: Analysis of a simple, single-move tale of class H-I, of the type: kidnapping of a person.

He had introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and given a proof of the Riemann – Roch theorem with them ( a version appeared in his Basic Number Theory in 1967 ).

The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space.

which can be viewed as a version of the Pythagorean theorem.

This position is a more refined version of the theorem first discovered by David Hume.

It was Pierre-Simon Laplace ( 1749 – 1827 ) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence.

It is also an example of a more generalized version of the central limit theorem that is characteristic of all stable distributions, of which the Cauchy distribution is a special case.

This is the Cartesian version of Pythagoras ' theorem.

An easier to state version of the theorem uses graph theory.

The simplest version of this theorem that suffices in practice for most needs, and has connections with the Löwenheim-Skolem theorem, says:

This theorem by Henkin is the most directly obtained version of the completeness theorem in its simplest proof.

The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 ( and a rewritten version of the dissertation, published as an article in 1930 ) is not easy to read today ; it uses concepts and formalism that are outdated and terminology that is often obscure.

" Another version of Hahn – Banach theorem is known as Hahn – Banach separation theorem or the separating hyperplane theorem, and has numerous uses in convex geometry.

Another version of Hahn – Banach theorem states that if V is a vector space over the scalar field K ( either the real numbers R or the complex numbers C ), if is a seminorm, and is a K-linear functional on a K-linear subspace U of V which is dominated by on U in absolute value,

Another version of Hahn – Banach theorem is known as the Hahn – Banach separation theorem.

One version of Ado's theorem is that every finite dimensional Lie algebra is isomorphic to a matrix Lie algebra.

Roughly speaking, in proving the first incompleteness theorem, Gödel used a slightly modified version of the liar paradox, replacing " this sentence is false " with " this sentence is not provable ", called the " Gödel sentence G ".

A version of the Stone – Weierstrass theorem is also true when X is only locally compact.

Shannon's version of the theorem states:

His Italian journey was a poet's version of those perennial thrusts across the Alps of the German emperors of the Middle Ages.

At a recent meeting of the Women's Association of the Trumbull Ave. United Presbyterian Church, considerable use was made of material from The Detroit News on the King James version of the New Testament versus the New English Bible.

Fing, a lean, chiseled, impeccable gentleman of the old school who was once mistaken on the street for Sir Cedric Hardwicke, is responsible for the rediscovery of Verdi's earliest, most raucous opera, Nabisco, a sumptuous bout-de-souffle with a haunting leitmotiv that struck me as being highly reminiscent of the Mudugno version of `` Volare ''.

It was heard again in Philadelphia in 1927 in the first version of `` Strike Up The Band '' and again abandoned shortly before the entire show was given up.

Fudo, the god of wisdom, was also thought of as the Japanese version of Acala.

As with most mythology, there is a tale which offers an alternative version of these events: in Argonautica ( iv. 760 ) Zeus ' sister and wife Hera alludes to Thetis ' chaste resistance to the advances of Zeus, that Thetis was so loyal to Hera's marriage bond that she coolly rejected him.

A version with Alicia Keys was included in Charles ' 2005 duets album Genius & Friends.

Its drafting by the Continental Congress began in mid 1776, and an approved version was sent to the states for ratification in late 1777.

The first version of the robot was first developed back in 2003.

Asteroids is also the first game to use Atari's " QuadraScan " vector-refresh system ; a full-color version known as " Color-QuadraScan " was later developed for games such as Space Duel and Tempest.

The Atari 7800 version was a launch title and featured co-operative play, it was the built in game on the European Atari 7800 release.

Also, a new version of Asteroids was developed for PlayStation, Nintendo 64, Windows, and the Game Boy Color in the late 1990s.

In 1960, Nicholas Poppe presented what was in effect a heavily revised version of Ramstedt ’ s volume on phonology that has since set the standard in Altaic studies.

In the 1998 version, Alliaceae were a distinct family ; in the 2003 version, combining the Alliaceae with the Agapanthaceae and the Amaryllidaceae sensu stricto was recommended but optional ; in the 2009 version, only the broad circumscription of the Amaryllidaceae is allowed, with the Alliaceae reduced to a subfamily, Allioideae.

