A Further Generalized Lagrangian Density and Its Special Cases
|
|
|
- Μητροφάνης Βασιλείου
- 7 χρόνια πριν
- Προβολές:
Transcript
1 A Furter eerlzed r Desty d Its Specl Cses F-Pe Ce Deprtet of Pyscs Dl Uversty of ecoloy Dl 64 C E-l: cefp@dluteduc Abstrct By surz d eted te r destes of te eerl reltvty d te Kbble s ue teory of rvtto furter eerlzed r desty for rvttol syste s obted d lyzed reter detl wc c be used for study ore etesve re of rvtto y specl cses c be derved fro ts eerlzed r desty ter eerl crcters d peculrtes wll be brefly descrbed PACS ubers: 4Cv 49e Keywords: r desty coupls betwee felds coservto lws eery-oetu tesor desty sp desty Itroducto I te teory of specl reltvty te r of tter feld c be deoted by te fuctol for: were s te ordry dervtve of It s well ow tt te reltvstc teores of rvtto te r desty of tter feld ust be deoted by te fuctol for : were s te covrt dervtve of : j 3 j For te Kbble s ue teory of rvtto te fre coecto j s depedet feld vrles d te torso ust pper te spce-te I ts cse te Eq c be eerlzed s j 4
2 For te reltvstc teores of rvtto te spce-te wtout torso j sould ot be depedet feld vrles d t wll be prove te Apped tt b d d j j j d d j j 5 I ts cse te Eq c be eerlzed s 6 Sce te ret jorty of te fudetl tter felds re spors t s ecessry to use tetrd feld e etrc feld s epressed s j j fro wc we ve j j etc I te reltvstc teores of rvtto 6 π 7 s lwys dopted s te r desty of rvttol feld For te Kbble s ue teory of rvtto Eq7 c be eerlzed s j j 8 For te reltvstc teores of rvtto te spce-te wtout torso e eerl reltvtyfter us Eq5 Eq7 c be eerlzed s 9 9 I ts pper order to coduct dept study o te eerl crcter d te peculrty of r destes for soe reltvstc teores of rvtto Eqs46 wll be eteded to te follow epresso: j j d Eqs89 wll be eteded to te follow epresso: j j
3 3 We wll e were d re deoted by Eq d Eq respectvelys furter eerlzed r desty represets te tter feld d j represet te rvttol felds s furter eerlzed r desty s sfctly ore eerl t te r destes deoted by Eqs46 d Eqs89 It ust be dcted tt prt fro descrb rvttol syste wt torso ts furter eerlzed r desty e Eqs c be used lso to descrbe rvttol syste wtout torso If Eqs re used to descrbe rvttol syste wtout torso t ust be oted tt j s fucto of d j s fucto of So te Eq c be epressed s d te Eq c be epressed s 3 Evdetly Eq6 s specl cse of Eq we Eq9 s equvlet to Eq3 For te reltvstc teores of rvtto te spce-te wt torso besdes Eq4 te follow r destes j 4 j j 5
4 re lso te specl cses of Eq By es of study te furter eerlzed r desty d ts specl cses ter eerl crcter d peculrty c be sow clerly e furter eerlzed r desty surzes y propertes of vrous teores of rvtto Below we sll prove tt Eq d Eq c be rewrtte s d j 6 j 7 j s te curvture tesor wt ed des j j j j j 8 s te torso tesor wt ed dees { } 9 e pyscl e of Eq6 s tt te rvttol felds could ct o te tter feld oly trou covrt dervtve curvture of spce-te d torso of spce-te erefore te fors of coupls betwee te rvttol felds d tter feld t be j j j j or etc e coupl j coted te covrt dervtve j s clled te l coupl wc s well ow te eerl reltvty d te ue teory of rvtto Eq6 tells us tt ddto to te l coupl tere t be oter coplcted coupls teory e pyscl e of Eq7 s tt te r of rvttol feld s coposed of curvture tesor feld d torso tesor feld Becuse s bot coordte sclr d fre sclr te possble ters volved 4
5 re sclrs costructed fro j Hece te study of furter eerlzed r destes sfctly eted te re of te studes of rvtto If Eq7 s used to descrbe rvttol syste wtout torso te d {} te possble ters volved re oly te sclr curvture {} {} j j d ts power suc s j Cosder oter requreets 6π s cose eerl reltvty We sll dscuss te ove probles te follow sectos e syetry of te r destes for rvttol syste Syetres est uverslly pyscl systes We suppose tt oe fudetl syetry of rvttol syste s tt te cto terls I d I d 4 4 d I I I d 4 I stsfy I I d respectvely uder te follow two sulteous trsfortos 4: te ftesl eerl coordte trsforto ξ te locl oretz trsforto of tetrd fre j e e e ε e j e suffcet codto of cto terl trsfortos s : I 4 d be I uder ove 5
6 6 ξ were represets te vrto t fed vlue of For te ost eerlzed r desty we ve j j j j 3 j j j j 4 et or or becuse of te depedet rbtrress of ε ε ε ξ ξ d ξ It s ot dffcult to derve te follow dettes 3 f : 5
7 7 6 7 j j j j 8 j j j j j 9 j j 3 Fro Eq3 d Eq7 t s foud tt tere ust est oter detty: 3 It wll be sow bellow tt y propertes of rvttol syste c be derved fro te ove dettes We Eqs re used to descrbe rvttol syste wtout torso fro Eq we ve
8 8 3 were deote te prtl dervtve t te costt vlues of d Hece we et Fro Eq3 we ve
9 9 38 Hece we et O te oter d t s evdet tt d relt to Eqs3 stsfy lso ξ were or or Ow to te depedet rbtrress of ε ε ε ξ ξ ξ d ξ we obt oter set of dettes 9 f :
10
