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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 Cortés
* Krabbe, N., P. Salaman, A. Cortés, A. Quevedo, L. A. Ortega and C. D. Cadena ( 2005 ) A new species of tapaculo from the upper Magdalena valley, Colombia.

P and Online
* Rodney P. Carlisle, " Fuchs, Klaus Emil Julius ", American National Biography Online February 2000, accessed 24 September 2005.
* Beginning in January 2000, David P. Goldman wrote a column for Asia Times Online under the pseudonym " Spengler.
* The Online Library of Liberty Project from Liberty Fund, Inc: The Aeneid ( Dryden translation, New York: P. F.
* Online verse translations in English by Judith P. Shoaf
* Online verse translations by Judith P. Shoaf
Software bundles usually included ClarisWorks, Quicken, a calendar / contact manager such as Touchbase and Datebook Pro, America Online, Apple's At Ease child-safe interface, educational software such as American Heritage Dictionary, The New Grolier Multimedia Encyclopedia, Microsoft Bookshelf ( on models equipped with a CD-Rom ), Mavis Beacon Teaches Typing, or Mario Teaches Typing, and games such as Spectre Challenger, Super Munchers, and Monopoly, all pre-installed over a slightly customized version of the Macintosh System software, denoted by a P in the version number ( e. g., System 7. 1P5 ).
* P. Cicogna, V. Natale, M. Occhionero, and M. Bosinelli, " Slow Wave and REM Sleep Mentation ," Sleep Research Online, vol.
Online finding aid to the gubernatorial papers of Tennessee Governor John P. Buchanan.
* Mione, P. 2006, " Job Enrichment ", Online paper.
* Samuel P. Goddard Papers Online from Arizona State University Libraries
Online references also include Thomas P. Hunt's Mafia Chonology, John Dickie's Cosa Nostra history and The Chronological History of La Cosa Nostra in the United States: January 1920-August 1987 compiled by the United States Department of Justice Criminal Division's Organized Crime Intelligence and Analysis Unit.
* S. P. Thompson ( 2004 ) Mary ( Mary of Blois ), suo jure countess of Boulogne ( d. 1182 ), Online Oxford Dictionary of National Biography
* Online text of Emily Hazen Reed's Life of A. P. Dostie, Or, The Conflict in New Orleans
* James P. Cassaro: " Vaclav Nelhybel ", Grove Music Online, ed.
* Lamar University, Online Math Notes-Phase Plane, P. Dawkins
* Lamar University, Online Math Notes-Systems of Differential Equations, P. Dawkins
A Professional MBA — with Evening, Weekend, and Online programs — and an Executive MBA are also available at the W. P. Carey School.
* MediaLab, Inc. Online ASCLS P. A. C. E.
* P. Cicogna, V. Natale, M. Occhionero, and M. Bosinelli, " Slow Wave and REM Sleep Mentation ," Sleep Research Online, vol.
The name was derived from the acronym of the service, S. A. P. O ( Servidor de Apontadores Portugueses Online ).

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