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In der Mathematik bezeichnet die Umkehrfunktion oder inverse Funktion einer bijektiven Funktion die Funktion, die jedem Element der Zielmenge sein eindeutig bestimmtes Urbildelement zuweist.

Eine Funktion  ordnet jedem  ein eindeutig bestimmtes Element  zu, das mit  bezeichnet wird.
Gilt für  die Beziehung , so sagt man auch, dass  ein Urbildelement von  unter  ist. Im Allgemeinen kann ein Element von  kein, ein oder mehrere Urbildelemente unter  besitzen.
Falls jedes Element von  genau ein Urbildelement unter  besitzt (man spricht dann von dem Urbildelement), nennt man  invertierbar. In diesem Fall kann man eine Funktion  definieren, die jedem Element von  ihr eindeutig definiertes Urbildelement unter  zuordnet.
Diese Funktion wird dann als die Umkehrfunktion von  bezeichnet.

Man kann leicht nachweisen, dass eine Funktion genau dann invertierbar ist, wenn sie bijektiv (also gleichzeitig injektiv und surjektiv) ist. Tatsächlich besagt die Injektivität nichts anderes, als dass jedes Element von  höchstens ein Urbildelement unter  besitzt. Die Surjektivität besagt gerade, dass jedes Element von  mindestens ein Urbildelement unter  besitzt.

Der Begriff der Umkehrfunktion gehört formal zum mathematischen Teilgebiet der Mengenlehre, wird aber in vielen Teilgebieten der Mathematik verwendet.

Definition

Seien  und  nicht-leere Mengen.
Neben der Definition aus der Einleitung gibt es weitere Möglichkeiten, die Begriffe der Invertierbarkeit einer Funktion  und der Umkehrfunktion einer invertierbaren Funktion formal einzuführen:

 Man sucht nach einer Funktion , sodass  für alle  und  für alle . Es stellt sich heraus, dass es höchstens ein solches  geben kann. Existiert dies, so nennt man  invertierbar und das eindeutig bestimmte  die Umkehrfunktion von .
 Unter Verwendung der Komposition von Funktionen kann die vorherige Bedingung auch etwas eleganter formuliert werden, indem man für  fordert:  und . Dabei ist  die identische Abbildung auf der Menge .
 Man führt zunächst die weiter unten erklärten Begriffe von Linksinversen und Rechtsinversen ein. Dann nennt man eine Funktion invertierbar, wenn sie sowohl eine Linksinverse als auch eine Rechtsinverse besitzt. Es zeigt sich, dass in diesem Fall Linksinverse und Rechtsinverse übereinstimmen müssen (womit auch folgt, dass es in diesem Fall davon nicht mehrere gibt). Diese eindeutig bestimmte Links- und Rechtsinverse ist dann die Umkehrfunktion.
 Man bezieht sich bei der Definition darauf, dass eine Funktion von  nach  immer auch eine Relation von  nach  ist. Daher besitzt sie auf jeden Fall eine Umkehrrelation. Man nennt  invertierbar, wenn diese Umkehrrelation eine Funktion von  nach  ist. In diesem Fall wird die Umkehrrelation auch als Umkehrfunktion bezeichnet.

Es stellt sich heraus, dass alle vorgestellten Invertierbarkeitsbegriffe äquivalent zum Begriff der Bijektivität sind. Auch führen alle Definitionen der Umkehrfunktion zum gleichen Ergebnis.

Notation

Wenn  eine bijektive Funktion ist, dann bezeichnet  die Umkehrfunktion. Dabei ist die hochgestellte  nicht mit einer negativen Potenz bezüglich der Multiplikation zu verwechseln. Es handelt sich vielmehr um die Umkehrung bezüglich der Komposition von Funktionen.
Die alternative Schreibweise  (f quer), kann leicht mit der komplexen Konjugation verwechselt werden. Sie wird daher in der mathematischen Literatur nur selten verwendet.

Allerdings besteht auch bei der Notation  eine Doppeldeutigkeit. Diese Notation wird nämlich auch für die Urbildfunktion verwendet, die für jede Funktion (also auch nicht bijektive) existiert.
Die Urbildfunktion ist eine Funktion von der Potenzmenge  in die Potenzmenge .
Es ist üblich, in der Notation der Urbildfunktion bei einelementigen Mengen die Mengenklammern wegzulassen. Für  wird also statt  auch einfach  geschrieben.
Identifiziert man nun in dieser notationellen Weise die einelementige Menge mit dem einen enthaltenen Element, dann ist die Umkehrfunktion eine Spezialisierung der Urbildfunktion, und frontale Widersprüche können nicht auftreten. Denn für bijektive  ist  das eine und einzige Element der Urbildmenge .

Wegen der genannten Verwechslungsmöglichkeit findet sich gelegentlich in der Literatur für die Umkehrfunktion (das ist die  Iteration) die Schreibweise
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für die Iteration
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für die Potenz
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und für die Ableitung
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Dann ist beispielsweise

und

Einfache Beispiele

 Sei  die Menge der 26 Buchstaben des lateinischen Alphabets und sei . Die Funktion , die jedem Buchstaben die entsprechende Nummer im Alphabet zuordnet, ist bijektiv, und  ist gegeben durch  "der n-te Buchstabe im Alphabet".

 Sei  die reelle Funktion mit . Diese ist bijektiv und die Umkehrfunktion ist gegeben durch
.

 Allgemeiner: Sind  und die Funktion  gegeben durch . Dann ist  genau dann bijektiv, wenn . In diesem Fall gilt .

Eigenschaften

 Die Umkehrfunktion ist selber bijektiv. Ihre Umkehrfunktion ist die ursprüngliche Funktion, d. h.
.

 Ist  eine bijektive Funktion, dann gilt für die Umkehrfunktion:
 für alle ,
 für alle .
Oder etwas eleganter:
,
.

 Sind  und  zwei Funktionen mit der Eigenschaft
 für alle ,
dann kann aus jeder der drei folgenden Eigenschaften bereits geschlossen werden, dass beide Funktionen bijektiv und ihre gegenseitigen Umkehrfunktionen sind:
 für alle
 ist injektiv
 ist surjektiv

 Sind die Funktionen  und  bijektiv, dann gilt dies auch für die Komposition . Die Umkehrfunktion von  ist dann .

 Eine Funktion  kann ihre eigene Umkehrfunktion sein. Dies gilt genau dann, wenn . In diesem Fall nennt man  eine Involution. Die einfachsten involutorischen Abbildungen sind die identischen Abbildungen.

 Ist  eine bijektive Funktion, wobei  und  Teilmengen von  sind, dann entsteht der Graph der Umkehrfunktion, indem man den Graph von  an der Geraden  spiegelt.

 Ist  differenzierbar,  und , dann gilt die folgende Umkehrregel:
.
Diese Aussage wird in der mehrdimensionalen Analysis zum Satz von der Umkehrabbildung verallgemeinert.

Umkehrfunktion für nicht bijektive Funktionen

In vielen Fällen besteht der Wunsch nach einer Umkehrfunktion für eine nicht bijektive Funktion. Hierzu kann man die folgenden Hilfsmittel heranziehen:

 Ist die Funktion nicht surjektiv, so kann man die Zielmenge verkleinern, indem man hierfür gerade das Bild der Funktion wählt. Die so erhaltene Funktion ist surjektiv und stimmt in ihren Wertepaaren mit der ursprünglichen Funktion überein. Dieser Ansatz ist immer möglich. Es kann allerdings sein, dass es schwierig ist, das Bild der betrachteten Funktion genau zu bestimmen. Außerdem kann beim Übergang auf diese Teilmenge eine wichtige Eigenschaft der ursprünglich betrachteten Zielmenge verloren gehen (in der Analysis etwa die Vollständigkeit).

 In manchen Fällen erweist es sich auch als fruchtbar, die gewünschte Surjektivität dadurch zu erreichen, dass man bei der betrachteten Funktion den Definitionsbereich erweitert. Oft geht das auch mit einer Erweiterung der Zielmenge einher. Ob dieser Weg gangbar und sinnvoll ist, muss aber jeweils individuell entschieden werden.

 Ist die Funktion nicht injektiv, so kann man auf ihrem Definitionsbereich eine geeignete Äquivalenzrelation definieren, sodass man die Funktion auf die Menge der entsprechenden Äquivalenzklassen übertragen kann. Diese Funktion ist dann automatisch injektiv. Dieser Ansatz ist allerdings anspruchsvoll und führt zu einem oft unerwünschten Wechsel in der Natur der Argumente der betrachteten Funktion.

 In der Praxis kann man die Injektivität der Funktion oft auch dadurch erreichen, dass man sich auf eine geeignete Teilmenge des Definitionsbereichs der Funktion einschränkt, die zu jedem Element des Bilds nur ein einziges Urbildelement enthält. Diese Einschränkung ist allerdings unter Umständen willkürlich. Man muss daher darauf achten, dass man diese Einschränkung an allen Stellen konsistent in gleicher Weise vornimmt.

Beispiele

 Man betrachte die Nachfolger-Funktion  auf der Menge  der natürlichen Zahlen ohne die Null. Diese Funktion ist injektiv. Sie ist aber nicht surjektiv, da die Zahl 1 nicht als Funktionswert vorkommt. Man kann nun die Zahl 1 aus der Zielmenge entfernen. Dann wird die Funktion surjektiv und die Vorgänger-Funktion  ist ihre Umkehrfunktion. Allerdings ist es unschön, dass bei der Funktion nun Definitionsbereich und Zielmenge nicht mehr übereinstimmen.
Die alternative Idee, den Definitionsbereich um das fehlende Urbildelement für die 1, nämlich die 0, zu erweitern, hat auf den ersten Blick denselben Nachteil. Fügt man, um dies zu beheben, die 0 ebenfalls zur Zielmenge hinzu, so besitzt diese wiederum kein Urbildelement. Man kann diesen Prozess aber gedanklich unendlich oft fortsetzen und gelangt dadurch zur Menge  der ganzen Zahlen. Auf dieser Menge ist die Nachfolger-Funktion bijektiv, und ihre Umkehrfunktion ist die Vorgänger-Funktion.

 Die Exponentialfunktion betrachtet als Funktion von  nach  ist injektiv, aber nicht surjektiv. Ihr Bild ist gerade die Menge der positiven reellen Zahlen. Schränkt man die Zielmenge darauf ein, so erhält man eine bijektive Funktion, deren Umkehrfunktion die Logarithmusfunktion ist. Eine natürliche Erweiterung des Zahlbereichs, wie im vorherigen Beispiel diskutiert, bietet sich hier nicht an. Daher muss man akzeptieren, dass bei den betrachteten Funktionen nun Definitionsbereich und Zielmenge nicht mehr übereinstimmen.

