Die LAV Stadtwerke Tübingen ist ein seit 1993 bestehender Zusammenschluss der Leichtathletik-Abteilungen des Post-SV Tübingen, des SV 03 Tübingen, der TSG Tübingen und des TV Derendingen als Gründungsvereine. Die Abkürzung LAV steht für Leichtathletik-Vereinigung. Die LAV Stadtwerke Tübingen ist eine Trainings- und Startgemeinschaft. Im Lauf der Jahre schlossen sich die Leichtathletikabteilungen des TSV Lustnau, des SV Pfrondorf und des TSV Hagelloch dieser Startgemeinschaft an.

Der Förderverein LAV Tübingen e. V. ist ein eingetragener Verein, der den Trainings- und Wettkampfbetrieb der LAV finanziell fördert, sowie die LAV-Veranstaltungen ausrichtet. Mitglieder sind alle Athleten der LAV Stadtwerke Tübingen. Erst die gemeinsame Mitgliedschaft in einem der acht Hauptvereine und im Förderverein LAV Tübingen e. V. ermöglicht ein Startrecht für die LAV Stadtwerke Tübingen.

Die LAV Stadtwerke Tübingen beschäftigt ca. 35 Trainer, die etwa 500 Athleten während ca. 45 Trainingsterminen pro Woche betreuen. Für Training und Wettkampf stehen neben den qualifizierten Trainern hochwertige Anlagen und Geräte zur Verfügung. Pro Jahr werden mehrere Trainingslager durchgeführt, die zum Teil disziplin- und trainingsgruppenabhängig an verschiedenen Orten und zu unterschiedlichen Zeiten stattfinden. Der Förderverein LAV Tübingen e. V. richtet pro Jahr mehrere Sportfeste aus, unter anderem die Bahneröffnung mit einem Wettkampf der Kinderleichtathletik, einen Wettkampf mit leichtathletischen Einzeldisziplinen für Jugendliche und Aktive sowie ein Abendsportfest mit wechselnden Themen und Disziplinen (z. B. Running & Music mit Sprint- und Laufdisziplinen, Jump & Sound mit Sprungdisziplinen und das soundtrack-meeting mit internationaler Beteiligung). Einer der Höhepunkte des Tübinger Sportjahres wird ebenfalls vom Förderverein LAV Tübingen e. V. veranstaltet: der Tübinger Erbelauf am ersten Sonntag nach Schulbeginn im September.

2014 und 2015 mussten einige bekannte Athleten aus finanziellen Gründen zu anderen Vereinen wechseln.

Seit 2021 wird die LAV Stadtwerke Tübingen von Puma ausgerüstet.

Bekannte Sportler
Bekannte Athleten der LAV Tübingen waren und sind:
 Dieter Baumann, Mittel- und Langstreckenlauf
Hanna Klein, Mittel- und Langstreckenlauf
 Jackie Baumann, Langhürden
Clemens Bleistein, Mittel- und Langstreckenlauf
 Marius Broening, Sprint
 Arne Gabius, Mittel- und Langstreckenlauf
 Filmon Ghirmai, Hindernis- und Langstreckenlauf
 Fabian Heinle, Weitsprung
 Marie-Laurence Jungfleisch, Hochsprung
 Wolfram Müller, Mittel- und Langstreckenlauf
 Peter Rapp, Weitsprung
 Lisa Steinkamp, Weitsprung
 Gregor Traber, Sprint
 Kerstin Werner, Mittelstreckenlauf

Weblinks
 LAV Tübingen

Einzelnachweise

LAV
Tubingen

LAV Tübingen


Charles Janet (; 15 de junho de 1849 - 7 de fevereiro de 1932) foi um engenheiro, diretor de empresa, inventor e biólogo francês. Ele também é conhecido por sua apresentação inovadora da tabela periódica dos elementos químicos.

Vida e trabalho
Janet se formou na École Centrale Paris e  então se casou com a filha do dono de uma empresa de manufatura e trabalhou nesta empresa pelo resto de sua vida, encontrando tempo para pesquisas em vários ramos da ciência. Sua coleção de 40.000 fósseis e outros espécimes infelizmente se dispersou após sua morte. Seus estudos da morfologia da cabeça de formigas, vespas e abelhas, e suas micrografias eram de notável qualidade. Ele também trabalhou em biologia vegetal e finalmente escreveu uma série de artigos sobre evolução. Ele foi um inventor prolífico e projetou muitos de seus próprios equipamentos, incluindo um viveiro de formigas, no qual uma colônia de formigas se tornava visível ao ser formada entre vidros. Em 1927, ele voltou sua atenção para a tabela periódica e escreveu uma série de seis artigos em francês, que foram impressos mas nunca tiveram ampla circulação. Seu único artigo em inglês foi mal editado e deu uma ideia confusa de seu pensamento.

Idéias químicas
Janet partiu do fato de que a série de elementos químicos é uma sequência contínua, que ele representou como uma hélice traçada nas superfícies de quatro cilindros concêntricos. Através de diversas transformações geométricas, ele criou vários desenhos impressionantes, um dos quais é sua "tabela periódica escalariforme", na qual o hidrogênio e o hélio são colocados acima do lítio e do berílio. Somente mais tarde percebeu que seu arranjo concordava perfeitamente com a teoria quântica e a estrutura eletrônica dos átomos. Ele colocou os actinídeos sob os lantanídeos vinte anos antes de Glenn Seaborg, e continuou a série até o elemento 120.

A tabela de Janet difere da tabela padrão ao colocar os elementos do bloco s à direita, de modo que os subníveis da tabela periódica são organizados na ordem , , , ns, da esquerda para a direita. Não há necessidade de interromper a sequência ou mover o bloco f para uma 'nota de rodapé'. Ele acreditava que nenhum elemento mais pesado que o número 120 seria encontrado, então ele não imaginou um bloco g. Em termos de números quânticos atômicos, cada linha corresponde a um valor da soma  onde n é o número quântico principal e ℓ o número quântico azimutal. A tabela, portanto, corresponde à regra de Madelung, que afirma que os subníveis atômicos são preenchidos na ordem de valores crescentes de . O filósofo da química Eric Scerri escreveu extensivamente em favor da tabela periódica escalariforme de Janet, e está sendo cada vez mais discutida como uma candidata à forma ideal ou mais fundamental da tabela periódica.Janet também imaginou um elemento zero cujo 'átomo' consistiria de dois nêutrons, e ele especulou que isso seria o link para uma tabela de imagem espelhada de elementos com números atômicos negativos - o que seria, antimatéria. Ele também concebeu o hidrogênio pesado (deutério). Ele morreu pouco antes da descoberta do nêutron, do pósitron e do hidrogênio pesado. Seu trabalho foi defendido principalmente por Edward G. Mazurs.

Família
Charles Janet é mais conhecido que seu irmão, Armand Janet, que também era engenheiro e entomologista. Armand Janet tornou-se conhecido como lepidopterista e serviu como presidente da Société entomologique de France em 1911. Armand Janet também é conhecido como espeleólogo e explorador  e foi um dos primeiros a explorar Verdon Gorge.

Referências

Links externos

  Biographie synthétique de Charles Janet
 Eric Scerri, 2020, The Periodic Table: Its Story and Its Significance, 2nd edition, Oxford University Press, New York,
Biólogos da França
Biólogos do século XX
Biólogos do século XIX
Químicos do século XX
Nascidos em 1849
Mortos em 1932

Charles Janet


සටහන්

සටහන්
 Dictionary of Hindu Lore and Legend () by Anna Dhallapiccola
 *

බාහිර සබැඳි

බෞද්ධ දේවතාවෝ
මහාභාරතයේ එන චරිත
අස්වනු දේවතාවෝ
හින්දු දෙවිවරු

යක්ෂ ගෝත්‍රිකයෝ


Zbigniew Kazimierz Brzezinski (28 Mart 1928 Varşova- 26 Mayıs 2017), Polonya kökenli Amerikalı siyaset bilimci, devlet adamıdır. Kendisi aslen bugün Ukrayna'ya bağlı Brzezany (bugün Berezhany, Berejani okunur) kasabası kökenlidir ki soyadı Brzezany'li anlamına gelir.

Dünyanın en önemli stratejistleri arasında ismi sayılan Brezezinski ABD'de 1977-1981 yılları arasında Jimmy Carter'ın Ulusal güvenlik yardımcılığını yaptı. Samuel Huntington'la birlikte çalışarak, 43 sayfalık gizli bir bülten yazdı. Bu bültende gelecek yönetimin 10 önemli dış ve ulusal güvenlik politikası hedefi açıklanıyordu.

Yetiştirdiği öğrencileri arasında Madeleine Albright, Condolezza Rice gibi ABD siyasetinin önemli isimleri vardır.

Ağustos 2007'de Barack Obama'nın başkan adaylığını destekledi. Aynı yıl Eylül ayında ise Obama Brzezinski'yi "en seçkin düşünürlerimizden biri" olarak tanımladı.

Brzezinski uluslararası düzen, ülkelerin siyasi düzenleri ve bunların arasındaki ilişkiler üzerine düşünce ve önerileriyle Uluslararası ilişkiler teorisi'nde Realist ekolün bir temsilcisi olarak kabul edilir.
Kendisi 26 Mayıs 2017'de ölmüştür.

Eserleri

Önemli Eserleri

 The Permanent Purge: Politics in Soviet Totalitarianism, Cambridge: Harvard University Press (1956)
 Soviet Bloc: Unity and Conflict, Harvard University Press (1967), ISBN 0-674-82545-4
 Between Two Ages : America's Role in the Technetronic Era, New York: Viking Press (1970), ISBN 0-313-23498-1
 Power and Principle: Memoirs of the National Security Adviser, 1977-1981, New York: Farrar, Strauss, Giroux (March 1983), ISBN 0-374-23663-1
 Game Plan: A Geostrategic Framework for the Conduct of the U.S.-Soviet Contest, Boston: Atlantic Monthly Press (June 1986), ISBN 0-87113-084-X
 Grand Failure: The Birth and Death of Communism in the Twentieth Century, New York: Charles Scribner's Sons (1989), ISBN 0-02-030730-6
 Out of Control: Global Turmoil on the Eve of the 21st Century, New York: Collier (1993), ISBN 0-684-82636-4
 The Grand Chessboard: American Primacy and Its Geostrategic Imperatives, New York: Basic Books (October 1997), ISBN 0-465-02726-1, subsequently translated and published in nineteen languages
 The Choice: Global Domination or Global Leadership, Basic Books (March 2004), ISBN 0-465-00800-3
 Second Chance: Three Presidents and the Crisis of American Superpower , Basic Books (March 2007), ISBN 0-465-00252-8
 America and the World: Conversations on the Future of American Foreign Policy , Basic Books (September 2008), ISBN 0-465-01501-8
 Stratejik Vizyon: Amerika ve Küresel Güç Buhranı (2012)

