On the Tangent Space of the Deformation Functor of Curves with Automorphisms Aristides Kontogeorgis
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On Inflation-Restriction Exact Sequences in Group and Amitsur Cohomology
ON INFLATION-RESTRICTION EXACT SEQUENCES IN GROUP AND AMITSUR COHOMOLOGY BY A. J. BERKSON AND ALAN McCONNELLC) 1. Introduction. Let H be a normal subgroup of a group G, M a G-module; a fundamental theorem of group cohomology [5] states: if H'(H, M)=0, 0</<«, then the sequence 0 —> Hn(GjH, MH) -A+ Hn(G, M) -^ 7Tn(7T,M)G -U Hn+1(GIH, MH)-^Hn+1(G, M) is exact. In §2 of this paper we show (under the assumption that «> 1) that this sequence is embedded in a considerably simpler exact sequence (for the precise statement see Theorem 1) and we are able to say something about the extent of deviation of the two sequences. Let C be a field, Fc F extension fields with [F: C] finite; a fundamental theorem of Amitsur cohomology [2], [6], [8] states: the sequence (2) 0 —> H2(KjC) -^U H2{FjC)-!-* H2((K <g>F)jK)° -U TY3(F/C)-^U H3(FjC) is exact. In §3 of this paper we show that this sequence is embedded in a con- siderably simpler exact sequence (for the precise statement see Theorem 2). In §4 we discuss the extent of deviation of the two sequences. Of course these two results are closely related (although neither implies the other) and upon careful analysis it can be seen that their proofs are essentially the same. The group cohomology proof is more elementary in that it does not use spectral sequences; this reflects the fact that the definition of the transgression map t can be stated without mentioning spectral sequences. -
Locally Compact Groups. Iv
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 221, Number 1, 1976 GROUP EXTENSIONSAND COHOMOLOGYFOR LOCALLYCOMPACT GROUPS. IV BY CALVIN C. MOOREÍ1) ABSTRACT. In this paper we shall apply the cohomology groups con- structed in [14] to a variety of problems in analysis. We show that cohomology classes admit direct integral decompositions, and we obtain as a special case a new proof of the existence of direct integral decompositions of unitary representa- tions. This also leads to a Frobenius reciprocity theorem for induced modules, and we obtain splitting theorems for direct integrals of tori analogous to known results for direct sums. We also obtain implementation theorems for groups of automorphisms of von Neumann algebras. We show that the splitting group to- pology on the two-dimensional cohomology groups agrees with other naturally de- fined topologies and we find conditions under which this topology is T2. Finally we resolve several questions left open concerning splitting groups in a previous paper [13]. 1. This paper will rely heavily on the development in [14] of cohomology groups whose properties were defined and discussed there. The object of this paper is to apply these constructions to a variety of problems in analysis. We obtain for instance a general theorem which guarantees the existence of direct integral decompositions of cohomology classes in appropriate contexts. This will contain for instance as a special case the existence of direct integral decomposi- tions of unitary representations. This will also give a kind of Frobenius reciproc- ity theorem for our induced modules, and in addition we obtain a splitting theo- rem for direct integrals of tori, analogous to the known theorems for products of tori. -