 Die Quadratfunktion  ist, betrachtet als Funktion von  nach , weder injektiv noch surjektiv. Die Surjektivität erreicht man dadurch, dass man als Zielmenge die Bildmenge  der nichtnegativen reellen Zahlen wählt. Um die Injektivität zu erreichen, kann man den Definitionsbereich einschränken. Am naheliegendsten ist es, hier ebenfalls  zu wählen. Die so erhaltene eingeschränkte Quadratfunktion ist bijektiv. Ihre Umkehrfunktion ist die Quadratwurzelfunktion.

 Die trigonometrischen Funktionen Sinus (sin), Kosinus (cos) und Tangens (tan) sind nicht bijektiv. Man schränkt sie jeweils auf geeignete Teilmengen des Definitionsbereichs und der Zielmenge ein und erhält bijektive Funktionen, deren Umkehrfunktionen die Arkusfunktionen: Arkussinus (arcsin), Arkuskosinus (arccos) und Arkustangens (arctan) sind.

 Ein entsprechendes Vorgehen für die Hyperbelfunktionen Sinus hyperbolicus (sinh), Cosinus hyperbolicus (cosh) und Tangens hyperbolicus (tanh) führt zu den Areafunktionen: Areasinus hyperbolicus (arsinh), Areakosinus hyperbolicus (arcosh) und Areatangens hyperbolicus (artanh).

Berechnung

Die effektive Bestimmung der Umkehrfunktion ist oft schwierig. Asymmetrische Verschlüsselungsverfahren beruhen darauf, dass die Bestimmung der Umkehrfunktion einer Verschlüsselungsfunktion effektiv nur möglich ist, wenn man einen geheimen Schlüssel kennt. Dabei ist die Berechnungsvorschrift für die Verschlüsselungsfunktion selbst öffentlich bekannt.

Reelle Funktionen sind oft durch eine Berechnungsvorschrift definiert, die durch einen arithmetischen Term  (mit einer Variablen ) beschrieben werden kann. Bei der Suche nach der Umkehrfunktion versucht man nun die Funktionsgleichung  durch Äquivalenzumformung in die Form  (für einen passenden Term ) zu bringen, also äquivalent nach  aufzulösen.
Gelingt dies, so ist die durch die Berechnungsvorschrift  definierte Funktion als bijektiv erwiesen und  ist eine Berechnungsvorschrift für die Umkehrfunktion. Man beachte, dass bei den Schritten der Äquivalenzumformung die Mengen, aus denen  und  gewählt werden sollen, genau zu beachten sind. Sie bilden dann Definitionsbereich und Zielmenge der betrachteten Funktion.

Beispiele:

 Sei  mit . Die folgenden Gleichungen sind äquivalent:

Die Umkehrfunktion von  lautet daher . Da es üblich ist, das Argument mit  zu bezeichnen, schreibt man auch: .

 Sei  mit . Die folgenden Gleichungen sind äquivalent (man beachte, dass  gilt):
 :
(Die zweite Lösung der quadratischen Gleichung entfällt, da  als positiv vorausgesetzt ist.) Die Umkehrfunktion lautet also .

Bemerkung: Bei dieser Lösung wurde die Quadratwurzel verwendet. Die Quadratwurzelfunktion ist gerade definiert als die Umkehrfunktion der einfachen Quadratfunktion . Diese einfache Funktion kann nämlich nicht unter Verwendung der Grundrechenarten "umgekehrt" werden.
Dieses Problem wurde dadurch gelöst, dass der Vorrat an mathematischen Standardoperationen um ein weiteres Mitglied (nämlich die Quadratwurzel) erweitert wurde.
Die Leistung der oben durchgeführten Umformung besteht also darin, die Berechnung für die Umkehrfunktion der Funktion  auf die Berechnung der Umkehrfunktion der Quadratfunktion zurückgeführt zu haben.
Die Quadratwurzel kann, wie gesagt, nicht auf elementare Weise berechnet werden. Tatsächlich hat sie selbst für ganzzahlige Argumente oft irrationale Werte. Es gibt aber gut verstandene Näherungsverfahren für die Quadratwurzel.
Daher wird obige Umformung als ausreichend angesehen. Tatsächlich lässt sich ein besseres Ergebnis auch nicht erzielen.
Man beachte, dass auch die anderen oben angegebenen Umkehrfunktionen (Logarithmus, Arcus- und Area-Funktionen) nicht mit Hilfe der Grundrechenarten (und der Exponentialfunktion und der trigonometrischen Funktionen) berechnet werden können. Sie erweitern daher, genau wie die Quadratwurzel, die Menge der mathematischen Standardoperationen (siehe auch Elementare Funktion).

Umkehrfunktionen und Morphismen

In der höheren Mathematik werden oft Mengen betrachtet, die noch mit zusätzlicher mathematischer Struktur versehen sind. Ein einfaches Beispiel hierfür ist die Menge der natürlichen Zahlen, auf der es unter anderem die durch die Kleiner-Relation definierte Ordnungsstruktur gibt.

Betrachtet man nun Funktionen zwischen zwei Mengen, die den gleichen Typ von Struktur tragen (also etwa zwei geordnete Mengen), so interessiert man sich besonders für Funktionen zwischen diesen Mengen, die mit den entsprechenden Strukturen "verträglich" sind. Diese Verträglichkeit muss dabei gesondert definiert werden. Die Definition ist aber in den meisten Fällen naheliegend.

Funktionen, die diese Verträglichkeit erfüllen, werden auch Morphismen genannt. Bei geordneten Mengen sind die Morphismen etwa die monotonen Funktionen.

Ist ein Morphismus bijektiv, so stellt sich die Frage, ob die Umkehrfunktion ebenfalls ein Morphismus ist.

In vielen Teilgebieten der Mathematik ist dies automatisch der Fall. So sind etwa die Umkehrfunktionen bijektiver Homomorphismen automatisch ebenfalls Homomorphismen.

In anderen Teilgebieten ist dies nicht der Fall. Bei den geordneten Mengen kommt es zum Beispiel darauf an, ob man sich auf Totalordnungen beschränkt (dann sind Umkehrfunktionen von monotonen Funktionen wieder monoton) oder ob man auch Halbordnungen zulässt (dann ist dies nicht immer der Fall).

Ein bijektiver Morphismus, dessen Umkehrfunktion ebenfalls ein Morphismus ist, wird auch Isomorphismus genannt.

Umkehrfunktionen von linearen Abbildungen

Ein besonders wichtiges Beispiel für den Morphismusbegriff ist der Begriff der linearen Abbildung (des Vektorraumhomomorphismus). Eine bijektive lineare Abbildung ist immer ein Isomorphismus. Oft stellt sich die Frage, wie deren Umkehrfunktion effektiv bestimmt werden kann.

Damit überhaupt ein solcher Isomorphismus existieren kann, müssen die beiden beteiligten Vektorräume dieselbe Dimension haben.
Ist diese endlich, so lässt sich jede lineare Abbildung zwischen den Räumen durch eine quadratische Matrix (mit entsprechender Spaltenzahl) darstellen. Die lineare Abbildung ist dann genau dann bijektiv, wenn diese Matrix eine Inverse besitzt. Diese Inverse beschreibt dann die Umkehrfunktion.

Im mathematischen Teilgebiet der Funktionalanalysis betrachtet man vor allem unendlichdimensionale Vektorräume, die neben der Vektorraumstruktur noch eine zusätzliche topologische Struktur tragen. Als Morphismen lässt man hier nur solche linearen Abbildungen gelten, die auch mit den topologischen Strukturen verträglich, das heißt stetig, sind.
Im Allgemeinen ist die Umkehrfunktion einer bijektiven stetigen linearen Abbildung zwischen zwei topologischen Vektorräumen nicht zwangsläufig stetig. Sind aber beide beteiligten Räume Banachräume, so folgt aus dem Satz über die offene Abbildung, dass dies der Fall sein muss.

Verallgemeinerungen

Für allgemeinere Anwendungen ist der oben eingeführte Begriff der Umkehrfunktion als Inverses einer Bijektion zu eng. Entsprechend existieren Verallgemeinerungen für solche Gegebenheiten, von denen zwei nachfolgend vorgestellt werden.

Linksinverse

Für eine Funktion  heißt eine Funktion  Linksinverse (oder Retraktion),
wenn

Das heißt, die Funktion  erfüllt

Das Verhalten von  auf dem Bild von  ist also festgelegt. Für Elemente aus , die nicht Resultat von  sind, kann  dagegen beliebige Werte annehmen. Eine Funktion  hat Linksinverse genau dann, wenn sie injektiv (linkseindeutig) ist.

Eine injektive Funktion kann mehrere Linksinverse haben. Dies ist genau dann der Fall, wenn die Funktion nicht surjektiv ist und der Definitionsbereich mehr als ein Element besitzt.

Beispiele
Linksinverse treten oft als "Inverse" von Einbettungen auf.

Sei zum Beispiel  die Menge der Vereine, die in der Saison 2018/19 mit einer Mannschaft in der ersten Fußball-Bundesliga der Männer vertreten sind.  sei die Menge der Kommunen in Deutschland. Die Funktion  ordne einem Verein die Kommune zu, in der sein Stadion steht.
Da in der betrachteten Saison keine zwei Bundesliga-Mannschaften aus derselben Stadt kommen, ist diese Funktion injektiv. Da es auch Kommunen ohne Bundesliga-Stadion gibt, ist sie nicht surjektiv.
Es gibt also mehrere Linksinverse zu . Eine einfach zu bildende Linksinverse ist die Funktion, die jeder Kommune, die ein Bundesliga-Stadion besitzt, den zugehörigen Verein und allen anderen Kommunen den FC Bayern München zuordnet. Ein in der Praxis sinnvolleres Beispiel wäre die Funktion, die jeder Kommune den Bundesliga-Verein mit dem am nächsten gelegenen Stadion zuordnet. Allerdings wäre es auch deutlich aufwändiger diese Funktion zu ermitteln, zumal erst einmal geklärt werden müsste, welcher Abstandsbegriff der Definition zu Grunde liegt (Luftlinie, kürzeste Entfernung mit dem PKW, …).

