Since ω is a differential two-form the skew-symmetric condition implies that M has even dimension.

Since ω

Since biological fatty acids can be of different lengths, the last position is labelled as a " ω ", the last letter in the Greek alphabet.

Since the physiological properties of unsaturated fatty acids largely depend on the position of the first unsaturation relative to the end position and not the carboxylate, the position is signified by ( ω minus n ).

Since ω and g are nondegenerate, each induces a bundle isomorphism TM → T * M, where the first map, denoted φ < sub > ω </ sub >, is given by the interior product φ < sub > ω </ sub >( u ) = < sub > u </ sub > ω = ω ( u, •) and the other, denoted φ < sub > g </ sub >, is given by the analogous operation for g. With this understood, the three structures ( g, ω, J ) form a compatible triple when each structure can be specified by the two others as follows:

Since the stress-energy operator has a conformal weight of 4, the AdS metric ought to go as ω < sup >- 2

Since ω is odd these algebras are mixed by α ( the linear map on V defined by ):

Since the symplectic form ω is nondegenerate, it sets up a fiberwise-linear isomorphism

Since the electrostatic force at ω depends on V < sub > DC </ sub > − V < sub > CPD </ sub >, the value of V < sub > DC </ sub > that minimizes the ω-term corresponds to the contact potential.

The number of neutrons, N, is known as the neutron number of the atom ; thus, A = Z + N. Since protons and neutrons have approximately the same mass ( and the mass of the electrons is negligible for many purposes ), and the mass defect is usually very small compared to the mass, the atomic mass of an atom is roughly equal to A.

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

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

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 1989-867 = 1122, we form a new pair of numbers

Since 612 − 255 = 357 our next pair is

Since the first part of the argument showed the reverse ( r < sub > N − 1 </ sub > ≤ g ), it follows that g = r < sub > N − 1 </ sub >.

Since each region is triangular and each edge is shared by two regions, we have that 2e = 3f.

Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour ( 360 °/ 24 hours = 15 ° per hour ).

Since p is prime q − 1 must be a multiple of p. Of course, if the number m = < sup >( q − 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.

Since they derive from a strong acid but weak base, they are both at about pH = 5 ; as a consequence, the morphine salts are mixed with small amounts of NaOH to make them suitable for injection.

Automobile exhaust gas capture has also been proposed to be economical but would require extensive design changes or retrofitting .< ref name = Musadi2011 > Since carbonic acid in seawater is in chemical equilibrium with atmospheric carbon dioxide, extraction of carbon from seawater has been studied.

Since the harmonic series, obtained when s = 1, diverges, Euler's formula ( which becomes ) implies that there are infinitely many primes.

Since the column vectors of A are the row vectors of the transpose of A ( denoted here by A < sup > T </ sup >), column rank of A equals row rank of A is equivalent to saying that the rank of a matrix is equal to the rank of its transpose, i. e. rk ( A ) = rk ( A < sup > T </ sup >).

Since 5 < sup > 2 </ sup > + 12 < sup > 2 </ sup > = 13 < sup > 2 </ sup >, ( 5, 12, 13 ) forms a Pythagorean triple.

Since τ refers to a vertical path, the optical depth for a slant path is τ ′ = m τ, where m is called the relative airmass, and for a plane-parallel

Since the E1 component of nuclear EMP depends on the prompt gamma ray output, which was only 0. 1 % of yield in Starfish Prime but can be 0. 5 % of yield in pure fission weapons of low yield, a 10 kiloton bomb can easily be 5 x 8 % = 40 % as powerful as the 1. 44 megaton Starfish Prime at producing EMP.

Since the surface area of a sphere of radius r is A = 4πr < sup > 2 </ sup >, then intensity I ( power per unit area ) of radiation at distance r is

Since 1 dB = 20 log < sub > 10 </ sub > 1. 122, we may say, in a voltage sense, that the 1dB compression point occurs when

Since ( 9 / 8 ) / ( 10 / 9 ) = ( 81 / 80 )— the syntonic comma — the fundamental characteristics of meantone systems are that all intervals are generated from fifths, and the syntonic comma is tempered to a unison.

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 >.

In the first step, the final nonzero remainder r < sub > N − 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N − 1 </ sub >; therefore, g must be less than or equal to r < sub > N − 1 </ sub >.

Since r < sub > N − 1 </ sub > is a common divisor of a and b, r < sub > N − 1 </ sub > ≤ g.

Since bosons carry one unit of angular momentum, the fermion's spin direction will flip from + to − ( or vice versa ) during such an exchange ( in units of the reduced Planck's constant ).

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

Since 2000, a small amateur experimental planting has been underway in the Lake Champlain valley of Vermont at the Vermont Experimental Cold-Hardy Cactus Garden where winter temperatures can reach − 37 ° C with variable snowcover.

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 methane clathrates are stable at a higher temperature than liquefied natural gas ( LNG ) (− 20 vs − 162 ° C ), there is some interest in converting natural gas into clathrates rather than liquifying it when transporting it by seagoing vessels.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since the topology on R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ( X )- adic topology and R < nowiki ></ nowiki > X < nowiki ></ nowiki > is complete, we can in particular apply power series to other power series, provided that the arguments don't have constant coefficients ( so that they belong to the ideal ( X )): f ( 0 ), f ( X < sup > 2 </ sup >− X ) and f ( ( 1 − X )< sup >− 1 </ sup > − 1 ) are all well defined for any formal power series f ∈ R < nowiki ></ nowiki > X < nowiki ></ nowiki >.