Social Media and Chatbots Use for Chronic Disease Patients Support: Case Study from an Online Community Regarding Therapeutic Use of Cannabis
MESTRADO MULTIMÉDIA - ESPECIALIZAÇÃO EM TECNOLOGIA Social Media and Chatbots use for chronic disease patients support: case study from an online community regarding therapeutic use of cannabis Alice Rangel Teixeira M 2019 FACULDADES PARTICIPANTES: FACULDADE DE ENGENHARIA FACULDADE DE BELAS ARTES FACULDADE DE CIÊNCIAS FACULDADE DE ECONOMIA FACULDADE DE LETRAS Social Media and Chatbots use for chronic disease patients support: case study from an online community regarding therapeutic use of cannabis Alice Rangel Teixeira Mestrado em Multimédia da Universidade do Porto Orientador: Carla Teixeira Lopes July 2019 © Alice Rangel Teixeira, 2019 Social Media and Chatbots use for chronic disease patients support: case study from an online community regarding therapeutic use of cannabis Alice Rangel Teixeira Mestrado em Multimédia da Universidade do Porto Approved in public by the jury President: Rui Pedro Amaral Rodrigues (Prof) External Examiner: Ana Margarida Pisco Almeida (Prof) Supervisor: Carla Alexandra Teixeira Lopes (Prof) Resumo A análise de redes sociais na área da saúde é recente e permite compreender a efetividade de políticas e práticas de saúde para a população, ajustando-as conforme(Paul & Dredze, 2017). Contudo, apesar do papel central da partilha de informação para o apoio social e emocional, no contexto das redes sociais, ainda são poucos os estudos que procuram analisar a dinâmica de produção e partilha desta informação. Este estudo analisa esta dinâmica de produção de conhecimento, tendo como caso de estudo as comunidades online de apoio ao tratamento de doenças crônicas com cannabis. O caso escolhido parte da perspetiva que as comunidades têm a produção de conhecimento como objetivo implícito dos agrupamentos, por não haver informação ou atenção ao tratamento satisfatória. -
Article 251 – 2013 Classification Et Définitions Classification and Definitions
FIA Annexe J / Appendix J – Art.251 Article 251 – 2013 Classification et Définitions Classification and Definitions ART. 1 CLASSIFICATION CLASSIFICATION 1.1 Catégories et groupes Categories and groups Les automobiles utilisées en compétition sont réparties dans The cars used in competition are divided up into the les catégories et groupes suivants : following categories and groups: Catégorie I : Category I: - Groupe N : Voitures de Production - Group N: Production Cars - Groupe A : Voitures de Tourisme - Group A: Touring Cars - Groupe R : Voitures de Tourisme ou de Grande - Group R : Touring Cars or Large Scale Series Production de Série Production Cars Catégorie II : Category II: - Groupe RGT : Voitures GT de Production - Group RGT: GT Production Cars - Groupe GT1 : Voitures de Grand Tourisme - Group GT1: Grand Touring Cars - Groupe GT2 : Voitures de Grand Tourisme - Group GT2: Grand Touring Cars - Groupe GT3 : Voitures de Grand Tourisme de Coupe - Group GT3 : Cup Grand Touring Cars - Groupe CN : Voitures de Sport-Production - Group CN: Production Sports Cars - Groupe D : Voitures de Course de Formule - Group D: International Formula Racing Cars Internationale - Groupe E : Voitures de Course de Formule Libre - Group E: Free Formula Racing Cars Catégorie III : Category III: - Groupe F : Camions de Course - Group F: Racing Trucks 1.2 Classes de cylindrée Cubic capacity classes Les voitures sont réparties d'après leur cylindrée-moteur, The cars are divided up into the following classes according dans les classes suivantes : to their cubic capacity: 1. jusqu'à 500 cm3 1. up to 500 cm3 2. de plus de 500 cm3 à 600 cm3 2. over 500 cm3 and up to 600 cm3 3. -
