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.

* Grimal, P. ( 1986 ).

P. Grimal has taken up this interpretation connecting it to a vase with red figures representing Boreas pursuing the nymph Oreithyia: Boreas is depicted as a two headed winged demon, the two faces with beards, one black and the other fair, perhaps symbolising the double movement of the winds Boreas and Antiboreas.

While there is no direct proof of an original solar meaning of Janus, this being the issue of learned speculations of the Roman erudits initiated into the mysteries and of emperors as Domitian, the derivation from a Syrian cosmogonic deity proposed by P. Grimal looks more acceptable.

One then considers metrics on the bundle P that are consistent with both the fiber metric, and the metric on the underlying manifold M. The consistency conditions are:

Starting from one point on the aggregate demand curve, at a particular price level and a quantity of aggregate demand implied by the IS-LM model for that price level, if one considers a higher potential price level, in the IS-LM model the real money supply M / P will be lower and hence the LM curve will be shifted higher, leading to lower aggregate demand ; hence at the higher price level the level of aggregate demand is lower, so the aggregate demand curve is negatively sloped.

P. Holland considers this lack of reciprocal action of particles and wave function to be one " mong the many nonclassical properties exhibited by this theory ".

According to Joseph P. Schultz, modern scholarship " considers the Maccabean revolt less as an uprising against foreign oppression than as a civil war between the orthodox and reformist parties in the Jewish camp ", while John J. Collins writes that while the civil war between Jewish leaders led to the king's new policies, it is wrong to see the revolt as simply a conflict between Hellenism and Judaism, since " The revolt was not provoked by the introduction of Greek customs ( typified by the building of a gymnasium ) but by the persecution of people who observed the Torah by having their children circumcised and refusing to eat pork.

According to Joseph P. Schultz, modern scholarship " considers the Maccabean revolt less as an uprising against foreign oppression than as a civil war between the orthodox and reformist parties in the Jewish camp.

One model considers that the P and S atoms ( in PCl < sub > 5 </ sub > and SF < sub > 6 </ sub > respectively ) form five and six true covalent bonds with the participation of d orbitals, in violation of the octet rule.

To obtain this, one considers two probability distributions P and Q, which are close to one another, so that

At least one herpetologist has considered the species a subspecies of Plestiodon tetragrammus under the scientific name P. tetragrammus callicephalus, but the more common classification considers it a separate species based on differences in appearance and the distinct geographic distribution.

If one considers a moving initial position, or equivalenty a moving origin ( e. g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track ), the velocity of P ( e. g. a point representing the position of a passenger walking on the train ) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be ' fixed in space ' ( such as, for instance, a point fixed on the floor of the train station ).

James P. Allen considers hnw a successor of hnnw as the pharaoh's m-r-pr.

Cutbush was the suspect advanced in the 1993 book Jack the Myth by A. P. Wolf, who suggested that Macnaghten wrote his memo to protect Cutbush's uncle who was a fellow police officer, and another recent writer, Peter Hodgson, considers that Cutbush is the most likely candidate.

At least one authority considers the American lion ( along with the cave lion ), to be more closely related to the tiger, P. tigris, citing a comparison of skull shapes ; the braincase, in particular, appears to be especially similar to the braincase of a tiger.

Guzmán considers Psilocybe tampanensis to be intermediate in form between P. mexicana and P. caerulescens.

In his 2009 review of Roman Catholic priest-scholar Kevin P. Spicer's Hitler's Priests: Catholic Clergy and National Socialism, he praises the book's admirable qualities but criticizes the work for its failure to distinguish between the small minority of " brown priests ", those priests who unequivocally supported the Nazi regime, with those who whom he considers to be " fellow travellers ", i. e. accepting the benefits that came with the Reichskonkordat but who failed to condemn the Nazi regime at the same time.

On the night of 15 / 16 April 1941 Axis ships were intercepted by Commander P. J Mack's 14th Destroyer Flotilla, comprising destroyers, HMS Janus, Jervis, Mohawk, Juno and Nubian.

With a market capitalization of under $ 1. 2 billion, Janus moves from the S & P 500 stock index to the S & P MidCap 400 after the close of business on November 22, 2011.