Als numerisches Beispiel sei  die Einbettung von  in . Dann bietet sich jede Rundungsfunktion (auf 0 Stellen nach dem Komma), also zum Beispiel die Gaußklammer, als Linksinverse an. Aber auch die Funktion auf , die jeder ganzen Zahl sich selbst und allen anderen Zahlen die 0 zuordnet, ist eine Linksinverse.

Rechtsinverse

Eine Rechtsinverse (Koretraktion) von  (oder, bei Faserbündeln, ein Schnitt von ) ist eine Funktion , sodass

Das heißt, die Funktion  erfüllt

 kann also jedes Urbildelement von  unter  sein.

Hat eine Funktion  eine Rechtsinverse, so muss sie surjektiv (rechtstotal) sein.

Umgekehrt scheint es offensichtlich, dass aus der Surjektivität von  die Existenz einer Rechtsinversen folgt. Zu jedem  kann man ja ein oder sogar mehrere Urbildelemente unter  in  finden.
Ist die Funktion allerdings "hochgradig nicht-injektiv", so muss hierzu für eine unüberschaubare Menge von Elementen der Zielmenge eine Entscheidung getroffen werden, welches der Urbildelemente man denn jeweils wirklich nimmt.
Eine solche simultane Entscheidung kann nicht immer konstruktiv getroffen werden. Das Auswahlaxiom (in geeigneter Formulierung) besagt gerade, dass eine Rechtsinverse trotzdem für alle surjektiven Funktionen existiert.

In vielen Fällen kann allerdings die Auflösung der Uneindeutigkeit durch eine globale Festlegung erfolgen. Dies ist etwa bei der Definition der Quadratwurzel der Fall, wo man die Uneindeutigkeit immer zu Gunsten der positiven Lösung auflöst.
In solchen Fällen wird das Auswahlaxiom nicht benötigt.

Die Funktion  ist offenbar genau dann Rechtsinverse von , wenn  Linksinverse von  ist. Hieraus folgt unmittelbar, dass Rechtsinverse immer injektiv und Linksinverse immer surjektiv sind.

Eine surjektive Funktion hat genau dann mehrere Rechtsinverse, wenn sie nicht injektiv ist.

Beispiele
Rechtsinverse treten oft als Funktionen auf, die Repräsentanten einer Menge bestimmen.

Sei beispielsweise  eine Funktion, die jeder Art ihre Gattung zuweist. Als Rechtsinverse  wählt man dann eine Funktion, die für jede Gattung eine typische Art benennt. Politische Vertretung liefert viele Beispiele. Hier könnte  etwa die Staatsangehörigkeit eines Menschen sein,  das Staatsoberhaupt eines Staates.

Die Hilbert-Kurve bildet das Einheitsintervall stetig (daher die Bezeichnung Kurve) auf das Einheitsquadrat ab. In der praktischen Anwendung wird aber häufig der Hilbert-Index benötigt, nämlich eine Linearisierung zweidimensionaler Daten (eine Umkehrung der Hilbert-Kurve). Dazu nimmt man eine der Rechtsinversen der Hilbert-Kurve, von denen es mehrere gibt – denn die Hilbert-Kurve kann als stetige Abbildung zwischen zwei Räumen unterschiedlicher Dimension nach dem Satz von der Invarianz der Dimension nicht bijektiv sein.

Links- und Rechtsinverse von Morphismen

Tragen die Mengen  und  eine zusätzliche mathematische Struktur und ist  eine injektive bzw. surjektive Funktion, die mit diesen Strukturen verträglich ist, so stellt sich die Frage, ob es möglich ist, die Links- bzw. Rechtsinverse so zu wählen, dass sie ebenfalls mit den Strukturen verträglich ist.
Für viele in der Mathematik untersuchte Strukturen ist dies nicht der Fall.
Ist  allerdings eine injektive bzw. surjektive lineare Abbildung, so kann man die Links- bzw. Rechtsinverse ebenfalls als lineare Abbildung wählen.

Verschiedenes

 Von besonderem Interesse sind oft Funktionen, bei denen Definitionsbereich und Zielmenge übereinstimmen. Für eine Menge  bildet die Menge der Funktionen von  in sich mit der Komposition als Verknüpfung ein Monoid. Die Begriffe der Invertierbarkeit sowie des Links- und Rechtsinversen, die hier eingeführt wurden, stimmen dann mit den entsprechenden Begriffen aus der Algebra überein.
Der Begriff der Umkehrfunktion ist in diesem Fall identisch mit dem Begriff des inversen Elements.

 Im allgemeinen Kontext wird der Begriff der Invertierbarkeit von Funktionen oft weggelassen, da er mit dem Begriff der Bijektivität übereinstimmt.

 Bei den obigen Überlegungen wurde vorausgesetzt, dass  und  nicht-leer sind. Ist  leer, so gibt es überhaupt nur dann eine Funktion von  nach , wenn  ebenfalls leer ist.
Diese ist dann die leere Funktion, die bijektiv und involutorisch ist.
Ist  leer,  aber nicht, so gibt es wieder genau eine Funktion von  nach , die ebenfalls leer ist. Diese Funktion ist injektiv aber nicht surjektiv. Sie besitzt weder Links- noch Rechtsinverse, da es überhaupt keine Funktionen von  nach  gibt.

 Bei der Einführung des Funktionsbegriffs in der Mathematik gibt es verschiedene Vorgehensweisen. Der in diesem Artikel verwendete Begriff der Surjektivität setzt voraus, dass die Zielmenge ein Teil der Identität der Funktion ist. Legt man einen anderen Funktionsbegriff zu Grunde, so muss man einige der Ausführungen entsprechend anpassen.

 Die meisten der Aussagen in diesem Artikel gelten auch für Funktionen zwischen Klassen.

Siehe auch

 Retraktion und Koretraktion, Links- bzw. Rechtsinverse in Kategorien

Weblinks

Einzelnachweise

Mathematischer Grundbegriff


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Image Title: Dino Dan Coloriages Coloring Pages Kerunaru Info In Prepare 13. Post Title: Dino Dan Coloring Pages. Filename: dino-dan-coloriages-coloring-pages-kerunaru-info-in-prepare-13.jpg. Image Dimension: 618 x 800 pixels. Images Format: jpg/jpeg. Publisher/Author: Rowan Wiegand. Uploaded Date: Monday - February 11th. 2019 14:16:18 PM. Category: Coloring Pages. Image Source: freshome.com. Regard Dino Coloring To Dan Decor 14. Page Prepare Vectories Inspirational Inspirations 0. Pages Surprising In Within 255032 Kerunaru Plans Adventures Parties Remodel With 3. 10. Boy Lively 18. 5 Dinosaur Sheet Ideas 5. 15. Kidtoons Throughout Trek Pertaining Info S 27 Lovely Decorations 13. Umazz 9. Pdf Pinterest Coloriages Printable 12.


text:
Brachyelytrum  P.Beauv. é um género botânico pertencente à família Poaceae, subfamília Pooideae, tribo Brachyelytreae.

Suas espécies ocorrem na América do Norte e regiões temperadas da Ásia.

Espécies
 Brachyelytrum africanum  Hack.ex Schinz
 Brachyelytrum aristatum  P.Beauv. ex Roem. & Schult.
 Brachyelytrum aristosum (Michx.)
 Brachyelytrum erectum  Beauv.
 Brachyelytrum pringlei  Vasey ex Beal
 Brachyelytrum procumbens  Hack.
 Brachyelytrum septentrionale  (Babel) G.C.Tucker
 Brachyelytrum silvaticum  Hack.

Referências

Ligações externas

Poaceae
Géneros de plantas

redpajama_set_name: RedPajamaWikipedia


text:
Tag Archives: former
Haddin replaces Blewett as Australia's fielding coach
"I am thrilled to get the opportunity to work with this young group of players"
Former Australia wicketkeeper-batsman Brad Haddin has succeeded Greg Blewett as the national team's fielding coach.
Smith: Philander 'can't seem to make it through a series'
"There's been too many times where you're fighting to get him onto the field"
Former South Africa captain Graeme Smith has lashed out at pace bowler Vernon Philander after he was ruled out of the fourth Test against England with a back injury.
MacGill to become Bangladesh's spin bowling coach?
"Our first choice for the spin-bowling coach is Stuart MacGill, initially for three months"
Nazmul Hasan has revealed that former Australia leg-spinner Stuart MacGill is the Bangladesh Cricket Board's (BCB) "first choice" for the role of spin bowling coach.
BCB decide not to renew Samaraweera's contract as batting consultant
"We had a contract with him till the Champions Trophy, so now we have parted ways"
The Bangladesh Cricket Board (BCB) has opted against renewing the contract of batting consultant Thilan Samaraweera.
Pietersen to play for South Africa?
"I'm going to be playing a lot of cricket in South Africa over the next two years, so we'll see"
Former England batsman Kevin Pietersen has hinted that he is contemplating resurrecting his international career with his native South Africa.
Was the 2011 World Cup final fixed?
"I think we should also inquire into what happened to the Sri Lanka team during the 2011 World Cup final"
Former Sri Lanka captain Arjuna Ranatunga has claimed that the 2011 World Cup final between India and Sri Lanka was fixed.
Gillespie appointed as Papua New Guinea's interim coach
"It broadens my experiences and broadens my learning and hopefully it will hold me in good stead going forward"
Former Australia pace bowler Jason Gillespie has been named as Papua New Guinea's coach on an interim basis.
Tsotsobe banned for eight years
"I was, at the time, in a very vulnerable financial state and this dilemma too easily persuaded me to participate in spot fixing"
Former South Africa left-arm seamer Lonwabo Tsotsobe has been handed an eight-year ban for his involvement in the 2015 Ram Slam T20 Challenge corruption scandal.
Smith: Rabada's suspension is 'ridiculous'
Posted on July 9, 2017 by bimalmirwani
"If it wasn't picked up by the stump mics he wouldn't have been done"
Former South Africa captain Graeme Smith has expressed his frustration towards the suspension given to Proteas pace bowler Kagiso Rabada.
What does the future hold for Anderson?
"The ambition to play one more Ashes in England is still strong"
England pace bowler James Anderson has revealed that he is eager to keep playing international cricket until the 2019 Ashes series.