Belcar Skylimit Sprint Cup
BELCAR SKYLIMIT SPRINT CUP TECHNICAL REGULATIONS 2021 PAGINA INDEX Art 1. DEFINITION – DESCRIPTION 2 Art 2. REGULATIONS 2 Art 3. BODYWORK AND OTHER EXTERNAL DIMENSIONS 6 Art. 4 WEIGHT 14 Art. 5 ENGINE 16 Art 6. FUEL LINES, FUEL PUMPS AND FUEL TANKS 19 Art 7. LUBRICATION SYSTEM 22 Art 8. ELECTRICAL EQUIPMENT 23 Art 9. TRANSMISSION 25 Art 10. SUSPENSION AND STEERING MECHANISM 26 Art 11. BRAKES 28 Art 12. WHEELS AND TIRES 30 Art 13. COCKPIT 31 Art 14. SAFETY EQUIPMENT 33 Art 15. SAFETY STRUCTURE 36 Art 16. FUEL 37 Art 17. CURRENT TEXT 37 Art 18. APPROVAL 37 VZW Terlamen is the promoter of the Belcar Sprint Championship 2021 in accordance with the regulations of the International Sporting Code of the FIA, the National Sporting Code of RACB sport, the current regulation and possibly the additional (special) regulation, to which all participants must submit through their participation. Every member of a participating team must take note of the full content of the current regulation. Art. 1 DEFINITION – DESCRIPTION A race car for the Belcar Sprint Championship is defined by RACB Sport, in agreement with the promoter. This car is suitable for sporting purposes and has at least one exit on each side. The base model has to be homologated for the public road or homologated for races by the FIA or by an ASN. T GT Applicable text x Applicable text for Touring cars x Applicable text for GT cars Art. 2 REGULATIONS 2.1 Role of RACB Sport The technical regulations of the Belcar Skylimit Sprint Cup 2021 are issued by RACB Sport, in agreement with the promoter. -
Kfz Teile, Reifen Und Zubehör Seit Über 30 Jahren Auf Der Überholspur
WWW.BERGRENNEN-MICKHAUSEN.COM KFZ TEILE, REIFEN UND ZUBEHÖR KOMPETENZ UND SERVICE AUS EINER HAND • 9.000 m² Lagerfläche • 180.000 verschiedene hochwertige Artikel im Kfz-Teile-Bereich rund um Ihr Fahrzeug • bis zu 150.000 Reifen lagernd • großes Lager – kurze Lieferzeit Zentrale: Melanderstr. 1-9 · 86441 Zusmarshausen Tel 08291 / 85 97-0 · Fax 08291 / 85 97-60 Filiale: Bahnhofstr. 49 · 86470 Thannhausen Tel 08281 / 29 49 [email protected] · www.kfz-teile-kastner.de SEIT ÜBER 30 JAHREN AUF DER ÜBERHOLSPUR CONTENT INHALT 03 WILLKOMMEN MICKHAUSEN 2017 – FINALE FURIOSO Grußworte / Greetings 4-11 Mickhausen 2017: Finale Furioso! 12-20 Ehrentafel der Gesamtsieger 1964-2016 22 ZUSCHAUERINFORMATION Bus-Shuttle-Service 24 Ab Seite 12 Impressum / Offizieller Text 25 Zeitplan / Time table 26 Streckenplan / Course map 28 GRUPPENBESCHREIBUNGEN DIE UNTERSCHIEDLICHEN FAHR- Der ASC Bobingen sagt Danke! 30 ZEUGTYPEN BEIM BERGRENNEN Bitte beachten: Zuschauerinformationen 32 Please pay attention: Information for spectators 33 GRUPPEN & NENNLISTEN Gruppenbeschreibungen 34-36 Ab Seite 34 Kategorie 1 / Category 1 Tourenwagen Gruppe G 38 NENNLISTE ALLER STARTER Tourenwagen Gruppe N, R1, CTC/CGT 38 VERPASSEN SIE Tourenwagen Gruppe S20 FIA über 2000 40 KEINEN FAHRER Tourenwagen Gruppe A, R2, R3, F, CTC/CGT 40-42 Tourenwagen Gruppe E1-FIA, E1-Bergrennen, H, R4, R5, CTC/CGT, FS, NSU 44-56 Kategorie 2 / Category 2 GrandTourismo Gruppe GT1, GT2, GT3, R-GT 58 Rennfahrzeuge Gruppe E2-SH 58 Sportwagen Gruppe E2-SC, CN, C3, CSC 60 Ab Seite 38 Sportwagen Gruppe D/E2-SS 62 04 GRUSSWORTE GREETINGS LIEBE MOTORSPORT- DEAR FRIENDS OF MOTORSPORTS, FREUNDE, right from the very first edition in 2001, which saw more schon beim Startschuss des than 25.000 motorsport fans, a lot of racing cars have Mickhauser Bergrennens im speeded up at the mountain-race in Mickhausen. -
