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.

The idea for blocking programs in this way was patented by Brett West and John P. Gardner in 1994 and tested in Canada.

* Brett, P., William Byrd and his Contemporaries ( Berkeley, 2007 )

* David B. Audretsch, Gilbert, Brett Anitra ; McDougall, Patricia P. ( 2004 ), The Emergence of Entrepreneurship Policy, Small Business Economics 22

The following season the club received its record outgoing transfer fee ; £ 1. 75million from for Brett Ormerod, eclipsing the £ 600, 000 Q. P. R.

* Brett Myers, P, Philadelphia ( 2002 – 09 ), Houston ( 2010 – present ) played in 26 games for Reading in 2001

George P. Brett, Jr. made the following comments in a letter dated 23 January 1947 to Daniel Macmillan about his family's devotion to the American publishing industry :" For the record my grandfather was employed by Macmillan's of England as a salesman.

Names he used for novels include Erle Barton, Lee Barton, Thornton Bell, Leo Brett, Bron Fane, L. P. Kenton, Phil Nobel, Lionel Roberts, Neil Thanet, Trebor Thorpe, Pel Torro, and Olaf Trent.

A. Williams-T. P. Cameron Wilson-W. B. Yeats-E. Hilton Young-Francis Brett Young

The Drawing Center named Brett Littman, former Deputy Director of P. S.

The final game featured a stellar pitching performance by Brett Cecil and a home run by J. P. Arencibia.

* Art by Alex Maleev, Dan Brereton, John Romita, Sr., Al Milgrom, Frank Cho, Jim Mahfood, Scott Morse, Craig Thompson, Michael Avon Oeming, Jason Pearson, Sean Phillips, Mark Bagley, Rodney Ramos, Bill Sienkiewicz, P. Craig Russell, Jacen Burrows, Walden Wong, Leonard Kirk, Terry Pallort, Dave Gibbons, Mike Gaydos, James Kochalka, David Mack, Brett Weldele, Ashley Wood, and Art Thibert

* Szatmary, David P. Shay's Rebellion: The Making of an Agrarian Insurrection ( 1984 ), 1787 in Massachusetts

** Watson, P. B. Marcus Aurelius Antoninus ( London, 1884 ), chap.

( see limit ), then we say that " P ( n ) holds for almost all positive integers n " ( formally, asymptotically almost surely ) and write

Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation ( C ), parity ( P ), and time reversal ( T ) operators.

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.

Several of ASU's graduate schools also appear among the top of the US News & World Report rankings, including the 30th-ranked W. P. Carey School of Business ( along with its 4th-ranked program in Supply Chain Management and the 15th-ranked program in Information Systems ), the 26th-ranked Sandra Day O ' Connor College of Law, the 43rd-ranked Ira A. Fulton School of Engineering ( including five individual programs ranked in the top 30 ), the 16th-ranked School of Public Affairs, the 26th-ranked Mary Lou Fulton Teachers College, the 21st-ranked College of Nursing and Health, and 25th-ranked Healthcare Management.

* Alexander, FM The Use of the Self, E. P. Dutton ( New York, 1932 ), republished by Orion Publishing, 2001, ISBN 0-7528-4391, ISBN 978-0-7528-4391-9

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

In particular, we cannot in general claim that " P or not P " is true ( the law of Excluded Middle ), since in some cases we may not be able to prove the statement " P " nor prove the statement " not P ".

It became the expectation — rather than the exception — that those in the public eye should write about themselves — not only writers such as Charles Dickens ( who also incorporated autobiographical elements in his novels ) and Anthony Trollope, but also politicians ( e. g. Henry Brooks Adams ), philosophers ( e. g. John Stuart Mill ), churchmen such as Cardinal Newman, and entertainers such as P. T. Barnum.

* Coffin, Tristram P .; Cohen, Hennig, ( editors ), Folklore in America ; tales, songs, superstitions, proverbs, riddles, games, folk drama and folk festivals, Garden City, N. Y.: Doubleday, 1966.

The running time of the new computation will be the length of time the unimproved fraction takes ( which is 1 − P ), plus the length of time the improved fraction takes.

In the case of parallelization, Amdahl's law states that if P is the proportion of a program that can be made parallel ( i. e., benefit from parallelization ), and ( 1 − P ) is the proportion that cannot be parallelized ( remains serial ), then the maximum speedup that can be achieved by using N processors is

In 1938, the first formal men's barbershop organization was formed, known as the Society for the Preservation and Encouragement of Barber Shop Quartet Singing in America ( S. P. E. B. S. Q. S. A ), and in 2004 rebranded itself and officially changed its public name to the Barbershop Harmony Society ( BHS ).

:* Les funérailles du général Marceau ( General Marceau's burial ), by P. H. Lamaire ( SOUTH façade, right ),