Diğer Kitap ve Monografileri

 Russo-Soviet Nationalism, M.A. Thesis, McGill University (1950)
 Political Control in the Soviet Army: A Study on Reports by Former Soviet Officers, New York, Research Program on the U.S.S.R (1954)
 with Carl J. Friedrich, Totalitarian Dictatorship and Autocracy, Cambridge: Harvard University Press (1956)
 Ideology and Power in Soviet Politics, New York: Praeger (1962)
 with Samuel Huntington, Political Power: USA/USSR, New York: Viking Press (April 1963), ISBN 0-670-56318-8
 Alternative to Partition: For a Broader Conception of America's Role in Europe, Atlantic Policy Studies, New York: McGraw-Hill (1965)
 The Implications of Change for United States Foreign Policy, Department of State (1967)
 International Politics in the Technetronic Era, Sofia University Press (1971)
 The Fragile Blossom: Crisis and Change in Japan, New York: Harper and Row (1972), ISBN 0-06-010468-6
 with P. Edward Haley, American Security in an Interdependent World, Rowman & Littlefield (September 1988), ISBN 0-8191-7084-4
 with Marin Strmecki, In Quest of National Security, Boulder: Westview Press (September 1988), ISBN 0-8133-0575-6
 The Soviet Political System: Transformation or Degeneration, Irvington Publishers (August 1993), ISBN 0-8290-3572-9
 with Paige Sullivan, Russia and the Commonwealth of Independent States: Documents, Data, and Analysis, Armonk: M. E. Sharpe (1996), ISBN 1-56324-637-6
 The Geostrategic Triad : Living with China, Europe, and Russia, Center for Strategic & International Studies (December 2000), ISBN 0-89206-384-X

Seçme Denemeleri ve Raporları

 with David Owen, Michael Stewart, Carol Hansen, and Saburo Okita, Democracy Must Work: A Trilateral Agenda for the Decade, Trilateral Commission (June 1984), ISBN 0-8147-6161-5
 with Brent Scowcroft and Richard W. Murphy, Differentiated Containment: U.S. Policy Toward Iran and Iraq, Council on Foreign Relations Press (July 1997), ISBN 0-87609-202-4
 U.S. Policy Toward Northeastern Europe: Report of an Independent Task Force, Council on Foreign Relations Press (July 1999), ISBN 0-87609-259-8
 with Anthony Lake, F. Gregory, and III Gause, The United States and the Persian Gulf, Council on Foreign Relations Press (December 2001), ISBN 0-87609-291-1
 with Robert M. Gates, Iran: Time for a New Approach, Council on Foreign Relations Press (February 2003), ISBN 0-87609-345-4

Dış bağlantılar
 Foreign Affairs'ta yer alan yazıları.
 Büyük Satranç Tahtası, Brzezinski(Kitabın Türkçe Özeti)
 Jeostratejik Üçlü, Brzezinski (Kitabın Türkçe Özeti)

Kaynakça

1928 doğumlular
2017 yılında ölenler
Varşova doğumlular
20. yüzyıl Amerikalı siyasetçileri
21. yüzyıl Amerikalı siyasetçileri
Amerikalı antikomünistler
Polonya asıllı Amerikalılar
Amerikalı siyaset bilimciler
Başkanlık Özgürlük Madalyası sahipleri
Amerikalı siyasetçiler

Zbigniew Brzezinski


Isla Brikama (en inglés: Brikama Island) es una isla fluvial en el río Gambia, en África Occidental parte del país de Gambia.

La isla se encuentra a unos siete kilómetros de distancia, entre las Islas Kai Hai, y las Islas Baboon, tiene casi 1.400 metros de largo y en su punto más ancho unos 270 metros.  La isla se encuentra cerca de la orilla izquierda del Gambia, en un canal de 15 metros de ancho.

Véase también
 Geografía de Gambia
 Geografía de África

Referencias

Enlaces externos
 Mapa de ubicación de la isla

Islas fluviales de Gambia

Isla Brikama


හාරිස්පත්තුව වරකාගොඩ දූල්දෙණිය රාජකරුණා නවරත්න අතපත්තු වාසලමුදියන්සේලාගේ මුදියන්සේ සහ හිඟුල්වල අලකොලදෙණියේ දුග්ගන්නාරාළලාගේ පිංචිඅම්මා දම්පතීන්ගේ තෙවන දරුවා ලෙස 1942 මාර්තු 18 වනදා උන්වහන්සේ   උපතලැබීය.

දොළොස්වනවියෙහිදීඋඩපිටියේශ්‍රීසුමංගල,මැදගොඩපඤ්ඤානන්ද,අළුදෙණියේරතනපාලහාරඹුක්වැල්ලේසද්ධානන්දයනමහාස්වාමින්ද්‍රයන්වහන්සේලාගේආචාර්යත්වයෙන්1955 අප්‍රේල්07වනදාඅස්ගිරිමහාවිහාරයීයමංගලඋපෝසථාගාරයේදීඑවකටඅස්ගිරිමහාවිහාරපාර්ශ්වයේමහානායකයටවත්තේධම්මරතනමහානාහිමියන්ගේඋපාධ්‍යායත්වයෙන්පැවිදිබිමටපත්වූහ. ඒවරකාගොඩඤාණරතනහිමිනාමයෙනි.

ශාසනිකවත්පිළිවෙත්මැනවින්හදාරා1962 ජූනි09 වනදාඅස්ගිරිමහාවිහාරයීයමංගලඋපෝසථාගාරයේදීඅධිසිල්ලැබූහ.

බදුල්ලවිද්‍යාත්තංසපිරිවෙනෙන්හාවත්තේගමශ්‍රීධර්මදීපපිරිවෙන්වෙතින්මූලිකපිරිවෙන්අධ්‍යාපනයලබාඅස්ගිරිමහාවිහාරපිරිවෙනින්හාපේරාදෙණියශ්‍රීසාරානන්දපිරිවෙනින්උසස්අධ්‍යාපනයලබා1970 දීවිද්‍යාලංකාරවිශ්වවිද්‍යාලයෙන්ශාස්ත්‍රවේදීඋපාධියලබාගත්හ. ශිෂ්‍යඅවදියේසිටමසුපේෂලශික්ෂාකාමීයතිවරයන්වහන්සේනමක්ලෙසගිහිපැවිදිසැමගේගෞරවයටපාත්‍රවූඋන්වහන්සේප්‍රාචීනභාෂාඅධ්‍යාපනයලබාප්‍රාචීනහාප්‍රතිචීනභාෂාපිළිබඳවියතෙකුවූහ. ස්වකීයගුරුදේවයන්වහන්සේලාවෙතගුරුබැතියෙන්කටයුතුකළදක්ෂස්වාමීන්වහන්සේනමක්වූහ.

1976දීගිනිගත්හේනබදුපොලවිද්‍යාලයෙන්සියගුරුභූමිකාවආරම්භකළවරකාගොඩඤාණරතනස්වාමීන්ද්‍රයන්වහන්සේමහනුවරවිද්‍යාර්ථවිද්‍යාලය, කොත්මලේමඩකුඹුරවිද්‍යාලය, වලලපාතදුම්බරමහාවිද්‍යාලය, හාපොල්ගොල්ලමහාවිද්‍යාලයයනපාසල්වලවිසිපස්වසරකපමණකාලයක්ගුරුවෘත්තියෙහිනිරතවූහ. ඉන්වැඩිකාලයක්සේවයකළපොල්ගොල්ලවත්තවිද්‍යාලයටයාබදවභූමිභාගයක්පිරිනැමීමදසුවිශේෂීවේ. ගුරුවරයෙකුවශයෙන්සේවයෙහිනිරතවෙමින්ශාස්ත්‍රයදානයකිරීමත්සමඟමහානාහිමියෝසමාජමෙහෙවරෙහිදනිරතවූහ.

වරකාගොඩඤාණරතනමහානාහිමිපාණන්වහන්සේශිෂ්‍යඅවදියේසිටමවත්පිළිවෙත්මෙන්මසංඝසභාවේකටයුතුපිළිබඳවමනාපුහුණුවක්දලැබූහ.

වරකාගොඩඤාණරතනමහානායකස්වාමීන්ද්‍රයන්වහන්සේපාර්ශ්වයටඅයත්ශාසනිකවිවිධකාර්යයන්හිනිරතවූහ. අස්ගිරිමහාවිහාරපාර්ශ්වයෙහිවැඩිසිටිඅතිපූජ්‍යමහානායකස්වාමීන්ද්‍රයන්වහන්සේලාගේමඟපෙන්වීමහාඇසුරලබමින්ශාසනිකපදවිඋසුලන්නටහැකිවීමත්ඊටඅදාළකටයුතුක්‍රමවත්වවගකීමෙන්සිදුකිරීමටත්උන්වහන්සේටශක්තියලැබිණි.

ශ්‍රීදළදාවහන්සේවෙනුවෙන්තේවාකටයුතුවලනිරතවීමේභාග්‍යබුද්ධශ්‍රාවකයන්වහන්සේනමක්ලබන්නේනම්එයඉතාදුර්ලභඅවස්ථාවකි. 1976 දීසිරිදළදාමාළිගාවෙහිතේවාවෙහිනිරතවීමටපත්වූවරකාගොඩඤාණරතනනායකස්වාමීන්ද්‍රයන්වහන්සේ2004 වර්ෂයේදීදශ්‍රීදළදාවහන්සේවෙතතේවාකටයුතුවලනිරතවූහ.

පලීපානශ්‍රීචන්දානන්දමහානායකස්වාමීන්ද්‍රයන්වහන්සේවිසින්1990 දීවරකාගොඩඤාණරතනස්වාමීන්ද්‍රයන්වහන්සේකාරකමහාසංඝසභාවටපත්කරනලදහ. උඩුගමශ්‍රීධම්මදස්සිරතනපාලබුද්ධරක්ඛිතමහානායකමාහිමිපාණන්වහන්සේවිසින්2009 ජ්‍යෙෂ්ඨකාරකසභිකතනතුරපිරිනමනලදඅතරකාරකසංඝසභාවේඋපාධ්‍යායධූරයට2006 දීඋඩුගමශ්‍රීබුද්ධරක්ඛිතමහනාහිමියන්විසින්මපත්කරනලදී.

2015 අප්‍රේල්07 වනදාඅස්ගිරිමහාවිහාරපාර්ශ්වයේඅනුනායකධූරයටපත්වූවරකාගොඩඤාණරතනමහාස්වාමීන්ද්‍රයන්වහන්සේලෝකශාසනිකසේවාවෙහිනිරතවූහ. ඓතිහාසිකබදුලුමුතියංගනරජමහාවිහාරයේවිහාරාධිපතිධූරයට2000 දීපමණපත්වූඋන්වහන්සේඅස්ගිරියවිජයසුන්දරාරාමයේසහපොල්ගොල්ලඋඩගුන්නෑපානබෝධිමල්කඩවිහාරයේවිහාරාධිපතිධූරයටපත්වඑමවිහාරස්ථානවලආගමිකකටයුතුමැනවින්සිදුකළහ. 1987 දීදඹදිවබුද්ධභූමියවන්දනාකරගත්උන්වහන්සේඋඩුගමශ්‍රීබුද්ධරක්ඛිතමහානායකස්වාමීන්ද්‍රයන්වහන්සේසහගලගමඅත්ථදස්සිමහානායකස්වාමීන්ද්‍රයන්වහන්සේසමඟසිංගප්පූරුවසහබුරුමයටවැඩමකළඅතර2002 දීතායිලන්තයේආගමිකඋත්සවරැසකටවැඩමකළහ.

ගලගමඅත්ථදස්සිමහානායකමාහිමියන්ගේඅපවත්වීමෙන්පසුඅස්ගිරිමහාවිහාරපාර්ශ්වයේමහානායකධූරයටවරකාගොඩධම්මසිද්ධිශ්‍රීපඤ්ඤානන්දඤාණරතනමහානායකමාහිමිපාණන්වහන්සේපත්වූහ.

