The close relationship of alternative algebras and composition algebras was given by Guy Roos in 2008: He shows ( page 162 ) the relation for an algebra A with unit element e and an involutive anti-automorphism such that a + a * and aa * are on the line spanned by e for all a in A.

* Conjugate ( graph theory ), an alternative term for a line graph

A recent alternative criterion for the Cassie – Baxter state asserts that the Cassie – Baxter state exists when the following 2 criteria are met: 1 ) Contact line forces overcome body forces of unsupported droplet weight and 2 ) The microstructures are tall enough to prevent the liquid that bridges microstructures from touching the base of the microstructures.

Another alternative ISDN configuration can be used in which the B channels of an ISDN BRI line are bonded to provide a total duplex bandwidth of 128 kbit / s.

As the book presents alternative resolutions for the Mage line, Chapter Two also presents an alternative interpretation that the tenth sphere is " Judgement " or " Telos " and that Anthelios ( the red star in the World of Darkness metaplot ) is its planet ( each sphere has an associated planet and Umbral realm ).

USC Literature Professor Henry Jenkins cited Dr. McCoy's " He's dead, Jim " line as an example of fans actively participating in the creation of an underground culture in which they derive pleasure by repeating memorable lines as part of constructing new mythologies and alternative social communities.

An alternative is Kingham railway station ( approximately 5 miles from Stow ) on the same line.

Also, it is difficult for a merchant transmission line to compete when the alternative transmission lines are subsidized by other utility businesses.

A surge of energy on a transmission line will see an impedance of Z < sub > 0 </ sub > prior to any reflections arriving, hence surge impedance is an alternative name for characteristic impedance.

Line numbers are an alternative to a named label ( and used in some languages such as Fortran and BASIC ), that are whole numbers placed at the beginning of each line of text within the source code.

After 1987, IBM PC compatibles dominated both the home and business markets of commodity computers, with other notable alternative architectures being used in niche markets, like the Macintosh computers offered by Apple Inc. and used mainly for desktop publishing at the time, the aging 8-bit Commodore 64 which was selling for $ 150 by this time and became the world's best-selling computer, the 16-bit Commodore Amiga line used for television and video production and the 16-bit Atari ST used by the music industry.

An alternative to preemption on slower links, such as dialup and digital subscriber line ( DSL ), is to reduce the maximum transmission time by reducing the maximum transmission unit.

His Queen consort, Margaret of Anjou, was pregnant, and even if she should miscarry, the marriage of the newly ennobled Edmund Tudor, 1st Earl of Richmond to Margaret Beaufort provided for an alternative line of succession.

An alternative plan was devised in the 1970s to extend the Jubilee line parallel to the River Thames: this would have taken the line from Fenchurch Street to Thamesmead via St Katharine Docks, Wapping, Surrey Docks North, Millwall ( near to South Quay DLR station ), North Greenwich, Custom House, Silvertown, Woolwich Arsenal, and thence to Thamesmead.

The resulting line became known as the Morden – Edgware line, although a number of alternative names were also mooted in the fashion of the contraction of Baker Street & Waterloo Railway to " Bakerloo ", such as " Edgmor ", " Mordenware ", " Medgway " and " Edgmorden ".

An alternative commenting convention affects an entire source code file, known as a " literate script ", in which every line is considered a comment unless it starts with a sign.

The alternative called for park and ride lots to be constructed along the Route 55 corridor, providing access to the line.

An ancient and alternative way in which women managed to rise to power, especially without displacing the direct male line descendants of the first monarchs, is the historical Consortium or Coregency between husband and wife or other relatives, the most notable of these being the cases of Hatshepsut and Thutmose III, as well as the Ptolemaic Dynasty's Kings and Queens.

However, increasingly, for many ' time critical ' applications such as air line reservation systems, point-of-sale applications, ATMs ( cash-point machines ), Airline Guidance systems, Collision avoidance systems and numerous modern web based applications-operating in a real-time environment where speed of response is fundamental-there is little alternative.

" An alternative explanation ( see Sam Davis Elliott's Soldier of Tennessee and sources cited therein ) of the name is that Peter Decherd, who donated the land for the railroad right-of-way ( and was therefore given the right to name two stations along the line ), named one station Decherd, and the other Tulkahoma ( later corrupted to Tullahoma ).

