idea homosexual partnerships parenting children evenly divided americans support americans asked think homosexual couples legal right adopt child americans said said n't


idea homosexual partnerships parenting children evenly divided americans support americans asked question right homosexual partnerships raise children adoption americans said said n't americans asked similar question results almost polarizing results found twenty years later americans said lesbian gay couples partnerships said n't federal laws prohibiting adoption child homosexual couple partnership


children raised families concerns like mental emotional even social development children raised sex couple partnership households plethora research conducted provides insight range issues including personal development gender development peer relationships family relationships children sex parents research suggests sexual identities including gender identity gender role behavior sexual orientation develop much ways among children lesbian mothers among children heterosexual parents evidence also suggests children


lesbian gay parents normal social relationships peers adults also studies aspects personal development including personality self concept conduct similarly reveal differences children lesbian mothers children heterosexual parents differences significant noticeable example study examined compared particular behaviors ideas belief performed sons daughters lesbian mothers studies found daughters lesbian mothers aspired pursue careers physicians attorneys engineers compared daughters


heterosexual mothers sons lesbian mothers also tended less aggressive nurturing sons heterosexual mothers general concern homosexual couples partnerships parenting children n't grounds argument children grow one two gay lesbian parents fare well emotional cognitive social sexual functioning children whose parents heterosexual children 's optimal development seems influenced nature relationships interactions within family unit particular structural form takes chosen


numerous empirical studies well intensive theoretical disputes starting scandinavian english speaking countries different approach adopted europe united states european sociologists interested actively promoting children rights time sociology approached children childhood mainly socialization perspective emergence new childhood sociological paradigm ran parallel feminist critique sociological traditions childhood sociologists attacked adultocentric approach separative view sociology towards children surprisingly key works sociology childhood quite interdisciplinary linking


history cultural studies ethnomethodology pedagogy key texts include james prout 's ''constructing reconstructing childhood'' james jenks prout ''theorizing childhood'' prout 's ''the future childhood'' methodological issues research children see ''research children'' edited christensen james recent trends current sociology childhood organized around three central discussions '''the child social actor''' approach derives youth sociology well ethnography focusing everyday life ways children orient society engages cultural performances social worlds


construct take part theory research methodology approach children active participants members society right beginning ref name mackay ref ref name speier ref ref name speier ref thus neither analyzed outsiders society merely 'emergent' members society therefore sociology childhood distinguishes established concepts socialisation ref name cromdal ref research developmental psychology last decades '''the generational order''' second approach centers socio structural socio theoretical questions concerning social equality social order society categorizes members age segregates many respects rights deeds economical participation


ascribed needs etc issues summarized overall concept '''generational order''' thus categorization societal members age far innocent representation natural distinctions rather social construction natural truth therefore relevant component social order deeply connected dimensions social inequality social economic changes socio political interventions thus become central topics childhood sociology analysis issues increased awareness generational inequality societies '''the hybridity childhood''' discussion critical though


dismissive social constructionist approaches dominated sociology childhood since open materialist perspectives seeks interdisciplinary path recognizes biological well social cultural shaping childhood holds open possibility interdisciplinary childhood studies emergent current multi disciplinary efforts scholarship two important influences firstly called 'new wave' childhood studies heavily influenced alan prout 's seminal book ''the future childhood'' work prout examines childhoods merely constructed socially via discourses laws institutions


materially toys food medicines since sociologists nick lee offered important analyses ways 'entanglements' children non human materialities technologies become ever important governance regulation children 's lives terms 'biopoliticisation' childhood secondly nonrepresentational approaches children 's geographies offered commensurate arguably broader series approaches move beyond social constructivism scholars peter kraftl john horton affrica taylor particularly influential examining childhoods produced experienced complex intersections


much research discussion effects society assumption gender roles childhood societal norms perpetuate gender differentiated interactions children psychologists sociologists suggest self gender identity result social learning peers role modeling within family unit genetic predisposition ref name raley raley bianchi sons daughters family processes gender children matter annual review sociology ref sociological implications follows '''peer interactions''' significant gender differences relationship styles among children particularly begin emerge early


childhood onset middle childhood around age grow prevalent age boys tend play larger groups girls friends boys likely become friends turn leads density social networks among boys boys also well defined dominance hierarchies girls within peer groups terms dyadic relationships girls likely longer lasting relationships nature literature suggests girls engage dyadic relationships boys girls also prosocial conflict


situations better collaborative work play boys also spend time social conversations boys likely self disclose among peers boys hand boys likely girls engage organized play sports activities well defined rules one theory suggests boys opportunities exhibit strength skill compare peers competitive activities girls' peer groups characterized strong interpersonal relations empathy others working towards connection oriented


friendships social networks ref name rose rose amanda j rudolph karen review sex differences peer relationship processes potential trade offs emotional behavioral development girls boys psychological bulletin ref '''family interactions''' overall literature implies biological gender children affects parents interact differentials interaction range amount time spent children much parents invest financially children 's futures average fathers tend exhibit differential treatment mothers fathers tend invested families sons families


daughters terms time money however association gender father investment weakening years differentials large parents tend enroll daughters cultural activities sons eg art classes dance classes musical instrument lessons tend invested school related parent involvement programs sons daughters ref name raley sons daughters treated differently parents based gender also receive different benefits parents based gender parents fathers mothers may


gender differentiated interactions benefits however sex minority siblings may difficulty receiving necessary sex specific treatment parents ref name raley current tasks questions socialization practices institutions remain central childhood research dealt new sociological way analyze socialization processes means therefore reconstruct historically culturally varying conceptions processes institutions disciplining civilization offspring addition strategies habitus formation practices status production considered sociology social inequality sociology family private life therefore


interests social order journals ''family matters'' australian institute family studies ref name aifs ref ''international journal sociology family'' ''journal family history'' ''journal marriage family'' ''journal family issues'' see also references reading alanen l mayall b eds ''conceptualizing child adult relations'' london routledge falmer christensen p james eds ''research children perspectives practices'' london falmerroutledge cohen philip n ''the family diversity inequality social change nd ed '' new york ww norton http bookswwnortoncom books webadaspxid bass l ed ''sociological studies children youth'' vol amsterdam


emerald publishing ''the blackwell companion sociology families'' hoboken nj oxford wiley blackwell buehler niederberger separative view scientific approach children dk behera ed ''children childhood contemporary societies'' delhi kamla raj enterprises pp nbsp randall collins scott coltrane ''sociology marriage family gender love property'' wadsworth pub co chicago corsaro william https wwwamazoncom dp ''the sociology childhood'' thousand oaks ca pine forge press edgar patricia ''the new child search smarter grown ups'' wilkinson publishing melbourne australia james prout


eds ''constructing reconstructing childhood'' london falmerroutledge nd revised edition james jenks c prout ''theorizing childhood'' cambridge polity press jenks chris ''childhood'' nd edition new york london routledge nicholas long rex forehand ''making divorce easier child effective ways help children adjust'' contemporary books chicago mayall barry ''towards sociology childhood'' open university press maidenhead berkshire uk david newman ''families sociological perspective'' mcgraw hill higher education boston mass parsons talcot robert f bales collaboration james olds philip slater morris zelditch


jr ''family socialization interaction process'' glencoe il free press prout ''the future childhood towards interdisciplinary study children'' london routledge prout hallett ch eds ''hearing voices children social policy new century'' london routledge qvortrup j bardy g sgritta h wintersberger eds ''childhood matters social theory practice politics'' avebury uk aldershot brian williams stacey sawyer carl wahlstrom ''marriages families intimate relationships practical introductions'' nd edition pearson boston zelizer vivianne ''pricing priceless child changing social value


'''philosophy space time''' branch philosophy concerned issues surrounding ontology epistemology character space time ideas central philosophy inception philosophy space time inspiration central aspect early analytic philosophy subject focuses number basic issues including whether time space exist independently mind whether exist independently one another accounts time 's apparently unidirectional flow whether times present moment exist questions