වරකාගොඩ ඥාණරතන හිමි


Gilbert Houcke (1914-1984) est un dompteur français. Il est considéré comme l'un des dresseurs de fauves ayant marqué le cirque européen du XXème siècle.

Biographie
Né le 28 mai 1918 à Grenoble, il est le troisième des cinq enfants de Jean Houcke, metteur en scène de cirque et Marcelle Rancy également issue d'une célèbre famille circassien. Issue d'une tradition familiale essentiellement équestre, il est formé dès son plus jeune âge aux arts du cirque dont principalement l'acrobatie et l'équitation. Dans un premier temps, il devient écuyer sous l'enseignement de son père et ses oncles André et Albert Rancy qui lui apprennent le dressage des chevaux  .

Carrière de dompteur
A l'âge de vingt ans, il apprend à dresser et à présenter des fauves. Il préconise notamment une bienveillance lors de l'apprivoisement des animaux tout en admettant des risques.  En 1952, lors d'un numéro à Munich, il est blessé par un tigre.

En 1951,  il réalise son premier engagement en France au Cirque d'Hiver-Bouglione où il se présente en "Tarzan" au d'un groupe de six fauves. Il décline son personnage  dans le film Le tigre de Colombo, réalisé sous le chapiteau du cirque Busch qui lui vaut le surnom le « Tarzan français ».

Il décède le 15 décembre 1984. En France, la presse relève son approche qualifiée de "bienveillante" de domptage dans un contexte où la maltraitance animale est la norme dans les arts du cirque d'après-guerre en déclarant  :

Références

Dompteur
Naissance en mai 1918
Naissance à Grenoble
Décès en décembre 1984
Décès à Uzès
Décès à 66 ans

Gilbert Houcke


Nordin El Hajjioui surnommé Dikke Nordin van den Dam ou Sponky, né le  à Anvers (Belgique), est un criminel belge d'origine marocaine spécialisé dans le trafic de drogue dans le conflit Mocro-oorlog à Anvers.

À la suite de l'opération Sky ECC menée par la police belge et néerlandaise, Nordin El Hajjioui figure parmi les personnes les plus recherchées dans cette affaire anti-drogue. Il figure parmi les hommes les plus recherchés en Belgique et figure dans le top 50 Interpol.

Biographie

Enfance
Nordin El Hajjioui naît à Anvers et grandit dans le quartier Dam situé dans sa ville natale.

Mocro-oorlog
Dans les années 2010, le grand baron Gwenette Martha établit des contacts avec Nordin El Hajjioui et les Turtles. En 2012, une livraison de 200 kilos de cocaïne destinée à la bande de Samir Bouyakhrichan, Benaouf Adaoui et Houssine Ait Soussan est livrée au hometerminal MSC du Port d'Anvers avant de se volatiliser. Nordin El Hajjioui prend rapidement son envol vers le Maroc pour se réfugier. La presse néerlandaise évoque le nom de ''Dikke Nordin'' comme ayant joué un rôle dans ce vol.

Le nom de Nordin El Hajjioui apparaît pour la première fois à la suite des enquêtes de la police belge menée à l'encontre du docker Frank De Tank actif au Port d'Anvers. Le criminel belge recevait d'énormes sommes d'argent de la part du chef de réseau Nordin El Hajjioui. Un travailleur du port d'Anvers est également poursuivi pour avoir reçu plusieurs dizaines de milliers d'euros de la part de Nordin El Hajjioui. En 2015, Nordin El Hajjioui encourt une peine de cinq ans d'emprisonnement pour trafic de drogues. En 2016, la police arrive à intercepter  de cocaïne destinés au groupe de Nordin El Hajjioui.

En , un cortège de mariage à la valeur de 7 millions d'euros en voitures sportives a lieu dans le quartier de Borgerhout à Anvers. Il s'agit du mariage de la sœur de Nordin El Hajjioui avec un membre de la famille El Yousfi, pour la plupart des membres de l'organisation The Turtles.

En , Nordin El Hajjioui entre en conflit avec Frank De Tank, et lui demande de payer une rançon de  après une perte de plusieurs kilos de cocaïne, chose refusée par le criminel belge. Plusieurs explosions s'ensuivent à Anvers dont le premier au domicile parental de Nordin El Hajjioui, survenu le . Le Marocain réplique avec une tentative d'assassinat au domicile de Frank De Tank situé à Brecht.

Au début de 2018, la police belge met la main sur une liste noire des personnes à abattre, dans laquelle figurent Frank De Tank et huit autres personnes de son entourage. La presse néerlandaise révèle également l'alliance de Nordin El Hajjioui avec la Drug Enforcement Administration.

Arrestations
Au début de mars 2020, les services secrets belges mènent une opération anti-drogue à Anvers, donnant lieu à 36 perquisitions. Dix personnes sont arrêtés dont Mehmet T., le successeur de Frank De Tank au port d'Anvers, mais également le fabricant de grenades albanais Fidan J. dans le quartier Cadixwijk. Le , Kristof Aerts du parquet d'Anvers déclare : "Les membres de cette organisation criminelle sont liés à une importation d'au moins 1,5 tonne de cocaïne. L'un des cerveaux de cette organisation se trouve actuellement à Dubaï."

Le , Nordin El Hajjioui est arrêté à Dubaï pour ses implications dans plusieurs actes violents survenus à Anvers et les environs sur fond de trafic international de cocaïne. Peu après son arrestation, la police émirati révèle la proposition de Nordin El Hajjioui de payer une énorme somme d'argent en échange d'une libération. Le , il est relâché de prison.

Opération Sky ECC
Le , la police belge lance la plus grande opération anti-drogue jamais réalisé en Belgique. Au moins 51 suspects sont arrêtés avec Nordin El Hajjioui comme cerveau d'une organisation qui importe de la cocaïne, qui tient un trafic d'armes et planifie des attentats à la grenade. Dans cette affaire, Nordin El Hajjioui risque une peine de quinze ans d'emprisonnement.

Voir aussi

Ouvrages
Cette bibliographie est indicative.

Références bibliographiques
Mocro Maffia

Wraak

Liens externes

Sources

Notes et références

Personnalité belge condamnée pour crime
Crime organisé en Belgique
Mocro Maffia
Naissance à Anvers
Naissance en octobre 1988
Personnalité marocaine condamnée pour crime
Personnalité belge née d'un parent marocain

Nordin El Hajjioui


Slobodan Milošević (okunuşu: Slobodan Miloşeviç, Sırpça: Слободан Милошевић; 20 Ağustos 1941, Pozarevać - 11 Mart 2006, Lahey), Sırbistan ve Yugoslavya'nın eski devlet başkanıdır.

Hayatı
Belgrad Üniversitesi Hukuk Fakültesinden mezun oldu. Çalışma hayatına Belgrad belediye başkanının ekonomi danışmanı olarak başladı. Komünist Parti'ye katıldı. 1984 yılında, Sırbistan Komünist Partisi Başkanı olan arkadaşı İvan Stambolić tarafından başkent Belgrad'daki parti liderliğine getirildi.

1989'da Sırbistan Cumhurbaşkanı oldu ve göreve gelir gelmez Kosova'nın özerk statüsüne son verdi. Kontrolü sağlamak için Yugoslav birliklerinin bölgeye gönderildiği 1990'da Sırbistan, Kosova hükûmetini feshetti.

Hırvatistan ve Slovenya'nın Yugoslavya'dan 1991'de bağımsızlığını ilan etmesi üzerine Slovenya sınırlarına tanklar gönderdi. Kısa süren bir savaşı tetikledi fakat Slovenya'nın ayrılışını engellemedi. Hırvatistan'daki Sırpları da silahlara sarılmaları için cesaretlendirdi.

1992 yılının Ocak ayında Hırvatistan'da BM gözetiminde ateşkes yürürlüğe girerken, Mart ayında Bosna-Hersek bağımsızlığını ilan etti. Bu kez Bosnalı Sırpların ayaklanması için destek verdi. Yaklaşık 250.000 kişinin öldüğü Bosna Savaşı'nın başlamasından üç yıl sonra, ABD'nin girişimiyle Dayton'da Hırvat ve Bosnalı liderlerle barış masasına oturmayı kabul etti.

Yugoslavya'da Kasım ve Aralık 1996'da yapılan seçimlerde, eski Sırp liderinin müttefikleri genel seçimleri kazandı. Muhalefetteki koalisyon, yerel seçimlerde başkent Belgrad da dâhil olmak üzere kentlerin çoğunda zafer kazandı. Ancak kendi kontrolündeki Seçim Komisyonu, yerel seçimleri iptal etti. Bu karar, ülkeyi 250.000 kişinin katıldığı seçim sonrası şiddetine sürükledi.

Düşüşü

Şiddet olayları yayılırken, 1997 Ocak ayında yenilgiyi kabullenerek, bazı kentlerin kontrolünü muhalefete bıraktı. 15 Temmuz'da parlamento tarafından Yugoslavya devlet başkanlığına getirildi.

Kosova'da Arnavutların ayaklanmasını bastırmak için Şubat 1998'de bölgeye birlikler gönderdi. Bölgede şiddet sürerken BM Güvenlik Konseyi, Eylül ayında derhâl ateşkes ve siyasi diyalog çağrısında bulunulan öneriyi kabul etti.

18-19 Mart'ta Fransa'da yapılan barış görüşmelerinde Kosovalı Arnavutlar bölgeye geçici özerklik tanınmasını öngören barış anlaşmasını imzaladı, ancak Sırplar anlaşmayı reddetti. Görüşmelerin başarısızlıkla sonuçlanması üzerine 24 Mart'ta NATO bombardımanı başladı.

Miloşeviç, 27 Mayıs'ta Lahey'deki Uluslararası Ceza Mahkemesi tarafından savaş suçu sanığı ilan edildi ve insanlığa karşı suç işlediği için Lahey Uluslararası Adalet Divanı'na verilen görev başındaki ilk devlet başkanı oldu. İnsanlığa karşı altı belirli suçtan oluşan iddianameye göre, Miloşeviç ve işbirlikçileri, doğrudan 750.000 Kosovalının mülteci durumuna getirilmesi ve etnik Arnavut oldukları için 6.000 kişinin öldürülmesinden sorumlu tutuldular. Bu arada, NATO bombardımanı Sırp askerlerinin Kosova'dan çekilmeye başladığı 10 Haziran'a kadar sürdü.

Yugoslavlar 24 Eylül 2000'de doğrudan devlet başkanını seçmek için ilk kez oy kullandı. Pek çok batılı vakıf bu seçimlerde Miloşeviç karşıtı muhalif adaylara para akıttı. Büyük kampanyalar düzenlendi. Miloşeviç'i zamanı geldiğinde iktidardan indirmek için eylemci bir rejim karşıtı gençlik grubu (Otpor adında) yaratıldı. Seçimde Miloşeviç karşıtları, Voyislav Koştunitsa'yı zafere taşırken, seçim komisyonu seçimlerin ikinci turunun yapılması gerektiğini açıkladı, ancak bu da ülke çapında gösterilerin başlangıcı oldu. 5 Ekim'de Belgrad caddelerine yürüyen Miloşeviç karşıtları parlamento, televizyon binası ve polis karakollarını ele geçirdi. Bu isyan Miloşeviç'in iktidardaki sonu oldu.

6 Ekim'de Milošević, Koštunica ile bir araya geldi ve alenen yenilgiyi kabul etti. Koštunica, Milošević'in duyurusunun ardından nihayet 7 Ekim'de Yugoslav cumhurbaşkanı olarak göreve başladı.