redpajama_set_name: RedPajamaCommonCrawl


text:
The Forums Curriculum
The Traditional Curriculum
Corruption, Governance and Institutions
This forum builds on the growing academic and policy interest in corruption. By now, there is consensus amongst international policy circles that corruption is not only a significant barrier to effective governance and the implementation of public programs, but that it undermines the formal and informal institutions that underpin government and the formation of public policies. The Forum will provide students with the capacity to engage contemporary policy debates about the causes and consequences of corruption, as well as to begin the process of formulating their own hypotheses about policy interventions that may reduce its incidence. Invited lectures from representatives of multi-lateral development lending organizations, such as the World Bank, IMF, and Inter-American Development Bank, as well as prosecutors and police officials personally tasked with investigating corruption. As a final project, students in the Forum will be tasked with creating a realistic and rigorous research design for their own anti-corruption intervention.
Daniel Gingerich, Department of Politics
Sandip Sukhtankar, Department of Economics
Sandip Sukhtankar is an Associate Professor in the Department of Economics at the University of Virginia, an affiliate of the Bureau for Research and Economic Analysis of Development (BREAD) and the Jameel Poverty Action Lab (J-PAL), and Lead Academic (India) for the International Growth Centre (IGC). He received his PhD from Harvard University in 2009, and a BA from Swarthmore College (with Highest Honors) in 2000.
Prof Sukhtankar's research interests are in development economics, political economy, and public economics, with a particular focus on governance and the delivery of public benefits and services. His research has been published in top economics journals such as the American Economic Review, American Economic Journal: Applied Economics, and the Journal of Public Economics. Prof Sukhtankar works with governments across India to design and evaluate projects that improve public service delivery. His work has been supported by the National Science Foundation, the Omidyar Network, and the Bill and Melinda Gates Foundation.
At UVA, Professor Sukhtankar teaches Econ 4610 (Economic Development) and Econ 8991 (Research Methods in Economics). He is also Co-Director of UVA-CLEAR (Corruption Lab for Ethics, Accountability, and Rule of Law).
Navigating the Forum
In the first semester (Fall 2019) you take an introductory seminar (FORU 1500): Making Sense of Corruption." This seminar begins by confronting students with three key questions: What are the types of corruption? How prevalent is corruption across the world? How can corruption be measured? After students have addressed these questions, the course considers the various theoretical approaches to understanding corruption. In this respect, the course elucidates the role of institutional structures and economic factors in explaining the form and incidence of corruption. Next, the course will present students with an overview of the theoretical and empirical work on the consequences of corruption. Finally, it will provide an initial examination of the effectiveness of policies that tackle corruption and improve governance.
Students must take three required courses in Politics, Economics, and Statistics (see below) which will provide them with the necessary tools for evaluating comparative institutional analyses and modern empirical studies. In addition, they must take an elective course in each of the three core issue areas at the heart of contemporary research into corruption: 1) information, accountability, and institutions; 2) the politics and economics of development; and 3) ethics. The Forum will conclude with a capstone seminar (FORU 2500) entitled, "Making a Better World: Policy Interventions for Good Government." The seminar will build on the learnings from the earlier coursework and focus on practical anti-corruption efforts.
Competency Requirements
First Writing Requirement (3 credits)
Second Writing Requirement (3 credits)
World Langugages (0-14 credits)
Core Required Courses (8 credits)
FORU 1500 (Fall '19)
FORU 1510 (Spring '20)
FORU 2500 Forum capstone, Spring '21
Other Required Courses (3 Credits Each)
PLCP 1010 (year 1)
ECON 2010 (year 1)
STAT 2120 (year 1 or Fall 2020)
Category 1: Information, Accountability, and Institutions (3 Credits - 1 course)
PLAP 3140 - Mass Media and American Politics
PLAP 3270 - Public Opinion and American Democracy
PLAP 3310 - American Presidency
PLAP 3350 - American Congress
PLAP 3610 – Introduction to Public Administration
PLCP 3110 – Politics of Western Europe
PLCP 3120 – Politics and Political Economy of the Welfare State
PLCP 3500 – Comparative Political Behavior
MDST 3404 - Democratic Politics in the New Media Environment
MDST 3680 – The News Media
Category 2: Politics and Economics of Development (3 Credits - 1 course)
PLAD 2500: Politics, Poverty, & Health
PLCP 3012 - The Politics of Developing Areas
PLCP 3130 - Political Economy of Development
PLCP 3500-001 - Grassroots Politics
PLCP 3210 – Russian Politics
PLCP 3330 – Politics of Latin America
PLCP 3410 – Politics of the Middle East and North Africa
PLCP 3610 – Chinese Politics
PLCP 3630 – Politics in India and Pakistan
ECON 3330 - Public Choice
GDS 3010 – Global Development, Theories and Case Studies I
GDS 3020 - Global Development, Theories and Case Studies II
GDS 3010 – Development on the Ground
SOC 3470 – Sociology of Development
Category 3: Ethics (3 Credits - 1 course)
PHIL 1730 - Introduction to Moral and Political Philosophy
PHIL 2060 – Philosophical Problem in Law
PHIL 2500 – Environmental Ethics
PHIL 2770 - Political Philosophy
PHIL 2750 - Democracy
PHIL 2850 – Ethics and Epistemology for Beginners
RELG 2210 – Religion, Ethics, & Global Environment
RELG 2630 – Business, Ethics, and Society
RELG 2650 – Theological Bioethics
PLIR 3310 – Ethics and Human Rights in World Politics
Category 4 - Science (Take 2 three-or-more credit classes in the sciences)
FAQ-Forums
Only for students who entered UVA before Fall 2020
askthecollege@virginia.edu
Last Modified: Tuesday, 14-Jun-2022 3:31 pm
© 2023 Maintained by UVA Arts & Sciences Digital Communications


text:
WISE Up Action – A Solidarity Network for Manning and Assange
WISE Up is a Welsh, Irish, Scottish, English grassroots solidarity network for Chelsea (formerly Bradley) Manning and Julian Assange
About this site and the WISE Up Action network
Julian Assange Upcoming Solidarity Actions
Donate to Manning and Assange
Ideas for Action
8 April – Public Meeting for Bradley Manning in Dublin
The article below makes reference to Chelsea Manning passing through Ireland's Shannon airport en route to Iraq.
We now know from direct communication with Chelsea that this was not the case and that she did not pass through Shannon airport at any time, although nearly 2.5 million other US soldiers have done so. The use of Shannon by the US military is an ongoing and contentious issue in Ireland.
The information apparently came from a member of Manning's Unit and was passed onto us in good faith by a trusted source. We apologise for this error and any confusion it has caused.
WISE Up, May 2015
Free Bradley Manning! Demilitarise Shannon Airport! End the War!
WHEN? Friday 8 April at 8pm
WHERE? Wynn's Hotel, 35-39 Lower Abbey St., Dublin 1.
"The last place Bradley Manning was before he was in a war zone, and then in chains, was Ireland. Like tens of thousands of young Americans who preceeded him, Manning passed through Shannon Airport (a defacto U.S. military base in neutral Ireland)… to his fate. 4,000 of these young Americans returned home in body bags (their corpses wisely shipped through Saudi not Shannon), 10,000 with injuries they will never recover from…
"We Irish slapped Bradley Manning, and these hundreds of thousands of young Americans, on the back, sold them duty free and sent them to their predictable fate! Under the ancient rules of Irish and global hospitality Bradley Manning is partly our responsibility. This young man was our guest in Ireland and we sent him on his way into a danger we were well aware of, without a word of warning." Ciaron O'Reilly
HARRY BROWNE, Journalism Lecturer D.I.T.
Author, Political Commentator.
CIARON O'REILLY, Giuseppe Conlon House, London.
Pitstop Ploughshares.
FRANK CORDARO, Des Moines Catholic Worker (U.S.A.)
B52 Plowshares.
MUSIC by Joe Black and Steve Jacobs (U.S.)
FREE ENTRY. Donations to cover costs appreciated.
MORE INFORMATION: Afri: 01 882 7563, Mairtin: 086 103 5091 or email ciaronx@yahoo.com
This event is supported by Afri, 134 Phibsborough Road, Dublin 7.


text:
Q: Intellij-IDEA gradle templates How can I change the template of "build.gradle" in IntelliJ IDEA 15.0.1 ?
I'd like to delete "sourceCompatibility", to add 'idea' plugin, and to modify the version of JUnit.
I'd tried to modify "Gradle Build Script" as below,
Perference > Editor > File and Code Templates > Gradle Build Script
apply plugin: 'java'
apply plugin: 'idea'

repositories {
    mavenCentral()
}

dependencies {
    testCompile 'junit:junit:4.12'
}

but I got a build.gradle as followed
apply plugin: 'java'
apply plugin: 'idea'

repositories {
    mavenCentral()
}

dependencies {
    testCompile 'junit:junit:4.12'
}

apply plugin: 'java'

sourceCompatibility = 1.5

repositories {
    mavenCentral()
}

dependencies {
    testCompile group: 'junit', name: 'junit', version: '4.11'
}

Best Regards,
-Mitsutaka Ohisa

A: The preferences you are interest are hard-coded in IDEA JetBrains gradle plugin:
<IDEA_base>\plugins\gradle\lib\gradle.jar\org\jetbrains\plugins\gradle\frameworkSupport\GradleJavaFrameworkSupportProvider.class