11 47 48 I ddto tere re te reltos: 49 5 Utlz tese reltos d tose Eqs d crry out soe coplcted clcultos t c be prove tt te dettes Eqs5-3 re equvlet to te dettes Eqs Possble fors of te rs uder te syetry of trsfortos Eqs I ts secto we wll prove tt due to te requreet of te cto terls of rvttol syste be vrt uder te trsfortos Eqs te possble fors of te r destes Eq d Eq t be: j 6 d j 7 respectvely e proof of Eq6 s ve te follow: Eq7 es tt j ppers oly trou curvture tesor feld j
12 becuse Eq3 es tt ppers j j oly trou torso tesor feld becuse Eq6 es tt ppers oly trou covrt dervtve d curvture tesor feld j d torso tesor feld becuse j j Hece te tter r desty sould te te for deoted by Eq6 O te oter d f tere ests te relto Eq6 we ust ve: j j erefore fro Eq5 j j j j 5
13 3 j j j j j j j j j j j j 5 us we ve
14 4 j j j j 57 j j 58 Us Eqs53-58 d Eqs5-3 we ve te follow dettes: 59 6
15 5 6 j j j j j j 6 ρ ρ ρ ρ j j j j j j j 63
16 6 j j O te oter d fro Eq6 we lso ve: 66 were 67 b b b b 68 } { 69 Substtut Eqs67-69 to Eq66 d us ξ becuse of te depedet rbtrress of ε ε ε ξ ξ d ξ fter soe lety clcultos we c obt te dettes Eqs59-64 oe by oe Hece te dettes obted drectly fro
17 7 re just te se s tose derved fro j j j j j j e ove lyss prove tt te relto j j j ust est Wt te se etod we c lso prove te follow reltos: j j j Prevously we tred to prove Eq6 ef However tere pper to be soe errors tt pper I te ove lyss we beleve we ve corrected te flws 4 Coservto lws for rvttol syste wt our furter eerlzed r desty Below we sll derve te coservto lws for rvttol syste wt our furter eerlzed r desty deoted by Eqs fro te dettes Eqs5-3 d equtos of felds: 7 7
18 8 j j j j j j 7 Fro te we c et te follow reltos: j j j j j j j _ 75 j j j j j _ 76
19 Eq73 t be rerded s coservto lws of eery-oetu tesor desty for te rvttol syste: t t 79 were j j t 8 d j j t 8 t be terpreted s te eery-oetu tesor desty of tter feld d of rvttol feld respectvely But we ust dcted tt t d t re ot tesor destes d Eq79 lcs te vrt crcter t sould ve te teores of reltvstc rvtto However f we use Eq 75 to defe
20 j j j j j _ 8 d use Eq 76 to defe j j j j j _ 83 te we et At ere d re tesor destes d Eq85 s covrt relto Hece we wll te Eqs8485 to be te coservto lws of eery-oetu tesor desty for te rvttol syste wt our furter eerlzed r destes Hstorclly Este d proposed oter coservto lws of eery- -oetu tesor desty for rvttol syste : ~ t 86 were u t ~ u u e vrtues d defects out Eq85 d Eq86 ve bee dscussed torouly efs9 Becuse Eqs8485 ve ore locl bss d rc pyscl cotets te utor beleves tt te coservto lws Eqs8485 t be better t Este s coservto lws Eq86 9 d could be tested by future eperets d observtos Eq74 t be rerded s coservto lws of sp desty for te rvttol syste: s s 87 were
21 s 88 d s 89 t be terpreted s te sp desty of tter feld d of rvttol feld respectvely But we ust dcted tt s s d Eq87 lc t ll te vrt crcter t sould ve te sprt of eerl reltvty However f we use Eq 77 to defe S 9 d use Eq 78 to defe S 9 te we et S S 9 S S 93 At ere S S d Eq93 ll ve te vrt crcter ece we wll te Eqs993 to be te coservto lws of sp desty for te rvttol syste wt our furter eerlzed r destes
22 5 Soe specl cses of Eq d Eq We ve dcted tt j j j j re ll te specl cses of Eq d It s evdet tt j j re ll te specl cses of Eq Wt te se etod to prove j j j we c lso prove te follow reltos: j 94 j j j 95 j 96
23 3 j j j It s ot dffcult to verfy tt for te ove specl cses of Eq d Eq te coservto lws for rvttol syste ll ve te se tetcl for: d S S S S Of course te deftos of eery-oetu tesor desty d sp desty for dfferet r destes re dfferet Fro te dscussos te ove sectos we ve see tt our furter eerlzed r desty c be used for descrb y teores of rvtto er eerl crcters re: te rvttol felds could ct o te tter feld oly trou covrt dervtve curvture of spce-te d torso of spce-te te r destes of rvttol feld re coposed of curvture tesor feld d torso tesor feld te coservto lws for rvttol syste ll ve te se tetcl for er peculrtes re: te cocrete fors of r destes for tter d rvttol feld re dfferet so te coupls betwee te rvttol felds d tter feld re dfferet te deftos of eery-oetu tesor desty d sp desty for dfferet r destes re dfferet Apped Ⅰ Proof of te relto Eq5 for te spce-te wtout torso e olooc coecto feld s relted to d j by 3 j j A
24 were j j I ddto j j EqA c be derved fro te requreet: A s requreet urtees tt lets d les re preserved uder prllel dsplceet 4 e torso tesor s defed by 5 A3 ere ests te relto 5: { } A4 were { } A5 s te Crstoffel sybol EqA4 c be derved fro EqsAA3A5 I te spce-te wtout torso fro EqA4 t s obvously { } I ts cse te relto j j j c be obted fro EqsAA5 d d b d d j j 5 Ⅱ Soe useful reltos of dfferetl eoetry At ere we troduce soe useful reltos of dfferetl eoetry wc wll be used ts pper e curvture tesor relted to coecto { } s defed by 8 {} ρ ρ { } { } { }{ } { }{ } A6 ρ ρ Slrly te curvture tesor relted to coecto s defed by ρ ρ ρ ρ A7 4