" The first well-known version of anarcho-capitalism was formulated by Austrian School economist and libertarian Murray Rothbard in the mid-twentieth century, synthesizing elements from the Austrian School of economics, classical liberalism, and nineteenth century American individualist anarchists Lysander Spooner and Benjamin Tucker ( rejecting their labor theory of value and the normative implications they derived from it ).

In the most famous version of her myth, her birth was the consequence of a castration: Cronus severed Uranus ' genitals and threw them behind him into the sea.

In another version of her origin, she was considered a daughter of Zeus and Dione, the mother goddess whose oracle was at Dodona.

As someone in constant contact with ( this watered-down version of ) “ nature ”, the farmer was positioned to experience moments that transcend the mundane material world.

" In the version that was offered by the Hellenistic poet Callimachus, which has become the standard setting, Artemis was bathing in the woods when the hunter Actaeon stumbled across her, thus seeing her naked.

Base also published a colouring book version for children to do their own colouring.

Several later books were original in Europe, and at least one novel has only ever appeared in Italian, no English version yet published.

Several editions featuring Newton's first three stanzas and the verse previously included by Harriet Beecher Stowe in Uncle Tom's Cabin were published by Excell between 1900 and 1910, and his version of " Amazing Grace " became the standard form of the song in American churches.

In 1960, Hill published an abridged version of the book containing the Andrew Carnegie formula for wealth creation.

Earlier version first published in New English Dictionary, 1913 .</ ref >

His version of Columbus ' life, published in 1829, was more a romance than a biography.

How to design and implement a stripped-down version of an interpreter for the BASIC language was covered in articles by Allison in the first three quarterly issues of the People's Computer Company newsletter published in 1975 and implementations with source code published in Dr. Dobb's Journal of Tiny BASIC Calisthenics & Orthodontia: Running Light without Overbyte.

In 1648 there appeared the play Le Gran Tamerlan et Bejezet by Jean Magnon, and in 1725 Handel's Tamerlano was first performed and published in London ; Vivaldi's version of the story, Bajazet, was written in 1735.

* The published version of Wellington's initial despatch describing the battle.

The following websites have either online material that supports the popular version of the Bermuda Triangle, or documents published from official sources as part of hearings or inquiries, such as those conducted by the United States Navy or United States Coast Guard.

Between then and 1764, when a more formal revised version was published, a number of things happened which were to separate the Scottish Episcopal liturgy more firmly from either the English books of 1549 or 1559.

In 1994, the prayers announced " allowed " by the 1982 Bishops Council of the Anglican Church of Korea was published in a second version of the Book of Common Prayers In 2004, the National Anglican Council published the third and the current Book of Common Prayers known as " seoung-gong-hwe gi-do-seo " or the " Anglican Prayers ", including the Daily Masses, Special Masses, Baptism, Confirmation, Funeral Mass, Wedding Mass, Rite of Ordination Mass, and all of the other events the Anglican Church of Korea celebrates.

Aside from the American version and the newly-published Philippine Book of Common Prayer, the Filipino-Chinese of Saint Stephen's Pro-Cathedral in the Diocese of the Central Philippines uses the English-Chinese Diglot Book of Common Prayer, published by the Episcopal Church of Southeast Asia.

* Bubble Trouble A detailed analysis of the arcade version, as published in Retro Gamer magazine.

The first, classified, edition of Factbook was published in August 1962, and the first unclassified version in June 1971.

A Spanish version, with a similar format and using a slightly revised version of the 1909 Reina-Valera translation, was published in 2009.

However, it is still printed in every version of the King James Bible published by the church.

Before there was an official standard for C, many users and implementors relied on an informal specification contained in a book by Ritchie and Brian Kernighan ; that version is generally referred to as " K & R " C. In 1989 the American National Standards Institute published a standard for C ( generally called " ANSI C " or " C89 ").

There is a board game based on the computer game version of Civilization that was published in 2002.

In 1974, ANSI published a revised version of ( ANS ) COBOL, containing a number of features that were not in the 1968 version.

In 1985, ANSI published still another revised version that had new features not in the 1974 standard, most notably structured language constructs (" scope terminators "), including,,, etc.