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.

* HTML Greek, in parallel with French translation: P. Remacle's collection

For two geometric objects P and Q represented by the relations P ( x, y ) and Q ( x, y ) the intersection is the collection of all points ( x, y ) which are in both relations.

* The Gentleman From Angell Street: Memories of H. P. Lovecraft ( ISBN 978-0-9701699-1-4 ), written by Muriel and C. M. Eddy, Jr. is a collection of personal remembrances and anecdotes from two of Lovecraft's closest friends in Providence.

David P. Wright argues that the Jewish law used Hammurabi's collection as a model, imitating both its structure and content.

Most of the rest of the poem has recently ( 2004 ) been published from a 3rd century BC papyrus in the Cologne University collection ( P. Köln XI 429 ).

P. G. Wodehouse published his first collection of comical stories about butler Jeeves in 1917.

* The Titan ( collection ), a collection of short stories by P. Schuyler Miller

For a collection T of subsets of X ( that is, for any subset of the power set P ( X ) of X ), let

More formally, a multivariate random variable is a column vector X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub >)< sup > T </ sup > ( or its transpose, which is a row vector ) whose components are scalar-valued random variables on the same probability space ( Ω,, P ), where Ω is the sample space, is the sigma-algebra ( the collection of all events ), and P is the probability measure ( a function returning every event's probability ).

The Silk Stocking National Historic District, located between Broadway and Seawall Boulevard and bounded by Ave. K, 23rd St., Ave. P, and 26th St., contains a collection of historic homes constructed from the Civil War through World War II.

The Nigerian pygmy hippopotamus ranged in the Niger River Delta, especially near Port Harcourt, but no reliable reports exist after the collection of the museum specimens secured by I. R. P. Heslop, a British colonial officer, in the early 1940s.

* L ' Enfant et l ' Art, a Love & Art Children's Foundation art collection created under the guidance of Alécia de Menezes Seidler, auctioned to benefit the children of Les P ' tits Cracks Le Figaro, May 2007.

P. T. Barnum was one of the earliest benefactors of Tufts College, and the Barnum Museum of Natural History was constructed in 1884 with funds donated by him to house his collection of animal specimens and the stuffed hide of Jumbo the elephant, who would become the university's mascot.

In 1986 the Lady Abingdon collection of French Empire furniture was bequeathed by Mrs T. R. P.

The African American collection is a body of historically significant and current books by and about African Americans and includes papers and memorabilia of such persons as the late Emmett P. Scott, secretary to Booker T. Washington, and Arthur J. Smith, who was associated with the Far East Consular Division of the State Department.

The collection includes: over 3, 000 textile items from the 1920s through the 1990s, including film and stage costumes as well as over a thousand items from Dietrich's personal wardrobe ; 15, 000 photographs, by Cecil Beaton, Horst P. Horst, George Hurrell, Lord Snowdon and Edward Steichen ; 300, 000 pages of documents, including correspondence with Burt Bacharach, Yul Brynner, Maurice Chevalier, Noël Coward, Jean Gabin, Ernest Hemingway, Karl Lagerfeld, Nancy and Ronald Reagan, Erich Maria Remarque, Josef von Sternberg, Orson Welles, and Billy Wilder ; as well as other items like film posters and sound recordings.

The art collection of 21 paintings auctioned by François Curiel, President of Christie's Europe, raised US $ 350, 000 for the children of Les P ' tits Cracks, a Parisian association dedicated to caring for children with cancer.

Most of Pletho's works can be found in J. P. Migne, Patrologia Graeca, collection ; for a complete list see Fabricius, Bibliotheca Graeca ( ed.

At the end of 1762, however, he was able to return to Dresden, where he was commissioned by P. D. Lippert to prepare the Latin text of the third volume of his Dactyliotheca ( art account of a collection of gems ).

In 1874, P. P. Bliss edited a collection titled Gospel Songs, and in 1875 P. P. Bliss and Ira Sankey issued Gospel Hymns, no ’ s.