25 EqA4 suests tt {} for te spce-te wt torso d {} oly for te spce-te wtout torso We c lso defe te curvture tesor relted to te fre coecto j 3: j j j j j A8 Us EqA t c be verfed tt torso tesor c lso be verfed: j j Us EqA te follow relto for j j j j A9 efereces Kbble WB 96 oretz Ivrce d te rvttol Feld J t Pys Weber S 97 rvtto d Cosoloy Wley New Yor 3 Ce F P 99 eerl equtos of oto for test prtcles spce-te wt torso Iter J eor Pys Hel F W vo der Heyde P d Kerlc D 976 eerl reltvty wt sp d torso: foudtos d prospects ev od Pys Scoute J A 954 cc Clculus Sprer Berl 8 du d fstz E 975 e Clsscl eory of Felds rslted by Heres Pero Press Oford 9 Ce F P 7 Feld equtos d coservto lws derved fro te eerlzed Este s r desty for rvttol syste d ter plctos to cosoloy Iter J eor Pys to be publsed Corso E 953 Itroducto to esors Spors d eltvstc Wve Equtos Blce & So odo F P Ce 993 e eerlzed rs of rvttol teory wt torso d ter vrce uder ξ trsfortos Scece I C Seres A 366 ε Ce F P e restudy o te debte betwee Este d ev-cvt d te eperetl tests Spcete & Substce 3 6 5
On Hypersurface of Special Finsler Spaces. Admitting Metric Like Tensor Field
It J otem Mat Sceces Vo 7 0 o 9 99-98 O Hyersurface of Seca Fser Saces Admttg Metrc Lke Tesor Fed H Wosoug Deartmet of Matematcs Isamc Azad Uversty Babo Brac Ira md_vosog@yaoocom Abstract I te reset work
r t t r t t à ré ér t é r t st é é t r s s2stè s t rs ts t s
r t r r é té tr q tr t q t t q t r t t rrêté stér ût Prés té r ré ér ès r é r r st P t ré r t érô t 2r ré ré s r t r tr q t s s r t t s t r tr q tr t q t t q t r t t r t t r t t à ré ér t é r t st é é
Physique des réacteurs à eau lourde ou légère en cycle thorium : étude par simulation des performances de conversion et de sûreté
Physique des réacteurs à eau lourde ou légère en cycle thorium : étude par simulation des performances de conversion et de sûreté Alexis Nuttin To cite this version: Alexis Nuttin. Physique des réacteurs
P r s r r t. tr t. r P
P r s r r t tr t r P r t s rés t t rs s r s r r t é ér s r q s t r r r r t str t q q s r s P rs t s r st r q r P P r s r r t t s rés t t r t s rés t t é ér s r q s t r r r r t r st r q rs s r s r r t str
A study on generalized absolute summability factors for a triangular matrix
Proceedigs of the Estoia Acadey of Scieces, 20, 60, 2, 5 20 doi: 0.376/proc.20.2.06 Available olie at www.eap.ee/proceedigs A study o geeralized absolute suability factors for a triagular atrix Ere Savaş
Couplage dans les applications interactives de grande taille
Couplage dans les applications interactives de grande taille Jean-Denis Lesage To cite this version: Jean-Denis Lesage. Couplage dans les applications interactives de grande taille. Réseaux et télécommunications
Oscillatory integrals
Oscilltory integrls Jordn Bell jordn.bell@gmil.com Deprtment of Mthemtics, University of Toronto August, 0 Oscilltory integrls Suppose tht Φ C R d ), ψ DR d ), nd tht Φ is rel-vlued. I : 0, ) C by Iλ)
Fourier Series. constant. The ;east value of T>0 is called the period of f(x). f(x) is well defined and single valued periodic function
Fourier Series Periodic uctio A uctio is sid to hve period T i, T where T is ve costt. The ;est vlue o T> is clled the period o. Eg:- Cosider we kow tht, si si si si si... Etc > si hs the periods,,6,..
P P Ó P. r r t r r r s 1. r r ó t t ó rr r rr r rí st s t s. Pr s t P r s rr. r t r s s s é 3 ñ
P P Ó P r r t r r r s 1 r r ó t t ó rr r rr r rí st s t s Pr s t P r s rr r t r s s s é 3 ñ í sé 3 ñ 3 é1 r P P Ó P str r r r t é t r r r s 1 t r P r s rr 1 1 s t r r ó s r s st rr t s r t s rr s r q s
ss rt çã r s t Pr r Pós r çã ê t çã st t t ê s 1 t s r s r s r s r q s t r r t çã r str ê t çã r t r r r t r s
P P P P ss rt çã r s t Pr r Pós r çã ê t çã st t t ê s 1 t s r s r s r s r q s t r r t çã r str ê t çã r t r r r t r s r t r 3 2 r r r 3 t r ér t r s s r t s r s r s ér t r r t t q s t s sã s s s ér t
Annulations de la dette extérieure et croissance. Une application au cas des pays pauvres très endettés (PPTE)
Annulations de la dette extérieure et croissance. Une application au cas des pays pauvres très endettés (PPTE) Khadija Idlemouden To cite this version: Khadija Idlemouden. Annulations de la dette extérieure
Finite Field Problems: Solutions
Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The
Émergence des représentations perceptives de la parole : Des transformations verbales sensorielles à des éléments de modélisation computationnelle
Émergence des représentations perceptives de la parole : Des transformations verbales sensorielles à des éléments de modélisation computationnelle Anahita Basirat To cite this version: Anahita Basirat.