redpajama_set_name: RedPajamaStackExchange


text:
Top 10 Successful South Indian Actor Male
Top 10 South Indian Actor Male: There are four major languages in South Indian Cinema which are Tamil, Telugu, Malayalam, and Kannada. Over the past few years, South Indian Cinema has given stiff competition to Bollywood. South Indian movies are very popular among fans all over India. A major reason behind the success of Tollywood movies is their talented actors.
Do you want to know who are the most famous South Indian actors in 2022? If yes, please follow the list of Top 10 Successful South Indian Actor Male. According to Twitter the most popular South Indian actor male is Vijay from the Tamil film industry (Kollywood). His recently launched movie "Beast" became the most tweeted about South Indian cinema in 2022.
READ ALSO:- Top 10 Most Popular Indian Actors
01. Vijay
Vijay is one of the most popular South Indian actors in 2022. He is widely known as Thalapathi Vijay by his followers. Vijay made his acting debut in 1984, acting as a child actor in dramas and films. Besides acting, he is a good singer, philanthropist, and dancer. Vijay was born in Chennai and works mainly in the Tamil Industry. In 1992, he played as lead with Naalaiya Theerpu, directed by his father.
Vijay's popularity knocked after the film Thirumalai in 2003. Vijay has own many awards such as Tamil Nadu State Film Awards, SIIMA Award, etc. V. V. Production, a film studio and Vijay Makkal Iyakkam, a welfare organization is founded by Vijay. He is married to Sangeetha Sornalingam and has two children, both of whom have appeared in cameos in films.
02. Rajinikanth
Rajinikanth is one of the most popular South Indian actor male, was born on 12th December 1950 in Madras. He is the most successful and most popular South Indian actor of all time in history. Rajinikanth made his debut in 1975 with the film Apoorva Ragangal. Early in his career mostly had negative characters. In 1983, he appeared in his first Hindi film Andha Kanoon and became famous across India.
In 1996, he received his first Filmfare and Tamil Nadu Award with Mullum Malarum and critical acclamation. He is the first Indian actor who work in a black & white, color, motion picture, and 3D. Rajinikanth has received many awards such as Dadasahab Phalke, Padma Vibhushan, N.T.R National, Padma Bhushan, etc.
03. Allu Arjun
Allu Arjun was born on April 8, 1982 in a Telugu family in Madras. He is a famous Tamil South Indian male actor, dancer and media personality. He is best known for his performances in Telugu cinema. He started acting at the age of 03 as a child artist in Vijetha (1985) and as a dancer in Daddy (1986). He made his debut in 2003 with the film Gangotri. His recently launched movie "Pushpa: The Rise" is one of the highest-grossing film.
04. Prabhas
Prabhas is another popular Tamil actor, was born on October 23, 1979. He made his debut in 2002 with the film Eeswar. He has a huge fan following all over India. His films Baahubali-The Beginning and Baahubali-The Conclusion are among the top highest-grossing films in India. He is the recipient of six awards and seven Filmfare nominations and has received a Nandy Award and a SIIMA Award.
05. Yash
Another successful South Indian Actor Male is Naveen Kumar Gowda. He is popularly known as Yash. He was born in Karnataka in January 1986. He started his acting career in 2004 with Nanda Gokula and other dramas. He made his debut in 2004 with the film Moggina Manasu, winning the Filmfare Award for Best Supporting Actor. After his film K.G.F: Chapter 1, he gained Pan-India recognition and superstar status. He is married to actress Radhika Pandit.
06. Dhanush
Venkatesh Prabhu Kasthuri Raja, popularly known as Dhanush, was born in 1983, Madras. He is is an Indian actor, producer, director, writer, lyricist, dancer and singer. He started his career in 2002 with the film Thulluvadho Ilamai, directed by his father. Dhanush's song "Why this Kolaveri Di" was the first Indian song on YouTube to gain over 100 Million views. Dhanush owns a production house Wunderbar Films, with his wife Aishwarya.
07. N. T. Rama Rao Jr.
N. T. Rama Rao Jr, popularly known as NTR was born on 20 May 1983 in Hyderabad. He made his debut at the age of 8 with the films Brahmarshi Vishwamitra and Ramayana directed by his grandfather. He debut on television as host of Bigg Boss in 2017, which was a huge success. He has received around 30 Awards, including 9 Filmfare Awards. He married Lakshmi Pranathi, with whom he has two sons.
08. Mahesh Babu
One of the Successful South Indian Actor Male is Mahesh Babu, was born on 9 August 1975 in Chennai. He is also known as the Salman Khan of the South Film Industry. He entered the film industry in 1999 with Raja Kumarudu in Telugu with the Hindi version A Prince. He is the first Telugu superstar to get a wax figure at Madame Tussauds. In 2015, he started a production house G. Mahesh Babu Entertainment. Mahesh is married to actress Namrata Shirodka and has two children.
09. Suriya Sivakumar
Saravanan Sivakumar is another popular South Indian actor male, was born on 23rd July 1975 in Chennai. He was started his career with the film Nerukku Ner in 1997. He is also a TV presenter, producer, and philanthropist. Suriya is actively involved in social work and founded the Agaram Foundation to carry out philanthropic activities. He is an ambassador of several brands like Intex, Quikr, Nescafe holds Edison Award. He is married actress Jyotika and has two children.
10. Ram Charan
One of the best South Indian Actor Male is Konidela Ram Charan Teja, was born on 27 March 1985 in Chennai. He is the son of Megastar Chiranjeevi. He is an Indian actor, producer, and entrepreneur. He made his debut with the film Chirutha in 2007. In 2009 his hit movie Maghadheera won the Filmfare Best Actor – Telugu, which is the highest grossing film till 2013. In 2018, Rangasthalam won Filmfare and SIIMA Award for Best Actor in Telugu as well as accolades.
Tags: south indian actors male, south indian top actors, tamil south indian actors, telugu south indian actors, top 10 south indian actors, top ten south indian actors
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This photograph shows AGA Geodimeters Models 4D (top) and 4L (bottom). These instruments worked by sending a light signal of known wavelength to a reflector. The wavelength of the returning signal was compared to the outgoing one, and the difference (called the "phase shift") was measured. Using multiple frequences of light, the instrument computed a distance based on the known lengths and measured phase shifts of returning light waves.
The control panel and optics of a Model 4D Geodimeter. Photos courtesy of Charlie Glover.
The control panel and optics of a Model 4L. Photos courtesy of Charlie Glover.
Geodimeters, first developed in the 1950s, evolved quickly in the 1960s. In the "4 series" (shown in the photo), weight was scaled down to 20 pounds and measuring time was reduced from 45 minutes to 10 minutes, compared to earlier Geodimeter models.
For lightwave instruments, a complete set of measurements consisted of four separate observations: two measurements with the prism over true center, then measurements with offsets of 0.4 meters. Two complete sets of these measurements, separated by 24 hours, were made. Accuracy of the measurements could be affected by optics alignment, frequency drift, and calibration curve errors in the phase readings. Wet and dry bulb thermometer readings were taken at one end of the line and temperature and pressure readings were taken at both ends of the line both before and after measurements. Altimeter readings were also taken.
The 4D used a high-pressure mercury vapor lamp rather than a common tungsten light bulb as its light source. First manufactured in 1963, the "D" in its designation indicated that it could be used in daylight. The Coast and Geodetic Survey (C&GS) used this model throughout the 1960s.
In 1966, the 4D was modified to use a laser as its light source, in order to increase its range in moderate haze and to measure longer distances in bright sunlight. C&GS technician George Lesley replaced the mercury vapor lamp with a three-milliwatt helium-neon gas laser. The modified 4D was designated "4L," and replaced the 2A and 4D models on the Transcontinental Traverse. Later, the three-milliwatt laser was replaced with a six-milliwatt laser and the model was renamed "4L 6A."
As a result of the technology developed by C&GS, AGA produced the first commercially available electronic distance measurement instrument with a laser light source, which it designated Model 8. These models were also used in Transcontinental Traverse observations.
Burger, T. C., Tomlinson, R. W. (1975). Electronic Distance Measuring Instruments. Washington, D. C.: American Congress on Surveying and Mapping.
Meade, B. K. (1967). Progress and Results of High-Precision Traverse Surveys. Presented to the Joint American Society of Photogrammetry-American Congress on Surveying and Mapping Convention, March 5-10, 1967.
Smith, J. R. (1983). Geodimeter 1947-1983. Unpublished.


