Since D and D' are both diagonalizable and they commute, they are simultaneously diagonalizable, and Af is diagonalizable.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

Since Groveland is primarily a bedroom community, there is naturally considerable traffic during the commute drive time.

Since det ( A ) and det ( B ) are just numbers and so commute, det ( AB )

Since the return, the Chief Executive of Hong Kong now exercises the power to grant pardons and commute penalties under section 12 of article 48 Basic Law of Hong Kong.

Since quaternion multiplication is associative, and real numbers commute with other quaternions, the norm of a product of quaternions equals the product of the norms:

Since the opening of Sakudaira station on the Nagano Shinkansen, many people have moved to Saku and commute to Tokyo by Shinkansen.

Since 1898, the town's main employer was " Dębieńsko " Coal Mine, which was closed up in 2000 causing a huge unemployment rate ( number of jobs in the commute dropped by 3, 536 which was almost a half of all jobs in the area ) and poverty.

Since bosons are symmetric in the single-particle state index we of course, demand that and commute,

Since the orthogonal projections corresponding to the subspaces in a nest commute, nests are commutative subspace lattices.

Since 1980 more workers commute out of Fahrwangen than commute in for jobs.

Since these operators commute with each other and with the Hamiltonian on the limit of negligible spin-orbit coupling, their eigenvalues may be used to describe a molecule state through the quantum numbers S, M < sub > S </ sub >, M < sub > L </ sub > and M < sub > J </ sub >.

Since then, many inhabitants commute to other areas where employment is easier to find.

Since the matrices in are symmetric and commute with each other, they can be diagonalized simultaneously.

Since 1993, the Nebraska Parole Board has voted unanimously and repeatedly to commute both men's sentences to time served.

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

Since 1944 he has also conducted regularly at the San Francisco Opera, where he made his debut with a memorable performance of Verdi's Falstaff.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Those famous lines of the Greek Anthology with which a fading beauty dedicates her mirror at the shrine of a goddess reveal a wise attitude: `` Venus, take my votive glass, Since I am not what I was, What from this day I shall be, Venus, let me never see ''.

Since the Connally amendment has the effect of giving the same right to the other party to a dispute with the United States, it also prevents us from using the court effectively.

Since ordinary breakfast-table conversation was impossible, it was at least something that they were able to offer Eugene the sugar bowl with their sugar in it, and the plate of bread and butter, and that Eugene could return the pitcher of hot milk to them handle first.

Since these duties fit neatly with those of the proposed presidential aide, one person, with adequate staff assistance, could fill both jobs.

Since brevity is the soul of ambiguity as well as wit, newspaper headlines continually provide us with amusing samples.

Since the absorption of radio waves in rocklike material varies with wave length, it should be possible to sample the temperature variation at different depths beneath the surface and possibly detect changes in the structure or composition of the lunar surface material.

Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

Since the writer had established this democratic procedure in the beginning he had to go along with their decision -- after, of course, pointing out whether he thought their decision was a wise or an unwise one.

Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.

Since this type of item was not in the statute when section 381 was enacted in 1954, one cannot say with certainty what effect the enactment of that section should have.

Since on the one hand school desegregation has come in Virginia hand-in-glove with pupil assignment, shall we support the plan??

Since this book is concerned only incidentally with railroad rates, it will not attempt to analyze the methods by which the staff of the Interstate Commerce Commission has estimated out-of-pocket costs and apportioned residue costs.

Since the strength of the Mexicans had been underrated, too small a posse had been collected, and since the deputy had not been provided with search warrants, MacPherson and his men decided it was much wiser to withdraw.

Since they commonly translate thoughts and feelings into deeds, hands naturally represent action, and since nearly half the characters in Great Expectations are of the underworld or closely allied to it, the linking of hands with crime or violence is not to be wondered at.

Since by the principle of optimality the remaining stages use an optimal Af-stage policy with respect to Af, we may enter section Af of the table at this state Af and read off the optimal policy for stage Af and the resulting state Af.

Since the earth is rotating and the unleveled gyro-stabilized platform is fixed with respect to a reference in space, an observer on the earth will see the platform rotating ( with respect to the earth ).

Since Mr. Clark believes firmly that the chewing of hard foods helps develop healthy gums and teeth, raw vegetables and raw whole-wheat grains are handed out with fresh fruit and whole-wheat cookies at snack time in the afternoons.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since two of these could be trustees of the college, actually it would be necessary to have the consent of only one elected official to impose a levy of millions of dollars of tax revenue.

Since she could not act, one part suited her as well as any other, and so she was the first person to offer Mr. Lincoln a glass of water, holding it up to the box, high above her head, to Miss Harris, who had asked for it.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since the same method of shaping and fitting the dogs and notches is used throughout, we will only describe the construction of one locking bar.

Since fly cutters are one sided and not balanced, they should be used at the slowest speed available, and fed very slowly to avoid binding.

Since charges are relatively the same, reserving a car before you leave for Europe will assure you of having one on tap when you want it.

Since a Skeletal Age rating can be made at any age during growth, from Elbow, Shoulder, Knee, or Foot as well as Hand, it seems to be the method of choice when one wishes to study most aspects of skeletal developmental progress during childhood.

Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man, in addition, by complex symbols, one would expect that the hypothalamus could be excited from the cortex.

Since the course, one member has lost her husband.

Since the company under review is supplying what we are here regarding as only one kind of service, we might suppose that the problem of total cost apportionment would be very simple ; ;

Since the 1946 disaster there have been 15 tsunami in the Pacific, but only one was of any consequence.

Since perforated tape at the time could record eight bits in one position, it also allowed for a parity bit for error checking if desired.

Since is the distance from a given number to the mean, one way to interpret this property is as saying that the numbers to the left of the mean are balanced by the numbers to the right of the mean.

Since a coulomb is approximately equal to elementary charges ( such as electrons ), one ampere is approximately equivalent to elementary charges moving past a boundary in one second, or the reciprocal of the value of the elementary charges in coulombs.

Since in practice it is not worth contrasting a zero probability with one that is nearly indistinguishable from zero, he prefers to categorize himself as a " de facto atheist ".

Since then, Alumni has played at the highest level of Argentinian rugby and its rivalry with Belgrano Athletic Club is one of the fiercest local derbies in Buenos Aires.

Since the evolution of the Aramaic alphabet out of the Phoenician one was a gradual process, the division of the world's alphabets into those derived from the Phoenician one directly and those derived from Phoenician via Aramaic is somewhat artificial.