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 October 1947, Li ' l Abner met Rockwell P. Squeezeblood, head of the abusive and corrupt Squeezeblood Comic Strip Syndicate.

* Cocteau, Jean, Le Coq et l ' Arlequin: notes autour de la musique – avec un portrait de l ' auteur et deux monogrammes par P. Picasso, Paris, Éditions de la Sirène, 1918

Thus the expression " point P is incident with line l " is used instead of either " P is on l " or " l passes through P ".

* P. Collart, Philippes ville de Macédoine de ses origines jusqu ' à la fin de l ' époque romaine, Paris, 1937.

* André Charles, marquis de La Jaille, Voyage au Sénégal pendant les années 1784 et 1785, avec des notes jusqu ’ à l ' an X par P. Labarthe, Paris, Denter, 1802.

While the status of the Asiatic lion ( P. l. persica ) as a subspecies is generally accepted, the systematic relationships among African lions are still not completely resolved.

The Asiatic lion persica was the most distinctive, and the Cape lion had characteristics allying it more with P. l. persica than the other sub-Saharan lions.

* P. l. leo, known as the Barbary lion, originally ranged from Morocco to Egypt.

* Franceschi, P. The Doomsday Argument and Hempel's Problem, English translation of a paper initially published in French in the Canadian Journal of Philosophy 29, 139-156, 1999, under the title Comment l ' urne de Carter et Leslie se déverse dans celle de Hempel

* Brunhes, J .; Rhaim, A .; Geoffroy, B .; Angel, G .; Hervy, J. P. Les Moustiques de l ' Afrique mediterranéenne French / English.

* J. Zenneck, ( translators: P. Blanchin, G. Guérard, É. Picot ), " Précis de télégraphie sans fil: complément de l ' ouvrage: Les oscillations électromagnétiques et la télégraphie sans fil ", Paris: Gauthier-Villars, 1911. viii, 385 p.: ill. ; 26 cm.

Mitochondrial sequence data from fossils suggest that American lions ( P. atrox ) are a sister lineage to Eurasian cave lions ( P. l. spelaea ), diverging about.

* Epipactis exilis P. Delforge-now a synonym of Epipactis persica subsp.

In 1935, the new film studio Photo Chemical Laboratories, known as P. C. L.

He also translated four books against the errors of the Greeks, by Manuel Kalekas, Patriarch of Constantinople, a Dominican friar ( Ingolstadt, 1608 ), P. G., CLII, col. 13-661, a work known only through Ambrose's translation.

In 1938, the first formal men's barbershop organization was formed, known as the Society for the Preservation and Encouragement of Barber Shop Quartet Singing in America ( S. P. E. B. S. Q. S. A ), and in 2004 rebranded itself and officially changed its public name to the Barbershop Harmony Society ( BHS ).

Quantum computers have gained widespread interest because some problems of practical interest are known to be in BQP, but suspected to be outside P. Some prominent examples are:

* the income statement, also known as the statement of financial results, profit and loss account, or P & L

That briefly means that there is no known algorithm that efficiently solves all instances of SAT, and it is generally believed ( but not proven, see P versus NP problem ) that no such algorithm can exist.

The problem of how many variable assignments satisfy a formula, not a decision problem, is in # P. UNIQUE-SAT or USAT or Unambiguous SAT is the problem of determining whether a formula known to have either zero or one satisfying assignments has zero or has one.

During this period, which has become known as baseball's dead-ball era, Cub infielders Joe Tinker, Johnny Evers, and Frank Chance were made famous as a double-play combination by Franklin P. Adams ' poem Baseball's Sad Lexicon.

This was renamed the African Union First Colored Methodist Protestant Church and Connection, more commonly known as the A. U. M. P.

It is known that there exists a unique Delaunay triangulation for P, if P is a set of points in general position ; that is, there exists no k-flat containing k + 2 points nor a k-sphere containing k + 3 points, for 1 ≤ k ≤ d − 1 ( e. g., for a set of points in < big > ℝ </ big >< sup > 3 </ sup >; no three points are on a line, no four on a plane, no four are on a circle, and no five on a sphere ).

constant and this relating the variables P. V and T of an ideal gas is known as the equation of state.

* World Thinking Day, also known as " B .- P. day " or " Founder's Day " ( World Association of Girl Guides and Girl Scouts )

The inverse transform, known as Fourier series, is a representation of s < sub > P </ sub >( t ) in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:

A sufficient condition for recovering s ( t ) ( and therefore S ( ƒ )) from just these samples is that the non-zero portion of s ( t ) be confined to a known interval of duration P, which is the frequency domain dual of the Nyquist – Shannon sampling theorem.

In favour of the Synoptic chronology, E. P Sanders observes that a short ministry accords with the careers of other known prophetic figures of the time — who appear in the desert, raise large scale public interest, but soon come to a bloody end at the hand of the Roman military.

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.

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

In order to enter at a talent competition at University High School, Berry and Torrence helped form a doo-wop group known as " The Barons " ( named after their high school's Hi-Y club, where they were members ), which comprised fellow University High students William " Chuck " Steele ( lead singer ), Arnold P. " Arnie " Ginsburg ( born November 19, 1939 ) ( 1st tenor ), Wallace S. " Wally " Yagi ( born 20 July 1940 ) ( 2nd tenor ), John ' Sagi " Seligman ( 2nd tenor ), with Berry singing bass, and Torrence providing falsetto.

* P. H. I. R. M., a 1980s computer hacking group originally known as Kilobaud

) and reestablish relations with the Republic of China ( commonly known by its main island as Taiwan ), it has since restored ties with the P. R. C.

She writes that only three fragmentary manuscripts are known to have survived into the modern period, two 3rd-century fragments ( P. Rylands 463 and P. Oxyrhynchus 3525 ) published in 1938 and 1983, and a longer 5th-century Coptic translation ( Berolinensis Gnosticus 8052, 1 ) published in 1955.

The complexity class P is contained in NP, but NP contains many important problems, the hardest of which are called NP-complete problems, for which no polynomial-time algorithms are known for solving them ( although they can be verified in polynomial time ).

" Oxfordian Louis P. Bénézet created the " Bénézet test " by which lines known to be by Oxford were compared with lines of Shakespeare.