text:
Cpt_0607_cy.indd
practice presents a threat to public health right balance in oversight of physician opioid discipline of physicians: assessing state and safety—have the ability to issue a prescribing for pain: the role of state medical medical boards through case studies. <http:// boards. J. Law Med. Ethics 31, 21–40 (2003).
aspe.hhs.gov/daltcp/reports/2006/stdiscp.
Hoffmann, D.E. & Tarzian, A.J. Achieving the right balance in oversight of physician opioid 10. Federation of State Medical Boards. Protecting prescribing for pain: a survey of state medical the public: how state medical boards regulate boards. J. Med. Licensing Discipline 89, 159–170
and discipline physicians. <http://www.fsmb.
used. It is more oft en the case that the org/smb_protecting_public.html>. Accessed Bovjberg, R.R., Aliaga, P. & Gittler, J. State to the DHHS study, case closure times "vary considerably according to how far through the disciplinary process a case See ARTICLE page 807
proceeds. Nationally, cases resolved before or during investigation averaged 180 days from intake to closure in 2003, "Personalized Medicine: Elusive
425 days for cases closed aft er investi-gation but before hearing, and 675 days Dream or Imminent Reality?": A
to reach hearing."9 Although a signifi -cant majority of cases are closed during Commentary
investigation, for those cases that require a hearing, board efficiency is poor. Moreover, many boards have a backlog of uninvestigated complaints.9 I was invited to comment on the article in this issue by Larry Lesko,
"Personalized Medicine: Elusive Dream or Imminent Reality?",1
especially with respect to three questions. There are several possible
and Willis, state boards would need an alternative, perhaps a "fast track" review approaches to discussing these questions. One is to simply answer the
question as directly and succinctly as possible; another is to expand
related to the prescribing of opioids for on the questions. For the purpose of this Commentary, I try to do both.
pain. Ideally such a committee would include pain-treatment experts. Argu-ably, boards would need additional In his article, Dr. Lesko lists the following Direct answers
as three of the many unresolved questions "No" would be my simple answer to the fi rst question. I do not believe that RCTs are necessary to establish the usefulness of 1. Are prospective, randomized con- a predictive safety (or a dosing safety) test. trolled trials (RCTs) necessary to qualify RCTs are expensive and used to establish or validate a predictive genetic test (e.g., CONFLICT OF INTEREST
for CYP2C9 activity) to inform dosing in that of a placebo. Safety tests are expected The author declared no conflict of interest.
clinical practice or for regulatory policies to be predictive for an individual. Safety signals are recognized by following treated 2. To what extent can prospective or Reidenberg, M.M. & Willis, O. Prosecution of retrospective observational studies sup- specifi c genetic variants associated with an physicians for prescribing opioids to patients. port genotype-phenotype associations for Clin. Pharmacol. Ther. 81, 903–906 (2007)
adverse event (AE)—including those due Code of Federal Regulations 21, §1306.04(a).
the purpose of qualifying or validating a to dosing related to drug metabolism vari- 3. United States v. Hurwitz, 459 F.3d 463, 468 (4th predictive genetic test to determining opti- ants—may well be the same as the allele 4. Hoover v. Agency for Health Care Administration, frequency in the placebo group. However, 676 So. 2d 1380, 1380–85 (Fla. Dist. Ct. App. 3. What clinical end points are appropri- placebo-treated patients do not receive the ate for qualifying or validating predictive Federation of State Medical Boards. Model genetic tests when given the choice between guidelines for the use of controlled substances of a drug-specifi c AE, even if they carry for the treatment of pain. <http://www.
a clinically relevant, causal biomarker, a painpolicy.wisc.edu/domestic/model.htm> surrogate end point used as a substitute for genetic variant is refl ected clinically only a clinical end point, or a clinical outcome? Federation of State Medical Boards. Model policy for the use of controlled substances for the treatment of pain. <http://www.fsmb.org/ 1Genetics Research and Development, GlaxoSmithKline, Research Triangle Park, North Carolina, USA. pdf/2004_grpol_Controlled_Substances.pdf> Correspondence: A Roses ([email protected]) Hoffmann, D.E. & Tarzian, A.J. Achieving the CLINICAL PHARMACOLOGY & THERAPEUTICS | VOLUME 81 NUMBER 6 | JUNE
defi nes the serious need for long-term, could be confi rmed in long-term prospec- tive observation studies rather than RCTs. and should be tested for CYP2C9 variants using a comprehensive screening tool that already been in place for years. An exam- at least covers tag single-nucleotide poly- abacavir as a treatment for HIV, which led to the identifi cation of a genetic marker genetic screening tool.2 When such chips begin with the fi rst patient treated in phase or similar platforms become inexpensive, I and continue through all clinical trials Box 1). It is thus not a totally new concept
their routine application (when mandated to monitor treated patients aft er marketing cussions of and proposals for new schemes has begun, including all patients in a man- will be available for established tests or datory provisional approval group (Figure
that would require fewer patients to defi ne 1). Predictive safety markers ascertained
prescribed "provisional" or "conditional" sake, this will no doubt be part of routine approval process involving continued sur- patients during the provisional approval veillance for safety signals in all patients. period. For a drug with the "approved" records and monitored databases. In fact, No one would argue that 10,000 patients is label, relevant prospective surveillance initial-phase, commercially available SNP platforms are being utilized routinely by cacy for major illnesses to be available to improve safety of coumadin in clinical variants of interest during clinical tri- earlier—under active and regulated risk- practice, based on retrospective studies, als for a drug as well as for combination interactions in adjunctive trials. Th observational in nature, and do not man-date RCTs but do require consistent and Box 1 Abacavir risk-management example.
Abacavir is a drug that is eff ective in treating HIV/AIDs that was developed in the early 1990s, when there was a huge unmet medical need for lifesaving drugs. There were also organized and eff ective patient advocacy groups who engaged the political system. Abacavir had been shown to be eff ective, but a signifi cant proportion of patients also developed a hypersensitivity syndrome (HSS). Abacavir was granted conditional approval in the late 1990s, subject to a comprehensive risk-management program that continues to this day. HSS was defi ned from studies of approximately 200,000 patients receiving the drug between 1996 sive safety databases by surveillance of and 2000 (ref. 8). In 2002, a report published in Lancet from an academic group reported the association with HLA-B5701 in 14 of 18 patients with HSS.9 In the same month the sponsor Large clinical databases, such as those of studies reported in Lancet that 39 of 84 patients were HLA-B57 positive.8 The regulated risk-management program has continued to test the marker in multiple eff ectively for well-informed provisional populations in order to evaluate prospective diagnostic value in diff erent ethnic groups approval studies without reinventing de and to gather information for the regulators. The drug is now widely used for HIV treatment. novo the clinical trial monitoring schemes HSS can be recognized clinically with clinical follow-up appointments, and, when HSS is observed, abacavir can be safely stopped and patients warned never to receive it again.10 stant is the clinical care and monitoring Patient medical records can refl ect this "allergy." Deaths due to HSS have virtually disappeared environment for prospective surveillance since the mid-1990s. The predictive value of the test is still being evaluated prospectively in that provides both the numerator (safety observational studies of multiple populations receiving the drug. This observational program calls for periodic clinical examinations for HSS. It has also been demonstrated that the test characteristics are diff erent in diff erent ethnic groups and, although highly effi Caucasians, would be dangerous to rely on as a sole predictive test in other ethnic groups cially those that will be mandated by reg- in which HIV is epidemic.11 The cost to GlaxoSmithKline of maintaining this one-off risk- management program is signifi cant, but the drug remains on the market, available to the indications, could also be used to identify "right" patients. In perspective, the cost of the program over 7 years is smaller than the cost new safety data, as well as testing for pro- of a single phase III clinical trial. The cost to patients not receiving the drug would have been spective prediction characteristics.
more than signifi cant; it would have been tragic.
In considering the third question, it is Similar conditional approvals for cancer drugs exist. Surely treatments with RCT- critical to understand that identifi cation of cacy for Alzheimer's disease, depression, chronic obstructive pulmonary a safety marker requires prospective obser- disease, rheumatoid arthritis, diabetes, and other major diseases could similarly benefi t from provisional approvals and closely monitored safety surveillance.
actually quite simple—no matter what may VOLUME 81 NUMBER 6 | JUNE 2007 | www.nature.com/cpt
defi ned in the drug label for selection of patients to treat. Aft er several decades of involvement with genomic technologies and their application to diagnosis and pharmacogenetics, I have formed views on drug development and surveillance that, in the current electronic world, seem ideas are not original; elements have been discussed in statements by offi Food and Drug Administration (FDA), reports by the Institute of Medicine and tion of various components of the health- Figure 1 A rendition of drug development with provisional or conditional approval. A GAO report says
that a "new expedited process" would "serve as an incentive to increase drug development".7 AEs, adverse events; Epi, epidemiology; FTIH, first time in humans; PGX, pharmacogenetics.
agencies (in the United States with suf-fi cient government support to regulate and safeguard health care in the twenty- be concluded from retrospective statistical fi rst century). It would involve formal data, predictive accuracy can be evaluated utilization of comprehensive health-care e power of counts is the clinical response to use of systems to provide electronic data in real an epidemiologic conclusion, usually per- the drug. Even if several drug candidates time as physicians are caring for patients formed retrospectively, could be confi rmed for its usefulness in prospective epidemiol- patients, full clinical trials are necessary ogy studies in populations using uniform, the curve in the use of electronic health for safety of a drug for at least the fi rst 200,000 patients need to be observed sys- tematically.5 Serious clinical safety signals, including those due to dosing, need to be defi ned in real time using as few aff ected Figure 1 is a simplistic diagram of
tested prospectively to defi ne patients who predict outcomes can shorten clinical tri- als once they have been established, but those being developed to treat important the time frame for the evaluation of sur- in-a-lifetime, comprehensive genetic vari- diseases or illnesses with major medical ant scans will allow in-time defi nitions of patient profi les that are highly correlated to be eff ective (see Box 1). Th
cholesterol as a surrogate marker, but the with a particular safety signal. Eventually drug discovery and development is still a such data will be routinely used in medi- "fl ow through a pipeline." However, for rent use were initiated over the past sev- cal care, when the genetic data have been standardized and are available on a "bank sulted with drug-development experts (in of a new drug for Alzheimer's disease.4 The right safe and effective drug at the
Region-specifi c brain glucose utilization right dose for the right patient at an
as a surrogate marker for the next class of appropriate cost
candidate drugs for Alzheimer's disease calls for "collaborative efforts among may allow faster screening than the small fi les can also be used to enrich patients CLINICAL PHARMACOLOGY & THERAPEUTICS | VOLUME 81 NUMBER 6 | JUNE
to . . . identify diseases in great need of approval. . . . To help ensure safety, the structures would be in place to follow a Targets would still be discovered, screen- medicines ascertained on the basis of data ing assays developed, leads processed by medicinal chemists, and candidates tested for preclinical safety and drug metabolism, Conclusion
and then drugs would be tested for the fi rst To return to Dr. Lesko's questions, large- scale observational studies in a prospec- to work, although certainly the defi nition of animal metabolism could be assisted by ing signals as they occur, and for rapidly performed starting with the FTIH studies. Organ toxicity markers might well be used routinely before FTIH, as is beginning to can provide for real-time individual and tify the adverse clinical signals to associ- ate with a safety test. Patients exhibiting those signals would be tested for genetic panels (including ethnic-specifi c variants) also be available for prospective observa- a new model (Figure 1) will allow
tional monitoring to assess predictability. With all parties in the provision of health Requirements for integrating drug
and eff ectively improve health care with development, safety surveillance,
a cradle-to-grave electronic observational and medical-outcome prospective
determined prospectively over years.
In its simplest form, a prospective moni- CONFLICT OF INTEREST
This article does not necessarily reflect the views Lesko, L.J. Personalized medicine: elusive dream or imminent reality? Clin. Pharmacol.
Ther. 81, 807–816 (2007).
metabolism and transport. Nat. Genet. 37,
84–89 (2005).
Roses, A.D. 2025: the practice of neurology: back from the future. Arch. Neurol. 58, 1766–
Alzheimer's disease in persons homozygous for the epsilon 4 allele for apolipoprotein E. N. Engl. J. Med. 334, 752–758 (1996).
Roses, A.D. Genome-based pharmacogenetics and the pharmaceutical industry. Nat. Rev. Drug Discov. 1, 541–549 (2002).
VOLUME 81 NUMBER 6 | JUNE 2007 | www.nature.com/cpt
Kelly, P., Stallard, N., Zhou, Y., Whitehead, abacavir. Lancet 359, 1121–1122 (2002).
J. & Bowman, C. Sequential genome-wide et al. Association between presence association studies for monitoring adverse events in the clinical evaluation of new drugs. hypersensitivity to HIV-1 reverse-transcriptase having adequate education or training in Stat. Med. 25, 3081–3092 (2006).
inhibitor abacavir. Lancet 359, 727–732 (2002).
10. Phillips, E.J. Genetic screening to prevent New Drug Development: Science, Business, abacavir hypersensitivity reaction: are we there Regulatory, and Intellectual Property Issues yet? Clin. Infect. Dis. 43, 103–105 (2006).
a critical question that the authors have Cited as Hampering Drug Development Efforts, 11. Hughes, A.R. et al. CNA30027 Study Team; not addressed as to whether, and to what GAO-07-49, 35–36 (Government Accountability CNA30032 Study Team. Association of genetic extent, the reluctance of some physicians variations in HLA-B region with hypersensitivity to abacavir in some, but not all, populations. to prescribe adequate pain medications is HLA-B region and hypersensitivity reactions to Pharmacogenomics 5, 203–211 (2004).
attributable to the education and training that physicians receive in medical school and postgraduate training as opposed to See ARTICLE page 903
what the authors term fear of government action. As the DEA stated in the policy The DEA's Balancing Act to
statement, it is not the agency's role to provide medical training to physicians Ensure Public Health and Safety
on the general practice of medicine or to specify the precise medical circumstances and patient characteristics that warrant JT Rannazzisi1
the use of opioids to treat pain. Rather, that responsibility is carried by the medi-cal community, and how it does so seems In their article in this issue, Reidenberg and Willis assert that there
likely to be the primary factor determina- are multiple barriers to the adequate treatment of pain and that one
of these barriers is fear of government action against a physician
state boards and associations have issued who prescribes opioids for patients in pain.1 At the same time, the
authors state that the risk of a physician's being punished by either a
ment of pain patients, while taking steps state medical board or the Drug Enforcement Administration (DEA)
for a patient in pain with adequate medical record documentation is
very small.
(CSA), the DEA is obligated to ensure the sional practice should in no way interfere availability of pharmaceutical controlled with the legitimate practice of medicine or cause any physician to be reluctant to pro- extremely small. Indeed, the DEA recently e DEA to prevent these controlled substances, published a policy statement that sought also stated in that document that it wishes to emphasize this very point and alleviate medical professionals that the agency has channels. In particular, the DEA's role prescribing controlled substances to treat embarked on a campaign to "target" physi- under the CSA is to ensure that controlled cians who prescribe controlled substances substances are prescribed, administered, the Federal Register on September 6, 2006, for the treatment of pain (or that physi- and dispensed only for legitimate medical can be accessed on the Web sites of both cians must curb their legitimate prescrib- purposes by DEA-registered practitioners the Federal Register and the DEA's Offi ing of pain medications to avoid liability). acting in the usual course of professional It appears that the fi ndings of Reidenberg and Willis are consistent with the DEA's assertion that there has been no upsurge in To protect public health and safety, the law that physicians may prescribe control- the number of cases initiated by the agency DEA has always had a legal obligation to led substances only for legitimate medical against physicians who prescribe control- investigate the extremely small fraction of physicians who use their DEA regis-tration to commit criminal acts or oth- 1Office of Diversion Control, Drug Enforcement Administration, Alexandria, Virginia, USA. Correspondence: JT Rannazzisi ([email protected]) this obligation seriously, because even a single physician who uses his or her DEA CLINICAL PHARMACOLOGY & THERAPEUTICS | VOLUME 81 NUMBER 6 | JUNE
Source: http://studwww.ugent.be/~smdkeyse/elusive_dream_imminent_reality.pdf
Microsoft word - cessation of a seizure disorder.doc
CESSATION OF A SEIZURE DISORDER: Correction of the Atlas Subluxation Complex Robert J. Goodman, D.C., John S. Mosby Jr., D.C., M.D. ABSTRACT Observations of one patient presenting with a seizure disorder are reported. Relief of symptoms is noted subsequent to correction of the misalignment of the occipito-atlanto-axial complex. The authors suggest a relationship between the misaligned skull and
dickensplacesurgery.co.uk
Weight Reduction - How to Lose Weight This leaflet provides a checklist of things that may help you to lose weight. A further separate leaflet called 'Obesity and Overweight in Adults' gives more general information about the topic. How weight loss works The science In some respects, it is quite simple. Your weight depends on how much energy you take in (the calories in food and dr


