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 Cycloped it was cutting-edge for 1829, lighter and considerably faster than the other locomotives in the competition.

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.

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 ).

One of my virtues or vices is a sort of three-dimensional imagination complete with sound effects and glorious living color.

So when textbooks, like that of Baker set out drawings of the ' Ptolemaic System ', complete with earth in the center and the seven heavenly bodies epicyclically arranged on their several deferents, we have nothing but a misleading 20th-century idea of what never existed historically.

The second reason for his popularity is his complete spontaneity with the guitar.

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.

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

He wondered how they could go on in poverty, superstition, ignorance, with a complete lack of desire to make either their land or their lives flourish.

The Commission shall complete its affairs in connection with settlement of United States-Yugoslav claims arising under the Yugoslav Claims Agreement of 1948 not later than December 31, 1954::

So with four complete Push-Pull Super-Sets No. 1, four of No. 2, four of No. 3 and four to six sets of the Incline Bench Press, you can see that Henri De Courcy has had a terrific mass-building, muscle-shaping, torso-defining workout that cannot be improved upon.

A great many writers are bewitched by the apparently overwhelming advantage an attacker would have if he were to strike with complete surprise using nuclear rockets.

Following arrowed signs, I veered right toward the former kitchens, complete with chimneys, which now house one of the world's greatest collections of Chinese porcelain and a fabulous array of silver dinner services.

In many cases, you must file a complete set of plans with the local building inspector.

Currently, there are some 6000 companies in the field, ranging from small firms with a handful of employees to major concerns having complete facilities for production of metal, electrical, and plastic components.

His thirteenth chapter includes many exciting accounts of huge serpents with prodigious strength, but these seem to be given to complete his picture, not to be believed.

Although we are still far from a complete understanding of these problems, as a first approximation, it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic-cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances, in experimental and clinical neurosis, and as the result of psychopharmacological agents.

The dictionary is a form dictionary, at least in the sense that complete forms are used as the basis for matching text occurrences with dictionary entries.

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.

Autocoder declarative statements provide the processor with the necessary information to complete the imperative operations properly.

He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.

They had winged over the Adriatic, they had taken Bari by complete surprise and now they were battering her, attacking with deadly skill.

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.

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.