Third Group Cohomology and Gerbes Over Lie Groups
THIRD GROUP COHOMOLOGY AND GERBES OVER LIE GROUPS JOUKO MICKELSSON AND STEFAN WAGNER Abstract The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space H is given 3 by the third cohomology H (H, Z). When H is a topological group the integral cohomology is often related to a locally continuous (or in the case of a Lie group, locally smooth) third group cohomology of H. We shall study in more detail this relation in the case of a group extension 1 N G H 1 when the gerbe is defined by an abelian extension → → → → 1 1 A Nˆ N 1 of N. In particular, when Hs(N, A) vanishes we shall construct a → → → →2 3 N N transgression map Hs(N, A) Hs(H, A ), where A is the subgroup of N-invariants in A and the subscript s denotes→ the locally smooth cohomology. Examples of this relation appear in gauge theory which are discussed in the paper. Keywords: Third group cohomology, gerbe, abelian extension, automorphisms of group extension, crossed module, transgression map, gauge theory. MSC2010: 22E65, 22E67 (primary), 20J06, 57T10 (secondary). 1. Introduction A gerbe over a topological space X is a principal bundle with fiber PU( ), the projective unitary group U( )/S1 of a complex Hilbert space . GerbesH are classified by the integral cohomologyH H3(X, Z). In real life gerbes mostH often come in the following way. We have a vector bundle E over a space Y with model fiber with a free right group action Y N Y with Y/N = X such that the action of NH can be lifted to a projective action× of→N on E. -
Historic Vehicles
„ÚSTECKÁ 21“ SUPPLEMENTARY REGULATIONS OF THE EVENT INTERNATIONAL HILL CLIMB CHALLENGE ÚSTÍ NAD ORLICÍ 26.5.-28.5.2006 MODERN VEHICLES: FIA CHALLENGE FIA EUROPEAN CUP GROUP E 1 CENTRAL EUROPE ZONE CHAMPIONSHIP (FIA TROPHY) CZECH REPUBLIC CHAMPIONSHIP HISTORIC VEHICLES: FIA HILL CLIMB CHAMPIONSHIP – EUROPE CHAMPIONSHIP CENTRAL EUROPE ZONE CHAMPIONSHIP (FIA TROPHY) CZECH REPUBLIC CHAMPIONSHIP AUTO-KLUB AND THE TOWN ÚSTÍ NAD ORLICÍ 1 C O N T E N T General program of the event 1 Organisation 2 General conditions 3 Eligible vehicles 4 Driver's safety equipment 5 Eligible competitors and drivers 6 Entries, Insurance 7 Reservations, official text 8 Participant's duties 9 Administrative checks and scrutineering 10 Running of the event 11 Parc Fermé, final checks 12 Classifications, protests, appeals 13 Prizes and cups, prize-giving ceremony 14 Special provisions Supplements: Supplement no. 1 – Czech Republic Hill-Climb Championship of Modern Vehicles Supplement no. 2 – Free International Hill-Climb Race of Modern Vehicles for the Coat-of-arms of the town Ústí nad Orlicí Supplement no. 3– Czech Republic Hill-Climb Championship of historic vehicles Supplement no. 4 – Free International Hill-Climb Race for the Coat-of-arms of the town Ústí nad Orlicí of historic vehicles 2 GENERAL PROGRAM OF THE EVENT 16.05.2006 24.00 h Close of entries 26.05.2006 14.00 - 20.00 h Administrative checks and scrutineering 26.05.2006 16.00 h Final check of the course 27.05.2006 06.30 - 07.00 h Administrative checks and scrutineering (special cases) 27.05.2006 08.00 h Posting official list of accepted drivers 27.05.2006 09.00 - 12.00 h Official practice (two heats) 27.05.2006 12.15 - 12.30 h Posting practice results and issue of starting list for the race 27.05.2006 13.00 - 13.10 h Ceremonial opening of the event 27.05.2006 13.30 - 17.30 h I. -