Humanities
Philosophy
Metaphysics
Philosophy of space and time


single concept named '''pacha''' plato ''timaeus'' identified time period motion heavenly bodies space things come aristotle book iv ''physics'' defined time number changes respect place object innermost motionless boundary surrounds book st augustine 's ''confessions'' ruminates nature time asking time one asks know wish explain


one asketh know goes comment difficulty thinking time pointing inaccuracy common speech things speak properly things speak improperly still things intended understood augustine presented first philosophical argument reality creation aristotle context discussion time saying knowledge time depends knowledge movement things therefore time cannot creatures measure


infinite temporal regress events cannot exist early th century muslim physicist ibn al haytham alhacen alhazen discussed space perception epistemological implications ''book optics'' also rejected aristotle 's definition ''topos'' ''physics'' iv way geometric demonstrations defined place mathematical spatial extension experimental proof intro mission model vision led changes understanding visual perception space contrary previous emission theory vision supported euclid ptolemy tying visual perception space prior bodily experience


alhacen unequivocally rejected intuitiveness spatial perception therefore autonomy vision without tangible notions distance size correlation sight tell us next nothing things realism anti realism traditional realist position ontology time space existence apart human mind idealists contrast deny doubt existence objects independent mind anti realists whose ontological position objects outside mind exist nevertheless doubt independent existence time space immanuel kant published ''critique pure reason''


space time held ''transcendentally ideal'' sense also ''empirically real'' mere illusions idealist writers j e mctaggart ''the unreality time'' argued time illusion see also flow time writers discussed part realists regard instance gottfried leibniz held monads existed least independently mind observer absolutism relationalism leibniz newton great debate defining notions space time real objects


absolute mere orderings upon actual objects relational began physicists isaac newton via spokesman samuel clarke gottfried leibniz papers leibniz clarke correspondence arguing absolutist position leibniz offers number thought experiments purpose showing contradiction assuming existence facts absolute location velocity arguments trade heavily two principles central philosophy principle sufficient reason identity indiscernibles principle sufficient reason holds every fact reason sufficient


explain way otherwise identity indiscernibles states way telling two entities apart one thing example leibniz uses involves two proposed universes situated absolute space discernible difference latter positioned five feet left first example possible thing absolute space exists situation however possible according leibniz universe 's position


absolute space would sufficient reason might well anywhere else therefore contradicts principle sufficient reason could exist two distinct universes ways indiscernible thus contradicting identity indiscernibles standing clarke 's newton 's response leibniz 's arguments bucket argument water bucket hung rope set spin start flat surface water begins spin bucket surface water become concave bucket stopped water


occurs rotating bucket well stationary bucket containing spinning water explained stating water rotating relation presence third thing absolute space leibniz describes space exists relation objects existence apart existence objects motion exists relation objects newtonian space provided absolute frame reference within objects motion newton 's system frame reference exists independently objects contained within


objects described moving relation space almost two centuries evidence concave water surface held authority mach another important figure debate th century physicist ernst mach deny existence phenomena like seen bucket argument still denied absolutist conclusion offering different answer bucket rotating relation fixed stars mach suggested thought experiments like bucket argument problematic imagine universe contains bucket


bucket could seen rotating water inside bucket could possibly slight curve account curve observe increase number objects universe also increases curvature water mach argued momentum object whether angular linear exists result sum effects objects universe mach 's principle einstein albert einstein proposed laws physics based principle relativity principle holds rules physics must


observers regardless frame reference used light propagates speed reference frames theory motivated maxwell 's equations show electromagnetic waves propagate vacuum speed light however maxwell 's equations give indication speed relative prior einstein thought speed relative fixed medium called luminiferous ether contrast theory special relativity postulates light propagates speed light inertial frames examines


implications postulate attempts measure speed relative ether failed seen confirmation einstein 's postulate light propagates speed reference frames special relativity formalization principle relativity contain privileged inertial frame reference luminiferous ether absolute space einstein inferred frame exists einstein generalized relativity frames reference non inertial achieved positing equivalence principle states force felt


force following geodesic object standing earth however experience force held geodesic surface planet einstein partially advocates mach 's principle distant stars explain inertia provide gravitational field acceleration inertia occur contrary leibniz 's account warped space time integral part object defining characteristics volume mass one holds contrary idealist beliefs objects exist independently mind seems


relativistics commits also hold space temporality exactly type independent existence conventionalism position conventionalism states fact matter geometry space time decided convention first proponent view henri poincar reacting creation new non euclidean geometry argued geometry applied space decided convention since different geometries describe set objects equally well based considerations sphere world view developed updated


include considerations relativistic physics hans reichenbach reichenbach 's conventionalism applying space time focuses around idea coordinative definition coordinative definition two major features first coordinating units length certain physical objects motivated fact never directly apprehend length instead must choose physical object say standard metre bureau international des poids et mesures international bureau weights measures wavelength cadmium stand unit length second feature deals separated


objects although presumably directly test equality length two measuring rods next one another find much two rods distant one another even supposing two rods whenever brought near one another seen equal length justified stating always equal length impossibility undermines ability decide equality length two distant objects sameness length contrary must set definition use coordinative definition


effect reichenbach 's conventionalism general theory relativity light assumed ie discovered mark equal distances equal times setting coordinative definition however geometry spacetime set absolutism relationalism debate contemporary philosophy still disagreement correctness conventionalist doctrine structure space time building mix insights historical debates absolutism conventionalism well reflecting import technical apparatus general theory relativity details structure space time


made large proportion discussion within philosophy space time well philosophy physics following short list topics relativity simultaneity according special relativity point universe different set events compose present instant used rietdijk putnam argument demonstrate relativity predicts block universe events fixed four dimensions invariance vs covariance bringing bear lessons absolutism relationalism debate powerful mathematical tools invented th th


century michael friedman draws distinction invariance upon mathematical transformation covariance upon transformation invariance symmetry applies ''objects'' ie symmetry group space time theory designates features objects invariant absolute dynamical variable covariance applies ''formulations'' theories ie covariance group designates range coordinate systems laws physics hold distinction illustrated revisiting leibniz 's thought experiment universe shifted five feet example position object seen property


object ie location invariant similarly covariance group classical mechanics coordinate systems obtained one another shifts position well translations allowed galilean transformation classical case invariance symmetry group covariance group coincide part ways relativistic physics symmetry group general theory relativity includes differentiable transformations ie properties object dynamical words absolute objects formulations general theory relativity unlike


classical mechanics share standard ie single formulation paired transformations covariance group general theory relativity covariance group every theory historical frameworks application modern mathematical methods league idea invariance covariance groups try interpret historical views space time modern mathematical language translations theory space time seen manifold paired vector spaces vector spaces facts objects


theory historical development spacetime theories generally seen start position many facts objects incorporated theory history progresses structure removed example aristotelian space time absolute position special places center cosmos circumference newtonian space time absolute position galilean invariant special positions holes general theory relativity traditional debate absolutism relationalism shifted whether spacetime substance


since general theory relativity largely rules existence eg absolute positions one powerful argument spacetime substantivalism offered john earman known hole argument technical mathematical argument paraphrased follows define function ' 'd'' identity function elements manifold excepting small neighbourhood h belonging h ' 'd'' comes differ identity smooth function use function ' 'd'' construct two mathematical models second generated applying ' 'd'' proper


elements first two models identical prior time ''t'' ''t'' time function created foliation spacetime differ ''t'' considerations show since substantivalism allows construction holes universe must view indeterministic earman argues case substantivalism case determinism indeterminism question physics commitment substantivalism direction time problem direction time arises directly two contradictory facts firstly fundamental physical laws


time reversal invariant cinematographic film taken process describable means aforementioned laws played backwards would still portray physically possible process secondly experience time macroscopic level ''not'' time reversal invariant glasses fall break shards glass cannot reassemble fly onto tables memories past none future feel ca n't change past influence future causation solution one solution problem takes metaphysical view direction time


follows asymmetry causation know past elements past causes effect perception feel ca n't affect past affect future ''ca n't'' affect past ''can'' affect future two main objections view first problem distinguishing cause effect non arbitrary way use causation constructing temporal ordering could easily become circular second problem view explanatory power causation account


