E. L. Doctorow

Edgar Lawrence "E. L." Doctorow (January 6, 1931 – July 21, 2015) was an American novelist, editor, and professor, best known internationally for his works of historical fiction. He has been described as one of the most important American novelists of the 20th century.

He wrote twelve novels, three volumes of short fiction and a stage drama. They included the award-winning novels Ragtime (1975), Billy Bathgate (1989), and The March (2005). These, like many of his other works, placed fictional characters in recognizable historical contexts, with known historical figures, and often used different narrative styles. His stories were recognized for their originality and versatility, and Doctorow was praised for his audacity and imagination.

A number of Doctorow's novels were also adapted for the screen, including, Welcome to Hard Times (1967), with Henry Fonda, Daniel (1983), starring Timothy Hutton, and Billy Bathgate (1991) starring Dustin Hoffman. His most notable adaptations were for the film, Ragtime (1981) and the Broadway musical of the same name (1988), which won four Tony Awards.

Eöl

Eöl, called the Dark Elf, is a fictional character in J. R. R. Tolkien's Middle-earth legendarium. He is introduced in The Silmarillion as an Elf of Beleriand and is a character existing in some form from the earliest to the latest writings.

Appearances

Eöl, the Dark Elf, was a Sinda and lord of the forest of Nan Elmoth, a fief, north-east of Doriath. Even before he encountered the Dwarves of the Blue Mountains in Eriador, he had close relationships with other Dwarves, whom he met (and learned much forging skills from) along his travel through Middle-earth. When he entered the lands of Beleriand, the Sindar from Doriath recognised Eöl's kinship, and accepted him fairly quickly among the high court of Menegroth, due to his skills.

He was vassal of the High-king of Beleriand, Thingol. Before the wars began he lived in Doriath. When Melian enclosed it with her magic Girdle of Melian to aid its defence he became uneasy and moved to Nan Elmoth outside the Girdle. One of the greatest Elven-smiths of Middle-earth, he forged Anglachel and Anguirel two great, black, magic swords. Made from a meteorite's metal, they can cut all earth-delved iron and have an entrapped sentience. His smithwork rivalled that of the greatest of the Elven-smiths, Fëanor and Celebrimbor, in both fame and fate. One sword, Anglachel, he gave to Thingol as tribute for living in Nan Elmoth and it was eventually used by Túrin to slay Glaurung the dragon. The other sword, Anguirel, he kept for himself. Eöl devised galvorn, a black metal of great strength and malleability, which he fashioned into armour that he wore when he went abroad. He was friend of the Dwarves of Nogrod and Belegost and, until the founding of the realms of the Noldor, all the traffic of goods between the Sindar and Dwarves passed through Nan Elmoth.

Euler–Lagrange equation

In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss-Russian mathematician Leonhard Euler and French-Italian mathematician Joseph-Louis Lagrange in the 1750s.

Because a differentiable functional is stationary at its local maxima and minima, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing (or maximizing) it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum, its derivative is zero.

In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler–Lagrange equation for the action of the system. In classical mechanics, it is equivalent to Newton's laws of motion, but it has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.

El

EL, El or el may refer to:

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