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P and .
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.

P and J
* W. S. Judd, C. S. Campbell, E. A. Kellogg, P. F. Stevens, M. J. Donoghue, 2002.
* W. S. Judd, C. S. Campbell, E. A. Kellogg, P. F. Stevens, M. J. Donoghue ( 2002 ).
J. P. Mallory and D. Q.
* Rhodes P. J.
Carnegie sold it in 1901 for $ 480 million to J. P. Morgan, who created U. S. Steel.
The Tycoons: How Andrew Carnegie, John D. Rockefeller, Jay Gould, and J. P. Morgan Invented the American Supereconomy.
* 1837 – J. P. Morgan, American financier ( d. 1913 )
* P. J. Rhodes: The Athenian Empire.
The current limited partners are Ronald E. Canakaris ; Warrick Dunn ; Douglas J. Hertz ; John P. Imlay, Jr .; Ed Mendel ; Derek V. Smith ; John A. Williams ; and Brian J. Barker.
* O ' Rourke, P. J., All the Trouble in the World.
J. P. de Florian's Gonsalve de Cordoue and Châteaubriand's Le dernier des Abencerrages are imitations of Perez de Hita's work.
* 1983 – J. P. Howell, American baseball player
* the Ligurian substrate hypothesis proposed in the 19th century by d ' Arbois de Joubainville, J. Pokorny, P. Kretschmer and several other linguists encompasses the Basco-Iberian hypothesis.
According to J. P. Mallory, in his 1989 book In Search of the Indo-Europeans, the hypothesis was also inspired by a Basque place-name ending in-adze.
The bundle theory of substance thus rejects the substance theories of Aristotle, Descartes, and more recently, J. P. Moreland, Jia Hou, Joseph Bridgman, Quentin Smith, and others.
* The Elements of Programming Style, with P. J. Plauger
* Software Tools, a book and set of tools for Ratfor, cocreated in part with P. J. Plauger
* Software Tools in Pascal, a book and set of tools for Pascal, with P. J. Plauger
* Sterling Quinlan, The Hundred Million Dollar Lunch ( Chicago, J. P. O ' Hara, 1974 ), ISBN 0-87955-310-3.
* Mallory, J. P. ( 1991 ) In Search of the Indo-Europeans: language, archaeology and myth.
* Sweet, J. P. M., ( 1979, Updated 1990 ) Revelation, London: SCM Press, and Philadelphia: Trinity Press International.
He asked her to have dinner with him that night at P. J. Clarke's.
Holly was offered a spot in the Winter Dance Party, a three-week tour across the Midwest opening on January 23, 1959, by the GAC agency, with other notable performers such as Dion and the Belmonts, Ritchie Valens, and J. P. " The Big Bopper " Richardson.

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