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 p is the star's parallax in arcseconds.

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.

It will be seen that where the scope is similar, the Athabascan ratios come out somewhat higher ( as indeed they ought to with a total ratio of 2.8 as against 3.5 or 4: 5 ) except for verbs, where alone the Athabascan ratio is lower.

He was elected to the U. S. House of Representatives, where he served a total of five terms.

where the total mass of all particles is given by

Therefore, it works as a neutron reflector and neutron moderator, effectively slowing the neutrons to the thermal energy range of below 0. 03 eV, where the total cross section is at least an order of magnitude lower – exact value strongly depends on the purity and size of the crystallites in the material.

The fact that in equivalent baseband models of communication systems, the signal spectrum consists of both negative and positive frequencies, can lead to confusion about bandwidth, since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as, where is the total bandwidth ( i. e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel ), and is the positive bandwidth ( the baseband bandwidth of the equivalent channel model ).

where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.

He is the enigmatic dictator of Oceania, a totalitarian state taken to its utmost logical consequence – where the ruling Party wields total power for its own sake over the inhabitants.

Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

Wherever the player goes before entering the dungeon, there is always a town which offers the basic services of a temple for healing and curing curses, a junk store where anything can be sold for a few copper coins, a sage who can identify items and ( from the second town onwards ) a bank for storing the total capacity of coins to lighten the player's load.

The total cross-section is related to the absorbance of the light intensity through Beer-Lambert's law, which says absorbance is proportional to concentration:, where C is the concentration as a number density, A < sub > λ </ sub > is the absorbance at a given wavelength λ, and is the path length.

Trance is the ability to communicate with, and mainly to receive from, other entities, incarnate and discarnate, and may sometimes be independent of time ; it is usually divided into deep trance ( obliterative and so dangerous, where the operative abdicates the throne, quite common ) and light trance ( a high or even total degree of awareness and thus safer for the practitioner, and extremely rare when well-done ).

If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed.

A typical dice game today is craps, where two dice are thrown at a time and wagers are made on the total value of the two dice.

Thus, if n < sub > r </ sub > is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be ( 1 + n < sub > r </ sub >), which is the actual reappearance factor added to the equation.

In the case of total life extinction, a similar factor may be applicable for f < sub > ℓ </ sub >, that is, how many times life may appear on a planet where it has appeared once.

where E < sub > cell </ sub > is the cell potential measured in volts ( V ) and C < sub > trans </ sub > is the cell current integrated over time and measured in coulombs ( C ); C < sub > trans </ sub > can also be determined by multiplying the total number of electrons transferred ( measured in moles ) times Faraday's constant ( F ).

where N is the total number of individuals in the population, B is the number of births, D is the number of deaths, b and d are the per capita rates of birth and death respectively, and r is the per capita rate of population change.

* the conclusion of supply and performance contracts where the total turnover provided for therein is more than the percentage of turnover for the previous financial year ;

* the raising or granting of loans, the issue of debt securities and the assumption of liabilities of a third party or suretyship for a third party where the total money value in each case is more than the percentage of subscribed capital ;

France is also one of the few countries where non-American productions have the biggest share: American films only represented 47. 7 % of total admissions in 2010.

Thus, if is the total number of trials and is the number of trials where the event occurred, the probability of the event occurring will be approximated by the relative frequency as follows:

Before the 2008 season, Fenway Park's capacity was increased to 37, 373, where it remains following additional renovations for the 2009 season, making its total capacity the fourth smallest, ahead of Marlins Park, the Oakland-Alameda County Coliseum, and Tropicana Field.

where is the total decay rate, the radiative decay rate and the non-radiative decay rate.