successful may account time asymmetric phenomena like perception action account many others however asymmetry causation observed non arbitrary way metaphysical case human hand dropping cup water smashes fragments hard floor spilling liquid order causes resultant pattern cup fragments water spill easily attributable terms trajectory cup irregularities structure angle impact floor etc however applying event


human hand ie capable non animal agency ie floors capable ii pieces cup came possess exactly nature number cup assembling short asymmetry attributable relationship temporal direction ii implications form functional capacity application ideas form functional capacity dictates temporal direction relation complex scenarios involving specific non metaphysical agency


merely dependent human perception time however last observation sufficient invalidate implications example progressive nature time general thermodynamics solution second major family solutions problem far one generated literature finds existence direction time relating nature thermodynamics answer classical thermodynamics states basic physical theory fact time reversal symmetric thermodynamics particular second law thermodynamics states


net entropy closed system never decreases explains often see glass breaking coming back together statistical mechanics things become complicated one hand statistical mechanics far superior classical thermodynamics thermodynamic behavior glass breaking explained fundamental laws physics paired statistical postulate statistical mechanics unlike classical thermodynamics time reversal symmetric second law thermodynamics arises statistical mechanics merely states ''overwhelmingly'' likely net entropy increase


absolute law current thermodynamic solutions problem direction time aim find fact feature laws nature account discrepancy laws solution third type solution problem direction time although much less represented argues laws time reversal symmetric example certain processes quantum mechanics relating weak nuclear force time reversible keeping mind dealing quantum mechanics time reversibility comprises complex definition type solution insufficient


time asymmetric phenomena quantum mechanics account uniformity macroscopic time asymmetry relies assumption quantum mechanics final correct description physical processes one recent proponent laws solution tim maudlin argues fundamental laws physics laws temporal evolution see maudlin however elsewhere maudlin argues passage time intrinsic asymmetry temporal structure world asymmetry grounds distinction sequences runs past future sequences run


future past ibid edition p nbsp thus arguably difficult assess whether maudlin suggesting direction time consequence laws primitive flow time problem flow time treated analytic philosophy owes beginning paper written j e mctaggart proposes two temporal series first series means account intuitions temporal becoming moving called series series orders events according


time unreal since series inconsistent b b series alone cannot account nature time series describes essential feature building framework two camps solution offered first theorist solution takes becoming central feature time tries construct b series series offering account b facts come facts second camp b theorist solution takes decisive mctaggart 's arguments series tries construct series


three spatial dimensions hence things mdash past present future mdash said real things present according theory homer really ' 'does'' exist though must still use special language talking somebody exists distant time mdash would use special language talking something far away words ''near'' ''far'' ''above'' ''below'' directly comparable phrases ''in past'' ''a minute ago'' endurantism perdurantism positions persistence objects somewhat


similar endurantist holds object persist time exist completely different times instance existence regard somehow separate previous future instances though still numerically identical perdurantist hand holds thing exist time exist continuous reality consider thing whole must consider aggregate temporal parts instances existing endurantism seen conventional view flows


within realities somehow exist outside reality whole even though realities wholes related however positions rarely adopted see also arrow time ''being time'' chronometry einstein 's thought experiments ''the end time'' eternal return metaphysics mili apek presentism philosophy time ''process reality'' process philosophy spacetime temporal parts time geography ''time reborn'' time travel science time travel fiction quentin smith zeno 's paradoxes notes references albert david ''time chance'' harvard univ press dainton barry ''time space second edition'' mcgill queens university


press earman john ''world enough space time'' mit press friedman michael ''foundations space time theories'' princeton univ press adolf gr nbaum ''philosophical problems space time'' nd ed boston studies philosophy science vol xii reidel publishing horwich paul ''asymmetries time'' mit press ialenti vincent ''deep time reckoning'' mit press lucas john randolph ''a treatise time space'' london methuen mellor dh ''real time ii'' routledge laura mersini houghton rudy vaas eds graham nerlich ''the shape space'' cambridge university press hans reichenbach ''the philosophy


space time'' dover hans reichenbach ''the direction time'' university california press rochelle gerald behind time ashgate lawrence sklar ''space time spacetime'' university california press turetzky philip ''time'' routledge bas van fraassen ''an introduction philosophy space time'' random house gal benjamin cosmology physics philosophy springer verlag new york external links stanford encyclopedia philosophy http platostanfordedu entries time time ned markosian http platostanfordedu entries spacetime bebecome becoming modern physics steven savitt http platostanfordedu entries spacetime theories absolute relational theories space motion nick huggett carl hoefer


internet encyclopedia philosophy http wwwieputmedu timehtm time bradley dowden https ieputmedu per time persistence time damiano costa brown cl https webarchiveorg web http wwwunrestrictedphilosophycom space largely wittgensteinian approach towards dissolution question space rea c https webarchiveorg web http wwwndedu mrea papers four dimensionalismpdf four dimensionalism ''the oxford handbook metaphysics'' oxford univ press describes presentism four dimensionalism ceitt time temporality research center https webarchiveorg web http wwwceittcom index enhtml time temporality https webarchiveorg web http wwwexactspentcom philosophy space timehtm related subjects http wwwbpslk olib wh wh phtml gods universe buddhist perspective essays buddhist cosmology francis story natural philosophy metaphysics space space thought experiments physics


synthesis amino acid n carboxyanhydrides high molecular weight products upon reaction nucleophiles stopped short referring polymers possibly due strong views espoused emil fischer direct supervisor denying possibility covalent molecule exceeding daltons cellophane invented jocques brandenberger treated sheets viscose rayon acid gallery widths heights caption leading figures polymer chemistry file hermann staudingerjpg hermann staudinger father polymer chemistry file wallace carothers labjpg wallace carothers inventor nylon file stephanie kwolek spinning elements harry kalishtif stephanie kwolek inventor kevlar gallery

Natural science
Chemistry
Polymer chemistry


structures electrically conductive polymers polyacetylene polyphenylene vinylene polypyrrole x nh polythiophene x polyaniline x nh n polyphenylene sulfide x structure polydimethylsiloxane illustrating polymer inorganic backbonethe chemist hermann staudinger first proposed polymers consisted long chains atoms held together covalent bonds called macromolecules work expanded chemical understanding polymers followed expansion field polymer chemistry polymeric materials neoprene nylon polyester invented staudinger polymers thought


clusters small molecules colloids without definite molecular weights held together unknown force staudinger received nobel prize chemistry wallace carothers invented first synthetic rubber called neoprene first polyester went invent nylon true silk replacement paul flory awarded nobel prize chemistry work polymer random coil configurations solution stephanie kwolek developed aramid aromatic nylon named kevlar patented karl ziegler giulio natta received nobel prize discovery


catalysts polymerization alkenes alan j heeger alan macdiarmid hideki shirakawa awarded nobel prize chemistry development polyacetylene related conductive polymers ref name nobel ref polyacetylene find practical applications organic light emitting diodes oleds emerged one application conducting polymers teaching research programs polymer chemistry introduced institute macromolecular chemistry founded freiburg germany direction staudinger america polymer research institute pri established herman mark polytechnic


institute brooklyn polytechnic institute nyu polymers properties viscosity polymer solutions valued parameter viscometers employed measurements polymers high molecular mass compounds formed polymerization monomers simple reactive molecule repeating structural units polymer derived called monomer polymer described many ways degree polymerisation molar mass distribution tacticity copolymer distribution degree branching end groups crosslinks crystallinity thermal properties glass transition temperature melting


temperature polymers solution special characteristics respect solubility viscosity gelation illustrative quantitative aspects polymer chemistry particular attention paid number average weight average molecular weights math n math math w math respectively br math n frac sum n sum n quad w frac sum n sum n quad math formation properties polymers rationalized many theories including scheutjens fleer theory flory huggins solution theory cossee arlman mechanism polymer field theory hoffman nucleation theory flory stockmayer theory many others segments polypropylene showing slightly different structures isotactic syndiotactic polymers study


polymer thermodynamics helps improve material properties various polymer based materials polystyrene styrofoam polycarbonate common improvements include toughening improving impact resistance improving biodegradability altering material solubility viscosity polymers get longer molecular weight increases viscosity tend increase thus measured viscosity polymers provide valuable information average length polymer progress reactions ways polymer branchescomposites formed combining polymeric materials form overall structure properties differ sum individual components classification


