Add holes in top, forming `` S '' for salt and `` P '' for pepper.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

Since Af and P divides Af for Af, we have Af.

It is clear that each vector in the range of Af is in Af for if **ya is in the range of Af, then Af and so Af because Af is divisible by the minimal polynomial P.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

Ten students act as managers for a high-school football team, and of these managers a proportion P are licensed drivers.

The word `` binomial '' means `` of two names '' or `` of two terms '', and both usages apply in our work: the first to the names of the two outcomes of a binomial trial, and the second to the terms P and Af that represent the probabilities of `` success '' and `` failure ''.

The constancy of P and the independence are the conditions most likely to give trouble in practice.

Obviously, very slight changes in P do not change the probabilities much, and a slight lack of independence may not make an appreciable difference.

We shall find a formula for the probability of exactly X successes for given values of P and N.

Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1, with probabilities Q and P respectively.

On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.

As S increases we consider the two free corner points of the square, Af and Af, adjacent to P and Q respectively.

We again consider a fixed point P at Af and a variable point Q at Af on C.

We erect a square with PQ as a side and with free corners Af and Af adjacent to P and Q respectively.

Now with P fixed at Af, Af-values occur when the corner Af crosses C, and are among the values of S such that Af.

Moreover, if Af and Af are two planes intersecting in a line l, tangent to Q at a point P, the two free intersections of the image curves Af and Af must coincide at P', the image of P, and at this point Af and Af must have a common tangent l'.

To do this we must first show that every line which meets **zg in a point P meets its image at P.

But if this is the case, then an arbitrary pencil of lines having a point, P, of **zg as vertex is transformed into a ruled surface of order Af having Af generators concurrent at P.

In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if

An example is the " divides " relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p ( and not with any integer that is not a multiple of p ).

Oxford U. P .; p. 251

There are a few coincidental identities between cirth and runic letters, i with runic ᛁ, k with Younger Futhark ᚴ and ch with the Futhorc ᚳ ; p is furthermore reminiscent of Latin P ( runic ᚹ w ).

: This term is used both for conventional p – n diodes used to monitor temperature due to their varying forward voltage with temperature, and for Peltier heat pumps for thermoelectric heating and cooling .. Peltier heat pumps may be made from semiconductor, though they do not have any rectifying junctions, they use the differing behaviour of charge carriers in N and P type semiconductor to move heat.

P. J. Riis " The Cult Image of Diana Nemorensis " in Acta Archaelogica Kopenhagen 37 1966 p. 69 ff.

* L. P. Hartley, ' Emily Bronte In Gondal And Galdine ', in L. P. Hartley, The Novelist's Responsibility ( 1967 ), p. 35-53

The only exception to the formula is the Klein bottle, which has Euler characteristic 0 ( hence the formula gives p = 7 ) and requires 6 colors, as shown by P. Franklin in 1934 ( Weisstein ).

11, No. 1, P. 35. p. 58

" Reading and playing: what makes interactive fiction unique " p. 276-298. in Williams, J. P., & Smith, J. H. ( 2007 ).

* The projection of to the horizontal subspace of the tangent space at point p ∈ P must be isomorphic to the metric g on M at π ( p ).

One obtains the value f ( r ) by substitution of the value r for the symbol X in P. One reason to distinguish between polynomials and polynomial functions is that over some rings different polynomials may give rise to the same polynomial function ( see Fermat's little theorem for an example where R is the integers modulo p ).

) Frank P. Ramsey, on the other hand, was skeptical about the existence of such objective logical relations and argued that ( evidential ) probability is " the logic of partial belief " (" Truth and Probability ", 1926, p. 157 ).

* Maxwell-Stuart, P. G. Chronicle of the Popes: The Reign-by-Reign Record of the Papacy from St. Peter to the Present, Thames & Hudson, 2002, p. 117 – 118.

* Maxwell-Stuart, P. G. Chronicle of the Popes: The Reign-by-Reign Record of the Papacy from St. Peter to the Present, Thames & Hudson, 2002, p. 119.

* Maxwell-Stuart, P. G. Chronicle of the Popes: The Reign-by-Reign Record of the Papacy from St. Peter to the Present, Thames & Hudson, 2002, p. 118.

Genèse et survivances d ' un mythe, d ' Homère à Bouchardon ( Paris, P. U. R., 2009 ), p. 139-164 ( Interférences ).

* Diop, Cheikh Anta, Modum, Egbuna P., " Towards the African renaissance: essays in African culture & development ", 1946 – 1960, p 28, Karnak House ( 1996 ).

# if x < sup > p </ sup > + y < sup > p </ sup > + z < sup > p </ sup > = 0 ( mod P ) then P divides xyz, and