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.

1876 ), and is dated by P Marchegay from 1121.

* P. Remacle's collection – Greek with French translation

* 1929 – Huey P. Long Governor of Louisiana is impeached by the Louisiana House of Representatives.

* 1899 – P. L. Travers, Australian author ( d. 1996 )

* 2012 – N. K. P. Salve, Indian politician ( b. 1921 )

* 1920 – P. D. James, English novelist

* 1992 – The Katina P. runs aground off of Maputo, Mozambique and 60, 000 tons of crude oil spill into the ocean.

* 1911 – United States Senate leaders agree to rotate the office of President pro tempore of the Senate among leading candidates to fill the vacancy left by William P. Frye's death.

* 1932 – Thomas P. Salmon, American politician, 75th Governor of Vermont

* 1919 – William P. Foster, American bandleader and educator ( d. 2010 )

* 1975 – Bus massacre in Lebanon: An attack by the Phalangist resistance kills 26 militia members of the P. F. L.

* Pei Wei Asian Diner – throughout the United States ; a subsidiary of P. F.

* P. F. Chang's China Bistro – throughout the United States ; features California-Chinese fusion cuisine

* 1954 – Michael P. Kube-McDowell, American novelist

* 1927 – Samuel P. Huntington, American political scientist ( d. 2008 )

Conversely, some elements do not maintain distinct allotropes in different phases – for example phosphorus has numerous solid allotropes, which all revert to the same P < sub > 4 </ sub > form when melted to the liquid state.

* 1837 – J. P. Morgan, American financier ( d. 1913 )

* 1995 – Oklahoma City bombing: The Alfred P. Murrah Federal Building in Oklahoma City, Oklahoma, USA, is bombed, killing 168.

* 1990 – Himchan, South Korean singer ( B. A. P )

A great part of the craft of parallel programming consists of attempting to reduce the component ( 1 – P ) to the smallest possible value.

* 1911 – Following the resignation and death of William P. Frye, a compromise is reached to rotate the office of President pro tempore of the United States Senate.

* Smyth, Alfred P., Warlords and Holy Men: Scotland AD 80 – 1000.

* 1983 – J. P. Howell, American baseball player

* 1891 – P. T. Barnum, American showman, businessman, scam artist, and entertainer ( b. 1810 )

of Docs., U. S. G. P. O., 1994 – 2002.

Additionally, though the Chronicler's principal source is the Deuteronomistic History, coming primarily, as stated above, from the books of 2 Samuel and 1 – 2 Kings and other public records and sources ( see above ), the Chronicler also uses other biblical sources, particularly from the Pentateuch, as redacted and put together by P ( the Priestly Source ).