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By exponentiating these operators, however, that is, by going to the continuous Heisenberg group, H < sub > 3 </ sub >( ℝ ), he showed that he could obtain ( his now eponymous ) braiding relations for the exponential operators U and V, ( which, incidentally, may also be effectively realized on finite-dimensional spaces, through Sylvester's celebrated clock and shift matrices in the finite Heisenberg group, as discussed below ).
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By and these
By extending this help, we hope to make possible the enthusiastic enrollment of these nations under freedom's banner.
By a combination of music, lighting effects, and narration, famous events that have transpired in these locations are evoked and re-created for large audiences usually to considerable acclaim.
By 1965, several or all of these systems will have been fully tested and their reliability established.
By using the appropriate version any one of these factors can be determined for any combination of the other three.
By these measures, Congress, so the Court ( in effect ) now decides, gave not only needless but inadequate relief, since it now appears that the federal courts have inherent power to sterilize the Act of 1875 against all proceedings challenging local regulation ''.
By these steps the final AIA list was reduced from 8,000 to 3,500.
By virtue of the legal responsibilities of the Department of Employment in the farm placement program, we necessarily found ourselves in the middle between these two forces.
By preying on the sick, by playing callously on the hopes of the desperate, by causing the sufferer to delay proper medical care, these medical ghouls create pain and misery by their very activity.
By no means are these isolated cases.
By 1926, when the mighty Yanks were at their mightiest, only a few of these were left but they still shone brightest, even beside able and agile rookies like Tony Lazzeri ( who managed never to have one of his epileptic fits on the field ), Mark Koenig, Lou Gehrig, George Pipgras, and gray-thatched Earl Combs.
By reminding ourselves of these factors in the situation, we should, I am sure, come to a fresh realization, however painful it be, that the battle between Parker and his neighbors was fought in earnest.
By studying these images, they can detect solar system objects by their movements relative to the background stars, which remain fixed.
By the beginning of the 8th century, these kingdoms had either been conquered by Nicene neighbors ( Ostrogoths, Vandals, Burgundians ) or their rulers had accepted Nicene Christianity ( Visigoths, Lombards ).
By reducing detail in one direction more than another, these effects can be reduced.
Whenever any result is sought by its aid, the question will then arise — By what course of calculation can these results be arrived at by the machine in the shortest time?
By and large the power exercised by these officials was routine administration and quite limited.
By 500 BC, Ionia appears to have been ripe for rebellion against these Persian clients.
By 454, the Delian League could be fairly characterized as an Athenian Empire ; at the start of the Peloponnesian War, only Chios and Lesbos were left to contribute ships, and these states were by now far too weak to secede without support.
By late 1983 it was clear that IBM's Token Ring would not be ready in time for the launch of the Mac, and might miss the launch of these other products as well.
By this point Apple had a wide variety of communications products under development, and many of these were announced along with AppleTalk Phase II.
By the help of these discoveries, Angle civilization in the age preceding the invasion of Britannia can be fitted together.
By the 1930s, statisticians and models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
By the time the federal environmental clearances were delivered in 1994, A $ 10 million contract, signed off as a cost overrun, was used to repair these leaks.
By making these data available to local public health officials in real time, most models of anthrax epidemics indicate that more than 80 % of an exposed population can receive antibiotic treatment before becoming symptomatic, and thus avoid the moderately high mortality of the disease.
By the early 2000s, these competitions were named Comic Idol ( in reference to Pop Idol.
By and operators
By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.
By analogy with classical mechanics, the Hamiltonian is commonly expressed as the sum of operators corresponding to the kinetic and potential energies of a system, in the form
By transferring upper triangularisation of operators of finite-dimensional complex vector space, there is an internal orthonormal Hilbert space basis for where runs from to, such that each of the corresponding-dimensional subspaces is-invariant.
By integrating varying delivery streams, hybrids enable pay-TV operators more flexible application deployment, which decreases the cost of launching new services, increases speed to market, and limits disruption for consumers.
By enabling a station to participate nearly simultaneously in many different HF networks, ALE allows for convenient cross-organization message passing and monitoring without requiring dedicated separate equipment and operators for each partner organization.
By 1926 quartz crystals were used to control the frequency of radio broadcasting stations and were popular with amateur radio operators.
By drawing bait on a wire towards the cage, tour operators lure the shark to the cage, possibly striking it, exacerbating this problem.
By 1984, only six of the original twelve operators were still working with MIC and the number of supervisory personnel was also halved.
By February 1904, the Marconi Wireless Company required all of its operators to use ' CQD ' for a ship in distress, or requiring URGENT assistance.
By the finite-dimensional spectral theorem, such operators can be associated with an orthonormal basis of the underlying space in which the operator is represented as a diagonal matrix with entries in the real numbers.
By Stone's theorem, self-adjoint operators are precisely the infinitesimal generators of unitary groups of time evolution operators.
By 1944, the term " foo fighter " was used by radar operators to describe a spurious or dubious trace.
By further use of arbitrary phase-changes, Wigner showed that the product of the representing unitary operators obeys
By modifying the direction and extent of the movement, operators can select different focal planes which contain the structures of interest.
By necessity field measurements have to be quick, safe and simple if they are to be widely applied by owners and operators of MV and HV assets
By the early part of the 21st century many of the mines had been closed as problems with high costs of operations have plagued the mine operators.
By 10: 26 p. m. EDT operators started a restoration procedure.
By concentrating its signal on the continental United States with a directional antenna, Westar 1 could transmit to TVRO (" TV, receive only ") dishes only a few meters in diameter, well within the means of local cable TV operators.
By 1912, the United States government began requiring radio operators to obtain licenses to send out signals.
By Hellinger – Toeplitz, such operators cannot be everywhere defined ( but they may be defined on a dense subset ).
By 1992, Flextech was a media-only group, having built up stakes in local cable operators selling off its non core asset ..
By Stone's theorem, there is a one-to-one correspondence between self-adjoint operators and ( strongly continuous ) one parameter unitary groups.
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