Many groups have translation checkers to reduce the chances of letting translation errors slip through, and / or to give an alternative wording / meaning of a certain line to aid in editing an ambiguous translation.

The largest hurdle the Republicans would have to face is a state law which says that before making a first race, one of two alternative courses must be taken: 1

The most common explanation suggests that the name was taken from the railway station in Marple, Stockport, through which Christie passed, with the alternative account that Christie took it from the home of a Marple family who lived at Marple Hall, near her sister Madge's home at Abney Hall.

" Although throughout his book Camus is concerned to present " the rebel " as a preferred alternative to " the revolutionary " he nowhere acknowledges that this distinction is taken from the one that Stirner makes between " the revolutionary " and " the insurrectionist ".

MIT has also taken steps to reduce its environmental impact by running alternative fuel campus shuttles, subsidizing public transportation passes, and building a low-emission cogeneration plant that serves most of the campus electricity, heating, and cooling requirements.

In 2001, the European Association for Palliative Care recommended that oral oxycodone could be taken as a second-line alternative to oral morphine for cancer pain.

This led to murmuring that the gods of Paganism had taken greater care of the city than that of the Christian God, inspiring St Augustine to write The City of God, alternative title " De Civitate Dei contra Paganos: The City of God against the Pagans ", in which he claimed that whilst the great ' city of Man ' had fallen, Christians were ultimately citizens of the ' city of God.

An alternative story was that when lost and wandering in Phrygia, Silenus was rescued by peasants and taken to King Midas, who treated him kindly.

He points out that several chronicles refer to him as Edward the Fourth ( the title he would have taken as King had he outlived his father ): this name would obviously have become confusing when the actual Edward IV succeeded in 1461, and this may have been the period when an alternative had to be found.

BART has served as a rapid transit and commuter rail system, and provided an alternative transportation route to highway transportation, though its critics counter its success has taken four decades to come to fruition at a steep cost during the interim.

The International Committee of the Fourth International ( ICFI ) was established by several sections of the International as an alternative centre to the International Secretariat, in which they felt a revisionist faction led by Michel Pablo had taken power.

For three years during the First World War, while Aintree Racecourse was taken over by the War Office, an alternative race was run at Gatwick Racecourse, a disused course on land now occupied by Gatwick Airport.

By the time the group released their first album in 1986 the Parisian alternative music scene had taken flight, and Manu, his brother Antoine Chao, and friends such as Alain from Les Wampas formed Los Carayos to incorporate this sound with the rockabilly and punk styles of Hot Pants.

James Roth, a U. S. gastroenterologist, advocated paracetamol as a gastric-friendly alternative to aspirin, which can irritate the stomach when taken without food.

If the customer wishes to be able to reproduce the photos themselves, they may discuss an alternative contract with the photographer in advance before the pictures are taken, in which a larger up front fee may be paid in exchange for reprint rights passing to the customer.

The rocks lie on one of two potential routes to Ithaca ; the alternative, which is taken by Odysseus, leads to Scylla and Charybdis.

In How Few Remain, an alternative history novel by Harry Turtledove, the town is mentioned as the only Confederate town taken by the US during the Second Mexican War.

* An alternative page featuring Rastapopoulos — this would have taken the place of pages 39 – 40.

Some manuscripts show evidence that particular care was taken in their composition, for example, by including alternative readings in their margins, demonstrating that more than one prior copy ( exemplar ) was consulted in producing the current one.

As the Dutch, however, had just ended their war with Spain and already taken over most Portuguese colonies in Asia, they saw little advantage in this grandiose scheme and proposed a free trade agreement as an alternative to a full political union.

Kaspar Hauser was taken as the name of an alternative rock band based in Amherst, Massachusetts in the early 1980s, as well as an experimental musician from Newcastle-Upon-Tyne, England.

In negotiation theory, the best alternative to a negotiated agreement or BATNA is the course of action that will be taken by a party if the current negotiations fail and an agreement cannot be reached.

Many students have assisted with the Special Olympics and have taken alternative spring break trips to hundreds of service sites across the United States.

In 1889, he arranged to have levels taken for alternative routes to Roma Street tunnel via Herschel Street, and to Central Station via a direct route between Turbot and Ann Streets.