Forêts aléatoires : aspects théoriques, sélection de variables et applications
Forêts aléatoires : aspects théoriques, sélection de variables et applications Robin Genuer To cite this version: Robin Genuer. Forêts aléatoires : aspects théoriques, sélection de variables et applications.
Radio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes.
Radio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes. Diego Torres Machado To cite this version: Diego Torres Machado. Radio
Modèles de représentation multi-résolution pour le rendu photo-réaliste de matériaux complexes
Modèles de représentation multi-résolution pour le rendu photo-réaliste de matériaux complexes Jérôme Baril To cite this version: Jérôme Baril. Modèles de représentation multi-résolution pour le rendu
Consommation marchande et contraintes non monétaires au Canada ( )
Consommation marchande et contraintes non monétaires au Canada (1969-2008) Julien Boelaert, François Gardes To cite this version: Julien Boelaert, François Gardes. Consommation marchande et contraintes
Transformations d Arbres XML avec des Modèles Probabilistes pour l Annotation
Transformations d Arbres XML avec des Modèles Probabilistes pour l Annotation Florent Jousse To cite this version: Florent Jousse. Transformations d Arbres XML avec des Modèles Probabilistes pour l Annotation.
Vers un assistant à la preuve en langue naturelle
Vers un assistant à la preuve en langue naturelle Thévenon Patrick To cite this version: Thévenon Patrick. Vers un assistant à la preuve en langue naturelle. Autre [cs.oh]. Université de Savoie, 2006.
Lecture 5: Numerical Integration
Lecture notes on Vritionl nd Approximte Metods in Applied Mtemtics - A Peirce UBC 1 Lecture 5: Numericl Integrtion Compiled 15 September 1 In tis lecture we introduce tecniques for numericl integrtion,
Μέθοδος Προσδιορισμού του Ισοδύναμου Ατομικού, από το Λόγο των Εντάσεων σύμφωνα και ασύμφωνα Σκεδαζόμενων Ακτινών-γ
Τεχν. Χρον. Επιστ. Έκδ. ΤΕΕ, V, τεύχ. - 4, Tech. hro. Sc. J. TG, V, No - 9 Μέθοδος Προσδιορισμού του Ισοδύναμου Ατομικού Αριθμού, από το Λόγο των Εντάσεων σύμφωνα και ασύμφωνα Σκεδαζόμενων Ακτινών-γ Κ.
ACI sécurité informatique KAA (Key Authentification Ambient)
ACI sécurité informatique KAA (Key Authentification Ambient) Samuel Galice, Veronique Legrand, Frédéric Le Mouël, Marine Minier, Stéphane Ubéda, Michel Morvan, Sylvain Sené, Laurent Guihéry, Agnès Rabagny,
www.absolualarme.com met la disposition du public, via www.docalarme.com, de la documentation technique dont les rιfιrences, marques et logos, sont
w. ww lua so ab me lar m.co t me la sit po dis ion du c, bli pu via lar ca do w. ww me.co m, de la ion nta t do cu me on t ed hn iqu tec les en ce s, rι fιr ma rq ue se t lo go s, so nt la pr op riι tι
Universal Levenshtein Automata. Building and Properties
Sofa Uversty St. Klmet Ohrdsk Faculty of Mathematcs ad Iformatcs Departmet of Mathematcal Logc ad Applcatos Uversal Leveshte Automata. Buldg ad Propertes A thess submtted for the degree of Master of Computer
rs r r â t át r st tíst Ó P ã t r r r â
rs r r â t át r st tíst P Ó P ã t r r r â ã t r r P Ó P r sã rs r s t à r çã rs r st tíst r q s t r r t çã r r st tíst r t r ú r s r ú r â rs r r â t át r çã rs r st tíst 1 r r 1 ss rt q çã st tr sã
Digital Signal Processing: A Computer-Based Approach
SOLUTIOS AUAL to accopay Digital Sigal Processig: A Coputer-Based Approac Tird Editio Sait K itra Prepared by Cowdary Adsuilli, Jo Berger, arco Carli, Hsi-Ha Ho, Raeev Gadi, Ci Kaye Ko, Luca Luccese, ad
SHORT REVISION. FREE Download Study Package from website: 2 5π (c)sin 15 or sin = = cos 75 or cos ; 12
SHORT REVISION Trigoometric Rtios & Idetities BASIC TRIGONOMETRIC IDENTITIES : ()si θ + cos θ ; si θ ; cos θ θ R (b)sec θ t θ ; sec θ θ R (c)cosec θ cot θ ; cosec θ θ R IMPORTANT T RATIOS: ()si π 0 ; cos
6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Edexcel FP3. Hyperbolic Functions. PhysicsAndMathsTutor.com
Eecel FP Hpeolic Fuctios PhsicsAMthsTuto.com . Solve the equtio Leve lk 7sech th 5 Give ou swes i the fom l whee is tiol ume. 5 7 Sih 5 Cosh cosh c 7 Sih 5cosh's 7 Ece e I E e e 4 e te 5e 55 O 5e 55 te
Jeux d inondation dans les graphes
Jeux d inondation dans les graphes Aurélie Lagoutte To cite this version: Aurélie Lagoutte. Jeux d inondation dans les graphes. 2010. HAL Id: hal-00509488 https://hal.archives-ouvertes.fr/hal-00509488
Perturbation Series in Light-Cone Diagrams of Green Function of String Field
Petuto Sees ht-coe Dms of ee Fucto of St Fel Am-l Te-So Km Chol-M So- m Detmet of Eey Scece Km l Su Uvesty Pyoy DPR Koe E-y Km l Su Uvesty Pyoy DPR Koe Detmet of Physcs Km l Su Uvesty Pyoy DPR Koe Astct
Ψηφιακή Επεξεργασία Εικόνας
ΠΑΝΕΠΙΣΤΗΜΙΟ ΙΩΑΝΝΙΝΩΝ ΑΝΟΙΚΤΑ ΑΚΑΔΗΜΑΪΚΑ ΜΑΘΗΜΑΤΑ Ψηφιακή Επεξεργασία Εικόνας Φιλτράρισμα στο πεδίο των συχνοτήτων Διδάσκων : Αναπληρωτής Καθηγητής Νίκου Χριστόφορος Άδειες Χρήσης Το παρόν εκπαιδευτικό
ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ
ΗΜΥ ΔΙΑΚΡΙΤΗ ΑΝΑΛΥΣΗ ΚΑΙ ΔΟΜΕΣ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΗΜΥ Διακριτή Ανάλυση και Δομές Χειμερινό Εξάμηνο 6 Σειρά Ασκήσεων Ακέραιοι και Διαίρεση, Πρώτοι Αριθμοί, GCD/LC, Συστήματα
Assessment of otoacoustic emission probe fit at the workfloor
Assessment of otoacoustic emission probe fit at the workfloor t s st tt r st s s r r t rs t2 t P t rs str t t r 1 t s ér r tr st tr r2 t r r t s t t t r t s r ss r rr t 2 s r r 1 s r r t s s s r t s t
Analysis of a discrete element method and coupling with a compressible fluid flow method
Analysis of a discrete element method and coupling with a compressible fluid flow method Laurent Monasse To cite this version: Laurent Monasse. Analysis of a discrete element method and coupling with a
Transfert sécurisé d Images par combinaison de techniques de compression, cryptage et de marquage
Transfert sécurisé d Images par combinaison de techniques de compression, cryptage et de marquage José Marconi Rodrigues To cite this version: José Marconi Rodrigues. Transfert sécurisé d Images par combinaison
Vidyamandir Classes. Solutions to Revision Test Series - 2/ ACEG / IITJEE (Mathematics) = 2 centre = r. a
Per -.(D).() Vdymndr lsses Solutons to evson est Seres - / EG / JEE - (Mthemtcs) Let nd re dmetrcl ends of crcle Let nd D re dmetrcl ends of crcle Hence mnmum dstnce s. y + 4 + 4 6 Let verte (h, k) then
4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
FORMULAE SHEET for STATISTICS II
Síscs II Degrees Ecoomcs d Mgeme FOMULAE SHEET for STATISTICS II EPECTED VALUE MOMENTS AND PAAMETES - Vr ( E( E( - Cov( E{ ( ( } E( E( E( µ ρ Cov( - E ( b E( be( Vr( b Vr( b Vr( bcov( THEOETICAL DISTIBUTIONS
Hygromécanique des panneaux en bois et conservation du patrimoine culturel. Des pathologies... aux outils pour la conservation
Hygromécanique des panneaux en bois et conservation du patrimoine culturel. Des pathologies... aux outils pour la conservation Bertrand Marcon To cite this version: Bertrand Marcon. Hygromécanique des
Markov Processes and Applications
Markov rocesses ad Applcatos Dscrete-Tme Markov Chas Cotuous-Tme Markov Chas Applcatos Queug theory erformace aalyss ΠΜΣ524: Μοντελοποίηση και Ανάλυση Απόδοσης Δικτύων (Ι. Σταυρακάκης - ΕΚΠΑ) Dscrete-Tme
τ τ VOLTERRA SERIES EXPANSION OF LASER DIODE RATE EQUATION The basic laser diode equations are: 1 τ (2) The expansion of equation (1) is: (3) )( 1
VOLTERR ERE EXO O LER OE RTE EQUTO The i ler diode eutio re: [ ][ ] V The exio of eutio i: [ ] ddig eutio d V V The iut urret i ooed of the u of,. ooet, Î, tie vryig ooet. We thu let 6 The Volterr exio
Robust Segmentation of Focal Lesions on Multi-Sequence MRI in Multiple Sclerosis
Robust Segmentation of Focal Lesions on Multi-Sequence MRI in Multiple Sclerosis Daniel García-Lorenzo To cite this version: Daniel García-Lorenzo. Robust Segmentation of Focal Lesions on Multi-Sequence
University of Kentucky Department of Physics and Astronomy PHY 525: Solid State Physics II Fall 2000 Final Examination Solutions
University of Kentucy Deprtment of Pysics nd stronomy PHY : Solid Stte Pysics II Fll Finl Emintion Solutions Dte: December, (Mondy ime llowed: minutes. nswer ll questions.. Het cpcity of ferromgnets. (
Homework for 1/27 Due 2/5
Name: ID: Homework for /7 Due /5. [ 8-3] I Example D of Sectio 8.4, the pdf of the populatio distributio is + αx x f(x α) =, α, otherwise ad the method of momets estimate was foud to be ˆα = 3X (where
Contribution à l évolution des méthodologies de caractérisation et d amélioration des voies ferrées
Contribution à l évolution des méthodologies de caractérisation et d amélioration des voies ferrées Noureddine Rhayma To cite this version: Noureddine Rhayma. Contribution à l évolution des méthodologies
Article Multivariate Extended Gamma Distribution
axoms Artcle Multvarate Exteded Gamma Dstrbuto Dhaya P. Joseph Departmet of Statstcs, Kurakose Elas College, Maaam, Kottayam, Kerala 686561, Ida; dhayapj@gmal.com; Tel.: +91-9400-733-065 Academc Edtor:
Cytotoxicity of ionic liquids and precursor compounds towards human cell line HeLa
Cytotoxcty of oc lqud ad precuror compoud toward huma cell le HeLa Xuefeg Wag, a,b C. Adré Ohl, a Qghua Lu,* a Zhaofu Fe, c Ju Hu, b ad Paul J. Dyo c a School of Chemtry ad Chemcal Techology, Shagha Jao
Quadruple Simultaneous Fourier series Equations Involving Heat Polynomials
Itertiol Jourl of Siee Reserh (IJSR ISSN (Olie: 39-764 Ie Coperius Vlue (3: 6.4 Ipt Ftor (3: 4.438 Quruple Siulteous Fourier series Equtios Ivolvig Het Poloils Guj Shukl, K.C. Tripthi. Dr. Aekr Istitute
1. For each of the following power series, find the interval of convergence and the radius of convergence:
Math 6 Practice Problems Solutios Power Series ad Taylor Series 1. For each of the followig power series, fid the iterval of covergece ad the radius of covergece: (a ( 1 x Notice that = ( 1 +1 ( x +1.
