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.

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

where J denotes the Jacobian matrix of partial derivatives of ƒ and is the induced norm on the matrix.

However, the region where a partial eclipse can be observed is much larger.

After mixing with water vapor and expired CO < sub > 2 </ sub > in the lungs, oxygen diffuses down a pressure gradient to enter arterial blood where its partial pressure is around 100 mmHg ( 13. 3 kPa ).

SSV run at partial atmospheres ( typically around 1 / 3 of full atmospheric pressure ) in a hybrid of vacuum and conventional kiln technology ( SSV kilns are significantly more popular in Europe where the locally harvested wood is easier to dry versus species found in North America ).

Without solid exterior walls, full-height draperies on a perimeter track allow freedom to provide full or partial privacy when and where desired.

A partial pre-alpha version of the client was demonstrated once at Comdex where a bemused Bill Gates stopped by the booth.

* is a partial function called the transition function, where L is left shift, R is right shift.

Stops contrast with nasals, where the vocal tract is blocked but airflow continues through the nose, as in and, and with fricatives, where partial occlusion impedes but does not block airflow in the vocal tract.

The supply-and-demand model is a partial equilibrium model of economic equilibrium, where the clearance on the market of some specific goods is obtained independently from prices and quantities in other markets.

* is a partial function called the transition function, where L is left shift, R is right shift.

where u < sub > x </ sub > is the first partial derivative of u with respect to x.

The middle zone, the yellow portion of the flame is an oxygen depleted zone, where partial oxidation has occurred, but insufficient oxygen exists to burn all of the vapors present.

Sequence divergence in flanking regions can lead to poor primer annealing, especially at the 3 ’ section, where extension commences ; preferential amplification of particular size alleles due to the competitive nature of PCR can lead to heterozygous individuals being scored for homozygosity ( partial null ).

At very low degrees of partial melting a silica undersaturated melt is produced, forming a nepheline syenite, where orthoclase is replaced by a feldspathoid such as leucite, nepheline or analcime.

where is the partial derivative of with respect to its first argument, evaluated at.

Study of functions defined in this more general setting thus provides a convenient method of deriving results about the way functions vary in space as well as time or, in more mathematical terms, partial differential equations, where this technique is known as separation of variables.

More commonly, where the lensing mass is complex ( such as galaxy groups and clusters ) and does not cause a spherical distortion of space – time, the source will resemble partial arcs scattered around the lens.

During the Russo-Turkish War, Alexandra was clearly partial against Turkey and towards Russia, where her sister was married to the Tsarevitch, and she lobbied for a revision of the border between Greece and Turkey in favour of the Greeks.

Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false.

In partial differential equations, a domain is an open connected subset of the euclidean space R < sup > n </ sup >, where the problem is posed, i. e., where the unknown function ( s ) are defined.

An early form of partial jus soli dates from the Cleisthenes ' reforms, and developed further in the Roman world where citizenship was extended to all free inhabitants of the Empire, especially with the Constitutio Antoniniana ( Edict of Caracalla ).

Canada's Medicare system and most of the UK's NHS general practitioner and dental services, which are systems where health care is delivered by private business with partial or total government funding, fit this broader definition, as do the health care systems of most of Western Europe.