Hakkında çok sayıda yolsuzluk suçlaması olan Miloşeviç'in, Belgrad'daki villasında polis ve Milošević'in korumaları arasında 36 saatlik silahlı çatışmanın ardından 1 Nisan 2001'de Yugoslav makamları tarafından tutuklandı. Resmi bir suçlama yapılmamasına rağmen, Milošević'in görevi kötüye kullanmaktan ve yolsuzluktan şüpheleniliyordu.

Tutuklanmasının ardından ABD, Yugoslav hükûmetine Milošević'i ICTY'ye iade etmesi veya IMF ve Dünya Bankası'ndan gelen mali yardımı kaybetmesi için baskı yaptı. Başkan Koštunica, Yugoslav anayasasını ihlal edeceğini savunarak Milošević'in iade edilmesine karşı çıktı. Başbakan Zoran Đinđić, iade kararı çıkarmak için bir hükûmet toplantısı düzenledi. Milošević'in avukatları, iade sürecini Yugoslav anayasa mahkemesine temyiz etti. Mahkeme, itirazı görüşmek için iki hafta talep etti. Đinđić, cumhurbaşkanının ve anayasa mahkemesinin itirazlarını görmezden gelerek Milošević'in ICTY'ye iade edilmesini emretti. 28 Haziran'da Milošević, helikopterle Belgrad'dan Bosna-Hersek'in Tuzla kentindeki bir ABD hava üssüne götürüldü ve oradan da uçakla Hollanda'nın Lahey kentine götürüldü.

İade, Yugoslavya'da siyasi kargaşaya neden oldu. Başkan Koštunica iadeyi yasadışı ve anayasaya aykırı olmakla suçlarken, Đinđić koalisyon hükûmetindeki küçük bir parti protesto için ayrıldı. Milošević'in avukatı Toma Fila, iadenin Yugoslavya'nın iadeye ilişkin anayasal yasağını ihlal ettiğini söyledi.
Đinđić, hükûmetin işbirliği yapmaması durumunda olumsuz sonuçları olacağını belirtti. Ek olarak hükûmet, Milošević'i ICTY'ye göndermenin, yabancı bir ülke değil bir BM kurumu olduğu için iade olmadığını savundu. İadenin ardından, bir grup bağışçı Yugoslavya'ya yaklaşık 1 milyar dolarlık mali yardım sözü verdi.}

Ağır savaş suçları hakkında 66 ayrı dava bulunan dört yıl Hollanda'nın Lahey kentindeki eski Yugoslavya için kurulan Savaş Suçları Mahkemesi'nde yargılandı. Lahey yakınında 13 yıl önce Bosna Savaşı'ndaki facialar yüzünden ABD öncülüğünde kurulan, BM'ye bağlı mahkemenin yaptırdığı özel cezaevinin bulunduğu Kuzey Denizi'ne nazır Scheveningen'de tutuldu. 11 Mart 2006 tarihinde savaş suçlarından yargılandığı sırada Lahey'de (Den Haag) hapishanede öldü.

Dış bağlantılar
 Slobodan Milošević, İddianame ve Tutanaklar (ICTY)
 Slobodan Milosevic websitesi

Kaynakça

1941 doğumlular
2006 yılında ölenler
Sırp ateistler
Yugoslavlar
Sırp komünistler
Yugoslav komünistler
Sırbistan cumhurbaşkanları
Yugoslavya devlet başkanları
Bosna Savaşı'nda kişiler
Belgrad Üniversitesinde öğrenim görenler
Hollanda'da kardiyovasküler hastalıktan ölenler
Kalp krizinden ölenler
Eski Yugoslavya Uluslararası Ceza Mahkemesi tarafından suçlanan kişiler
Yugoslav siyasetçiler
Savaş suçlarıyla suçlanan kişiler
Lahey'de ölenler
Soykırım failleri
Ateist siyasetçiler

Slobodan Milošević


Seeking Major Tom ist das vierte Studioalbum von William Shatner. Veröffentlicht wurde das Album am 11. Oktober 2011 in den USA beim Label Cleopatra Records.

Am Album haben einige bekannte Musiker mitgewirkt, so z. B. Sheryl Crow, John Wetton, Patrick Moraz, Ritchie Blackmore, Alan Parsons, Peter Frampton, Warren Haynes, Nick Valensi, Zakk Wylde, Mike Inez, Chris Adler, Steve Howe, Michael Schenker, Dave Davies, Johnny Winter, Brad Paisley, Bootsy Collins, Carmine Appice, Ian Paice und Toots.

Titelliste
Die meisten Stücke auf dem Album haben einen Bezug zu der Figur Major Tom oder dem Weltraum bzw. zu Weltraumreisen.

 Major Tom (Coming Home) (David Lodge/Peter Schilling)
 Space Oddity (David Bowie)
 In a Little While (Bono, Adam Clayton, The Edge, Larry Mullen junior)
 Space Cowboy (Steve Miller, Ben Sidran)
 Space Truckin' (Ritchie Blackmore, Ian Gillan, Roger Glover, Jon Lord, Ian Paice)
 Rocket Man (Elton John, Bernie Taupin) (previously performed by Shatner in 1978)
 She Blinded Me with Science (Thomas Dolby, Jo Kerr)
 Walking on the Moon (Sting)
 Spirit in the Sky (Norman Greenbaum)
 Bohemian Rhapsody (Freddie Mercury)
 Silver Machine (Robert Calvert, Dave Brock)
 Mrs. Major Tom (Kirby Ian Andersen)
 Empty Glass
 Lost in the Stars (Kurt Weill, Maxwell Anderson)
 Learning to Fly (David Gilmour, Anthony Moore, Bob Ezrin, Jon Carin)
 Mr. Spaceman (Roger McGuinn)
 Twilight Zone (George Kooymans)
 Struggle (William Shatner, Adam Hamilton)
 Iron Man (Tony Iommi, Ozzy Osbourne, Geezer Butler, Bill Ward)
 Planet Earth (Simon Le Bon, Nick Rhodes, John Taylor, Roger Taylor, Andy Taylor)

Quellen

Weblinks

Album (Rock)
Album 2011
Konzeptalbum

Seeking Major Tom


In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory.

In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements. For instance, the class P is the set of decision problems solvable by a deterministic Turing machine in polynomial time. There are, however, many complexity classes defined in terms of other types of problems (e.g. counting problems and function problems) and using other models of computation (e.g. probabilistic Turing machines, interactive proof systems, Boolean circuits, and quantum computers).

The study of the relationships between complexity classes is a major area of research in theoretical computer science. There are often general hierarchies of complexity classes; for example, it is known that a number of fundamental time and space complexity classes relate to each other in the following way: NL⊆P⊆NP⊆PSPACE⊆EXPTIME⊆EXPSPACE (where ⊆ denotes the subset relation). However, many relationships are not yet known; for example, one of the most famous open problems in computer science concerns whether P equals NP. The relationships between classes often answer questions about the fundamental nature of computation. The P versus NP problem, for instance, is directly related to questions of whether nondeterminism adds any computational power to computers and whether problems having solutions that can be quickly checked for correctness can also be quickly solved.

Background
Complexity classes are sets of related computational problems. They are defined in terms of the computational difficulty of solving the problems contained within them with respect to particular computational resources like time or memory. More formally, the definition of a complexity class consists of three things: a type of computational problem, a model of computation, and a bounded computational resource. In particular, most complexity classes consist of decision problems that can be solved by a Turing machine with bounded time or space resources. For example, the complexity class P is defined as the set of decision problems that can be solved by a deterministic Turing machine in polynomial time.

Computational problems
Intuitively, a computational problem is just a question that can be solved by an algorithm. For example, "is the natural number  prime?" is a computational problem. A computational problem is mathematically represented as the set of answers to the problem. In the primality example, the problem (call it ) is represented by the set of all natural numbers that are prime: . In the theory of computation, these answers are represented as strings; for example, in the primality example the natural numbers could be represented as strings of bits that represent binary numbers. For this reason, computational problems are often synonymously referred to as languages, since strings of bits represent formal languages (a concept borrowed from linguistics); for example, saying that the  problem is in the complexity class NP is equivalent to saying that the language  is in NP.

Decision problems

The most commonly analyzed problems in theoretical computer science are decision problems—the kinds of problems that can be posed as yes–no questions. The primality example above, for instance, is an example of a decision problem as it can be represented by the yes–no question "is the natural number  prime". In terms of the theory of computation, a decision problem is represented as the set of input strings that a computer running a correct algorithm would answer "yes" to. In the primality example,  is the set of strings representing natural numbers that, when input into a computer running an algorithm that correctly tests for primality, the algorithm answers "yes, this number is prime". This "yes-no" format is often equivalently stated as "accept-reject"; that is, an algorithm "accepts" an input string if the answer to the decision problem is "yes" and "rejects" if the answer is "no".

While some problems cannot easily be expressed as decision problems, they nonetheless encompass a broad range of computational problems. Other types of problems that certain complexity classes are defined in terms of include function problems (e.g. FP), counting problems (e.g. #P), optimization problems, and promise problems (see section "Other types of problems").

Computational models
To make concrete the notion of a "computer", in theoretical computer science problems are analyzed in the context of a computational model. Computational models make exact the notions of computational resources like "time" and "memory". In computational complexity theory, complexity classes deal with the inherent resource requirements of problems and not the resource requirements that depend upon how a physical computer is constructed. For example, in the real world different computers may require different amounts of time and memory to solve the same problem because of the way that they have been engineered. By providing an abstract mathematical representations of computers, computational models abstract away superfluous complexities of the real world (like differences in processor speed) that obstruct an understanding of fundamental principles.

The most commonly used computational model is the Turing machine. While other models exist and many complexity classes are defined in terms of them (see section "Other models of computation"), the Turing machine is used to define most basic complexity classes. With the Turing machine, instead of using standard units of time like the second (which make it impossible to disentangle running time from the speed of physical hardware) and standard units of memory like bytes, the notion of time is abstracted as the number of elementary steps that a Turing machine takes to solve a problem and the notion of memory is abstracted as the number of cells that are used on the machine's tape. These are explained in greater detail below.

It is also possible to use the Blum axioms to define complexity classes without referring to a concrete computational model, but this approach is less frequently used in complexity theory.

Deterministic Turing machines

A Turing machine is a mathematical model of a general computing machine. It is the most commonly used model in complexity theory, owing in large part to the fact that it is believed to be as powerful as any other model of computation and is easy to analyze mathematically. Importantly, it is believed that if there exists an algorithm that solves a particular problem then there also exists a Turing machine that solves that same problem (this is known as the Church–Turing thesis); this means that it is believed that every algorithm can be represented as a Turing machine.

Mechanically, a Turing machine (TM) manipulates symbols (generally restricted to the bits 0 and 1 to provide an intuitive connection to real-life computers) contained on an infinitely long strip of tape. The TM can read and write, one at a time, using a tape head. Operation is fully determined by a finite set of elementary instructions such as "in state 42, if the symbol seen is 0, write a 1; if the symbol seen is 1, change into state 17; in state 17, if the symbol seen is 0, write a 1 and change to state 6". The Turing machine starts with only the input string on its tape and blanks everywhere else. The TM accepts the input if it enters a designated accept state and rejects the input if it enters a reject state. The deterministic Turing machine (DTM) is the most basic type of Turing machine. It uses a fixed set of rules to determine its future actions (which is why it is called "deterministic").

