In contrast, infinite-dimensional normed vector spaces may or may not be complete ; those that are complete are Banach spaces.

In contrast all finite-dimensional inner product spaces over or, such as those used in quantum computation, are automatically metrically complete and hence Hilbert spaces.

In contrast to classical mechanics, where accurate measurements and predictions can be calculated about location and velocity, in the quantum mechanics of a subatomic particle, one can never specify its state, such as its simultaneous location and velocity, with complete certainty ( this is called the Heisenberg uncertainty principle ).

By contrast a four-straight including the bug can have as many as sixteen outs to complete the straight-Q-J-10-Joker can catch any ace, king, nine, or eight.

In complete contrast to Tyre, Sogdian Rock was captured by stealthy attack.

Parnell's movement campaigned for ' Home Rule ', by which they meant that Ireland would govern itself as a region within the United Kingdom, in contrast to O ' Connell who wanted complete independence subject to a shared monarch and Crown.

In contrast, optical activity occurs only in a material, and a complete rotation occurs in a length of millimeters to meters, depending on the material.

Wilhelm's character was a complete contrast to that of his brother.

By the 18th century, samplers were a complete contrast to the scattered samples sewn earlier on.

In contrast, aerosol dynamics explains the evolution of complete aerosol populations.

In contrast to the theology held by other Jewish thinkers, Jewish theologian Louis Jacobs argues, Gersonides held that God does not have complete foreknowledge of human acts.

This is in contrast to a unitary republic whereby the national government has complete sovereignty over all aspects of political life.

By contrast Brzezinski was careful, in managing his own weekly luncheons with Secretaries Vance and Brown in preparation for NSC discussions, to maintain a complete set of careful notes.

Spielberg wanted Willie to be a complete contrast to Marion Ravenwood from Raiders of the Lost Ark, so Capshaw dyed her brown hair blonde for the part.

Without the benefits of modern training, men of the era were, in contrast, expected to run themselves to complete exhaustion during competitions.

In complete contrast with this work is the lyrical, nostalgic Symphony No. 4, subtitled " Deliciae Basilienses " (" The Delights of Basel ") and written as a tribute to days of relaxation spent in that Swiss city during the war.

The later workers took as their aim the complete reconstruction of the ancient life, in contrast with members of the school of Hermann, who were disposed to limit the field to the language and text of the Greek and Roman writers.

The song failed to make the UK Chart, in complete contrast to " All Around My Hat ", despite having much in common with its predecessor-a 12 / 8 time signature, upbeat tempo, solo verses and full harmony chorus.

Medieval Islamic metalwork offers a complete contrast to its European equivalent, which is dominated by modelled figures and brightly coloured decoration in enamel, some pieces entirely in precious metals.

But in contrast to Descartes, who considered it possible to form a clear and distinct idea of the mind, Malebranche argues in the Dialogues on Metaphysics, a dialogue between Theodore and Aristes, that we do not have a complete conception of the powers of the mind, and thus no clear conception of the nature of the mind.

In contrast to its earlier place amongst the wealthy, during the 17th and 18th centuries the pasty became popular with working people in Cornwall, where tin miners and others adopted it due to its unique shape, forming a complete meal that could be carried easily and eaten without cutlery.

Jämtland has been linked to the lands west and east of itself, which has been in complete contrast to the competitive Dano-Norwegian and Swedish state's interest.

Aside from the film gauge selection — 8 mm ( amateur ), 16 mm ( semi-professional ), 35 mm ( professional ) and 65 mm ( epic photography, rarely used except in special event venues ) — the cinematographer has a selection of stocks in reversal ( which, when developed, create a positive image ) and negative formats along with a wide range of film speeds ( varying sensitivity to light ) from ISO 50 ( slow, least sensitive to light ) to 800 ( very fast, extremely sensitive to light ) and differing response to color ( low saturation, high saturation ) and contrast ( varying levels between pure black ( no exposure ) and pure white ( complete overexposure ).

Matsuo puzzled and grew anxious over the complete passiveness, concluding that he was the butt of a devilish joke.

But a few days after Fred's return he began hemorrhaging and that was the beginning of early and complete disintegration.

He was a learned and brilliant man, one of the best jurists in Europe and with flashes of penetrating insight, and yet in his dealings with other people, particularly when he tried to be ingratiating, he was capable of an abysmal stupidity that can have come only from a complete incomprehension of human nature and human motives.

They, however much they were in disagreement with the late Victorians over the method by which Britain was Germanized, agreed with them that the end result was the complete extinction of the previous Celtic population and civilization.

A recent editorial discussing a labor-management agreement reached between the Southern Pacific Co. and the Order of Railroad Telegraphers has been criticized on the grounds that it was not based on complete information.

The prize was an old-fashioned, woven cloth hammock, complete with cross-top pillow, fringed side pieces, and hooks for hanging.

Despite several years of front-page stories, the average citizen was unable to get a complete picture of McCarthy until he saw on the television screen what the reporters had been seeing all along but had no effective way of communicating.

The work program, as it was originally proposed, was to take five years to complete.

Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.

Cuban S.S.R.: Whatever may have been the setbacks resulting from the unsuccessful attempt of the Cuban rebels to establish a beachhead on the Castro-held mainland last week, there was at least one positive benefit, and that was the clear-cut revelation to the whole world of the complete conversion of Cuba into a Russian-dominated military base.

This was later known to be the result of concentrating the minute amount of complete antibody found in these sera ; ;

when the insoluble fraction was suspended in a volume of saline equal to that of the original serum sample, no complete antibody activity could be detected.

It was nevertheless almost incredible that four years after Yalta there should be a complete split over Germany, with hot heads on both sides planning to use the Germans against their former allies, and with Nazi-minded Germans expecting to recover their power by fighting on one side or the other.

For the use of students and future restorers, a full, day-by-day record was kept of all three undertakings, complete technical reports on what we found and what we did.

If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.

Milman Parry rigorously defended the observation that the extant Homeric poems are largely formulaic, and was led to postulate that they could be shown entirely formulaic if the complete corpus of Greek epic survived ; ;

Some time later the missing part of the relic was found and the complete inscription, together with other new evidence, fully corroborated the ancient priest's information.

As a natural outgrowth of this approach it was often suggested that the doctor should complete the preparation for painless intercourse by dilating the vagina.

So filled was Mel Chandler with the spirit of Garryowen that after Korea was over, he took on the job of writing the complete history of the regiment.