From these results, one sees that the study of linear operators on vector spaces over an algebraically closed field is essentially reduced to the study of nilpotent operators.

From this it follows that correctness of drawing depends solely upon the principal rays ; and is independent of the sharpness or curvature of the image field.

From 1969 to 1993, home field advantage was alternated between divisions each year regardless of regular season record and from 1995 to 1997 home field advantage was predetermined before the season.

From 1969-1993, home field advantage alternated between the two divisions, and from 1995-1997 home field advantage was predetermined before the season.

From the beginning of each playing period with a stroke-off ( a set strike from the centre-spot by one team ) until the end of the playing period, the ball is in play at all times, except when either the ball leaves the field of play, or play is stopped by the referee.

From a classical perspective, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner ; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles.

From a more modern perspective, Haeckel's drawings were the beginnings of the field of evolutionary developmental biology ( evo-devo ).

From May 1934 until October 1935, Armstrong conducted the first large scale field tests of his FM radio technology from a laboratory constructed by RCA on the 85th floor of the Empire State Building.

** Eddy currents: From Faraday's law of induction, the changing magnetic field can induce circulating loops of electric current in the conductive metal core.

From early beginnings with the invention of the phonograph using purely mechanical techniques, the field has advanced with the invention of electrical recording, the mass production of the 78 record, the magnetic wire recorder followed by the tape recorder, the vinyl LP record.

From mycology arose the field of phytopathology, the study of plant diseases, and the two disciplines remain closely related because the vast majority of " plant " pathogens are fungi.

From there, the Raiders advanced to the Vikings 23-yard line, aided by an 18-yard run by Davis and a 10-yard reception by wide receiver Cliff Branch, to set up Mann's 40-yard field goal to increase the their lead, 19 – 0.

From here, the sousaphone players run in a snake around the field jumping to drum line cadence.

From the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle.

From this rotation, we can calculate the difference in orthogonal velocity components, find the anisotropic permittivity, find the gyration vector, and calculate the applied magnetic field.

From the late-1990s, the field has expanded to explore such wide-ranging topics as the origins and rate of change of political institutions, and the role of culture in explaining economic outcomes and developments.

From the end of the twentieth century, courage has been a concept generating interest in the field of psychology.

From 1965 – 1993, Texaco participated in a consortium to develop the Lago Agrio oil field in Ecuador.

From 2002 to 2005, the RiverHawks ' home field was Marinelli Field in Rockford, Illinois.

From 24 April to 5 May, he held a council of war attended by his nephew and most renowned field commander, Prince Rupert.

From there Alaric escaped with difficulty, and not without some suspicion of connivance by Stilicho, who supposedly had again received orders to depart.

From it she was rescued by a priest named Martin, who dug a subterraneous passage, by which she escaped, and remained concealed in the woods, her rescuer supporting her, meantime, by the fish he caught in the lake.

From an original contingent of 190 12 officials, 116 company " employees " ( indentured servants ), and 62 felons and former prostitutes only 104 remained, 9 having escaped and 77 having died in transit.

> From ( should be escaped ).

From there Perdiccas turned west towards Phrygia in order to humble Antigonus, who escaped with his son Demetrius to Greece, where he obtained the favour of Antipater, regent of Macedonia ( 321 BC ), and Craterus.

From there it escaped or was deliberately released into the wild.

From his interviews with a range of witnesses and study of surviving documents he demonstrated to the satisfaction of most analysts that Hitler was dead and had not escaped from Berlin.

The Spy Who Came in From the Cold misleads the reader, by changing a key plot element of its predecessor, Call for the Dead, wherein Hans-Dieter Mundt escaped capture by Smiley and Guillam and returned to East Germany.

From Oedipus onward, Greek and Roman tales are filled with exposed children who escaped death to be reunited with their families — usually, as in Longus's Daphnis and Chloe, more happily than in Oedipus's case.

From there, Te Kooti escaped into the Urewera and made an alliance with the Tuhoe leadership.

From the skull, it appears to have been relatively large ( perhaps the size of N. amplus or a little more ) and to have escaped collection by early 19th century naturalists by chance.

From there, in 1809, he escaped in the company of a British colonel named Clutchwell and eventually reached German territory.

From this wall ascended two stairs on either side of the baptistry, and the excess water from the rite would have escaped along this path.

From this he escaped, going first to Morocco and then to Zaire.

From there he escaped and fled with his wife to what became Yugoslavia where he lived incognito.

From a work ascribed to Albert the Great, " Compilatio de Novo Spiritu ", in the Munich Library, we learn further that in consequence of the condemnation, David fled from France, and so escaped punishment.

From 1 March to 4 March, the remaining Italian submarines at Massawa escaped destruction by sailing south.

From this disaster the Earl escaped, with considerable losses, which included his wife's brother, John Randolph, 3rd Earl of Moray.

From 1910 to 1940, rubber production was desired by colonialists, and forced labor of the tribesmen with whom the Aka were associated increased the demand for bushmeat, and some villagers escaped into the forest, where they put added demands on the Aka.

From police photographs, witnesses identified the man who shot Berriman as Richard Buckley and his accomplice as Angus Murray, an escaped prisoner from Geelong Gaol.

From 1907 he was imprisoned and exiled several times for his political activities by the Tsarist authorities, but at the end of 1913 he escaped the Russian Empire.

* From Justice Holmes ’ opinion: " According to the allegations and affidavits there never was a chance for the petitioners to be acquitted ; no juryman could have voted for an acquittal and continued to live in Phillips County and if any prisoner by any chance had been acquitted by a jury he could not have escaped the mob.

From there the family could raise a lantern on a flagpole to signal fleeing slaves in Kentucky when it was safe for them to cross the Ohio River .< sup ></ sup > Rankin also constructed a staircase leading up the hill to the house for slaves to climb up to safety on their way further north .< sup ></ sup > For over forty years leading up to the Civil War, many of the 2000 slaves who escaped to freedom through Ripley stayed at the family's home, and none was ever recaptured there.

From that time until 1972, when he escaped from legal custody, he spent his life in a number of orphanages, boys ' homes and youth training centres.