A computational problem can then be defined in terms of a Turing machine as the set of input strings that a particular Turing machine accepts. For example, the primality problem  from above is the set of strings (representing natural numbers) that a Turing machine running an algorithm that correctly tests for primality accepts. A Turing machine is said to recognize a language (recall that "problem" and "language" are largely synonymous in computability and complexity theory) if it accepts all inputs that are in the language and is said to decide a language if it additionally rejects all inputs that are not in the language (certain inputs may cause a Turing machine to run forever, so decidability places the additional constraint over recognizability that the Turing machine must halt on all inputs). A Turing machine that "solves" a problem is generally meant to mean one that decides the language.

Turing machines enable intuitive notions of "time" and "space". The time complexity of a TM on a particular input is the number of elementary steps that the Turing machine takes to reach either an accept or reject state. The space complexity is the number of cells on its tape that it uses to reach either an accept or reject state.

Nondeterministic Turing machines

The deterministic Turing machine (DTM) is a variant of the nondeterministic Turing machine (NTM). Intuitively, an NTM is just a regular Turing machine that has the added capability of being able to explore multiple possible future actions from a given state, and "choosing" a branch that accepts (if any accept). That is, while a DTM must follow only one branch of computation, an NTM can be imagined as a computation tree, branching into many possible computational pathways at each step (see image). If at least one branch of the tree halts with an "accept" condition, then the NTM accepts the input. In this way, an NTM can be thought of as simultaneously exploring all computational possibilities in parallel and selecting an accepting branch. NTMs are not meant to be physically realizable models, they are simply theoretically interesting abstract machines that give rise to a number of interesting complexity classes (which often do have physically realizable equivalent definitions).

The time complexity of an NTM is the maximum number of steps that the NTM uses on any branch of its computation. Similarly, the space complexity of an NTM is the maximum number of cells that the NTM uses on any branch of its computation.

DTMs can be viewed as a special case of NTMs that do not make use of the power of nondeterminism. Hence, every computation that can be carried out by a DTM can also be carried out by an equivalent NTM. It is also possible to simulate any NTM using a DTM (the DTM will simply compute every possible computational branch one-by-one). Hence, the two are equivalent in terms of computability. However, simulating an NTM with a DTM often requires greater time and/or memory resources; as will be seen, how significant this slowdown is for certain classes of computational problems is an important question in computational complexity theory.

Resource bounds
Complexity classes group computational problems by their resource requirements. To do this, computational problems are differentiated by upper bounds on the maximum amount of resources that the most efficient algorithm takes to solve them. More specifically, complexity classes are concerned with the rate of growth in the resources required to solve particular computational problems as the input size increases. For example, the amount of time it takes to solve problems in the complexity class P grows at a polynomial rate as the input size increases, which is comparatively slow compared to problems in the exponential complexity class EXPTIME (or more accurately, for problems in EXPTIME that are outside of P, since ).

Note that the study of complexity classes is intended primarily to understand the inherent complexity required to solve computational problems. Complexity theorists are thus generally concerned with finding the smallest complexity class that a problem falls into and are therefore concerned with identifying which class a computational problem falls into using the most efficient algorithm. There may be an algorithm, for instance, that solves a particular problem in exponential time, but if the most efficient algorithm for solving this problem runs in polynomial time then the inherent time complexity of that problem is better described as polynomial.

Time bounds

The time complexity of an algorithm with respect to the Turing machine model is the number of steps it takes for a Turing machine to run an algorithm on a given input size. Formally, the time complexity for an algorithm implemented with a Turing machine  is defined as the function , where  is the maximum number of steps that  takes on any input of length .

In computational complexity theory, theoretical computer scientists are concerned less with particular runtime values and more with the general class of functions that the time complexity function falls into. For instance, is the time complexity function a polynomial? A logarithmic function? An exponential function? Or another kind of function?

Space bounds

The space complexity of an algorithm with respect to the Turing machine model is the number of cells on the Turing machine's tape that are required to run an algorithm on a given input size. Formally, the space complexity of an algorithm implemented with a Turing machine  is defined as the function , where  is the maximum number of cells that  uses on any input of length .

Basic complexity classes

Basic definitions
Complexity classes are often defined using granular sets of complexity classes called DTIME and NTIME (for time complexity) and DSPACE and NSPACE (for space complexity). Using big O notation, they are defined as follows:
 The time complexity class  is the set of all problems that are decided by an  time deterministic Turing machine.
 The time complexity class  is the set of all problems that are decided by an  time nondeterministic Turing machine.
 The space complexity class  is the set of all problems that are decided by an  space deterministic Turing machine.
 The space complexity class  is the set of all problems that are decided by an  space nondeterministic Turing machine.

Time complexity classes

P and NP

P is the class of problems that are solvable by a deterministic Turing machine in polynomial time and NP is the class of problems that are solvable by a nondeterministic Turing machine in polynomial time. Or more formally,

P is often said to be the class of problems that can be solved "quickly" or "efficiently" by a deterministic computer, since the time complexity of solving a problem in P increases relatively slowly with the input size.

An important characteristic of the class NP is that it can be equivalently defined as the class of problems whose solutions are verifiable by a deterministic Turing machine in polynomial time. That is, a language is in NP if there exists a deterministic polynomial time Turing machine, referred to as the verifier, that takes as input a string  and a polynomial-size certificate string , and accepts  if  is in the language and rejects  if  is not in the language. Intuitively, the certificate acts as a proof that the input  is in the language. Formally:
 NP is the class of languages  for which there exists a polynomial-time deterministic Turing machine  and a polynomial  such that for all ,  is in  if and only if there exists some  such that  accepts.

This equivalence between the nondeterministic definition and the verifier definition highlights a fundamental connection between nondeterminism and solution verifiability. Furthermore, it also provides a useful method for proving that a language is in NP—simply identify a suitable certificate and show that it can be verified in polynomial time.

The P versus NP problem
While there might seem to be an obvious difference between the class of problems that are efficiently solvable and the class of problems whose solutions are merely efficiently checkable, P and NP are actually at the center of one of the most famous unsolved problems in computer science: the P versus NP problem. While it is known that PNP (intuitively, deterministic Turing machines are just a subclass of nondeterministic Turing machines that don't make use of their nondeterminism; or under the verifier definition, P is the class of problems whose polynomial time verifiers need only receive the empty string as their certificate), it is not known whether NP is strictly larger than P. If P=NP, then it follows that nondeterminism provides no additional computational power over determinism with regards to the ability to quickly find a solution to a problem; that is, being able to explore all possible branches of computation provides at most a polynomial speedup over being able to explore only a single branch. Furthermore, it would follow that if there exists a proof for a problem instance and that proof can be quickly be checked for correctness (that is, if the problem is in NP), then there also exists an algorithm that can quickly construct that proof (that is, the problem is in P). However, the overwhelming majority of computer scientists believe that PNP, and most cryptographic schemes employed today rely on the assumption that PNP.

EXPTIME and NEXPTIME

EXPTIME (sometimes shortened to EXP) is the class of decision problems solvable by a deterministic Turing machine in exponential time and NEXPTIME (sometimes shortened to NEXP) is the class of decision problems solvable by a nondeterministic Turing machine in exponential time. Or more formally,

EXPTIME is a strict superset of P and NEXPTIME is a strict superset of NP. It is further the case that EXPTIMENEXPTIME. It is not known whether this is proper, but if P=NP then EXPTIME must equal NEXPTIME.

Space complexity classes

L and NL

While it is possible to define logarithmic time complexity classes, these are extremely narrow classes as sublinear times do not even enable a Turing machine to read the entire input (because ). However, there are a meaningful number of problems that can be solved in logarithmic space. The definitions of these classes require a two-tape Turing machine so that it is possible for the machine to store the entire input (it can be shown that in terms of computability the two-tape Turing machine is equivalent to the single-tape Turing machine). In the two-tape Turing machine model, one tape is the input tape, which is read-only. The other is the work tape, which allows both reading and writing and is the tape on which the Turing machine performs computations. The space complexity of the Turing machine is measured as the number of cells that are used on the work tape.

L (sometimes lengthened to LOGSPACE) is then defined as the class of problems solvable in logarithmic space on a deterministic Turing machine and NL (sometimes lengthened to NLOGSPACE) is the class of problems solvable in logarithmic space on a nondeterministic Turing machine. Or more formally,

It is known that . However, it is not known whether any of these relationships is proper.

PSPACE and NPSPACE

The complexity classes PSPACE and NPSPACE are the space analogues to  P and  NP. That is, PSPACE is the class of problems solvable in polynomial space by a deterministic Turing machine and NPSPACE is the class of problems solvable in polynomial space by a nondeterministic Turing machine. More formally,

While it is not known whether P=NP, Savitch's theorem  famously showed that PSPACE=NPSPACE. It is also known that PPSPACE, which follows intuitively from the fact that, since writing to a cell on a Turing machine's tape is defined as taking one unit of time, a Turing machine operating in polynomial time can only write to polynomially many cells. It is suspected that P is strictly smaller than PSPACE, but this has not been proven.

EXPSPACE and NEXPSPACE

The complexity classes EXPSPACE and NEXPSPACE are the space analogues to EXPTIME and NEXPTIME. That is, EXPSPACE is the class of problems solvable in exponential space by a deterministic Turing machine and NEXPSPACE is the class of problems solvable in exponential space by a nondeterministic Turing machine. Or more formally,

Savitch's theorem showed that EXPSPACE=NEXPSPACE. This class is extremely broad: it is known to be a strict superset of PSPACE, NP, and P, and is believed to be a strict superset of EXPTIME.

Properties of complexity classes

Closure
Complexity classes have a variety of closure properties. For example, decision classes may be closed under negation, disjunction, conjunction, or even under all Boolean operations. Moreover, they might also be closed under a variety of quantification schemes. P, for instance, is closed under all Boolean operations, and under quantification over polynomially sized domains. Closure properties can be helpful in separating classes—one possible route to separating two complexity classes is to find some closure property possessed by one class but not by the other.

Each class X that is not closed under negation has a complement class co-X, which consists of the complements of the languages contained in X (i.e. co-X= X ). co-NP, for instance, is one important complement complexity class, and sits at the center of the unsolved problem over whether co-NP=NP.

Closure properties are one of the key reasons many complexity classes are defined in the way that they are. Take, for example, a problem that can be solved in  time (that is, in linear time) and one that can be solved in, at best,  time. Both of these problems are in P, yet the runtime of the second grows considerably faster than the runtime of the first as the input size increases. One might ask whether it would be better to define the class of "efficiently solvable" problems using some smaller polynomial bound, like , rather than all polynomials, which allows for such large discrepancies. It turns out, however, that the set of all polynomials is the smallest class of functions containing the linear functions that is also closed under addition, multiplication, and composition (for instance, , which is a polynomial but ). Since we would like composing one efficient algorithm with another efficient algorithm to still be considered efficient, the polynomials are the smallest class that ensures composition of "efficient algorithms". (Note that the definition of P is also useful because, empirically, almost all problems in P that are practically useful do in fact have low order polynomial runtimes, and almost all problems outside of P that are practically useful do not have any known algorithms with small exponential runtimes, i.e. with  runtimes where  is close to 1.)

Reductions

Many complexity classes are defined using the concept of a reduction. A reduction is a transformation of one problem into another problem, i.e. a reduction takes inputs from one problem and transforms them into inputs of another problem. For instance, you can reduce ordinary base-10 addition  to base-2 addition by transforming  and  to their base-2 notation (e.g. 5+7 becomes 101+111). Formally, a problem  reduces to a problem  if there exists a function  such that for every ,  if and only if .