We are excited to play a couple gigs in July. The band has been rehearsing and I think it's gonna be smokin'. We'll have all six ep's with us too. Here is the Facebook invite page.
Pink Moth will play this year's Kelp Records BBQ this Friday afternoon, June 17, 1:30pm set time. Free food starting at 1! It is happening at Global Village Backpackers, King and Spadina. Take the day off from that pesky job- it's summertime! Here's the facebook invite.
This is the last show of the tour. Really feeling the pull of my home and bed in Canada. What a wimp! I get my bits together and hop on the train through the former East to Erfurt, a nice town south of Berlin. The venue is excellent and the father/son team of Ralph and Phillip run the show and look after us to the T. It is an honour to play here and it feels good to be welcomed and treated well. Great food and kind people. I am supporting another Canadian act tonight, Brasstronaut from Vancouver. Nice to connect with these guys. We have some good laughs. The place fills up and i do my thing for the last time. It feels and sounds good but the ipod betrays me on the last song. I don't think anyone noticed. A very drunk spaniard talks my ear off for i while, then i escape to bed down in the band flat while the others go out to party. The next day it's back to Berlin to squeeze the most out of my last 3 days in the flat before heading to Paris, and home.
Back to Berlin. I miss my little balcony and the hammock. We head to Schokoladen to see fellow Canadians Olympic Symphonium, who are amazing, as well as being lovely people. The next day is the house show at Tobin's place with Snailhouse. We get things ready and make a big dinner for 10 before the show. I play my set to a lovely, attentive audience and it feels great. Lots of energy flying around the room. Such a nice intimate show. Then Snailhouse take the stage. They are so darn good. Singing harmonies and that upright bass and those fantastic songs. Inspiring. A very special night where everything seems to fall perfectly into place. I feel lucky to be a part of all this.
I am not used to being on a plane for such a short time. I did some reading, had a coffee, looked up, and we were there. Easy peasy to Gothenburg. Hopped on a bus into town and ran into B. Kleinhenz in the street. Funny! He lives across the water, so we get on the ferry. Nice to relax and hang out. Gothenburg has a small town feel and its good to be by the ocean. The show is in a small theater. The Black Atlantic roll into town and we get things going, good to see those guys again! This is a great show in every way. Best one yet. Thanks, Bjorn!


Glenmark Pharmaceuticals has signed a strategic development and licensing agreement with Celon Pharma, a Poland-based company, for the development and marketing of its generic version of Seretide Accuhaler in Europe targeting the treatment of lung diseases. GSK's Seretide Accuhaler product, fluticasone and salmeterol, is a dry powder inhaler to treat chronic obstructive pulmonary disease.
"As per the terms of the agreement, Glenmark has obtained semi-exclusive marketing and distribution rights of the product across 15 European countries including Great Britain, Germany, Belgium, the Netherlands, Italy, Sweden, Norway and Romania, among others," Glenmark said in a statement.
As per the deal, Celon will earn an upfront payment and certain milestone payments at different stages of the product's development, including royalties on sales, from Glenmark.
The period of the distribution agreement was for 10 years, extendable to two years.
Glenmark Pharmaceuticals Chairman & MD Glenn Saldanha said, "The deal reinforces Glenmark's growing capabilities in the respiratory segment and is a significant step forward towards building a strong respiratory franchise in Europe."
Celon Pharma CEO Maciej Wieczorek said, "The common experiences of both companies in the area of manufacturing, commercialisation and distribution of inhaled drugs will translate into greater availability of combination therapy in a DPI inhaler in many European countries."


An internet urban legend about a supposedly haunted Jewish wine cabinet auctioned on eBay in 2004 spawned not only a book and a blockbuster horror film but also a rising trend in selling so-called "haunted" items on eBay.
The tale of the dybbuk box has appeared on the internet on and off since 2004 but it only came to media attention with the release of The Possession, a 2012 film about a girl who is possessed by an evil spirit residing in an old wooden box. Her parents seek help from an Orthodox Jewish rabbi.
In Jewish mythology, a dybbuk ( from Hebrew adhere or cling) is a malicious spirit.
The film is inspired by an urban legend recounted by eBay user Spasmolytic. He chronicled the events that he, the original owner Kevin Mannis and several other people experienced while they were in possession of the box.
The box is now in the possession of Jason Haxton, the director of the Museum of Osteopathic Medicine in Kirksville, Missouri.
Haxton has written a book about the wine cabinet, and claims that he has managed to seal the dybbuk back into its box and has hidden it.
The publicity from the film and book has spawned an online market in the UK and the US in objects said to be possessed by a spirit.
Spooky-looking vintage china dolls are so popular on eBay that it has given them their own section on the website. There are also haunted vintage photographs "with eyes that follow you", haunted mirrors, haunted boxes, haunted Regency-style furniture, and even a pair of haunted earrings.
A recent auction featured a "haunted old doll" which sold for £108 after 46 bids by mummyrose27, of Stoke-on-Trent.
The sale description read: "Need this doll gone NOW!! We hear odd sounds and my son has been scratched on his face in his sleep. He's started to sleepwalk. I've done EVPs and caught a childlike voice talking back! I don't want this doll in the house anymore!"
The seller updated the page to add that she woke up with bruises on her leg and that her eldest son saw a boy in his room one night that "walked by and just flew out the window".
Accompanying the auction were photos of an doll that looked like it came from the 1960s, together with a close-up image of a child's chin that has been scratched.
IBTimes UK contacted the seller but did not receive a reply.
According to several of the auctions we looked at, the sellers state that eBay requires them to list the item as "for entertainment". They also maintain that they are not responsible if something bad happens to the new owner by buying the item, or if nothing happens at all.
The site said: "eBay allows sellers to describe intangible aspects of physical items which are for sale."
Currently being sold on eBay by starcent17 in New Jersey is a "haunted charging box". This silver vessel, lined with red velvet, is also the home of a female "Madden Jinn", a good spirit that grants wishes if you put coins, jewellery or lottery tickets into the vessel.
This user claims to be a paranormal investigator who has been working with spirits for 30 years. The objects she sells are picked up during investigations. She writes on her auctions that "spirits can attach themselves to many types of things" including dolls and jewellery.
She has 12 items on sale, most of them haunted porcelain dolls that are vessels for spirits.
She claims to have recorded over 18,000 examples of Electronic Voice Phenomenon (EVP): unexplained "other" voices recorded alongside the investigator's own voice on a digital recorder.
Starcent17 adds the disclaimer: "If you are not a firm believer, your haunted item is not going to communicate with you. The only type of items I have all possess good spirits. I never deal in anything evil in any way. My items have brought me much joy over the years, and I love to pass them on so they can continue their journey."
A look at starcent17's feedback shows an overwhelmingly positive response. A few buyers claim that they have experienced supernatural activity but it seems that most of the buyers were content with owning a doll with nightmarish potential.
"If you did not know, haunted dolls have been recorded throughout our history and continue even today. There are many famous people who own huge displays of haunted dolls," she writes on all her auction pages.
If the haunted doll you bought starts doing a Chucky in your living room, eBay can offer you a remedy - for a price.
A guide by eBay user The Haunted Store advises buyers on what they should do if they want to invest in haunted items. One tip is: "Make sure you have some sea salt and holy water/oil available to you in the event that things turn bad with your item, to bless your home with."


