Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Experiment where p is not constant.

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

where k has the same p, and opposite σ and sign of the energy.

where p is a program in L < sub > 2 </ sub >.

where p is the frequency of one allele and q is the frequency of the alternative allele, which necessarily sum to unity.

where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.

where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.

where is called the lever arm distance to p.

where is the component of p that is perpendicular to r. As above, the sign is decided based on the sense of rotation.

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.

where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

Since the early 20th century it has been commonly accepted that Old Irish Bel ( l ) taine is derived from a Common Celtic * belo-te ( p ) niâ, meaning " bright fire " ( where the element * belo-might be cognate with the English word bale in ' bale-fire ' meaning ' white ' or ' shining '; compare Anglo-Saxon bael, and Lithuanian / Latvian baltas / balts, found in the name of the Baltic ; in Slavic languages byelo or beloye also means ' white ', as in Беларусь ( White Russia or Belarus ) or Бе ́ лое мо ́ ре Sea ).

In some applications it is useful to be able to compute the Bernoulli numbers B < sub > 0 </ sub > through B < sub > p − 3 </ sub > modulo p, where p is a prime ; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime.

But California is where we're goin ''.

He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.

Now I wish to enter the American market, where the competition is very strong.

from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.

The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.

Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.

Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.

A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.

In a society where everything is for sale, Marlowe is the only man who cannot be bought.

This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.

As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.

`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.

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.

Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.

She was exposing herself to temptation which it is best to avoid where it can consistently be done.

Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.

but it is perennially restructured in situations where anchors are dragged or lost.

`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.

Finally we may note that the idea appears in educational theory where its influence is at present widespread.

where is the star's luminosity distance in parsecs, wherein 1 parsec is approximately 3. 2616 light-years.

Semidetached binary stars are binary stars where one of the components fills the binary star's Roche lobe and the other does not.

where δ equals Rasalgheti's angular diameter in arcseconds, d < sub > R </ sub > the star's diameter in AU, and D < sub > R </ sub > the Distance from Earth in parsecs.

* Star lifting is a process where an advanced civilization could remove a substantial portion of a star's matter in a controlled manner for other uses.

Outside of this region, in the star's envelope, energy is carried to the photosphere by plasma convection, where it radiates into space.

where M is the star's total mass.

Current theories of stellar dynamics also suggest that there is very little mixing between the bulk of a star's atmosphere and the material of its core, where fusion takes place, so most of a large star's fuel will never be used naturally.

The radiation zone or radiative zone is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion, rather than by convection.

where equals the angular diameter of Schedar in arcseconds, the star's diameter in AU, and the Distance from Earth in parsecs.

The outermost planet discovered appears to be within the system's habitable zone, where liquid water would remain stable ( more accurate data on the primary star's luminosity will be required to know for sure where the habitable zone is ).

As the novel begins, a glitch — an instability of the magnetic field inside the star caused by changes in the star's rotation — is about to destroy a net made up of ropes, where a group of 50 humans live.