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.

At this period the thirty-year old Helion was ranked `` as one of the mature leaders of the modern movement '', according to Herbert Read, `` and in the direct line of descent from Cezanne, Seurat, Gris and Leger ''.

And those still with us, Herbert C. Hoover, Harry S. Truman, Dwight D. Eisenhower and John F. Kennedy.

In an effort to fortify himself against the unforseen upsets sure to arise in the future, Herbert A. Leggett, banker-editor of the Phoenix `` Arizona Progress '', reflects upon a few of the depressing experiences of the feverish fifties.

Francesca and Herbert were among the few people we knew in Catatonia.

Francesca and Herbert considered themselves violently nonconformist and showed the world they were by filling their Colonial house with contemporary furniture and paintings and other art objects ( expensive, but not necessarily valuable, contemporary things ).

Like Herbert, they were all in communications: radio, television, magazines, and advertising.

Incidentally, one cannot miss the significance of this gesture, for Dickens reintroduces it associatively in Pip's mind at another moral and psychological crisis -- his painful recognition, in a talk with Herbert Pocket, that his hopeless attachment to Estella is as self-destructive as it is romantic.

The respectability which money confers implies a different etiquette, and, upon taking up the life of a London gentleman, Pip must learn from Herbert Pocket that `` the spoon is not generally used over-hand, but under ''.

Sent to Montpelier by Secretary Herbert Hoover, Red Cross Aide Reuben Sleight had been killed, and his pilot, Lt. Franklin Wolfe, badly injured.

Herbert Heilman in town for a day.

Writing to his colleague George Herbert Palmer -- `` Glorious old Palmer '', as he addresses him -- James says that if only the students at Harvard could really understand Royce, Santayana, Palmer, and himself and see that their varying systems are `` so many religions, ways of fronting life, and worth fighting for '', then Harvard would have a genuine philosophic universe.

Richard and George Herbert Mead as well, and that although Korzybski analyzes knowing, he doesn't fully analyze doing.

Herbert Sutcliffe sweeps Arthur Mailey during the first Ashes Test in Sydney, 1924.

Jack Hobbs and Herbert Sutcliffe took the score to 49 – 0 at the end of the second day, a lead of 27.

* 1921 – John Herbert Chapman, Canadian physicist ( d. 1979 )

Lists of phenomena, from the contemplation of which " the savage " was led to believe in animism, have been given by Sir E. B. Tylor, Herbert Spencer, Andrew Lang, and others ; a controversy arose between the former as to the priority of their respective lists.

The physicist Nick Herbert has argued for " quantum animism " in which mind permeates the world at every level.

* In the 1976 science fiction novel Children of Dune, written by Frank Herbert, Agamemnon is mentioned as an ancestor of the Atreides family.

* Benario, Herbert W., Alexander Severus ( A. D. 222 – 235 ), De Imperatoribus Romanis ( 2001 )

In reply to this the French sovereign dispatched Andrew as his ambassador to Güyük Khan ; with Longjumeau went his brother William ( also a Dominican ) and several others — John Goderiche, John of Carcassonne, Herbert " Le Sommelier ," Gerbert of Sens, Robert ( a clerk ), a certain William, and an unnamed clerk of Poissy.

* 1912 – Herbert Mills, American singer ( The Mills Brothers ) ( d. 1989 )

* Ebeling, Herbert C .: Johann Jakob Astor.