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.

After this Confederate defeat at the Battle of Mill Springs, Davis sent Johnston a brigade and a few other scattered reinforcements, and he sent Gen. P. G. T.

P. G. T.

He also " gallantly stepped forward " to contribute a quarter of the costs of dramatising P. G. Wodehouse's A Damsel in Distress.

Second edition, 1883, New York: G. P.

He also translated from Greek into Latin a life of St. John Chrysostom ( Venice, 1533 ); the Spiritual Wisdom of John Moschus ; The Ladder of Divine Ascent of St. John Climacus ( Venice, 1531 ), P. G., LXXXVIII.

He also translated four books against the errors of the Greeks, by Manuel Kalekas, Patriarch of Constantinople, a Dominican friar ( Ingolstadt, 1608 ), P. G., CLII, col. 13-661, a work known only through Ambrose's translation.

P. G. Walsh.

* Pope, Saxton ( 1925 ) Hunting with the Bow and Arrow New York: G. P. Putnam's Sons

Former P & G logo

* Robinson, Jerry, The Comics: An Illustrated History of Comic Strip Art ( 1974 ) G. P.

Classics Professor G. P. Goold at University College, wrote of Housman's scholarly accomplishments: " The legacy of Housman's scholarship is a thing of permanent value ; and that value consists less in obvious results, the establishment of general propositions about Latin and the removal of scribal mistakes, than in the shining example he provides of a wonderful mind at work ....

( When measured in decibels it is logarithmically related to the power ratio: G ( dB )= 10 log ( P < sub > out </ sub > /( P < sub > in </ sub >)).

Washington, D. C .: U. S. G. P. O., 1999.

of Docs., U. S. G. P. O., 1994 – 2002.

" By the Way " was originally a column in the Globe, consisting of unsigned humorous pieces ; P. G. Wodehouse was assistant editor of the column from August 1903 and editor from August 1904 to May 1909, during which time he was assisted by Herbert Westbrook.

For example " GOOD DOG " can be encrypted as " PLLX XLP " where " L " substitutes for " O ", " P " for " G ", and " X " for " D " in the message.

( 1911 ); Star Lore of All Ages, G. P. Putnam's Sons, New York, New York, U. S. A., hardcover ; reprint 2004 as Star Lore: Myths, Legends, and Facts, Dover Publications, Inc., Mineola, New York, U. S. A., ISBN 978-0-486-43581-7 softcover.

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 ".

* Robinson, Jerry, The Comics: An Illustrated History of Comic Strip Art ( 1974 ) G. P.

Formerly using the call-sign, WA4CZD, he obtained the vanity call sign W4CGP in 1998 to reflect the C. G. P.

New York: G. P.

* Benton, P ; Ibanex, D .; Southon, G ; Southon, P. Dianetic Processing: A Brief Survey of Research Projects and Preliminary Results, Hubbard Dianetic Research Foundation, 1951