polymers classified many ways polymers strictly speaking comprise solid matter minerals ie earth 's crust largely polymers metals polymers organisms living dead composed largely polymers water often polymers classified according origin biopolymers vs synthetic polymers vs inorganic polymers strand cellulose showing hydrogen bonds dashed within chains biopolymers structural functional materials comprise organic matter organisms one major class biopolymers proteins derived amino acids polysaccharides


cellulose chitin starch biopolymers derived sugars polynucleic acids dna rna derived phosphorylated sugars pendant nucleotides carry genetic information synthetic polymers structural materials manifested plastics synthetic fibers paints building materials furniture mechanical parts adhesives synthetic polymers may divided thermoplastic polymers thermoset plastics thermoplastic polymers include polyethylene teflon polystyrene polypropylene polyester polyurethane poly methyl methacrylate polyvinyl chloride nylons rayon thermoset plastics include vulcanized rubber bakelite kevlar polyepoxide almost synthetic polymers derived petrochemicals themes self repairing polymers


characterized self healing designed automatically repair damage thermodynamic principles guided formation polymers subjecting polymers specific heat temperature regimes overcome activation energy forward polymerization reaction encouraging polymer reform diels alder reaction sustainability polymer chemistry polymer thermodynamics widely studied sustainability life cycle assessments lca polymer electrolyte membranes considered important sustainability widespread us fuel cells polymer electrolyte membrane pem fuel cell hydrogen fuel cell directly converts hydrogen oxygen


electrical energy water waste heat without generating harmful gases emitted conventional internal combustion engines general pem fuel cells advantages compact structure low operating temperature fast startup speed long working life zero pollution see also polymer polymer science polymer physics chemistry polymer topology references


white bags filled contaminated stones line shore near industrial oil spill raahe finland '''environmental chemistry''' scientific study chemical biochemical phenomena occur natural places confused green chemistry seeks reduce potential pollution source defined study sources reactions transport effects fates chemical species air soil water environments effect human activity biological activity environmental chemistry interdisciplinary science includes atmospheric aquatic soil

Natural science
Chemistry
Environmental chemistry


chemistry well heavily relying analytical chemistry related environmental areas science environmental chemistry involves first understanding uncontaminated environment works chemicals concentrations present naturally effects without would impossible accurately study effects humans environment release chemicals environmental chemists draw range concepts chemistry various environmental sciences assist study happening chemical species environment important general concepts chemistry include understanding chemical


reactions equations solutions units sampling analytical techniques ref name williams williams ian ''environmental chemistry modular approach'' wiley ref contaminant contaminant substance present nature level higher fixed levels would otherwise may due human activity bioactivity term contaminant often used interchangeably ''pollutant'' substance detrimental impact surrounding environment whilst contaminant sometimes defined substance present environment result human activity without harmful effects


aromatic hydrocarbon large bodies water contaminated oil spills leaks many pahs carcinogens extremely toxic regulated concentration ppb using environmental chemistry chromatography laboratory testing nutrients leaching agricultural land water courses lead algal blooms eutrophication urban runoff pollutants washing impervious surfaces roads parking lots rooftops rain storms typical pollutants include gasoline motor oil hydrocarbon compounds metals nutrients sediment soil organometallic compounds methods quantitative chemical analysis key part environmental chemistry since provides


data frame environmental studies ref name vanloonduffyp ref common analytical techniques used quantitative determinations environmental chemistry include classical wet chemistry gravimetric titrimetric electrochemical methods sophisticated approaches used determination trace metals organic compounds metals commonly measured atomic spectroscopy mass spectrometry atomic absorption spectrophotometry aas inductively coupled plasma atomic emission icp aes inductively coupled plasma mass spectrometric icp ms techniques organic compounds including pahs commonly measured also using mass spectrometric methods gas chromatography mass spectrometry gc ms liquid chromatography mass spectrometry lc ms tandem mass spectrometry ms ms


high resolution accurate mass spectrometry hr offer sub part per trillion detection non ms methods using gcs lcs universal specific detectors still staples arsenal available analytical tools parameters often measured environmental chemistry radiochemicals pollutants emit radioactive materials alpha beta particles posing danger human health environment particle counters scintillation counters commonly used measurements bioassays immunoassays utilized toxicity evaluations chemical effects various organisms polymerase chain reaction pcr able identify species bacteria


organisms specific dna rna gene isolation amplification showing promise valuable technique identifying environmental microbial contamination published analytical methods peer reviewed test methods published government agencies private research organizations approved published methods must used testing demonstrate compliance regulatory requirements notable environmental chemists joan berkowitz br paul crutzen nobel prize chemistry br philip gschwend br alice hamilton br john hayes br charles david keeling br ralph keeling br mario molina nobel prize chemistry br james j morgan br clair patterson br roger revelle br sherry roland nobel prize chemistry br robert


list links environmental chemistry www virtual library http wwwtandfcouk journals titles asp international journal environmental analytical chemistry biochemistry chemistry water pollution


'''japanese studies''' japanese '''japan studies''' sometimes '''japanology''' europe sub field area studies east asian studies involved social sciences humanities research japan incorporates fields study japanese language culture history literature art music science roots may traced back dutch dejima nagasaki edo period foundation asiatic society japan yokohama men ernest satow frederick victor dickins important event development japanese studies academic discipline

Social science
Sociology
Area studies
Japanese studies


japanese studies organizations publications united states society japanese studies published ''journal japanese studies'' jjs since biannual academic journal dealing research japan united states jjs supported grants japan foundation georgetown university university washington addition endowments kyocera corporation national endowment humanities british association japanese studies bajs founded association primarily sponsored toshiba japan foundation bajs publishes academic journal called ''japan forum''


europe european association japanese studies eajs also funded toshiba japan foundation held triennial conferences around europe since academic journals dealing japanese studies include ''monumenta nipponica'' biannual english language journal affiliated sophia university tokyo ''social science japan journal'' published oxford university press scholarship japan also within purview many organizations publications dealing general field east asian studies association asian studies duke university publication ''positions asia critique'' studies meiji period


published yevgeniya suda ref name suda publisher location kyiv year pages ref ury eppstein ref name eppstein ref international research center japanese studies nichibunken maintains comprehensive date database institutions japanese studies outside united states japan database includes information institutions japanese studies continents database found according nichibunken database country institutions japanese studies outside united states japan china institutions countries containing highest number institutions include south korea england germany canada


australia france notable japanologists boris akunin ruth benedict basil hall chamberlain serge eliss eff carol gluck conrad totman lafcadio hearn algernon freeman mitford st baron redesdale also known b mitford lord redesdale donald keene fosco maraini edwin reischauer donald richie ernest mason satow edward seidensticker francis xavier judit hidasi steponas kairys scholarly journals ''bulletin national museum japanese history'' japanese ''east asian history'' ''japan forum'' ''japanese studies'' ''japanese journal religious studies'' ''journal japanese studies'' ''monumenta nipponica'' japanese studies english ''sino japanese studies'' ''social science japan journal'' online resources


http wwwkajaorkr korea association japanology kaja http ijssnuackr japan research center seoul national university '''japanese studies associations institutions canada''' japan studies association canada jsac promotes japanese studies canada contributes towards increased knowledge japan canada japan relations jsac website contains information japan related events conferences institutions across canada reached http bunayorkuca jsac '''japanese studies associations institutions europe''' european association japanese studies eajs association begun london oxford currently members countries roughly personal members institutional


impression systems thinking society '''systems science''' also referred '''systems research''' simply '''systems''' interdisciplinary field concerned understanding systems simple complex nature society cognition engineering technology science field diverse spanning formal natural social applied sciences systems scientists world understood system systems field aims develop interdisciplinary foundations applicable variety areas psychology biology medicine communication business management technology computer science engineering social sciences systems science covers formal sciences

