Then the previous expression is equal to the product of two factors:

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

Then, the relativistic expression for the angular distribution of the bremsstrahlung ( considering only the dominant dipole radiation contribution ), is

Then, still black with smoke and with his uniform in shreds, Nelson went on board Victory where he was received on the quarter-deck by Admiral Jervis – " the Admiral embraced me, said he could not sufficiently thank me, and used every kind expression which could not fail to make me happy.

Then combining the last two expression with Beer's law, molar ellipticity becomes:

Then one faces the problem of expression sin ( θ ) and cos ( θ ) as functions of x.

Then, for this expression, one has

Then for each input to that machine, build a Boolean expression which says that the input is passed to the machine, the machine runs correctly, and the machine halts and answers " yes ".

Then the expression can be satisfied if and only if there is a way for the machine to run correctly and answer " yes ", so the satisfiability of the constructed expression is equivalent to asking whether or not the machine will answer " yes ".

Then expression ( 2 ) becomes:

Then figures become more animated in pose and facial expression, tend to be smaller in relation to the background of scenes, and are arranged more freely in the pictorial space, where there is room.

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Then the general expression of a structural form is, where f is a function, possibly from vectors to vectors in the case of a multiple-equation model.

Then, as Wally leaves the room with a parting bon mot and the canned laughter kicks in, the camera catches June's bewildered, dazed, or amused facial expression.

" Fans find the expression useful, too ... Avoidism: Not originally fannish at all, but a philosophy devised in a rather stomach-turning book, In One Head and Out the Other, this doctrine became confused / associated with the Gandhi-following folk of Eric Frank Russell's " And Then There Were None ".

Then, the set of the Hamiltonian's equations given in the introduction can be expressed in a single expression as

Then, the expression given above for is not the only one that is compatible with such distribution for, and.

Then, unless, then number q has a parent in the Stern – Brocot tree given by the continued fraction expression

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,, and the constant function turns into the identity by substitution.

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 she goes into another room and returns, bringing with her the blonde-haired two-year-old boy who is her constant reminder of her American husband.

Then, recalling that the likelihood function is defined up to a multiplicative constant, it is just as valid to say that the likelihood function is approximately

Then, there exists a constant satisfying: for every ground term in such that, there exists a context, a nontrivial context and a ground term such that and, for all.

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Then add to T a collection of sentences that say that the objects denoted by any two distinct constant symbols from the new collection are distinct ( this is a collection of κ < sup > 2 </ sup > sentences ).

Suppose the rod rotates at a constant rate so that the mass moves at speed v. Then the kinetic energy T of the mass is:

Then NA < sup > 2 </ sup >+ NB < sup > 2 </ sup >+ NC < sup > 2 </ sup >+ NH < sup > 2 </ sup > = 3R < sup > 2 </ sup > where R is the common circumradius and if PA < sup > 2 </ sup >+ PB < sup > 2 </ sup >+ PC < sup > 2 </ sup >+ PH < sup > 2 </ sup > = K < sup > 2 </ sup >, where K is kept constant, then the locus of P is a circle centered at N with a radius.

Then, extending with a zero again, and defining an error constant where necessary:

Then it discusses how de Sitter space describes a distinct variant of the ordinary spacetime of general relativity ( called Minkowski space ) related to the cosmological constant, and how anti de Sitter space differs from de Sitter space.

Then is the Verdet constant for the material.

Then specific cutaneous cold and warm receptors conduct units that exhibit a discharge at constant skin temperature.

Then there is a constant C depending only on b such that ( g < sub > b </ sub >( n ))< sub > n ≥ 1 </ sub > satisfies

Then there is a constant C depending only on b < sub > 1 </ sub >, ..., b < sub > s </ sub >, such that sequence

Then, we can use this formula to compute the next hash value in constant time:

Then, using the Cauchy-Riemann equations we show that f ( z )= 0, and thus that f ( z ) is constant as well.

Then f is called weak if there exists a constant C such that the distribution of f satisfies the following inequality for all t > 0:

: Then the kernel of D consists of all functions in C < sup >∞</ sup >( R ) whose derivatives are zero, i. e. the set of all constant functions.

Then, a straight tunnel of length A and constant width W can be approximated as a sequence of N evenly spaced goals, each separated from its neighbours by a distance of A / N.

Then also the total energy is no longer a constant ( because the four vector energy with linear momentum is ).

Then the integral of the incoming waveform over the summing interval reduces to the integral of the constant and when that integral is divided by the summing interval it becomes the mean over that interval.