Generally, reductions are used to capture the notion of a problem being at least as difficult as another problem. Thus we are generally interested in using a polynomial-time reduction, since any problem  that can be efficiently reduced to another problem  is no more difficult than . Formally, a problem  is polynomial-time reducible to a problem  if there exists a polynomial-time computable function  such that for all ,  if and only if .

Note that reductions can be defined in many different ways. Common reductions are Cook reductions, Karp reductions and Levin reductions, and can vary based on resource bounds, such as polynomial-time reductions and log-space reductions.

Hardness
Reductions motivate the concept of a problem being hard for a complexity class. A problem  is hard for a class of problems C if every problem in C can be polynomial-time reduced to . Thus no problem in C is harder than , since an algorithm for  allows us to solve any problem in C with at most polynomial slowdown. Of particular importance, the set of problems that are hard for NP is called the set of NP-hard problems.

Completeness
If a problem  is hard for C and is also in C, then  is said to be complete for C. This means that  is the hardest problem in C (since there could be many problems that are equally hard, more precisely  is as hard as the hardest problems in C).

Of particular importance is the class of NP-complete problems—the most difficult problems in NP. Because all problems in NP can be polynomial-time reduced to NP-complete problems, finding an NP-complete problem that can be solved in polynomial time would mean that P = NP.

Relationships between complexity classes

Savitch's theorem

Savitch's theorem establishes the relationship between deterministic and nondetermistic space resources. It shows that if a nondeterministic Turing machine can solve a problem using  space, then a deterministic Turing machine can solve the same problem in  space, i.e. in the square of the space. Formally, Savitch's theorem states that for any ,

Important corollaries of Savitch's theorem are that PSPACE = NPSPACE (since the square of a polynomial is still a polynomial) and EXPSPACE = NEXPSPACE (since the square of an exponential is still an exponential).

These relationships answer fundamental questions about the power of nondeterminism compared to determinism. Specifically, Savitch's theorem shows that any problem that a nondeterministic Turing machine can solve in polynomial space, a deterministic Turing machine can also solve in polynomial space. Similarly, any problem that a nondeterministic Turing machine can solve in exponential space, a deterministic Turing machine can also solve in exponential space.

Hierarchy theorems

By definition of DTIME, it follows that  is contained in  if , since  if . However, this definition gives no indication of whether this inclusion is strict. For time and space requirements, the conditions under which the inclusion is strict are given by the time and space hierarchy theorems, respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined by constraining the respective resources. The hierarchy theorems enable one to make quantitative statements about how much more additional time or space is needed in order to increase the number of problems that can be solved.

The time hierarchy theorem states that
.

The space hierarchy theorem states that
.

The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem establishes that P is strictly contained in EXPTIME, and the space hierarchy theorem establishes that L is strictly contained in PSPACE.

Other models of computation
While deterministic and non-deterministic Turing machines are the most commonly used models of computation, many complexity classes are defined in terms of other computational models. In particular,
 A number of classes are defined using probabilistic Turing machines, including the classes BPP, PP, RP, and ZPP
 A number of classes are defined using interactive proof systems, including the classes IP, MA, and AM
 A number of classes are defined using Boolean circuits, including the classes P/poly and its subclasses NC and AC
 A number of classes are defined using quantum Turing machines, including the classes BQP and QMA

These are explained in greater detail below.

Randomized computation

A number of important complexity classes are defined using the probabilistic Turing machine, a variant of the Turing machine that can toss random coins. These classes help to better describe the complexity of randomized algorithms.

A probabilistic Turing machine is similar to a deterministic Turing machine, except rather than following a single transition function (a set of rules for how to proceed at each step of the computation) it probabilistically selects between multiple transition functions at each step. The standard definition of a probabilistic Turing machine specifies two transition functions, so that the selection of transition function at each step resembles a coin flip. The randomness introduced at each step of the computation introduces the potential for error; that is, strings that the Turing machine is meant to accept may on some occasions be rejected and strings that the Turing machine is meant to reject may on some occasions be accepted. As a result, the complexity classes based on the probabilistic Turing machine are defined in large part around the amount of error that is allowed. Formally, they are defined using an error probability . A probabilistic Turing machine  is said to recognize a language  with error probability  if:
 a string  in  implies that
 a string  not in  implies that

Important complexity classes

The fundamental randomized time complexity classes are ZPP, RP, co-RP, BPP, and PP.

The strictest class is ZPP (zero-error probabilistic polynomial time), the class of problems solvable in polynomial time by a probabilistic Turing machine with error probability 0. Intuitively, this is the strictest class of probabilistic problems because it demands no error whatsoever.

A slightly looser class is RP (randomized polynomial time), which maintains no error for strings not in the language but allows bounded error for strings in the language. More formally, a language is in RP if there is a probabilistic polynomial-time Turing machine  such that if a string is not in the language then  always rejects and if a string is in the language then  accepts with a probability at least 1/2. The class co-RP is similarly defined except the roles are flipped: error is not allowed for strings in the language but is allowed for strings not in the language. Taken together, the classes RP and co-RP encompass all of the problems that can be solved by probabilistic Turing machines with one-sided error.

Loosening the error requirements further to allow for two-sided error yields the class BPP (bounded-error probabilistic polynomial time), the class of problems solvable in polynomial time by a probabilistic Turing machine with error probability less than 1/3 (for both strings in the language and not in the language). BPP is the most practically relevant of the probabilistic complexity classes—problems in BPP have efficient randomized algorithms that can be run quickly on real computers. BPP is also at the center of the important unsolved problem in computer science over whether P=BPP, which if true would mean that randomness does not increase the computational power of computers, i.e. any probabilistic Turing machine could be simulated by a deterministic Turing machine with at most polynomial slowdown.

The broadest class of efficiently-solvable probabilistic problems is PP (probabilistic polynomial time), the set of languages solvable by a probabilistic Turing machine in polynomial time with an error probability of less than 1/2 for all strings.

ZPP, RP and co-RP are all subsets of BPP, which in turn is a subset of PP. The reason for this is intuitive: the classes allowing zero error and only one-sided error are all contained within the class that allows two-sided error, and PP simply relaxes the error probability of BPP. ZPP relates to RP and co-RP in the following way: . That is, ZPP consists exactly of those problems that are in both RP and co-RP. Intuitively, this follows from the fact that RP and co-RP allow only one-sided error: co-RP does not allow error for strings in the language and RP does not allow error for strings not in the language. Hence, if a problem is in both RP and co-RP, then there must be no error for strings both in and not in the language (i.e. no error whatsoever), which is exactly the definition of ZPP.

Important randomized space complexity classes include BPL, RL, and RLP.

Interactive proof systems

A number of complexity classes are defined using interactive proof systems. Interactive proofs generalize the proofs definition of the complexity class NP and yield insights into cryptography, approximation algorithms, and formal verification.

Interactive proof systems are abstract machines that model computation as the exchange of messages between two parties: a prover  and a verifier . The parties interact by exchanging messages, and an input string is accepted by the system if the verifier decides to accept the input on the basis of the messages it has received from the prover. The prover  has unlimited computational power while the verifier has bounded computational power (the standard definition of interactive proof systems defines the verifier to be polynomially-time bounded). The prover, however, is untrustworthy (this prevents all languages from being trivially recognized by the proof system by having the computationally unbounded prover solve for whether a string is in a language and then sending a trustworthy "YES" or "NO" to the verifier), so the verifier must conduct an "interrogation" of the prover by "asking it" successive rounds of questions, accepting only if it develops a high degree of confidence that the string is in the language.

Important complexity classes
The class NP is a simple proof system in which the verifier is restricted to being a deterministic polynomial-time Turing machine and the procedure is restricted to one round (that is, the prover sends only a single, full proof—typically referred to as the certificate—to the verifier). Put another way, in the definition of the class NP (the set of decision problems for which the problem instances, when the answer is "YES", have proofs verifiable in polynomial time by a deterministic Turing machine) is a proof system in which the proof is constructed by an unmentioned prover and the deterministic Turing machine is the verifier. For this reason, NP can also be called dIP (deterministic interactive proof), though it is rarely referred to as such.

It turns out that NP captures the full power of interactive proof systems with deterministic (polynomial-time) verifiers because it can be shown that for any proof system with a deterministic verifier it is never necessary to need more than a single round of messaging between the prover and the verifier. Interactive proof systems that provide greater computational power over standard complexity classes thus require probabilistic verifiers, which means that the verifier's questions to the prover are computed using probabilistic algorithms. As noted in the section above on randomized computation, probabilistic algorithms introduce error into the system, so complexity classes based on probabilistic proof systems are defined in terms of an error probability .

The most general complexity class arising out of this characterization is the class IP (interactive polynomial time), which is the class of all problems solvable by an interactive proof system , where  is probabilistic polynomial-time and the proof system satisfies two properties: for a language
 (Completeness) a string  in  implies
 (Soundness) a string  not in  implies

An important feature of IP is that it equals PSPACE. In other words, any problem that can be solved by a polynomial-time interactive proof system can also be solved by a deterministic Turing machine with polynomial space resources, and vice versa.

A modification of the protocol for IP produces another important complexity class: AM (Arthur–Merlin protocol). In the definition of interactive proof systems used by IP, the prover was not able to see the coins utilized by the verifier in its probabilistic computation—it was only able to see the messages that the verifier produced with these coins. For this reason, the coins are called private random coins. The interactive proof system can be constrained so that the coins used by the verifier are public random coins; that is, the prover is able to see the coins. Formally, AM is defined as the class of languages with an interactive proof in which the verifier sends a random string to the prover, the prover responds with a message, and the verifier either accepts or rejects by applying a deterministic polynomial-time function to the message from the prover. AM can be generalized to AM[k], where k is the number of messages exchanged (so in the generalized form the standard AM defined above is AM[2]). However, it is the case that for all , AM[k]=AM[2]. It is also the case that .

Other complexity classes defined using interactive proof systems include MIP (multiprover interactive polynomial time) and QIP (quantum interactive polynomial time).

Boolean circuits

An alternative model of computation to the Turing machine is the Boolean circuit, a simplified model of the digital circuits used in modern computers. Not only does this model provide an intuitive connection between computation in theory and computation in practice, but it is also a natural model for non-uniform computation (computation in which different input sizes within the same problem use different algorithms).

Formally, a Boolean circuit  is a directed acyclic graph in which edges represent wires (which carry the bit values 0 and 1), the input bits are represented by source vertices (vertices with no incoming edges), and all non-source vertices represent logic gates (generally the AND, OR, and NOT gates). One logic gate is designated the output gate, and represents the end of the computation. The input/output behavior of a circuit  with  input variables is represented by the Boolean function ; for example, on input bits , the output bit  of the circuit is represented mathematically as . The circuit  is said to compute the Boolean function .

Any particular circuit has a fixed number of input vertices, so it can only act on inputs of that size. Languages (the formal representations of decision problems), however, contain strings of differing lengths, so languages cannot be fully captured by a single circuit (this contrasts with the Turing machine model, in which a language is fully described by a single Turing machine that can act on any input size). A language is thus represented by a circuit family. A circuit family is an infinite list of circuits , where  is a circuit with  input variables. A circuit family is said to decide a language  if, for every string ,  is in the language  if and only if , where  is the length of . In other words, a string  of size  is in the language represented by the circuit family  if the circuit  (the circuit with the same number of input vertices as the number of bits in ) evaluates to 1 when  is its input.