Applied science
Business
Systems science


complex systems cybernetics dynamical systems theory information theory linguistics systems theory applications field natural social sciences engineering control theory systems design operations research social systems theory systems biology system dynamics human factors systems ecology computer science systems engineering systems psychology themes commonly stressed system science holistic view b interaction system embedding environment c complex often subtle trajectories dynamic behavior sometimes stable thus reinforcing various 'boundary conditions' become wildly unstable thus destructive concerns


earth scale biosphere geosphere dynamics example nature problems systems science seeks contribute meaningful insights associated fields systems notes henk bikker tu delft systems sciences broad array fields one way conceiving three groups fields developed systems ideas primarily theory done primarily practical engagements problem situations applied systems ideas context disciplines theoretical fields chaos dynamical systems complexity control theory affect control theory control engineering


control systems cybernetics autopoiesis conversation theory engineering cybernetics perceptual control theory management cybernetics second order cybernetics information theory general systems theory systems theory anthropology biochemical systems theory ecological systems theory developmental systems theory general systems theory living systems theory lti system theory social systems sociotechnical systems theory mathematical system theory world systems theory hierarchy theory practical fields critical systems heuristics critical systems thinking operations research management science soft systems methodology soft systems methodology developed england academics university lancaster systems department ten year action research programme main contributor peter checkland


multi stakeholder situations systems dynamics system dynamics approach understanding behavior complex systems time offers simulation technique modeling business social systems deals internal feedback loops time delays affect behavior entire system makes using system dynamics different approaches studying complex systems use feedback loops stocks flows systems engineering systems engineering se interdisciplinary field engineering focuses development organization complex systems art science creating


general systems scientists divided different generations founders systems movement like ludwig von bertalanffy kenneth boulding ralph gerard james grier miller george j klir anatol rapoport born came different natural social science disciplines joined forces establish general systems theory paradigm along organization efforts first generation systems scientists rose among scientists like ackoff ashby margaret mead churchman popularized systems concept scientists


inspired educated second generation notable scientists like ervin laszlo fritjof capra wrote systems theory others got acquainted started studying works started writing since debora hammond seen typical representative third generation general systems scientists organizations international society systems sciences isss organisation interdisciplinary collaboration synthesis systems sciences isss unique among systems oriented institutions terms breadth


scope bringing together scholars practitioners academic business government non profit organizations based fifty years tremendous interdisciplinary research scientific study complex systems interactive approaches management community development society initially conceived stanford center advanced study behavioral sciences ludwig von bertalanffy kenneth boulding ralph gerard anatol rapoport field systems science international federation systems research ifsr international federation global local societies field systems science federation non profit scientific


educational agency founded constituted thirty member organizations various countries overall purpose federation advance cybernetic systems research systems applications serve international systems community best known research institute field santa fe institute sfi located santa fe new mexico united states dedicated study complex systems institute founded george cowan david pines stirling colgate murray gell mann nick metropolis herb anderson peter carruthers richard slansky pines gell mann scientists


pp kenneth bailey fifty years systems science reflections ''systems research behavioral science'' pp nbsp robert l flood ewart r carson '' https booksgooglecom booksid x bwaaqbaj printsec frontcover dq introduction theory application systems science hl en sa x ved ahukewju pbpilrjahucbc khzpqcugq aeikjaa v onepage q introduction theory application systems science f false dealing complexity introduction theory application systems science nd edition '' george j klir '' https booksgooglecom booksid nhgbwaaqbaj printsec frontcover dq facets systems science hl en sa x ved ahukewis lxxilrjahuvbs khz csoq aeikjaa v onepage q facets systems science f false facets systems science nd edition '' kluwer academic plenum publishers jiri kroc karel balihar martin matejovic ''complex systems use medicine concepts methods bio medical applications'' researchgate ervin l szl ''systems science world order selected studies'' g e mobus c kalton ''principles systems science''


new york springer anatol rapoport ed ''general systems yearbook society advancement general systems theory'' society general systems research vol li xu contributions systems science information systems research ''systems research behavioral science'' pp nbsp graeme donald snooks general theory complex living systems exploring demand side dynamics ''complexity'' vol july august john n warfield proposal systems science ''systems research behavioral science'' pp nbsp michael c jackson ''critical systems thinking management complexity'' wiley


external links http pespmc vubacbe principia cybernetica web institute system science knowledge isskorg http isssorg world international society system sciences http wwwukssorguk uk systems society http wwwcybsocorg cybernetics society science cybernetics formal sciences science emergence


onlyinclude '''community psychology''' studies individuals' contexts within communities wider society ref name jimorford jim orford ''community psychology challenges controversies emerging consensus'' john wiley sons ref relationships individual communities society community psychologists seek understand quality life individuals within groups organizations institutions communities society aim enhance quality life collaborative research action ref name dalton dalton jh elias mj wandersman community psychology linking individuals communities stamford ct wadsworth ref community psychology employs various perspectives within outside psychology address issues

Social science
Psychology
Community psychology


work applied anthropology community development ref name maton maton k perkins saegert community psychology crossroads prospects interdisciplinary research american journal community psychology ref community psychology grew community mental health movement evolved dramatically early practitioners incorporated understandings political structures community contexts perspectives client services ref name levine levine perkins dv principles community psychology nd ed new york oxford university press ref onlyinclude society community research action division american psychological association community psychology


division apa called society community research action scra society 's mission follows scra website resources teaching learning community psychology information events field related research action become involved additional information field members undergraduate graduate programs community psychology history community psychology us many factors contributed beginning community psychology us factors include shift away socially conservative individual focused practices health


care psychology progressive period concerned issues public health prevention social change world war ii ref name dalton social psychologists' growing interest racial religious prejudice poverty social issues perceived need larger scale mental illness treatment veterans ref name rappaport psychologists questioning value psychotherapy alone treating large numbers people mental illness ref name rappaport development community mental health centers de institutionalization people mental illnesses communities ref name dalton swampscott conference several psychologists met discuss future community mental health well


discuss issue involved problems mental health instead community whole swampscott conference considered birthplace community psychology published report conference calls community psychologists political activists agents social change participant conceptualizers ref name dalton theories concepts values community psychology ecological levels analysis james kelly trickett developed ecological analogy used understand ways settings individuals interrelated unlike ecological framework developed bronfenbrenner focus kelly 's framework much


different levels environment may impact individual understanding human communities function specifically kelly suggests important principles govern people settings ''adaptation'' ie individuals adaptive given demands surrounding context two way process individuals adapt restrictions constraints quality environment environment adapts members examples regards adaption individual take instance individual adapts demands new job adapt environment learning


principle applies families organizations communities implication noting understanding succession units psychologists must understand history unit family organization community attempting implement intervention plan ''cycling resources'' setting resources need identified possibilities new resources developed resource perspective emphasizes focus strengths individuals groups institutions within setting interventions likely succeed build existing strengths rather introduce new external mechanisms


change ''personal resources'' include individual talents strengths specialties well ' 'social resources'' shared norms beliefs values aspects physical environment considered resources calm resting places library qualities space particular ''interdependence'' settings systems change one aspect setting consequences aspects setting intervention needs anticipate impact across entire setting prepared unintended consequences look school instance real world


example interdependent parts include students teachers administrators students' parents faculty staff secretaries janitors counselors nurses board members taxpayers first order second order change community psychologists often work social issues often working toward positive social change watzlawick et al differentiated first order second order change second order change often focus community psychology ''first order change'' positively changing individuals setting attempt fix problem ' 'second order change'' attending systems structures involved problem adjust person environment fit example methods


differ consider homelessness first order change fix homelessness would offer shelter one many homeless people second order change would address issues policy regarding affordable housing prevention health promotion community psychology emphasizes principles strategies preventing social emotional behavioral problems wellness health promotion individual community levels borrowed public health preventive medicine rather passive waiting mode treatment based medical model universal selective primary indicated secondary prevention early identification intervention particularly emphasized community psychology 's contributions prevention science substantial


including development evaluation head start program empowerment one goals community psychology involves empowerment individuals communities marginalized society one definition term intentional ongoing process centered local community involving mutual respect critical reflection caring group participation people lacking equal share resources gain greater access control resources cornell empowerment group rappaport 's definition includes empowerment viewed process mechanism people organizations communities gain mastery lives empowerment


