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.

In a letter to P. Schuyler Miller and John D. Clark in 1936 only three months before Howard's death, Conan is described as standing and weighing when he takes part in an attack on Venarium at only 15 years old, though being far from fully grown.

Completed by P. Schuyler Miller and John D. Clark, the chronology was later revised by Clark and L. Sprague de Camp in An Informal Biography of Conan the Cimmerian ( 1952 ).

" Reviewing the book for Astounding Science Fiction, P. Schuyler Miller characterized the title piece as " one of Bradbury's bitter, almost hysterical diatribes ," although he praised its " emotional drive and compelling, nagging detail.

The term was first used in print in 1957 by P. Schuyler Miller in a review of John W. Campbell, Jr .' s Islands of Space in Astounding Science Fiction.

For example, P. Schuyler Miller called Arthur C. Clarke's 1961 novel A Fall of Moondust hard SF, and the designation remains valid even though a crucial plot element, the existence of deep pockets of " moondust " in lunar craters, is now known to be incorrect.

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

* Genus Homo ( 1950 ) ( with P. Schuyler Miller )-first science fiction novel de Camp had a hand in, possibly the earliest work of fiction dealing with the " Planet of the Apes " theme

P. Schuyler Miller compared Sixth Column to " the old E. Phillips Oppenheim or modern Eric Ambler intrigue, thrust and counterthrust with civilization at stake.

P. Schuyler Miller, noting that the novel's " climactic situations seem to be telegraphed ", suggested that Heinlein presented his background situations so effectively that readers solve the story's mysteries more quickly than Heinlein allowed his characters to.

P. Schuyler Miller reviewed the novel favorably, saying " in true Heinlein manner the basic theme of the book smashes the screen of action only in the closing pages.

P. Schuyler Miller praised the novel as " very smoothly and logically put together ," although he noted that it lacked the level of " elaboration of background detail " that he expected from Heinlein.

" P. Schuyler Miller ranked it " close to the best in mainline science fiction.

" P. Schuyler Miller found The Star Beast to be " one of the best of 1954.

" P. Schuyler Miller recommended the novel unreservedly, saying that Heinlein's " minute attention to detail.

P. Schuyler Miller, reviewing the original edition, praised the novel's " verisimilitude, the attention to detail which Heinlein's adult readers know well.

P. Schuyler Miller said that " Heinlein is a master of concealed technology.

" P. Schuyler Miller found Revolt in 2100 to be " a distinctly minor Heinlein contribution,.

P. Schuyler Miller cited the novel's " freshness and simplicity ," characterizing it as " a life-size portrait-gallery of real people living in a real world of the future, every detail of which fits into place with top-tolerance precision ".

" P. Schuyler Miller characterized the novel as " all imagination and poetry ," but concluded it was " not up to some of Clarke's other writing " due to weakness in its " episodic structure.

Active in Republican politics, he was the Platform Committee chairman at the 1868 Republican National Convention in Chicago, he offered Vice President Schuyler Colfax's name for renomination at the 1872 Republican National Convention in Philadelphia, and gave the nominating speech for Oliver H. P. Morton for President at the 1876 Republican National Convention in Cincinnati.

* L. Sprague de Camp and P. Schuyler Miller-Genus Homo

P. Schuyler Miller received the volume favorably, but noted that the " revision and inter-writing " of the component stories was " not quite so successful a job " as Asimov had managed with I, Robot.

" P. Schuyler Miller reported it to be " good, sound, middle-of-the-road science fiction with a carefully hidden surprise.

P. Schuyler Miller, noting that Healy had managed to commission stories from the editors of the major science fiction magazines of the time, described the anthology as " one of the best anthologies you'll see in 1954.