While complexity classes defined using Turing machines are described in terms of time complexity, circuit complexity classes are defined in terms of circuit size — the number of vertices in the circuit. The size complexity of a circuit family  is the function , where  is the circuit size of . The familiar function classes follow naturally from this; for example, a polynomial-size circuit family is one such that the function  is a polynomial.

Important complexity classes
The complexity class P/poly is the set of languages that are decidable by polynomial-size circuit families. It turns out that there is a natural connection between circuit complexity and time complexity. Intuitively, a language with small time complexity (that is, requires relatively few sequential operations on a Turing machine), also has a small circuit complexity (that is, requires relatively few Boolean operations). Formally, it can be shown that if a language is in , where  is a function , then it has circuit complexity . It follows directly from this fact that . In other words, any problem that can be solved in polynomial time by a deterministic Turing machine can also be solved by a polynomial-size circuit family. It is further the case that the inclusion is proper, i.e.  (for example, there are some undecidable problems that are in P/poly).

P/poly has a number of properties that make it highly useful in the study of the relationships between complexity classes. In particular, it is helpful in investigating problems related to P versus NP. For example, if there is any language in NP that is not in P/poly, then . P/poly is also helpful in investigating properties of the polynomial hierarchy. For example, if NP ⊆ P/poly, then PH collapses to . A full description of the relations between P/poly and other complexity classes is available at "Importance of P/poly". P/poly is also helpful in the general study of the properties of Turing machines, as the class can be equivalently defined as the class of languages recognized by a polynomial-time Turing machine with a polynomial-bounded advice function.

Two subclasses of P/poly that have interesting properties in their own right are NC and AC. These classes are defined not only in terms of their circuit size but also in terms of their depth. The depth of a circuit is the length of the longest directed path from an input node to the output node. The class NC is the set of languages that can be solved by circuit families that are restricted not only to having polynomial-size but also to having polylogarithmic depth. The class AC is defined similarly to NC, however gates are allowed to have unbounded fan-in (that is, the AND and OR gates can be applied to more than two bits). NC is a notable class because it can be equivalently defined as the class of languages that have efficient parallel algorithms.

Quantum computation

The classes BQP and QMA, which are of key importance in quantum information science, are defined using quantum Turing machines.

Other types of problems
While most complexity classes studied by computer scientists are sets of decision problems, there are also a number of complexity classes defined in terms of other types of problems. In particular, there are complexity classes consisting of counting problems, function problems, and promise problems. These are explained in greater detail below.

Counting problems

A counting problem asks not only whether a solution exists (as with a decision problem), but asks how many solutions exist. For example, the decision problem  asks whether a particular graph  has a simple cycle (the answer is a simple yes/no); the corresponding counting problem  (pronounced "sharp cycle") asks how many simple cycles  has. The output to a counting problem is thus a number, in contrast to the output for a decision problem, which is a simple yes/no (or accept/reject, 0/1, or other equivalent scheme).

Thus, whereas decision problems are represented mathematically as formal languages, counting problems are represented mathematically as functions: a counting problem is formalized as the function  such that for every input ,  is the number of solutions. For example, in the  problem, the input is a graph  (a graph represented as a string of bits) and  is the number of simple cycles in .

Counting problems arise in a number of fields, including statistical estimation, statistical physics, network design, and economics.

Important complexity classes

#P (pronounced "sharp P") is an important class of counting problems that can be thought of as the counting version of NP. The connection to NP arises from the fact that the number of solutions to a problem equals the number of accepting branches in a nondeterministic Turing machine's computation tree. #P is thus formally defined as follows:
 #P is the set of all functions  such that there is a polynomial time nondeterministic Turing machine  such that for all ,  equals the number of accepting branches in 's computation tree on .

And just as NP can be defined both in terms of nondeterminism and in terms of a verifier (i.e. as an interactive proof system), so too can #P be equivalently defined in terms of a verifier. Recall that a decision problem is in NP if there exists a polynomial-time checkable certificate to a given problem instance—that is, NP asks whether there exists a proof of membership (a certificate) for the input that can be checked for correctness in polynomial time. The class #P asks how many such certificates exist. In this context, #P is defined as follows:
 #P is the set of functions  such that there exists a polynomial  and a polynomial-time Turing machine  (the verifier), such that for every , . In other words,  equals the size of the set containing all of the polynomial-size certificates for .

Function problems

Counting problems are a subset of a broader class of problems called function problems. A function problem is a type of problem in which the values of a function  are computed. Formally, a function problem  is defined as a relation  over strings of an arbitrary alphabet :

An algorithm solves  if for every input  such that there exists a  satisfying , the algorithm produces one such . This is just another way of saying that  is a function and the algorithm solves  for all .

Important complexity classes
An important function complexity class is FP, the class of efficiently solvable functions. More specifically, FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial time. FP can be thought of as the function problem equivalent of P. Importantly, FP provides some insight into both counting problems and P versus NP. If #P=FP, then the functions that determine the number of certificates for problems in NP are efficiently solvable. And since computing the number of certificates is at least as hard as determining whether a certificate exists, it must follow that if #P=FP then P=NP (it is not known whether this holds in the reverse, i.e. whether P=NP implies #P=FP).

Just as FP is the function problem equivalent of P, FNP is the function problem equivalent of NP. Importantly, FP=FNP if and only if P=NP.

Promise problems

Promise problems are a generalization of decision problems in which the input to a problem is guaranteed ("promised") to be from a particular subset of all possible inputs. Recall that with a decision problem , an algorithm  for  must act (correctly) on every . A promise problem loosens the input requirement on  by restricting the input to some subset of .

Specifically, a promise problem is defined as a pair of non-intersecting sets , where:
  is the set of all inputs that are accepted.
  is the set of all inputs that are rejected.

The input to an algorithm  for a promise problem  is thus , which is called the promise. Strings in  are said to satisfy the promise. By definition,  and  must be disjoint, i.e. .

Within this formulation, it can be seen that decision problems are just the subset of promise problems with the trivial promise . With decision problems it is thus simpler to simply define the problem as only  (with  implicitly being ), which throughout this page is denoted  to emphasize that  is a formal language.

Promise problems make for a more natural formulation of many computational problems. For instance, a computational problem could be something like "given a planar graph, determine whether or not..." This is often stated as a decision problem, where it is assumed that there is some translation schema that takes every string  to a planar graph. However, it is more straightforward to define this as a promise problem in which the input is promised to be a planar graph.

Relation to complexity classes
Promise problems provide an alternate definition for standard complexity classes of decision problems. P, for instance, can be defined as a promise problem:
 P is the class of promise problems that are solvable in deterministic polynomial time. That is, the promise problem  is in P if there exists a polynomial-time algorithm  such that:
 For every
 For ever

Classes of decision problems—that is, classes of problems defined as formal languages—thus translate naturally to promise problems, where a language  in the class is simply  and  is implicitly .

Formulating many basic complexity classes like P as promise problems provides little additional insight into their nature. However, there are some complexity classes for which formulating them as promise problems have been useful to computer scientists. Promise problems have, for instance, played a key role in the study of SZK (statistical zero-knowledge).

Summary of relationships between complexity classes
The following table shows some of the classes of problems that are considered in complexity theory.  If class X is a strict subset of Y, then X is shown below Y with a dark line connecting them.  If X is a subset, but it is unknown whether they are equal sets, then the line is lighter and dotted. Technically, the breakdown into decidable and undecidable pertains more to the study of computability theory, but is useful for putting the complexity classes in perspective.

See also
 List of complexity classes

Notes

References

Bibliography

Further reading
The Complexity Zoo : A huge list of complexity classes, a reference for experts.
 Includes a diagram showing the hierarchy of complexity classes and how they fit together.
Michael Garey, and David S. Johnson: Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman & Co., 1979.  The standard reference on NP-Complete problems - an important category of problems whose solutions appear to require an impractically long time to compute.

Measures of complexity
Theoretical computer science

Complexity class


Thoreaceae, porodica crvenih algi smještena u vlastiti red Thoreales, i dio je podrazreda Nemaliophycidae. Priznato je 20 vrsta, a ime je došlo po rodu Thorea.

Rodovi
 Nemalionopsis Skuja   (3)
 Thorea Bory   (17)

Izvori

Nemaliophycidae

Thoreaceae


Abraham Mansfarroll, né le 13 avril 1974, est un musicien, auteur, compositeur et percussionniste cubain. Diplômé de l'E.N.A (École Nationale d'Art), il continue ses études à l'Institut Supérieur des Arts de La Havane (ISA), l'équivalent d'un conservatoire national de musique, où après son diplôme, il reste en tant que professeur de percussions.

En 1997, il a créé son projet de percussions Pi-A-Pa et entame une tournée en France en collaboration avec l'ensemble vocal Soli-Tutti. Avec le groupe Sintesis et celui du flûtiste cubain Orlando « Maraca » Valle dont il fait partie, il participe aux divers festivals de la Havane, ainsi qu'à l'étranger (Espagne, Belgique, France, Suisse, États-Unis…)

En 2002, en tournée avec Las Hermanas Faez et Casa de la Trova, il retrouve la France et décide de s'y installer définitivement.Depuis, il a poursuivi une collaboration régulière avec des musiciens et des formations d'univers variés tels que : Ernesto Tito Puentes, Patrice Caratini, Julien Lourau, Alfredo Rodriguez, Charles Aznavour, Patrice Caratini, Julien Lourau, David Murray, Michel Fugain, Fred Pallem, Papa Wemba, aussi Chucho Valdes (Jazz Bata 2), Ibrahim Maalouf (S3NS), Clara Luciani...

Mansfarroll participe à l'enregistrement de nombreux CD sous divers labels en France et à l'étranger comme Rosalia, Starmania...

En 2014, Mansfarroll crée le groupe Campana Project autour du jazz afro-cubain. Il y fédère des percussionnistes, violoncellistes, bassistes, cuivres et bois du Pérou, Cuba, Grèce, Maroc, Madagascar... preuve vivante de l'universalité de la musique telle que la conçoit Mansfarroll.

Il a composé et édité deux CD : Utopia Guantanamera (2016) et Dizzy el Afrocubano (2021)qu'il a présenté au Festival Jazz à La Villette en septembre 2021.

En 2023, Mansfarroll a été sélectionné "Artiste Génération Spedidam" dans la catégorie "Jazz et musique du monde" et ce, jusqu'en 2025.

Notes et références

Liens externes

Naissance en avril 1974
Musicien cubain de jazz

Abraham Mansfarroll


Jay Harry Feaster, né le  à Harrisburg, dans l'État de la Pennsylvanie aux États-Unis, est un dirigeant américain de Hockey sur glace. Il est le directeur général des Bears de Hershey de 1989 à 1997, puis du Lightning de Tampa Bay de 2002 à 2008 et des Flames de Calgary de 2010 à 2013. Depuis , il occupe le  poste de Directeur exécutif de la promotion du hockey au sein de la communauté du Lightning de Tampa Bay.

Biographie

Éducation
Feaster est diplômé de l'Université de Susquehanna. Durant ces études, il est également président d'une fraternité de musiciens professionnels, le Phi Mu Alpha Sinfonia.

Il poursuit ses études à l'Université de Georgetown et obient un doctorat en droit.

En 1988, il travaille dans un cabinet d'avocat à Harrisburg, McNees, Wallace & Nurick. Pour eux, il est chargé de traiter avec la Hershey Entertainment and Resorts Company (HERCO), la société commerciale derrière les Bears de Hershey.

