When the coefficients belong to a finite field or are rational numbers, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials.

When a DCT has been used, the coefficients are typically scanned using a zig-zag scan order, and the entropy coding typically combines a number of consecutive zero-valued quantized coefficients with the value of the next non-zero quantized coefficient into a single symbol, and also has special ways of indicating when all of the remaining quantized coefficient values are equal to zero.

When the solubility of the salt is very low the activity coefficients of the ions in solution are nearly equal to one.

When activity coefficients are used, they are usually defined in terms of Raoult's law,

When the coefficients a, b, and c, are real or complex, the roots are

When the algebra can be endowed with a metric, then the structure coefficients are written with upper and lower indices, so as to distinguish their transformation properties under coordinate transformations.

When a model does not converge this indicates that the coefficients are not meaningful because the iterative process was unable to find appropriate solutions.

When applying spectral methods to time-dependent PDEs, the solution is typically written as a sum of basis functions with time-dependent coefficients ; substituting this in the PDE yields a system of ODEs in the coefficients which can be solved using any numerical method for ODEs.

When k is even the coefficients of all its Euler factors are non-negative, so that each of the Euler factors has coefficients bounded by a constant times the coefficients of Z ( E < sup > k </ sup >, T ) and therefore converges on the same region and has no poles in this region.

When a stochastic matrix, A, acts on a column vector, B, the result is a column vector whose entries are affine combinations of B with coefficients from the rows in A.

When combined with the central limit theorem, the FT also implies the famous Green-Kubo relations for linear transport coefficients, close to equilibrium.

When the model coefficients sum to one, as in this example, the production function is first-order homogeneous, which implies constant returns to scale, that is, if all inputs are scaled by a common factor greater than zero, output will be scaled by the same factor.

When the Fourier coefficients for a square wave were input to the machine, the graph would oscillate at the discontinuities.

When in a polynomial in of arbitrary degree the coefficient of the highest term is = 1, and all following coefficients are whole ( real, complex ) numbers, into which a certain ( real resp.

Formal group laws over a ring R are often constructed by writing down their logarithm as a power series with coefficients in R ⊗ Q, and then proving that the coefficients of the corresponding formal group over R ⊗ Q actually lie in R. When working in positive characteristic, one typically replaces R with a mixed characteristic ring that has a surjection to R, such as the ring W ( R ) of Witt vectors, and reduces to R at the end.

When an integer can be represented as a polynomial with small coefficients, the norms that arise are much smaller than those that arise when an integer is represented by a general polynomial.

When doing the calculation by hand it is useful to write down the coefficients in a triangle scheme as

When the coefficients depends only on present and past values of X, the defining equation is called a stochastic delay differential equation.

When combined with the central limit theorem, the FT also implies the famous Green – Kubo relations for linear transport coefficients, close to equilibrium.

When I show up he will know you are a good wife to have told him about it ''.

When the Know-nothings get control, it will read, All men are created equal except Negroes and foreigners and Catholics.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

She used to tell me, `` When I stand there and look at the flag blowing this way and that way, I have the wonderful, safe feeling that Americans are protected no matter which way the wind blows ''.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When these fields are surveyed together, important patterns of relationship emerge indicating a vast community of reciprocal influence, a continuity of thought and expression including many traditions, primarily literary, religious, and philosophical, but frequently including contact with the fine arts and even, to some extent, with science.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When finally the two bedraggled men reach their friend's home, Voltaire's fears are once again aroused.

`` When are you to leave ''??

When the roof blocks are all in place, the final rows of wall blocks are mortared into position.

When the aid operations are reorganized the Peace Corps should remain a semi-autonomous, functional unit.

When the budget goes to trustees for approval it is the president's budget, to which his faith and credit are committed ; ;

When they have 4 to 6 leaves and are thrifty little plants, it's time to set them out where they are to remain.

When aircraft are no longer helpless on airfields, they are no longer vulnerable to Aj.

When more than two figures are separated by subtraction symbols the subtraction must be carried out from the left to right if the result is to be correct.

When they're on, the top edges are planed even with the sheer batten.

When painting, Mason's physical eyes are half-closed, while his mind's eye is wide open, and this circumstance accounts in part for the impression he wishes to convey.

When improvements are recommended in working conditions -- such as lighting, rest rooms, eating facilities, air-conditioning -- do you try to set a measure of their effectiveness on productivity??

When sufficiently accurate and complete measurements are available, it will be possible to set limits on the thermal and electrical characteristics of the surface and subsurface materials of the moon.

When some thirteen records of newly and recently born individuals are collated, little or no correlation between length and distribution can be detected.

When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??