Résolution de problème inverse et propagation d incertitudes : application à la dynamique des gaz compressibles
Résolution de problème inverse et propagation d incertitudes : application à la dynamique des gaz compressibles Alexandre Birolleau To cite this version: Alexandre Birolleau. Résolution de problème inverse
Ημιγραμμικοποίηση και Διαγωνοποίηση των Διδιάστατων Εξισώσεων Euler για Ροές με Ελεύθερη Επιφάνεια
Τεχν. Χρον. Επιστ. Έκδ. ΤΕΕ Ι τεύχ. Te. Cro... TCG I No 47 Ημιγραμμικοποίηση και Διαγωνοποίηση των Διδιάστατων Εξισώσεων Eer για Ροές με Ελεύθερη Επιφάνεια ΑΛΕΞΑΝΔΡΟΣ Γ. ΠΑΝΑΓΙΩΤΟΠΟΥΛΟΣ Δρ. Πολιτικός Μηχανικός
Langages dédiés au développement de services de communications
Langages dédiés au développement de services de communications Nicolas Palix To cite this version: Nicolas Palix. Langages dédiés au développement de services de communications. Réseaux et télécommunications
DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Constant Elasticity of Substitution in Applied General Equilibrium
Constant Elastct of Substtuton n Appled General Equlbru The choce of nput levels that nze the cost of producton for an set of nput prces and a fed level of producton can be epressed as n sty.. f Ltng for
1 B0 C00. nly Difo. r II. on III t o. ly II II. Di XR. Di un 5.8. Di Dinly. Di F/ / Dint. mou. on.3 3 D. 3.5 ird Thi. oun F/2. s m F/3 /3.
. F/ /3 3. I F/ 7 7 0 0 Mo ode del 0 00 0 00 A 6 A C00 00 0 S 0 C 0 008 06 007 07 09 A 0 00 0 00 0 009 09 A 7 I 7 7 0 0 F/.. 6 6 8 8 0 00 0 F/3 /3. fo I t o nt un D ou s ds 3. ird F/ /3 Thi ur T ou 0 Fo
On Generating Relations of Some Triple. Hypergeometric Functions
It. Joural of Math. Aalysis, Vol. 5,, o., 5 - O Geeratig Relatios of Some Triple Hypergeometric Fuctios Fadhle B. F. Mohse ad Gamal A. Qashash Departmet of Mathematics, Faculty of Educatio Zigibar Ade
INTEGRAL INEQUALITY REGARDING r-convex AND
J Koren Mth Soc 47, No, pp 373 383 DOI 434/JKMS47373 INTEGRAL INEQUALITY REGARDING r-convex AND r-concave FUNCTIONS WdAllh T Sulimn Astrct New integrl inequlities concerning r-conve nd r-concve functions
Discrete Fourier Transform { } ( ) sin( ) Discrete Sine Transformation. n, n= 0,1,2,, when the function is odd, f (x) = f ( x) L L L N N.
Dscrete Fourer Trasform Refereces:. umercal Aalyss of Spectral Methods: Theory ad Applcatos, Davd Gottleb ad S.A. Orszag, Soc. for Idust. App. Math. 977.. umercal smulato of compressble flows wth smple
Solutions 3. February 2, Apply composite Simpson s rule with m = 1, 2, 4 panels to approximate the integrals:
s Februry 2, 216 1 Exercise 5.2. Apply composite Simpson s rule with m = 1, 2, 4 pnels to pproximte the integrls: () x 2 dx = 1 π/2, (b) cos(x) dx = 1, (c) e x dx = e 1, nd report the errors. () f(x) =
8.324 Relativistic Quantum Field Theory II
Lecture 8.3 Relatvstc Quantum Feld Theory II Fall 00 8.3 Relatvstc Quantum Feld Theory II MIT OpenCourseWare Lecture Notes Hon Lu, Fall 00 Lecture 5.: RENORMALIZATION GROUP FLOW Consder the bare acton
Self and Mutual Inductances for Fundamental Harmonic in Synchronous Machine with Round Rotor (Cont.) Double Layer Lap Winding on Stator
Sel nd Mutul Inductnces or Fundmentl Hrmonc n Synchronous Mchne wth Round Rotor (Cont.) Double yer p Wndng on Sttor Round Rotor Feld Wndng (1) d xs s r n even r Dene S r s the number o rotor slots. Dene
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES. Reading: QM course packet Ch 5 up to 5.6
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES Readig: QM course packet Ch 5 up to 5. 1 ϕ (x) = E = π m( a) =1,,3,4,5 for xa (x) = πx si L L * = πx L si L.5 ϕ' -.5 z 1 (x) = L si
CE 530 Molecular Simulation
C 53 olecular Siulation Lecture Histogra Reweighting ethods David. Kofke Departent of Cheical ngineering SUNY uffalo kofke@eng.buffalo.edu Histogra Reweighting ethod to cobine results taken at different
Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών. ΗΥ-570: Στατιστική Επεξεργασία Σήµατος. ιδάσκων : Α. Μουχτάρης. εύτερη Σειρά Ασκήσεων.
Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών ΗΥ-570: Στατιστική Επεξεργασία Σήµατος 2015 ιδάσκων : Α. Μουχτάρης εύτερη Σειρά Ασκήσεων Λύσεις Ασκηση 1. 1. Consder the gven expresson for R 1/2 : R 1/2
Θωμάς ΣΑΛΟΝΙΚΙΟΣ 1, Χρήστος ΚΑΡΑΚΩΣΤΑΣ 2, Βασίλειος ΛΕΚΙΔΗΣ 2, Μίλτων ΔΗΜΟΣΘΕΝΟΥΣ 1, Τριαντάφυλλος ΜΑΚΑΡΙΟΣ 3,
Αξιοποίηση Έξι Σεισμών στην Πελοπόννησο για την Συσχέτιση Φασματικών Επιταχύνσεων με την Απόκριση του Δομημένου Περιβάλλοντος Correlation of Spectral Accelerations with the Response of the Built Environment
If ABC is any oblique triangle with sides a, b, and c, the following equations are valid. 2bc. (a) a 2 b 2 c 2 2bc cos A or cos A b2 c 2 a 2.
etion 6. Lw of osines 59 etion 6. Lw of osines If is ny oblique tringle with sides, b, nd, the following equtions re vlid. () b b os or os b b (b) b os or os b () b b os or os b b You should be ble to
3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Minimum density power divergence estimator for diffusion processes
A Ist Stat Math 3) 65:3 36 DOI.7/s463--366-9 Mmum desty power dvergece estmator for dffuso processes Sagyeol Lee Jumo Sog Receved: 3 March 7 / Revsed: Aprl / ublshed ole: July The Isttute of Statstcal
ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE ΑΠΟ ΑΤΟΜΑ ΜΕ ΤΥΦΛΩΣΗ
ΠΑΝΕΠΙΣΤΗΜΙΟ ΜΑΚΕΔΟΝΙΑΣ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΚΠΑΙΔΕΥΤΙΚΗΣ ΚΑΙ ΚΟΙΝΩΝΙΚΗΣ ΠΟΛΙΤΙΚΗΣ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE
Some Geometric Properties of a Class of Univalent. Functions with Negative Coefficients Defined by. Hadamard Product with Fractional Calculus I
Itrtol Mthtcl Foru Vol 6 0 o 64 379-388 So otrc Proprts o Clss o Uvlt Fuctos wth Ntv Cocts Dd y Hdrd Product wth Frctol Clculus I Huss Jr Adul Huss Dprtt o Mthtcs d Coputr pplctos Coll o Sccs Uvrsty o
Outline. M/M/1 Queue (infinite buffer) M/M/1/N (finite buffer) Networks of M/M/1 Queues M/G/1 Priority Queue
Queueig Aalysis Outlie M/M/ Queue (ifiite buffer M/M//N (fiite buffer M/M// (Erlag s B forula M/M/ (Erlag s C forula Networks of M/M/ Queues M/G/ Priority Queue M/M/ M: Markovia/Meoryless Arrival process
Stéphane Bancelin. Imagerie Quantitative du Collagène par Génération de Seconde Harmonique.
Imagerie Quantitative du Collagène par Génération de Seconde Harmonique Stéphane Bancelin To cite this version: Stéphane Bancelin. Imagerie Quantitative du Collagène par Génération de Seconde Harmonique.
Estimators when the Correlation Coefficient. is Negative
It J Cotemp Math Sceces, Vol 5, 00, o 3, 45-50 Estmators whe the Correlato Coeffcet s Negatve Sad Al Al-Hadhram College of Appled Sceces, Nzwa, Oma abur97@ahoocouk Abstract Rato estmators for the mea of
Homework 4.1 Solutions Math 5110/6830
Homework 4. Solutios Math 5/683. a) For p + = αp γ α)p γ α)p + γ b) Let Equilibria poits satisfy: p = p = OR = γ α)p ) γ α)p + γ = α γ α)p ) γ α)p + γ α = p ) p + = p ) = The, we have equilibria poits
Bessel function for complex variable
Besse fuctio for compex variabe Kauhito Miuyama May 4, 7 Besse fuctio The Besse fuctio Z ν () is the fuctio wich satisfies + ) ( + ν Z ν () =. () Three kids of the soutios of this equatio are give by {
UNIVERSITE DE PERPIGNAN VIA DOMITIA
Délivré par UNIVERSITE DE PERPIGNAN VIA DOMITIA Préparée au sein de l école doctorale Energie et Environnement Et de l unité de recherche Procédés, Matériaux et Énergie Solaire (PROMES-CNRS, UPR 8521)
Review-2 and Practice problems. sin 2 (x) cos 2 (x)(sin(x)dx) (1 cos 2 (x)) cos 2 (x)(sin(x)dx) let u = cos(x), du = sin(x)dx. = (1 u 2 )u 2 ( du)
. Trigonometric Integrls. ( sin m (x cos n (x Cse-: m is odd let u cos(x Exmple: sin 3 (x cos (x Review- nd Prctice problems sin 3 (x cos (x Cse-: n is odd let u sin(x Exmple: cos 5 (x cos 5 (x sin (x
MATRICES WITH CONVOLUTIONS OF BINOMIAL FUNCTIONS, THEIR DETERMINANTS, AND SOME EXAMPLES
Journl of Alger umer Teor: Avne n Applon Volume umer 9 Pge -7 MATRICES WITH COVOLUTIOS OF BIOMIAL FUCTIOS THEIR DETERMIATS AD SOME EXAMPLES ORMA C SEVERO n PAUL J SCHILLO Meove Lne Wllmvlle Y USA e-ml:
Développement d un nouveau multi-détecteur de neutrons
Développement d un nouveau multi-détecteur de neutrons M. Sénoville To cite this version: M. Sénoville. Développement d un nouveau multi-détecteur de neutrons. Physique Nucléaire Expérimentale [nucl-ex].
