Often one assumes a priori that the algebra under consideration is unital: for one can develop much of the theory by considering and then applying the outcome in the original algebra.

Often, this type of compression is virtually indistinguishable from the original uncompressed sound or images, depending on the codec and the settings used.

The original scores, which dated from 1804 when the composer was twelve, were found in the Library of Congress in Washington D. C. Often transcribed for string orchestra, these sonatas reveal the young composer's affinity for Haydn and Mozart, already showing signs of operatic tendencies, punctuated by frequent rhythmic changes and dominated by clear, songlike melodies.

Often it is recommended that each loop should only have one entry point ( and in the original structural programming, also only one exit point, and a few languages enforce this ).

Often, one release is duplicated, renamed, then re-uploaded to different sites so that eventually, it can become impossible to trace the original file.

Often called the Shinji Shōbōgenzō ( shinji :” original or true characters ” and shōbōgenzō, variously translated as “ the right-dharma-eye treasury ” or “ Treasury of the Eye of the True Dharma ” ).

Often, these businesses owe money to suppliers and to tax authorities, and the proprietors do not withdraw all their original capital and profits at the end of each period.

The original quote is, " The best-laid schemes o ' mice an men / Gang aft agley " ( translation: " Often go awry ").

Often the scale of the work indicates a great deal about its original function.

Often called " the father of American landscape painting ," Inness is best known for these mature works that not only exemplified the Tonalist movement but also displayed an original and uniquely American style.

Often, operas are presented in their original languages, which may be different from the first language of the audience.

Often, they explain the background which led to the events in the original, but sometimes the connections are not as explicit.

Often there were only several months between the publication of the original book and the translation to other European languages.

Often, the samples featured on these records do not have the blessing of the original copyright holders.

Often as these myths evolve from their original source, the role of the storm god ( himself often the head of a pantheon ) is adopted by culture heroes or a personage symbolizing royalty.

Often, this will take on the crystal form and habit of the original protolith assemblage ; actinolite pseudomorphically replacing pyroxene is an indication that the amphibolite may not represent a peak metamorphic grade in the amphibolite facies.

Often samplers offer filters, modulation via low frequency oscillation and other synthesizer-like processes that allow the original sound to be modified in many different ways.

Often working independently of each other and with widely different starting points, these original photorealists routinely tackled mundane or familiar subjects in traditional art genres -- landscapes ( mostly urban rather than naturalistic ), portraits, and still lifes.

Often a prologue, epilogue, and intermissions are added in which the characters discuss a topic on the same theme as the original text, although intermission segments are usually dropped if the original work is short.

Often described as shy, Adams was referred to by Ethel Barrymore as the " original ' I want to be alone ' woman ".

Often, putting the system into production results in a need to maintain backward compatibility ( as many additional components now depend on it ) with the original, incomplete design.

He continued touring throughout the U. S. until shortly before he became ill. Often, he worked with a reconstituted version of the Brazos Valley Boys that included a few original members.

Often, compromises are called bipartisan if they reconcile the desires of both parties from an original version of legislation or other proposal.

Often, it matters little each way whether these examples are restored or original as the value is determined on a case by case bases by the individual buyer.

Often, I heard my uncles and cousins speak of it when I was a small boy growing up in Rabaul.

Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.

Often, threading through the overcast, he was forced to fly close to the ground by a low ceiling, skimming above the Winooski or the White River along the line of the broken railroad.

Often he was terribly despondent and talked to no one.

This led to the first of a number of periods in which an outside power controlled Athens ; Often the outside power set up a local agent as political boss in Athens ; but when Athens was independent, it operated under its traditional form of government ; even the bosses, like Demetrius of Phalerum, kept the traditional institutions in formal existence.

Often the Aegis is described as the bag in which Athene carried her shield and the serpent who was her son.

Often his research was simple: he would review period newspapers of the dates of reported incidents and find reports on possibly relevant events like unusual weather, that were never mentioned in the disappearance stories.

Often assumed to be illiterate, Catherine is acknowledged by Raymond in his life of her as capable of reading both Latin and Italian, and another hagiographer, Tommaso Caffarini, claimed that she could write in her own hand, though the majority of her written work was dictated.

Often dialogue was changed, and the show became less " Serious " in tone compared to the Japanese version, instead featuring more jokes and added dialogue, along with a completely different musical score ( usually orchestral music ) and completely different sound effects, due to licensing issues.

Often the work of these auteurs was first recognised abroad rather than in Germany itself.

Often this means making the central bank very aggressive about maintaining price stability, as was the case with the German Bundesbank or moving to some hard basis of currency such as a currency board.

Often Zeus ( or Jupiter ) was considered the supreme, all-powerful and all-knowing, king and father of the Olympian gods.

Often enormously complicated matters, ICJ cases ( of which there have been less than 150 since the court was created from the Permanent Court of International Justice in 1945 ) can stretch on for years and generally involve thousands of pages of pleadings, evidence, and the world's leading specialist public international lawyers.

Often the technology was purchased from Britain or British engineers and entrepreneurs moved abroad in search of new opportunities.

Often some attempt was made to smooth and shape the blade so it had less water resistance.

Often, the midwife would call for the assistance of a physician when a more difficult birth was anticipated.

Often the entrance was protected by a lifting bridge, a drawbridge or a timber gate tower.

Often an oil, such as linseed, was boiled with a resin, such as pine resin or even frankincense ; these were called ' varnishes ' and were prized for their body and gloss.

Often in the past, some Oromo communities used Galla to label themselves, as was exemplified by western Oromo leaders who established the " Western Galla Confederation " in the 1930s.

Often this point was made by referring to " ordinary English ," since the school of philosophy that most vigorously promoted this meta-philosophy was Oxford.

Often, the center of the blade was a core of soft steel, and the edges were solid high carbon steel, similar to the laminates of the Japanese.

Often these were ex-servicemen or ex-policemen ; retiring to run a pub was popular amongst military officers at the end of their service.

Often called the " dean of science fiction writers ", he was one of the most influential and controversial authors of the genre in his time.