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. and P
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.

. and U
The appointment of U Thant of Burma as the U.N.'s Acting Secretary General -- at this writing, the choice appears to be certain -- offers further proof that in politics it is more important to have no influential enemies than to have influential friends.
With the neutralists maintaining pressure for one of their own to succeed Mr. Hammarskjold, U Thant emerged as the only possible candidate unlikely to be waylaid by a veto.
U Thant of course, will hold office until the spring of 1963, when Mr. Hammarskjold's term would have come to an end.
the West may or not remain satisfied with the kind of neutralism that U Thant represents.
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
Near Q, both curves can be represented by analytic functions of U.
In a neighborhood of Q the difference between these functions is also a single-valued, analytic function of U.
The restrained gyro-stabilized platform with reasonable response characteristics operates with an approximate equation of motion, neglecting transient effects, as follows: Af where U is a torque applied about the output axis of the controlling gyro.
Lincoln's assassination was the first assassination of a U. S. president and sent the nation into mourning.
Lincoln has been consistently ranked by scholars and the public as one of the three greatest U. S. presidents.
In 1846, Lincoln was elected to the U. S. House of Representatives, where he served one two-year term.
Lincoln also supported the Wilmot Proviso, which, if it had been adopted, would have banned slavery in any U. S. territory won from Mexico.
Lincoln disapproved of slavery, and the spread of slavery to new U. S. territory in the west.

. and Studio
That's because the good professor teaches only Weider methods at his famous Montreal Health Studio which is located at 1821 Mt. Royal East in Montreal.
The Heritage collection, to be shown by Sanger-Harris and Anderson's Studio, has perhaps more different types of woods and decorations than any one manufacturer ever assembled together at one time.
Make no mistake, this Gorky Studio drama is a respectable import -- aptly grave, carefully written, performed and directed.
Studio audio processing is limited in the modern era due to digital audio systems ( mixers, routers ) being pervasive in the studio.
Starring the Kinsey Sicks " at New York's legendary Studio 54.
This unique RF box was also where the power supply connected in a unique dual power / television signal setup similar to the RCA Studio II's.
* Intersection of Ventura blvd and Laurel Canyon blvd in Studio City, Los Angeles is named Andrei Sakharov Square.
A production is scheduled at the Mill Studio in Guildford in September 2010, to be staged by PH Productions.
A London production of Anyone can Whistle opened at the Jermyn Street Studio Theatre, London, in association with Primavera Productions, running from March 10, 2010 to April 17, 2010.
Years later on Inside the Actor's Studio, Goldie Hawn claimed that Capp had sexually propositioned her during her auditions for the 1964 New York World's Fair.
* By Kanten Clay Studio as a natural ingredient to form modelling clay for young children to play with.
In 2009 radio market share in the Dutch speaking region was 63. 08 % for the VRT channels ( Radio 1, Radio 2, MNM, Studio Brussel and Klara, 23. 13 % for the VMMa channels ( Q-Music and Joe FM ) and 2. 65 % for the Corelio / Concentra joint venture channel ( Radio Nostalgie ).
Studio 100 and Woestijnvis.
C # Builder was released in 2003 as a native C # development tool, competing with Visual Studio. NET.
As of the 2005 release, C # Builder, Delphi for Win32, and Delphi for. NET have been combined into a single IDE called " Borland Developer Studio " ( though the combined IDE is still popularly known as " Delphi ").
More recently, software with similar capabilities has been developed to allow manipulation of digital audio files stored on computers using turntables with special vinyl records ( e. g. Final Scratch, M-Audio Torq, Serato Scratch Live ) or computer interface ( e. g. Traktor DJ Studio, Mixxx, Virtual DJ ).
He also had ambitions to work in film, like Elvis Presley and Eddie Cochran, and registered for acting classes with Lee Strasburg's Actors ' Studio, where the likes of Marlon Brando and James Dean had trained.
The BBC News Channel moved from the Studio N8 set ( now home to BBC World News ) to what was the home of the national news in Studio N6, allowing the Channel to share its set with the BBC News at One and the BBC News at Ten – with other bulletins moving to studio TC7.

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