CS 1675 Introduction to Machine Learning Lecture 7. Density estimation. Milos Hauskrecht 5329 Sennott Square
CS 675 Itroducto to Mache Learg Lecture 7 esty estmato Mlos Hausrecht mlos@cs.tt.edu 539 Seott Square ata: esty estmato {.. } a vector of attrbute values Objectve: estmate the model of the uderlyg robablty
The Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Points de torsion des courbes elliptiques et équations diophantiennes
Points de torsion des courbes elliptiques et équations diophantiennes Nicolas Billerey To cite this version: Nicolas Billerey. Points de torsion des courbes elliptiques et équations diophantiennes. Mathématiques
derivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
MATH 38061/MATH48061/MATH68061: MULTIVARIATE STATISTICS Solutions to Problems on Matrix Algebra
MATH 38061/MATH48061/MATH68061: MULTIVARIATE STATISTICS Solutios to Poblems o Matix Algeba 1 Let A be a squae diagoal matix takig the fom a 11 0 0 0 a 22 0 A 0 0 a pp The ad So, log det A t log A t log
Fusion de données multicapteurs pour la construction incrémentale du modèle tridimensionnel texturé d un environnement intérieur par un robot mobile
Fusion de données multicapteurs pour la construction incrémentale du modèle tridimensionnel texturé d un environnement intérieur par un robot mobile Ayman Zureiki To cite this version: Ayman Zureiki. Fusion
CHAPTER (2) Electric Charges, Electric Charge Densities and Electric Field Intensity
CHAPTE () Electric Chrges, Electric Chrge Densities nd Electric Field Intensity Chrge Configurtion ) Point Chrge: The concept of the point chrge is used when the dimensions of n electric chrge distriution
C.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Tridiagonal matrices. Gérard MEURANT. October, 2008
Tridiagonal matrices Gérard MEURANT October, 2008 1 Similarity 2 Cholesy factorizations 3 Eigenvalues 4 Inverse Similarity Let α 1 ω 1 β 1 α 2 ω 2 T =......... β 2 α 1 ω 1 β 1 α and β i ω i, i = 1,...,
One and two particle density matrices for single determinant HF wavefunctions. (1) = φ 2. )β(1) ( ) ) + β(1)β * β. (1)ρ RHF
One and two partcle densty matrces for sngle determnant HF wavefunctons One partcle densty matrx Gven the Hartree-Fock wavefuncton ψ (,,3,!, = Âϕ (ϕ (ϕ (3!ϕ ( 3 The electronc energy s ψ H ψ = ϕ ( f ( ϕ
Optimal stopping under nonlinear expectation
Avalable ole at www.scecedrect.com SceceDrect Stochastc Processes ad ther Applcatos 124 (2014) 3277 3311 www.elsever.com/locate/spa Optmal stoppg uder olear expectato Ibrahm Ekre a, Nzar Touz b, Jafeg
Time Invariant Regressor in Nonlinear Panel Model with Fixed Effects 1
me Ivarat Regressor Nolear Pael Model wt Fxed ffects Jyog Ha UCLA February 26, 23 I am grateful to Da Ackerberg ad Jerry Hausma for elpful commets. Abstract s paper geeralzes Hausma ad aylor s (98) tuto,
Studies on Properties and Estimation Problems for Modified Extension of Exponential Distribution
Iteratoal Joural of Computer Applcatos (975 8887) Volume 5 No. September 5 Studes o Propertes ad Estmato Problems for odfed Exteso of Expoetal Dstrbuto.A. El-Damcese athematcs Departmet Faculty of Scece
E fficient computational tools for the statistical analysis of shape and asymmetryof 3D point sets
E fficient computational tools for the statistical analysis of shape and asymmetryof 3D point sets Benoît Combès To cite this version: Benoît Combès. E fficient computational tools for the statistical
Solutions_3. 1 Exercise Exercise January 26, 2017
s_3 Jnury 26, 217 1 Exercise 5.2.3 Apply composite Simpson s rule with m = 1, 2, 4 pnels to pproximte the integrls: () x 2 dx = 1 π/2 3, (b) cos(x) dx = 1, (c) e x dx = e 1, nd report the errors. () f(x)
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ Μελέτη των υλικών των προετοιμασιών σε υφασμάτινο υπόστρωμα, φορητών έργων τέχνης (17ος-20ος αιώνας). Διερεύνηση της χρήσης της τεχνικής της Ηλεκτρονικής Μικροσκοπίας
6.642 Continuum Electromechanics
MIT OpenCourseWre http://ocw.mit.edu 6.64 Continuum Electromechnics Fll 8 For informtion out citing these mterils or our Terms of Use, visit: http://ocw.mit.edu/terms. 6.64, Continuum Electromechnics,
La naissance de la cohomologie des groupes
La naissance de la cohomologie des groupes Nicolas Basbois To cite this version: Nicolas Basbois. La naissance de la cohomologie des groupes. Mathématiques [math]. Université Nice Sophia Antipolis, 2009.
On Inclusion Relation of Absolute Summability
It. J. Cotemp. Math. Scieces, Vol. 5, 2010, o. 53, 2641-2646 O Iclusio Relatio of Absolute Summability Aradhaa Dutt Jauhari A/66 Suresh Sharma Nagar Bareilly UP) Idia-243006 aditya jauhari@rediffmail.com
Logique et Interaction : une Étude Sémantique de la
Logique et Interaction : une Étude Sémantique de la Totalité Pierre Clairambault To cite this version: Pierre Clairambault. Logique et Interaction : une Étude Sémantique de la Totalité. Autre [cs.oh].