Then, dividing the units of energy ( such as eV ) by a fundamental constant that has units of velocity ( M < sup > 0 </ sup > L < sup > 1 </ sup > T < sup >-1 </ sup >), facilitates the required conversion of using energy units to describe momentum.

Then for a specific value x of X, the function L ( θ | x )

Then L < sub > 1 </ sub > is Kripke incomplete.

Then is already an angle variable, and the canonical momentum conjugate is L, the angular momentum.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Then Aristaeus, on his civilizing mission, visited Arcadia, where the winged male figure who appears on ivory tablets in the sanctuary of Ortheia as the consort of the goddess has been identified as Aristaeus by L. Marangou.

Then, in 1986, the Sauk Village Library District Board of Trustees changed the district's name to the Nancy L. McConathy Public Library District in order to honor library district trustee and Village Clerk Nancy L. McConathy, who had died suddenly.

Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.

... Then one day somebody from the L. A. Times actually bothered to call me up and ask me how I felt, and I finally had a chance to talk about it.

For such a subgroup G, define Fix ( G ) to be the field consisting of all elements of L that are held fixed by all elements of G. Then the maps E Gal ( L / E ) and G Fix ( G ) form an antitone Galois connection.

Pick a fixed subset L of U. Then the maps F and G, where F ( M ) is the intersection of L and M, and G ( N ) is the union of N and ( U

Then, Flipper's brother Gator ( Samuel L. Jackson ) shows up with his girlfriend Vivian ( Halle Berry ).

Then the set of fixed points of f in L is also a complete lattice.

Then f + g is in L < sup > p </ sup >( S ), and we have the triangle inequality

Using the natural isomorphism between and the space of linear transformations from V to V ,< ref name =" natural iso "> Let L ( V, V ) be the space of linear transformations from V to V. Then the natural map

Then, he meets the Queen of Trash ( Vanessa L. Williams ).

Then on September 18, 2009, John Rzeznik stated in an interview on Good Day L. A., that the new album had tentatively been titled Something for the Rest of Us.

Then, in the 1950s, Merrill revised the Stanford-Binet and created a new version that included what he considered to be the best test items from Forms L and M. This version was published in 1960 and renormed in 1973.

Let X be a g-dimensional torus given as X = V / L where V is a complex vector space of dimension g and L is a lattice in V. Then X is an abelian variety if and only if there exists a positive definite hermitian form on V whose imaginary part takes integral values on L × L.

Then the energy of the vacuum is exactly E < sub > 0 </ sub >.

Then, p < sup > 2 </ sup > is the fraction of the population homozygous for the first allele, 2pq is the fraction of heterozygotes, and q < sup > 2 </ sup > is the fraction homozygous for the alternative allele.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Then X is reflexive if and only if each X < sub > j </ sub > is reflexive.

Then the cotangent space at x is defined as the dual space of T < sub > x </ sub > M:

Then I < sub > x </ sub > and I < sub > x </ sub >< sup > 2 </ sup > are real vector spaces and the cotangent space is defined as the quotient space T < sub > x </ sub >< sup >*</ sup > M = I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup >.

Then the complex derivative of ƒ at a point z < sub > 0 </ sub > is defined by

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.

Then the overall runtime is O ( n < sup > 2 </ sup >).

Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.

Then in 1702 the French astronomer Philippe de la Hire used a year he labeled at the end of years labeled ante Christum ( BC ), and immediately before years labeled post Christum ( AD ) on the mean motion pages in his Tabulæ Astronomicæ, thus adding the designation 0 to Kepler's Christi.

Then divide 12 by 6 to get a remainder of 0, which means that 6 is the gcd.

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

Then b < sub > 0 </ sub > is the value of p ( x < sub > 0 </ sub >).

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Then, for OpenGL 2. 0 and beyond:

Then Fischer and Rabin ( 1974 ) proved that any decision algorithm for Presburger arithmetic has a worst-case runtime of at least, for some constant c > 0.

Then x is a rational number greater than 0 and less than r < sub > 0 </ sub >.

Then, the Colts avenged their sole regular-season loss against the Cleveland Browns by crushing them, 34 – 0, in the NFL Championship Game.

Then after throwing an incomplete pass, Terry Bradshaw completed 2 consecutive passes, the second one a 28-yard touchdown completion to Stallworth to take a 7 – 0 lead.

Then they beat the Tampa Bay Buccaneers in the NFC Championship Game, 9 – 0, scoring only three field goals.

Then γ < sub > 1 </ sub > and γ < sub > 2 </ sub > are called equivalent at 0 if the ordinary derivatives of φ ∘ γ < sub > 1 </ sub > and φ ∘ γ < sub > 2 </ sub > at 0 coincide.

Then every subset of X is either considered " almost everything " ( has measure 1 ) or " almost nothing " ( has measure 0 ).

Then one might define the glass as being 0. 7 empty and 0. 3 full.

Then for arbitrary ε > 0 there is an embedding ( or immersion ) ƒ < sub > ε </ sub >: M < sup > m </ sup > → R < sup > n </ sup > which is