important place community psychology research literature criticized use riger example points paradoxical nature empowerment masculine individualistic construct used community research community psychologist guy holmes critiqued empowerment vague concept replete wolf wolfensberger called 'high craze value' ie fashionable term means different things different people ultimately means everything nothing certainly community psychologists would agree mao 'power grows barrel gun' support empowerment paradigm racino


proposed organizing concept replace complement prior rehabilitation paradigm acknowledge diverse groups community based work emerging community disciplines social justice core value community psychology seeking social justice research action community psychologists often advocates equality policies allow wellbeing people particularly marginalized populations ref name dalton diversity another value community psychology involves embracing diversity rappaport includes diversity defining aspect field calling research done benefit diverse populations gaining equality


justice value seen much research done communities regardless ethnicity culture sexual orientation disability status socioeconomic status gender age ref name rappaport individual wellness individual wellness physical psychological wellbeing people research community psychology focuses methods increase individual wellness particularly prevention second order change ref name dalton citizen participation citizen participation refers ability individuals voice decision making defining addressing problems dissemination information gathered ref name dalton basis usage participatory action research community


psychology community members often involved research process sharing unique knowledge experience research team working co researchers contrast citizen participation sought community developers community planners ie public administrators assure governmental funds best meet needs local citizenry three key values participation building support governmental planning raising political consciousness furthering democratic values citizen participation policymaking long history particular strong neighborhood action poverty programs activist led initiatives collaboration community strengths collaboration


community members construct research action projects makes community psychology exceptionally applied field allowing communities use knowledge contribute projects collaborative fair equal manner process research empowering citizens requires ongoing relationship researcher community research begins research ref name dalton psychological sense community psychological sense community simply sense community introduced seymour sarason major step taken david mcmillan david chavis


publication theory sense community sense community index originally designed primarily reference neighborhoods sense community index sci adapted study communities well including workplace schools religious communities communities interest etc empirical grounding community psychology grounds advocacy social justice action empiricism empirical grounding separates community psychology social movement grassroots organization methods psychology adapted use field acknowledge value driven subjective research involving community members methods used


community psychology therefore tailored individual research question quantitative well qualitative methods innovative methods embraced ref name dalton american psychological association sponsored two major conferences community research methods recently published edited book topic comparison community clinical psychology uk community psychology differentiated traditional clinical psychology practiced uk following ways class wikitable '''clinical psychology''' '''community psychology''' likely work individuals likely work groups communities work


confined clinical populations work likely involve diverse groups local community likely take place consulting room clinic likely take place community setting focus symptomatic change individual individually focused therapies focus community level change collective action work influenced psychiatric diagnosis work influenced mapping needs community level identifying sources oppression work influenced top treatment guidelines eg nice work influenced bottom


feedback community collaborators evidence base privileges rcts evidence base privileges diverse research methods especially emphasise community action participation likely short term time limited likely long term build grow time reactive ameliorative aim preventative transformational aim eg advocacy campaigning acting bring social change examples community psychology uk documented carolyn kagan mark burton jim orford ref name jimorford guy holmes education many programs related


community psychology housed psychology departments others interdisciplinary students earning community psychology degree complete courses focus history concepts field human diversity cultural competence public health community research methods statistics collaborative work communities organizational community development consultation prevention intervention program evaluation grantwriting research large component phd master 's degrees community psychologists base interventions theory research use action oriented research promote positive change students generally find niches faculty mentors institutions related


''the australian community psychologist'' journal australian psychological society ''journal community applied social psychology'' international journal ''journal community psychology'' international journal ''journal rural community psychology'' e journal ref name socpsynet social psychology network http wwwsocialpsychologyorg communityhtm commpsychjournals professional journals retrieved december ref http wwwpsychosocial interventionorg ''psychosocial intervention intervenci n psicosocial'' published spanish english ''rivista di psicologia di comunit '' italian journal http wwwgjcpporg en ''global journal community psychology practice'' gjccp addition number interdisciplinary journals ''community mental health journal'' ref name socpsynet articles field community health deal aspects community psychology see


also asset based community development behavior settings community organizing cultural historical activity theory ethnography grounded theory group dynamics institution large group capacitation multilevel model photovoice program evaluation psychotherapy social action model social capital social support systems thinking notes references bronfenbrenner u ecology human development experiments nature design cambridge harvard university press dalton jh elias mj wandersman community psychology linking individuals communities stamford ct wadsworth chavis dm wandersman sense community urban environment catalyst participation community development ''american journal community psychology'' kelly


jg ecological constraints mental health services american psychologist levine perkins perkins v principles community psychology perspectives applications rd ed new york oxford university press mcmillan dw chavis dm sense community definition theory ''american journal community psychology'' moritsugu j community psychology th ed allyn bacon inc rappaport j community psychology values research action new york holt rinehart winston rappaport j studies empowerment introduction issue prevention human services riger


st century invitation peer reviewed article global journal community psychology practice https geterikacom community psychology community psychology interactive video explainer community applied psychology


visualisation solution two dimensional heat equation temperature represented vertical direction color mathematics '''partial differential equation''' '''pde''' equation imposes relations various partial derivatives multivariable function function often thought unknown solved similarly thought unknown number solved algebraic equation like however usually impossible write explicit formulas solutions partial differential equations correspondingly vast amount modern

Formal science
Mathematics
Pure mathematics
Analysis
Partial differential equations


mathematical scientific research methods numerically approximate solutions certain partial differential equations using computers partial differential equations also occupy large sector pure mathematical research usual questions broadly speaking identification general qualitative features solutions various partial differential equations among many open questions existence smoothness solutions navier stokes equations named one millennium prize problems partial differential equations ubiquitous mathematically oriented scientific fields physics engineering instance foundational modern scientific


understanding sound heat diffusion electrostatics electrodynamics thermodynamics fluid dynamics elasticity general relativity quantum mechanics schrodinger equation pauli equation etc also arise many purely mathematical considerations differential geometry calculus variations among notable applications fundamental tool proof poincar conjecture geometric topology partly due variety sources wide spectrum different types partial differential equations methods developed dealing many individual equations arise usually acknowledged


general theory partial differential equations specialist knowledge somewhat divided several essentially distinct subfields ordinary differential equations form subclass partial differential equations corresponding functions single variable stochastic partial differential equations nonlocal equations particularly widely studied extensions pde notion classical topics still much active research include elliptic parabolic partial differential equations fluid mechanics boltzmann equations dispersive partial differential equations introduction one says function three variables ''harmonic'' solution ''the


laplace equation'' satisfies condition math display block frac partial u partial x frac partial u partial frac partial u partial z math functions widely studied nineteenth century due relevance classical mechanics explicitly given function usually matter straightforward computation check whether harmonic instance math display block u xyz frac sqrt x x z math math display block u xyz x z math harmonic math display block u xyz sin xy z math may surprising two given examples harmonic functions strikingly different form


one another reflection fact ''not'' immediate way special cases general solution formula laplace equation striking contrast case ordinary differential equations odes roughly similar laplace equation aim many introductory textbooks find algorithms leading general solution formulas laplace equation large number partial differential equations solution formulas fail exist nature failure seen concretely case following pde


function two variables consider equation math display block frac partial v partial x partial math directly checked function form single variable functions whatsoever satisfy condition far beyond choices available ode solution formulas typically allow free choice numbers study pde one generally free choice functions nature choice varies pde pde understand given equation ''existence uniqueness theorems'' usually important organizational principles many


introductory textbooks role existence uniqueness theorems ode somewhat opaque existence half usually unnecessary since one directly check proposed solution formula uniqueness half often present background order ensure proposed solution formula general possible contrast pde existence uniqueness theorems often means one navigate plethora different solutions hand reason also fundamental carrying purely numerical simulation one must


question similar striking difference behavior first pde one free prescription single function second pde one free prescription two functions let denote unit radius disk around origin plane continuous function unit circle exactly one function math display block frac partial u partial x frac partial u partial math whose restriction unit circle given functions real line


u partial sqrt left frac partial u partial x right left frac partial u partial right math numbers contrast earlier examples pde '''nonlinear''' owing square roots squares '''linear''' pde one homogeneous sum two solutions also solution constant multiples solution also solution well posedness well posedness refers common schematic package information pde say pde well posed one must existence uniqueness theorem


