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.

Gilbert, O. P., " Iona: monks, pastors and missionaries " in Broun & Clancy ( 1999 ).

Gilbert, O. P., " Religious life: early medieval " in Lynch ( 2001 ).

Gilbert, O. P., " Conversion to Christianity " in Lynch ( 2001 ).

* Machado, Carlos A., Nancy Robbins, M. Thomas P. Gilbert, and Edward Allen Herre.

Fate of Atlantis is based on the SCUMM story system by Ron Gilbert, Aric Wilmunder, Brad P. Taylor, and Vince Lee, thus employing similar gameplay to other point-and-click adventures developed by LucasArts in the 1980s and 1990s.

He commissioned the architect C. P. H. Gilbert to construct the Essex County Bank in 1921.

Two other tracts containing 39 acres were sold to Gilbert Bailey, by William P. Downs and Frederick Parks in 1838.

* Gilbert, Martin ( editor ) A Century of Conflict, 1850 – 1950 ; Essays for A. J. P.

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

* Gilbert, P. ( 2002 ) Body Shame: Conceptualisation, Research and Treatment.

* Gilbert, P. ( 1998 ) Shame: Interpersonal Behavior, Psychopathology and Culture.

**" Tho ' P ' raps I May Incur Your Blame " ( w. W. S. Gilbert m. Arthur Sullivan )

In the pedagogical method of Forte / Gilbert diminutions are classified as passing notes ( P ), neighboring notes ( N, upper or lower, complete or incomplete, direct or indirect ), consonant skips ( CS ), and arpeggiations ( Arp ).

Ezekiel Gilbert ( P )

One of his later relatives was the architect C. P. H. Gilbert.

Famous MSU alumni include former Michigan governors James Blanchard and John Engler, U. S. Senators Debbie Stabenow and Tim Johnson, U. S. Ambassador to Brazil Donna Hrinak, former Jordan Prime Minister Adnan Badran, billionaire philanthropists Tom Gores and Eli Broad, Chief Justice of the Texas Supreme Court Wallace B. Jefferson, trial lawyer Geoffrey Feiger, former Food and Drug Administration official Peter Rheinstein, Pulitzer Prize-winning novelist Richard Ford, Teamsters president James P. Hoffa, Quicken Loans founder and Cleveland Cavaliers owner and billionaire Dan Gilbert, Sergeant at Arms of the U. S. House of Representatives Wilson Livingood, former Michigan U. S. Senator and Secretary of Energy Spencer Abraham, former Vice President of the Republic of Liberia Harry Moniba, and former U. S. Ambassador to Italy Peter Secchia.

Miriam arranges a reunion with Gilbert, who supposedly is recuperating in the Outback, and this charade lands Ruth in the clutches of P. J.

* Gilbert P. Williamson, San Jose State ' 58, Former President and CEO, NCR Corporation

Following his acquisition in 1913 of the property at 1 East 91st Street in New York City from Andrew Carnegie, Kahn commissioned J. Armstrong Stenhouse and Charles P. H. Gilbert to design his Carnegie Hill mansion.

The Oxford Dictionary of National Biography also compares his verse with that of W. S. Gilbert and suggests that his prose was an early influence on P. G. Wodehouse.

Alternatively, an inker may do the basic layout of the page, give the work to another artist to do more detailed pencil work, and then ink the page himself ( as Joe Simon often did when inking Jack Kirby, or when Michael T. Gilbert collaborated with penciller P. Craig Russell on the Elric of Melniboné series ).

* Gilbert, P. 2000: Butterfly Collectors and Painters.

Some of the most recognized artists that have been produced by Varney, or have featured on his labels, include Yngwie Malmsteen, David Lee Roth, Kansas, Shawn Lane, Victor Wooten, Frank Gambale, Eric Johnson, John Scofield, Dennis Chambers, Warren Haynes, Scott Henderson, Stuart Hamm, Tony MacAlpine, Eric Gales, Marty Friedman, Jason Becker, Steve Smith, Greg Howe, Liquid Tension Experiment, Doug Pinnick, Mike Portnoy, Great White, Paul Gilbert, Nicole Couch, Michelle Meldrum, Phantom Blue, Michael Landau, Mike Stern, Winger, W. A. S. P., Steeler and Racer X.

* Fabes, Gilbert H., The First Editions of A. E. Coppard, A. P. Herbert and Charles Morgan, 1933 London: Myers.