text:
Fela and Afrika 70: Zombie (1977)
The original "F— The Police".
THE SCENE: In 1977 the government of Nigeria was thick with corrupt brutish thugs, the type who denied civil rights to its populace as a matter of principle. Of the many activists who spoke out against the regime none was more popular than bandleader Fela Kuti, who released numerous top-selling albums criticizing the governments' wide-ranging incompetence, peaking with the incendiary Zombie.
Over a twelve-minute percolation of tart guitar skanks, brisk funk beats and hard horns bleats, his band Afrika 70 tightly rages through the title track, in a sound Fela dubbed "Afrobeat". Muscular as a bicep yet deft as a finger, the song pulses large and small, hot and cold, sometimes reducing down to a mere guitar pluck and a shaker that sounds like sizzling rice soup.
The frenetic, danceable humanity of the music sets up the dispassionate precision of Fela's voice, coolly spitting out his opinion of the puppet-like Nigerian military:
Zombie no go go, unless you tell am to go
Zombie no go stop, unless you tell am to stop
Zombie no go turn, unless you tell am to turn
Zombie no go think, unless you tell am to think
Eventually he begins barking orders like a power-drunk drill sergeant:
Quick march/Slow march/Left turn /Right turn
About turn /Double time/Sa-lute /Open your hat
Stand at ease/Fall in/Fall out/Fall down
At twelve minutes long and the entirety of Side One, "Zombie" is a energetic full-body release of frustration, from the legs to the brain, simultaneously an exhortation and an exorcism.
THE FALLOUT: Due to its relentless negative critique of the current government, a new Fela album would usually result in a police interrogation of his crew, followed by a totally illegal beatdown. With Zombie, however, he had really pissed off the military, who somehow took offense when civilians would continually point at them in the street and shout "Zombie!" As payback for his mockery, over one thousand soldiers stormed his private compound, beat every man, woman and child they could find and burnt his house to the ground, but not before tossing Fela's mother out the window to her death. (No, that's not acting like a zombie at all…)
In retaliation he delivered his mother's coffin to the main army barracks in Lagos, then wrote about the experience in the title song of his subsequent album Coffin for Head of State. Even in mourning, Fela was uncompromising about the nature of right and wrong.
Zombie is available from Amazon and you can sample tracks here:
American musicians, even with their freedom of speech under attack, have it pretty easy, "Cop Killer" got Ice-T dropped from his label, but 15 years later he's made millions playing a cop on a television. The 15 years following Zombie found Fela surviving additional police beatings, plus a two-year jail sentence on trumped-up currency fraud charges. He consistently put his livelihood and his life on the line with each album, and Zombie was his fearless masterpiece.
See you next Wednesday.
NEXT WEEK: Rufus Harley and his electric…bagpipes?
Author Mark Montgomery FrenchPosted on November 21, 2007 July 27, 2016 Categories Afrobeat, Fela, Funk
One thought on "Fela and Afrika 70: Zombie (1977)"
holymansound says:
…and a shaker that sounds like sizzling rice soup…
-nice
Zombie, Sorrow Tears and Blood, and Expensive Shit stand as Mr. Kuti's triple punch to the government in Nigeria. There were many more songs that criticized the regime but these three were the most scathing and outright dancable. We need a Fela for these times.
Once again, big up Mr. French
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On January 9th Patently Apple posted a report on the FTC-Qualcomm trial noted that "Some of the largest phone makers in the world have had Qualcomm's licensing gun put to their head".
But a regional court in the city of Mannheim dismissed the Qualcomm suit as groundless in an initial verbal decision, saying the patent in question was not violated by the installation of its chips in Apple's smartphones.
Qualcomm continues to provide chips for Apple's older devices, but the ongoing dispute has left Apple without a clear path to a 5G-capable iPhone unless it strikes a deal with another chipmaker.
Talking about the current year, Tony Blevins, Apple supply chain executive, has affirmed that the company will now consider MediaTek and Samsung along with Intel to manufacture and supply 5G modem chips to Apple.
In a testimony last Friday, we have heard new details about the Qualcomm - Apple relationship, the $1 billion incentive Apple received, and what Qualcomm demanded in return.
"The strategy was to dual source in 2018 as well". It is reported that Qualcomm will appeal the decision.
He added that Apple had looked at using Intel chips for the iPad Mini 2 in 2013 but abandoned the idea because it would be required to forfeit those rebates. And earlier this month Apple was forced to withdraw the iPhone 7 and 8 from its retail stores in Germany, after Qualcomm posted €1.34BN in security bonds to enforce the December court decision - which related to a power management patent.
Also, Apple won't be able to launch 5G iPhones this year because Intel's 5G chips won't be ready until 2020.
The apple company is undoubtedly very closely monitoring the FTC case, considering that it is dealing with its own pending legal action that is generating comparable assertions in opposition to Qualcomm. Qualcomm charges a percentage of the selling price of each handset sold regardless of whether the device uses its chips. "We have been unable to get them to support us on new design wins past that time [when Apple filed a lawsuit against Qualcomm]", Williams said.
Qualcomm will naturally appeal the decision but it might already be too busy defending itself in a different major case. No offense to (Intel) but we don't want to be a single supplier with them. The regulatory agency called Apple chief operating officer Jeff Williams as a witness to help show that Qualcomm has abused its global dominance in the smartphone market. When Mollenkopf refused to play ball, Williams had to contact Intel which "had to scramble" to meet Apple's supply needs.


Automotive News Europe will host an hour-long Webinar highlighting the need for clear and streamlined business models in the auto industry. Among the speakers will be Hyundai Europe's Chief Operating Officer Allan Rushforth.
Other speakers will be Daniela Craemer-Kuehn, head of training operations at Raytheon Professional Services, and Ralf Landmann, senior partner at Roland Berger.
ANE Editor-in-Chief Harald Hamprecht will moderate the event, which is sponsored by Raytheon. It takes place at 3 p.m. Central European Time on Tuesday, May 31.


text:
Prison ministry sees 15-year dream become reality
By Lindsay SteeleNovember 18, 2014
International (MNN/CBI) — It's been a long road for Crossroad Bible Institution to get where they are. CBI is a ministry that helps prisoners come to know God.
This year they launched Tier 2 Life Skills Program, which features practical courses on the Christian work ethic, family, addiction recovery, financial stewardship, and community. The launch was a 15-year dream come true, and the lessons are pouring into CBI offices around the world.
The international program has expanded to include 20 established satellite campuses, with several more emerging.
But that wasn't the only 15-year dream in the making. The next dream up and coming is the development of Crossroad College International.
In the mid-90s, Congress cut off Pell Grants for people in prison. Since many prisoners are among the poorest of the poor, this termination of Pell Grants, combined with the increasing tuition costs of financially-driven colleges and universities, cut many prisoners off from the opportunity to take college courses.
However, CBI has been piloting a handful of college-level courses known as Tier 3. So far, over 3,500 students have participated in Tier 3, which helped CBI perfect their delivery system.
For the last five years, CBI has been in Phase 1, developing the college and functioning as a licensed post-secondary school by the State of Michigan, authorized to grant diplomas.
The next big leap is into Phase 2. This project is a three-year plan. It involves a $1.2 million endeavor to become a fully accredited two-year degree granting institution. Professors with PhDs are preparing courses, and Tier 3 Instructors will continue serving as students' Teaching Assistants. A College Advisory Board of experts has also been appointed to guide the process.
Instead of the institution being a Bible college, it will be a Christian liberal arts college, preparing students to think critically as Christians. CBI says, "We envision that such a well-rounded education can be applied to any line of work that our students will undertake when they reenter society."
As Phase 2 begins, pray for opportunities for more students to sign up for courses.
crossroad bible instituteprison ministry
Carolyn Luce says:
Would love to write to fellow Christians in prison. I have for years
with Chuck Colson's ministry but that no longer exists. Do you have
such a program? If so send me names. Iam elderly and would love
to encourage others.
Lucille Brumbaugh says:
Praise the Lord! Do you have anything in any Arizona prisons?
Sorry, no data found.
Crossroads Prison Ministries
Pray that more prisoners will surrender their lives to Christ.
Iraqi refugees begging for money and food
La Gonave, clean water, and the Gospel
How to stop child trafficking: pray, shop, give
Russia openly violating truce with Ukraine


text:
HALCYON JETS INC v. JET ONE GROUP INC
HALCYON JETS, INC., Plaintiff-Respondent, v. JET ONE GROUP, INC., et al., Defendants-Appellants.
MAZZARELLI, J.P., SWEENY, MOSKOWITZ, MANZANET-DANIELS, ROMÁN, JJ. Steven G. Legum, Mineola, for appellants. Schrader & Schoenberg, LLP, New York (Bruce A. Schoenberg of counsel), for respondent.
Order, Supreme Court, New York County (Emily Jane Goodman, J.), entered March 16, 2009, which, insofar as appealed from, denied defendants' motion pursuant to CPLR 3211(a)(7) to dismiss plaintiff's cause of action for defamation, unanimously affirmed, without costs.
The parties are business competitors. After filing a federal court complaint setting forth fraud and RICO claims for various alleged wrongdoing by plaintiff, defendants disseminated what the parties characterize as a "press release" reporting the filing of their federal complaint and summarizing its allegations. Plaintiff then instituted this action for defamation, alleging that the press release was false and resulted in significant consequential business losses; defendants moved to dismiss on the basis of the protections afforded by New York Civil Rights Law § 74 to fair and accurate reports of judicial proceedings; and the motion court denied the motion on the basis of Williams v. Williams (23 N.Y.2d 592 [1969] ).
Williams created a judicial exception to the statutory protections if it appears that the public policy goals of the statute are being thwarted by the commencement of litigation intended as a device to protect a report thereof and thereby disseminate defamatory information (see id. at 599). Defendants' intention to use the federal action as such a device is a factual issue that is sufficiently pleaded and cannot be presently be decided. We note, as did the motion court, that the press release here, unlike that in Williams, was not the reportage of an independent publisher but rather was issued by defendants themselves. While not dispositive, defendants' self-publication tends to connect the litigation and report thereof more closely than in Williams, making this an a fortiori case, and undermining defendants' argument that because their press release, unlike that in Williams, was not directed at members of the parties' industry but was disseminated as a general news item, Williams does not apply as a matter of law.


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