asserting prescription freely chosen functions one single one specific solution pde continuously changing free choices one continuously changes corresponding solution necessity applicable several different pde somewhat vague requirement continuity particular ambiguous since usually many inequivalent means rigorously defined however somewhat unusual study pde without specifying way well posed existence local solutions slightly weak form cauchy kowalevski theorem essentially states


terms partial differential equation made analytic functions certain regions necessarily exist solutions pde also analytic functions although fundamental result many situations useful since one cannot easily control domain solutions produced furthermore known examples linear partial differential equations whose coefficients derivatives orders nevertheless analytic solutions surprising example discovered hans lewy cauchy kowalevski theorem


necessarily limited scope analytic functions context precludes many phenomena physical mathematical interest classification notation writing pdes common denote partial derivatives using subscripts example math display block u x frac partial u partial x quad u xx frac partial u partial x quad u xy frac partial u partial partial x frac partial partial left frac partial u partial x right math general situation function variables denotes first partial derivative relative th input denotes second partial derivative relative th


th inputs greek letter denotes laplace operator function variables math display block delta u u u cdots u nn math physics literature laplace operator often denoted mathematics literature may also denote hessian matrix equations first order linear nonlinear equations pde called '''linear''' linear unknown derivatives example function second order linear pde


derivatives math display block u x u u x u xx u x u u x u xy u x u u x u yx u x u u x u yy f u x u u x math many fundamental pdes physics quasilinear einstein equations general relativity navier stokes equations describing fluid motion pde without linearity properties called '''fully nonlinear''' possesses nonlinearities one highest order derivatives example monge amp equation arises differential geometry ref name princetoncompanion ref linear equations second order elliptic


parabolic hyperbolic partial differential equations order two widely studied since beginning twentieth century however many important types pde including korteweg de vries equation also hybrids euler tricomi equation vary elliptic hyperbolic different regions domain also important extensions basic types higher order pde knowledge specialized elliptic parabolic hyperbolic classification provides guide appropriate initial boundary conditions smoothness solutions assuming general linear second order pde


two independent variables form math display block au xx bu xy cu yy cdots mbox lower order terms math coefficients may depend upon region plane pde second order region form analogous equation conic section math display block ax bxy cy cdots math precisely replacing likewise variables formally done fourier transform converts constant coefficient pde polynomial degree terms


highest degree homogeneous polynomial quadratic form significant classification one classifies conic sections quadratic forms parabolic hyperbolic elliptic based discriminant done second order pde given point however discriminant pde given due convention term rather formally discriminant associated quadratic form factor dropped simplicity ''elliptic partial differential equation'' solutions elliptic pdes


smooth coefficients allow within interior region equation solutions defined example solutions laplace 's equation analytic within domain defined solutions may assume boundary values smooth motion fluid subsonic speeds approximated elliptic pdes euler tricomi equation elliptic ''parabolic partial differential equation'' equations parabolic every point transformed form analogous heat equation change independent variables solutions smooth


transformed time variable increases euler tricomi equation parabolic type line ''hyperbolic partial differential equation'' hyperbolic equations retain discontinuities functions derivatives initial data example wave equation motion fluid supersonic speeds approximated hyperbolic pdes euler tricomi equation hyperbolic independent variables general linear partial differential equation second order form math display block l u sum n sum j n ij frac partial u partial x partial x j quad text plus lower order terms math


classification depends upon signature eigenvalues coefficient matrix elliptic eigenvalues positive negative parabolic eigenvalues positive negative save one zero hyperbolic one negative eigenvalue rest positive one positive eigenvalue rest negative ultrahyperbolic one positive eigenvalue one negative eigenvalue zero eigenvalues limited theory ultrahyperbolic equations courant hilbert


systems first order equations characteristic surfaces classification partial differential equations extended systems first order equations unknown vector components coefficient matrices matrices partial differential equation takes form math display block lu sum nu n nu frac partial u partial x nu b math coefficient matrices vector may depend upon hypersurface given implicit form math display block varphi x x ldots x n math non zero gradient


'''characteristic surface''' operator given point characteristic form vanishes math display block q left frac partial varphi partial x ldots frac partial varphi partial x n right det left sum nu n nu frac partial varphi partial x nu right math geometric interpretation condition follows data prescribed surface may possible determine normal derivative differential equation data differential equation determine normal derivative non characteristic data differential equation ' 'do


reduced systems ordinary differential equations important technique separation variables technique rests characteristic solutions differential equations one find solution solves equation satisfies boundary conditions ''the'' solution also applies odes assume ansatz dependence solution parameters space time written product terms depend single parameter see made solve problem method


separation variables one reduces pde pde fewer variables ordinary differential equation one variable turn easier solve possible simple pdes called separable partial differential equations domain generally rectangle product intervals separable pdes correspond diagonal matrices thinking value fixed coordinate coordinate understood separately generalizes method characteristics also used integral transforms method characteristics special cases one


find characteristic curves equation reduces ode changing coordinates domain straighten curves allows separation variables called method characteristics generally one may find characteristic surfaces integral transform integral transform may transform pde simpler one particular separable pde corresponds diagonalizing operator important example fourier analysis diagonalizes heat equation using eigenbasis sinusoidal waves domain finite periodic infinite sum solutions fourier series


appropriate integral solutions fourier integral generally required infinite domains solution point source heat equation given example use fourier integral change variables often pde reduced simpler form known solution suitable change variables example black scholes equation math display block frac partial v partial tfrac sigma frac partial v partial rs frac partial v partial rv math reducible heat equation math display block frac partial u partial


tau frac partial u partial x math change variables math display block begin align v st v x tau px x ln left right px tau tfrac sigma px v x tau e alpha x beta tau u x tau end align math fundamental solution inhomogeneous equations often solved constant coefficient pdes always solved finding fundamental solution solution point source taking convolution boundary conditions get solution analogous signal processing understanding filter impulse response superposition principle superposition principle applies linear system including linear systems pdes


common visualization concept interaction two waves phase combined result greater amplitude example principle observed pdes solutions may real complex additive solutions linear pde function space constants also solution pde function space methods non linear equations generally applicable methods solve nonlinear pdes still existence uniqueness results cauchy kowalevski theorem


often possible proofs important qualitative quantitative properties solutions getting results major part analysis computational solution nonlinear pdes split step method exist specific equations like nonlinear schr dinger equation nevertheless techniques used several types equations h principle powerful method solve underdetermined equations riquier janet theory effective method obtaining information many analytic overdetermined systems method characteristics used special cases solve nonlinear partial differential equations cases pde


solved via perturbation analysis solution considered correction equation known solution alternatives numerical analysis techniques simple finite difference schemes mature multigrid finite element methods many interesting problems science engineering solved way using computers sometimes high performance supercomputers lie group method sophus lie 's work put theory differential equations satisfactory foundation showed integration theories older mathematicians introduction called lie groups


referred common source ordinary differential equations admit infinitesimal transformations present comparable difficulties integration also emphasized subject transformations contact general approach solving pdes 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 pde symmetry methods


recognized study differential equations arising mathematics physics engineering many disciplines semianalytical methods adomian decomposition method lyapunov artificial small parameter method homotopy perturbation method special cases general homotopy analysis method series expansion methods except lyapunov method independent small physical parameters compared well known perturbation theory thus giving methods greater flexibility solution generality numerical solutions three widely used numerical methods solve pdes finite element method fem finite volume methods


fvm finite difference methods fdm well kind methods called meshfree methods made solve problems aforementioned methods limited fem prominent position among methods especially exceptionally efficient higher order version hp fem hybrid versions fem meshfree methods include generalized finite element method gfem extended finite element method xfem spectral finite element method sfem meshfree finite element method discontinuous galerkin finite element method dgfem element free galerkin method efgm interpolating element free galerkin method iefgm etc finite element method finite element method fem


practical application often known finite element analysis fea numerical technique finding approximate solutions partial differential equations pde well integral equations solution approach based either eliminating differential equation completely steady state problems rendering pde approximating system ordinary differential equations numerically integrated using standard techniques euler 's method runge kutta etc finite difference method finite difference methods numerical methods approximating solutions differential equations using finite difference equations approximate derivatives finite volume method similar finite