Current Groups and the Hamiltonian Anomaly
CURRENTGROUPSANDTHEHAMILTONIANANOMALY ossi niemimäki Doctoral dissertation to be presented for public examination with the permission of the Faculty of Science of the University of Helsinki, in Auditorium 107, Athena Building, on the 27th of May 2020 at 14 o’clock. Department of Mathematics and Statistics Faculty of Science University of Helsinki Helsinki 2020 isbn 978-951-51-5976-2 (paperback) isbn 978-951-51-5977-9 (pdf) http://ethesis.helsinki.fi Unigraa Oy Helsinki 2020 if you’re going to try, go all the way. there is no other feeling like it. you will be alone with the gods and the nights will ame with re. — Charles Bukowski ABSTRACT Gauge symmetry invariance is an indispensable aspect of the eld-theoretic models in classical and quantum physics. Geometrically this symmetry is often modelled with current groups and current algebras, which are used to capture both the idea of gauge invariance and the algebraic structure of gauge currents related to the symmetry. The Hamiltonian anomaly is a well-known problem in the quantisation of massless fermion elds, originally manifesting as additional terms in current algebra commutators. The appearance of these anomalous terms is a signal of two things: that the gauge invariance of quantised Hamiltonian operators is broken, and that consequently it is not possible to coherently dene a vacuum state over the physical conguration space of equivalent gauge connections. In this thesis we explore the geometric and topological origins of the Hamiltonian anomaly, emphasising the usefulness of higher geometric structures in the sense of category theory. Given this context we also discuss higher versions of the gauge-theoretic current groups. -
Date: 18 September 2010 FIA GT1
Date: 18 September 2010 FIA GT1 Championship - Portimao (P) - Qualifying Race Bartels/Bertolini Second in the Algarve Qualifying Race Bartels/Bertolini’s Maserati MC12 no.1 ended today’s Qualifying Race in second place during the seventh round of the FIA GT1 World Championship held in Algarve, Portugal. The Vitaphone Racing Team pair made an excellent show of top-notch driving, starting off from second row after Martin/Leinders’s Ford GT no. 40 was sent back to the last grid position. They (Bartels/Bertolini) concluded the race just behind the Dumbreck/Krumm duo in Sumo Power GT’s Nissan GT-R no.23. In the initial agitated stages Bartels was able to advance to third position, enabling Bertolini, after the pit stop, to fight until the end for the lead in the race. In the last few laps and thanks to less-worn tires, the Italian driving the Maserati was able to overtake Phoenix Racing Team/Carsport’s Corvette Z06 no. 13 driven by Hennerici/Margaritis after an intense head-to-head. With today’s second place, Bartels/Bertolini earn another 6 crucial points toward the drivers’ classification, moving further from their followers and gaining first row for tomorrow’s Championship Race. It turned out to be an unfortunate race for the Vitaphone Racing Team’s second Maserati MC12, driven by Bernoldi/Ramos. After a difficult start-off, the Trident’s car no. 2 was involved in collisions that made it slide to thirteenth position. A good final sixth place was obtained by Heger/Mueller on Triple H Team Hegersport’s Maserati MC12 no. -
