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.

Following an unexpected visit from P. R.

: R. I. P.

* Grant, P. R.

Additional peripheral cartridge-holders by companies such as P. R. E. S.

Because the WD1770 is capable of single density mode and uses the same IBM360 derived floppy disc format as the Intel 8271 found in the BBC Micro, it was also possible to run a DFS filing system with an alternate ROM, such as the P. R. E. S AP4 interface.

Alternative WD1770 / DFS Interfaces such as the P. R. E. S AP4 left & PAGE at E00h.

This provided an alternative to buying the combination of the P. R. E. S.

Let P be the root of the unbalanced subtree, with R and L denoting the right and left children of P respectively.

* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.

* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).

* Hanson, R. P. C., The Search for the Christian Doctrine of God: The Arian Controversy, 318-381 ( T .& T.

Spoofs include the " Eric Conspiracy " of moustachioed hackers named " Eric "; ex-members of the P. H. I. R. M.

Pentel R. S. V. P.

* Vientiane Buffalos RUFC, a semi-pro rugby union football club from Vientiane, Lao P. D. R., consisting mostly of expatriate players

P & R Publishing ( 2005 ).

The 21 consonant letters in the English alphabet are B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, X, Z, and usually W and Y: The letter Y stands for the consonant in " yoke ", the vowel in " myth " and the vowel in " funny ", and " yummy " for both consonant and vowel, for examples ; W almost always represents a consonant except in rare words ( mostly loanwords from Welsh ) like " crwth " " cwm ".

* P. v. R. Schleyer ( Editor-in-Chief ).

( E ) exhaust camshaft, ( I ) intake camshaft, ( S ) spark plug, ( V ) poppet valve | valve s, ( P ) piston, ( R ) connecting rod, ( C ) crankshaft, ( W ) water jacket for coolant flow.

* 1984 – Pleasure P, American R & B Singer ( Pretty Ricky )

The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true.

" Elaine Donnelly called such efforts " a big P. R.

( 1986 ), " Provision for the families of the Montfortians disinherited after the Battle of Evesham ", in P. R.

* Maddicott, J. R. ( 1986 ), " Edward I and the lessons of baronial reform: local government, 1258-80 ", in P. R.