Since energy and momentum are related in the same way as frequency and wavenumber in special relativity, it followed that the momentum p of a photon is proportional to its wavenumber k.

Since is the phase speed in terms of the angular frequency and the wavenumber, the gravity wave angular frequency can be expressed as

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k − 1 </ sub > is less than its predecessor r < sub > k − 2 </ sub >.

Since 2 < sup >( q − 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q − 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.

Since the probability per distance traveled for a neutron to collide with a nucleus is proportional to the material density, increasing the density of a fissile material can increase k. This concept is utilized in the implosion method for nuclear weapons.

Since ω = − dΦ / dt and k = + dΦ / dx, the wave velocity is v = dx / dt = ω / k.

Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i – th component in the k – th reaction is defined as

Since no energy is lost ( elastic, not inelastic scattering ), the wavelengths are the same as are the magnitudes of the wave-vectors | k < sub > in </ sub >|=| k < sub > out </ sub >|.

Since most of these organizations are generally perceived to be associated with right-wing and liberal parties of Slovakia ( with the perception being particularly strong among Slovak nationalists ), findings and proposals made by these organizations are generally resented or ignored by left-wing supporters and nationalists., ,, k. h.

Since the kth leading principal minor of a triangular matrix is the product of its diagonal elements up to row k, Sylvester's criterion is equivalent to checking whether its diagonal elements are all positive.

Since the r < sup > th </ sup > failure comes last, it remains to choose the k trials with successes out of the remaining k + r − 1 trials.

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

Since the profit sharing percentage must be uniform for all employees, this had the intended result of making more equitable contributions to 401 ( k )' s and other types of DC pension plans.

Since the Supreme Court's decision of that year this is more doubtful ; ;

( 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 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 attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.

Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the difficulty of drawing the net is great, we will merely discuss it.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

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.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

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 the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since the apparatus is new, it requires experimentation and changes in technique.

Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Since the inverse DFT is the same as the DFT, but with the opposite sign in the exponent and a 1 / N factor, any FFT algorithm can easily be adapted for it.

Since *- regular semigroups generalize inverse semigroups, the unique element defined this way in a *- regular semigroup is called the generalized inverse or Penrose-Moore inverse.

Since < sup > </ sup > the bulk density of a solid chemical element is strongly related to its molar mass ( usually about 3 R per mole, as noted above ), there exists noticeable inverse correlation between a solid ’ s density and its specific heat capacity on a per-mass basis.

Since this is equal to the inverse period at all times, the variable θ increases steadily from 0 to 1 over one period.

Since is a rotation matrix its inverse is its transpose.

Since wavelength and frequency are tied together through a simple directly inverse relationship, the two terms actually describe the same concept.

Since a double negation has no logical effect, the inverse of the inverse is logically equivalent to the original conditional.

In field theory, the expression is only shorthand for the formal expression ab < sup >− 1 </ sup >, where b < sup >− 1 </ sup > is the multiplicative inverse of b. Since the field axioms only guarantee the existence of such inverses for nonzero elements, this expression has no meaning when b is zero.

Since the residue classes ( mod p ) are a field, every non-zero a has a unique multiplicative inverse, a < sup >− 1 </ sup >.

Since this theorem applies in infinite-dimensional ( Banach space ) settings, it is the tool used in proving the infinite-dimensional version of the inverse function theorem ( see " Generalizations ", below ).

w / MPL Since the wage rate is assumed constant marginal cost and marginal product of labor have an inverse relationship-if marginal cost is increasing ( decreasing ) the marginal product of labor is decreasing ( increasing ).< ref > Note also that AVC

Since a and n are coprime, this implies that a has an inverse element a < sup >- 1 </ sup > and we can multiply both sides of the congruence with a < sup >- t </ sup >, yielding a < sup > s-t </ sup > ≡ 1 ( mod n ).

Since its early statement for radiolocation, many applications have been found for inverse scattering techniques, including echolocation, geophysical survey, nondestructive testing, medical imaging, quantum field theory.

Since the inverse Fourier transform is

Since the set of complex numbers λ with | λ |< sup > 2 </ sup > = 1 form the unit circle in the complex plane, it follows that for each point m in S < sup > 2 </ sup >, the inverse image p < sup >− 1 </ sup >( m ) is a circle, i. e., p < sup >− 1 </ sup > m ≅ S < sup > 1 </ sup >.

Since 1997, the draft has consisted of six rounds, with teams drafting in inverse order of their records in the previous season.

Since the acceleration of a trajectory at constant is equal to, the actual inverse temperature observed is:

Since is the inverse of this function, is less than 5 for all remotely practical values of.

Since the corner frequency is proportional to the inverse root of the moving mass, geophones with low corner frequencies (< 1 Hz ) become impractical.

Since YAP supports inverse search ( when the DVI file was compiled with source specials ), it can be configured to launch a LaTeX editor for the source file, placing the cursor on the corresponding word under the cursor in YAP.