Super Tour Southwest Shootout Group 2
Super Tour Southwest Shootout Group 2 - GT1, GT2, GT3, AS, T1 Circuit of the Americas 3.410 miles Sunday Race Grid Pos No. Name Class Overall BestTm In Session Hometown Region Make-Model Member_ID 1 07 Scott Walton GT1 2:10.688 Grp 2 Saturday Qualifying Horseshoe Bay TX LnSt Other GT1 381553 2 12 Michael Lewis GT1 2:10.876 G rp 2 Saturday Official Race ResultsPoway CA SanD 2001 Jaguar XKR 113617 3 05 David Fershtand GT1 2:13.285 Grp 2 Saturday Qualifying Fort Worth TX Tex 1993 Oldsmobile Cutlass 225386 4 88 Don Noe GT1 2:18.192 G rp 2 Saturday Official Race ResultsArlington TX Tex 1994 Ford Mustang 266856 5 15 John Vining GT2 2:20.683 Grp 2 Friday Qualifying Azle TX Tex 2002 Chevrolet Monte Carlo 475146 6 27 Marc Sherrin GT2 2:22.336 Grp 2 Saturday Qualifying Lucas tx Tex 2015 Chevrolet Camaro 481361 7 98 Marc Hoover T1 2:23.277 Grp 2 Saturday Qualifying Shingle Springs CA AZ 1994 Mazda MX5 Miata 112715 8 86 Joseph Gaudette T1 2:23.506 Grp 2 Saturday Qualifying Manassas Va WDC 2002 Chevrolet Corvette Z06358228 9 11 Len Gilmore GT1 2:24.234 Grp 2 Saturday Qualifying Austin TX Tex 2000 Chevrolet camaro 184778 10 77 Steven Pounds GT2 2:25.266 G rp 2 Saturday Official Race ResultsCypress TX Hous 2009 Maserati GranTurismo 363187 11 41 Michael Pettiford T1 2:25.281 Grp 2 Saturday Qualifying Louisville CO Colo 2006 Chevrolet Corvette Z06149585 12 60 Tim Gray GT2 2:25.326 Grp 2 Saturday Qualifying Minneapolis MN LOL 2016 Ford Mustang 253560 13 13 Brad Gross GT2 2:25.371 Grp 2 Saturday Qualifying Grapevine TX Tex 2013 Chevrolet Camaro 463052 14 -
Cocyclic Hadamard Matrices Kshitija Vaidya
Cocyclic Hadamard Matrices Kshitija Vaidya Supervised by Dr Santiago Barrera Acevedo Monash University Vacation Research Scholarships are funded jointly by the Department of Education and Training and the Australian Mathematical Sciences Institute. T Abstract: A square {±1g-matrix H is Hadamard if HH = nIn. The existence of a Hadamard matrix of order 4n for each n 2 N is conjectured. A recent algebraic approach to constructing Hadamard matrices connects cohomology with combinatorics, giving rise to cocyclic Hadamard matrices. Flannery's paper 'Calculation of Cocyclic Matrices' [4], which is the focus of this report addresses the problem of computing cocyclic martrices. 1 Introduction T A Hadamard matrix H is an n × n {±1g-array such that HH = nIn, where In is the n × n identity matrix and HT is the transpose of H. Hadamard proved that all Hadamard matrices have order 1, 2 or 4n for some n 2 N [4]. The following conjecture, known as the Hadamard conjecture, remains an open problem: Conjecture 1.1. There exists a Hadamard matrix of order 4n for each n 2 N. Central to the study of Hadamard matrices is the notion of Hadamard equivalence. Definition 1.2. Two {±1g-matrices M1 and M2 are said to be Hadamard equivalent (written M1 ∼ M2) if M1 = PM2Q where P and Q are signed permutation matrices. This defines an equivalence relation on the set of Hadamard matrices of order n. Some classical constructions of Hadamard matrices include the Sylvester, Williamson and Ito constructions [7]. Cocyclic Hadamard matrices constitute another family of Hadamard matrices. The connection between 2-cocycles in cohomology and Hadamard matrices was established by Horadam and de Launey [6].