Bears de Hershey
Alors qu'il ne se sent pas heureux avec ses collègues du cabinet d'avocat, Feaster s'entend à merveille avec ses clients de HERCO. Il propose alors à ses derniers de l'embaucher directement dans leur société. En 1989, il est ainsi embauché à titre de juriste par HERCO et nommé Assistant du directeur général des Bears de Hershey. La saison suivante, il est promu Directeur général de l'équipe. Dans un premier temps, son rôle se limite à l'aspect commercial, les Flyers de Philadelphie fournissant et gérant l'ensemble du contingent de joueurs.

Lors de la saison 1993-1994, Russ Farwell, alors directeur général des Flyers, l'informe qu'il ne peut lui fournir un contingent complet. Feaster fait donc ces premiers pas dans la gestion des opérations hockey, alors qu'il n'a lui-même jamais pratiqué ce sport. Il prolonge Tim Tookey et engage Mitch Lamoureux, Mike McHugh, Denis Metlyuk et Toni Porkka.

Pour la saison 1996-1997, il doit trouver un nouveau club-parent, Robert Clarke, le nouveau directeur général des Flyers décide de stopper le partenariat avec les Bears. Il se tourne vers l'Avalanche du Colorado. Avec Robert Hartley comme entraîneur et un contingent complètement changé, les Bears remportent la Coupe Calder dès la première saison de cette nouvelle collaboration. Feaster remporte le , remis au meilleur directeur général de la Ligue américaine de hockey.

La saison suivante, Les Bears terminent deuxième de la division Mid-Atlantic, derrière les Phantoms de Philadelphie, le nouveau club-école des Flyers. Ironie du sort, c'est ces derniers qui les éliminent en deuxième ronde des Séries éliminatoires. Au terme de la saison, Hartley est promu entraîneur de l'Avalanche.

Lightning de Tampa Bay
Jacques Demers, le directeur général du Lightning de Tampa Bay, se cherche un adjoint. Possédant beaucoup d'expérience dans le domaine hockey, mais peu dans la gestion, il trouve l'entente parfaite avec Feaster. Ce dernier est embauché pour la saison 1998-1999 et s'occupe principalement des affaires légales ainsi que de la gestion de la convention collective.

Lorsque Demers prend sa retraite au terme de la saison, les propriétaires nomme Richard Dudley directeur général et  Feaster reste son assistant. Mais lorsque ce dernier est remercié, Feaster est nommé Directeur Général, le .

Alors que l'équipe a terminé à l'avant-dernière place de la ligue avant sa nomination, il parvient à assembler un effectif qui remporte la Coupe Stanley deux ans plus tard, en 2004. Il est nommé directeur de la LNH de l'année 2004 par vote de ses pairs dans The Sporting News et est classé deuxième parmi les directeurs généraux de sports professionnels par le magazine Forbes en 2007.

En , le Lightning change de propriétaires, William Davidson le cède à Oren Koules et à Len Barrie. Ne s'entendant pas avec ses nouveaux patrons, Feaster donne sa démission le , malgré un contrat valable encore 3 ans.

Flames de Calgay
Après sa démission, il est approché par le Wild du Minnesota et par les Panthers de la Floride, sans que rien se concrétise. Il attend jusqu'au  pour retrouver un emploi avec les Flames de Calgary. Il est nommé Assistant du directeur général, Darryl Sutter.

Le , après avoir demandé à Sutter de poser sa démission, les propriétaires des Flames nomment Feaster Directeur général par intérim. Le , il est définitivement nommé et devient le  Directeur Général de l'histoire des Flames. Le , après avoir congédié le frère de Sutter, Brent, Feaster engage Bob Hartley à titre d'entraîneur-chef des Flames. Après un mauvais départ lors de la saison 2013-2014, Feaster est congédié pour la première fois de sa carrière.

Lightning de Tampa Bay, deuxième passage
Le , le Lightning le nomme Directeur exécutif de la promotion du hockey au sein de la communauté. Sa mission est de travailler avec les associations et établissements de la région de Tampa Bay pour sensibiliser les jeunes au hockey.

Feaster travaillera avec les jeunes locaux pour aider à développer le hockey dans la région de Tampa Bay. Il supervisera et gérera la sensibilisation du Lightning aux programmes de hockey pour les jeunes et les écoles secondaires et augmentera davantage la participation et établira des relations avec les arénas locaux. Le Lightning s'appuiera sur Feaster pour ses excellentes compétences en gestion afin de poursuivre et d'étendre l'empreinte du département dans la région de Tampa Bay.

En , Jeffrey Vinik, le propriétaire du Lightning, débloque 6 millions de dollars avec l'aide de la LNH répartis sur 5 ans, pour permettre de développer un nouveau programme, Build the Thunder. Ce programme vise à donner une chance de pratiquer du hockey à 100'000 jeunes, en leur fournissant du matériel et des installations de qualité.

Vie privée
Avec son épouse, Anne, ils ont cinq enfants : Theresa, Bobby, Libby, Ryan et Kevin. Theresa travaille pour les Friars de Providence en tant que Directrice des opérations hockey et à remporter la médaille d'or avec la sélection américaine lors des Championnat du monde junior en 2021.

Trophées et honneurs
1993-1994
 Champion de la Division Nord de la LAH avec le Bears de Hershey en tant que Directeur général.

1996-1997
 Vainqueur de la Coupe Calder avec les Bears de Hershey en tant que Directeur général.
  remis au meilleur directeur général de la Ligue américaine de hockey.

2002-2003
 Champion de la Division Sud-Est de la LNH avec le Lightning de Tampa Bay en tant que Directeur général.

2003-2004
 Champion de la Division Sud-Est de la LNH avec le Lightning de Tampa Bay en tant que Directeur général.
 Vainqueur du Trophée Prince de Galles avec le Lightning de Tampa Bay.
 Vainqueur de la Coupe Stanley avec le Lightning de Tampa Bay.

Références

Naissance en juillet 1962
Naissance à Harrisburg
Étudiant de l'université de Georgetown
Dirigeant américain de hockey sur glace
Dirigeant du Lightning de Tampa Bay

Jay Feaster


أمرابالي Ambapāli وتعرف أيضا باسم أمباباليكا Ambapālika وأمرابالي Amrapāli كانت تعتبر عروس المدينة، وعروس المدينة هي ترجمة للكلمة Nagarvadhu وتعني عاهرة من الطراز الرفيع الذي لا يناله إلا الطبقات الرفيعة من المجتمع كالملوك وكانت الفتيات في بعض أجزاء الهند قديما يتنافسن على هذا اللقب دون أن يعد الأمر هذا محرما لتحظى أجملهن به، وقد كانت أمبابالي عروس جمهورية فيشالي Vaishali في الهند حوالي 500 سنة قبل الميلاد، وقد ذكرت في نصوص بالي القديمة والأدبيات البوذية.
كانت أمبابالي لقيطة مجهولة الأبوين وجدت عند شجرة المانجا في إحدى الحدائق الملكية ومن اسم هذه الشجرة اشتق اسمها. لقد كانت أمبابالي فائقة الحسن والجمال مما رغب فيها العديد من نبلاء البلدة، ولكي يتجنب الصراع بين الراغبين فيها تم تنصيبها منصب «عروس المدينة»، وسرعان ما تطايرت الأنباء حول حسنها وفتنتها إلى أسماع الملك بيمبيسارا زعيم مملكة ماكادا المجاورة، فقام بالهجوم على المدينة واستدرج أمبابالي حتى ولعت بقدراته في العزف الموسيقي ووقعت في حبه، ولكنها بمجرد أن علمت بأنه الملك المحتل لبلدتها ابتعدت عنه وطلبت منه إنهاء الحرب، وفعلا قام الملك بإنهاء الحرب والانسحاب مما صوره جبانا في عيون أهل جمهورية فيشالي.
و في أحد الأيام اعترت أمبابالي رغبة في التشرف بتقديم الطعام لبوذا، وكما تنقل النصوص البوذية فإن بوذا قام بإجابة دعوتها متجاهلا إرادة الطبقة الارستقراطية آنذاك التي رفضت هذه الدعوة، وعندما جاء بوذا إليها قامت باستقباله استقبالا حاشدا هي وحاشيتها وقدمت له الطعام، وبعد هذه الحادثة سرعان ما اعتزلت أمبابالي الدعارة واعتنقت البوذية وظلت مؤيدة وداعية إلى بوذا.

مراجع

أشخاص في القرن 5 ق م
المرأة في القرن 5 ق م
النساء والبوذية
بوذيون هنود
راقصون قدماء
سنة الوفاة غير معروفة
سنة الولادة غير معروفة
محظيات
هنديات قديمات

أمرابالي


El de Havilland Canada DHC-3 Otter («nutria» en inglés) es un avión utilitario con capacidad STOL desarrollado por la compañía canadiense de Havilland Canada. Fue concebido como una versión con mejores prestaciones que el DHC-2 Beaver, pero acabó siendo un avión de mayor tamaño.

Variantes
 DHC-3 Otter : Versión original.
 CSR-123 Otter : Versión de transporte para la Real Fuerza Aérea Canadiense.
 YU-1 Otter : 6 ejemplares de evaluación para el Ejército de los Estados Unidos.
 U-1A Otter : Versión de transporte para el Ejército de los Estados Unidos.
 UC-1 Otter : Versión de transporte para la Armada de los Estados Unidos. Posteriormente denominada como U-1B Otter.
 DHC-3-T Turbo-Otter : Versiones del Otter equipadas con turbopropulsores PT6A-27 o PT6A-34.

Véase también

Referencias
 Hayes, Karl E. DHC-3 Otter - A History (CD-ROM). Crakaig, Killiney Hill Road, Killiney, Co. Dublin, Ireland: Karl E. Hayes Publisher, 2006. (also available via CANAV Books, Toronto)
 Hotson, Fred W. The de Havilland Canada Story. Toronto: CANAV Books, 1983. ISBN 0-07-549483-3.
 Michell, Simon. (ed.). Jane's Civil and Military Aircraft Upgrades 1994-95. Coulsdon, UK: Jane's Information Group, 1994. ISBN 0-7106-1208-7.
Milberry, Larry. Aviation In Canada. Toronto: McGraw-Hill Ryerson Ltd., 1979. ISBN 0-07-082778-8.
 Molson, Ken M. and Harold A. Taylor. Canadian Aircraft Since 1909. Stittsville, Ontario: Canada's Wings, Inc., 1982. ISBN 0-920002-11-0.
 Rossiter, Sean. The Immortal Beaver: The World's Greatest Bush Plane. Vancouver: Douglas & McIntyre, 1999. ISBN 1-55054-724-0.
 Rossiter, Sean. Otter & Twin Otter: The Universal Airplanes. Vancouver: Douglas & McIntyre, 1998. ISBN 1-55054-637-6.
 Taylor, John W.R., ed. Jane's All The World's Aircraft 1988-89. Coulsdon, UK: Jane's Defence Data, 1988. ISBN 0-7106-0867-5.

Enlaces externos

 de Havilland Canada DHC-3 CC-123 Otter
 De Havilland Canada D.H.C.3 'Otter'

DHC-3
Aeronaves de ala alta
Aeronaves de cola cruciforme
STOL
Aviones tractores monomotores
Aeronaves civiles utilitarias de Canadá de los años 1950
Aeronaves utilitarias militares de Canadá de los años 1960

De Havilland Canada DHC-3 Otter