difference method finite element method values calculated discrete places meshed geometry finite volume refers small volume surrounding node point mesh finite volume method surface integrals partial differential equation contain divergence term converted volume integrals using divergence theorem terms evaluated fluxes surfaces finite volume flux entering given volume identical leaving adjacent volume methods conserve mass design energy method energy method


brezis h browder f partial differential equations th century advances mathematics doi aima external links http eqworldipmnetru en pde enhtm partial differential equations exact solutions eqworld world mathematical equations http eqworldipmnetru en solutions eqindex eqindex pdehtm partial differential equations index eqworld world mathematical equations http eqworldipmnetru en methods meth pdehtm partial differential equations methods eqworld world mathematical equations https webarchiveorg web http wwwexampleproblemscom wiki indexphptitle partial differential equations example problems solutions exampleproblemscom http mathworldwolframcom partialdifferentialequationhtml partial differential equations mathworldwolframcom https referencewolframcom language femdocumentation tutorial solvingpdewithfemhtml partial differential equations mathematica http wwwmathworkscom moler pdespdf partial differential equations cleve moler numerical computing matlab http wwwnagcom numeric fl nagdoc fl html introhtml partial differential equations nagcom multivariable calculus mathematical physics


'''competition law''' law promotes seeks maintain market competition regulating anti competitive conduct companies ref name papersssrncom ref ref name taylor ref competition law implemented public private enforcement also known ''anti monopoly law'' china ref name papersssrncom russia previous years known ''trade practices law'' united kingdom australia european union referred ''antitrust'' ''competition law'' history competition law reaches back roman empire business practices market traders guilds governments always subject


scrutiny sometimes severe sanctions since th century competition law become global two largest influential systems competition regulation united states antitrust law european union competition law national regional competition authorities across world formed international support enforcement networks modern competition law historically evolved national level promote maintain fair competition markets principally within territorial boundaries nation states national competition law usually cover activity beyond territorial borders unless significant effects nation state level ref name taylor countries may allow


extraterritorial jurisdiction competition cases based called effects doctrine ref name taylor protection international competition governed international competition agreements negotiations preceding adoption general agreement tariffs trade gatt limited international competition obligations proposed within ''charter international trade organisation'' obligations included gatt conclusion uruguay round gatt multilateral negotiations world trade organization wto created ''agreement establishing wto'' included range limited provisions various cross border


competition issues sector specific basis principle competition law antitrust law three main elements prohibiting agreements practices restrict free trading competition business includes particular repression free trade caused cartels banning abusive behavior firm dominating market anti competitive practices tend lead dominant position practices controlled way may include predatory pricing tying price gouging refusal deal supervising mergers acquisitions large corporations including joint ventures transactions considered threaten competitive process


prohibited altogether approved subject remedies obligation divest part merged business offer licenses access facilities enable businesses continue competing substance practice competition law varies jurisdiction jurisdiction protecting interests consumers consumer welfare ensuring entrepreneurs opportunity compete market economy often treated important objectives competition law closely connected law deregulation access markets state aids subsidies privatization state owned assets establishment independent sector


regulators among market oriented supply side policies recent decades competition law viewed way provide better public services robert bork argued competition laws produce adverse effects reduce competition protecting inefficient competitors costs legal intervention greater benefits consumers history roman legislation early example enacted roman republic around nbsp bc protect grain trade heavy fines imposed anyone directly deliberately insidiously stopping supply ships ref name wilberforce p wilberforce p ref diocletian ad edict imposed


death penalty anyone violating tariff system example buying concealing contriving scarcity everyday goods ref name wilberforce p legislation came constitution zeno ad traced florentine municipal laws provided confiscation property banishment trade combination joint action monopolies private ''or'' granted emperor zeno rescinded previously granted exclusive rights ref name wilberforce p wilberforce p ref justinian subsequently introduced legislation pay officials manage state monopolies ref name wilberforce


outlawed trade combination blockquote nbsp ordained established merchant shall make confederacy conspiracy coin imagination murmur evil device point may turn impeachment disturbance defeating decay said staples anything pertaineth may pertain blockquote continental europe competition principles developed ''lex mercatoria'' examples legislation enshrining competition principles include ''constitutiones juris metallici'' wenceslaus ii bohemia condemning combination ore traders increasing prices municipal statutes florence followed zeno 's legislation


state monopolies emperor charles v holy roman empire law passed prevent losses resulting monopolies improper contracts many merchants artisans made netherlands henry viii england reintroduced tariffs foodstuffs designed stabilize prices face fluctuations supply overseas legislation read whereas blockquote hard difficult put certain prices things nbsp necessary prices victuals many times enhanced raised greedy covetousness appetites


owners victuals occasion ingrossing regrating upon reasonable ground cause great damage impoverishing king 's subjects blockquote around time organizations representing various tradesmen handicrafts people known guilds developing enjoyed many concessions exemptions laws monopolies privileges conferred abolished municipal corporations act early competition law europe coke th century thought general restraints trade unreasonable english common law restraint trade direct


predecessor modern competition law later developed us based prohibition agreements ran counter public policy unless reasonableness agreement could shown effectively prohibited agreements designed restrain another 's trade ''dyer 's'' first known restrictive trade agreement examined english common law dyer given bond exercise trade town plaintiff six months plaintiff promised nothing return hearing plaintiff 's attempt enforce restraint hull j exclaimed


overseas trade plunder pouring wealth international economy attitudes among businessmen shifting system industrial monopoly licenses similar modern patents introduced england reign queen elizabeth system reputedly much abused used merely preserve privileges encouraging nothing new way innovation manufacture response english courts developed case law restrictive business practices statute followed unanimous decision ''darcy v allein'' also known case monopolies king 's bench declare


void sole right queen elizabeth granted darcy import playing cards england ref name papadopoulos darcy officer queen 's household claimed damages defendant 's infringement right court found grant void three characteristics monopoly price increases quality decrease tendency reduce artificers idleness beggary put end granted monopolies king james began grant parliament passed statute monopolies part excluded patent rights


prohibitions well guilds king charles civil war king charles ii monopolies continued especially useful raising revenue ''east india company v sandys'' decided exclusive rights trade outside realm legitimate grounds large powerful concerns could trade conditions prevailing overseas development early competition law england europe progressed diffusion writings ''the wealth nations'' adam smith first established concept ''market economy''


time industrialisation replaced individual artisan group artisans paid labourers machine based production commercial success increasingly dependent maximizing production minimizing cost therefore size company became increasingly important number european countries responded enacting laws regulate large companies restricted trade following french revolution law june declared agreements members trade fixed price industry labour void unconstitutional hostile liberty similarly austrian penal code established agreements


raise price commodity disadvantage public punished misdemeanours austria passed law abolishing penalties though agreements remained void however germany laws clearly validated agreements firms raise prices throughout th th centuries ideas dominant private companies legal monopolies could excessively restrict trade developed europe however late th century depression spread europe known panic ideas competition lost favour felt companies co operate


forming cartels withstand huge pressures prices profits modern competition law development competition law stalled europe late th century canada enacted considered first competition statute modern times ''act prevention suppression combinations formed restraint trade'' passed one year united states enacted famous legal statute competition law sherman act named senator john sherman argued act announce new principle law applies


old well recognised principles common law ref name bare url ref united states antitrust senatorial round house thomas nast sherman act attempted outlaw restriction competition large companies co operated rivals fix outputs prices market shares initially ''pools'' later ''trusts'' trusts first appeared us railroads capital requirement railroad construction precluded competitive services scarcely settled territories trust allowed railroads discriminate rates imposed services provided consumers businesses destroy potential competitors different trusts could dominant


different industries standard oil company trust controlled several markets including market fuel oil lead whiskey ref name bare url vast numbers citizens became sufficiently aware publicly concerned trusts negatively impacted act became priority major parties primary concern act competitive markets provide primary regulation prices outputs interests profits instead act outlawed anticompetitive practices codifying common law restraint trade doctrine prof rudolph peritz argued competition law united states