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.

The photocathode sensitivities S, phosphor efficiencies P, and anode potentials V of the individual stages shall be distinguished by means of subscripts 1, and 2, in the text, where required.

* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).

For example, P might be the circle with radius 1 and center ( 0, 0 ): P =

The running time of the new computation will be the length of time the unimproved fraction takes ( which is 1 − P ), plus the length of time the improved fraction takes.

In the case of parallelization, Amdahl's law states that if P is the proportion of a program that can be made parallel ( i. e., benefit from parallelization ), and ( 1 − P ) is the proportion that cannot be parallelized ( remains serial ), then the maximum speedup that can be achieved by using N processors is

In the limit, as N tends to infinity, the maximum speedup tends to 1 / ( 1 − P ).

In practice, performance to price ratio falls rapidly as N is increased once there is even a small component of ( 1 − P ).

As an example, if P is 90 %, then ( 1 − P ) is 10 %, and the problem can be sped up by a maximum of a factor of 10, no matter how large the value of N used.

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

Illustrative is the hydration of phenylacetylene gives acetophenone, and the ( Ph < sub > 3 </ sub > P ) AuCH < sub > 3 </ sub >- catalyzed hydration of 1, 8-nonadiyne to 2, 8-nonanedione:

Alcohol sales are prohibited on Sunday in West Virginia until 1: 00 P. M. EST.

The resultant ciphertext replaces P < sub > 1 </ sub > and P < sub > 2 </ sub >.

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 ).

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

A quadratic Bézier curve is the path traced by the function B ( t ), given points P < sub > 0 </ sub >, P < sub > 1 </ sub >, and P < sub > 2 </ sub >,

which can be interpreted as the linear interpolant of corresponding points on the linear Bézier curves from P < sub > 0 </ sub > to P < sub > 1 </ sub > and from P < sub > 1 </ sub > to P < sub > 2 </ sub > respectively.

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.

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.

Because Palinpinon is such a big source of geothermal energy, Gloria Macapagal-Arroyo said it received P 250 million in royalties, applied for livelihood, education, related projects, and also for the 50 % subsidy on Valencia electric bills consumers.

Informally, the " P vs. NP " question asks whether every optimization problem whose answers can be efficiently verified for correctness / optimality can be solved optimally with an efficient algorithm.

Given the abundance of such optimization problems in everyday life, a positive answer to the " P vs. NP " question would likely have profound practical and philosophical consequences.

Cook conjectures that there are optimization problems ( with easily checkable solutions ) which cannot be solved by efficient algorithms, i. e., P is not equal to NP.

* In 2011 a Rutgers University / IBM / University of Texas team linked the KAUST Shaheen installation together with a Blue Gene / P installation at the IBM Watson Research Center into a " federated high performance computing cloud ", winning the IEEE SCALE 2011 challenge with an oil reservoir optimization application.

* Green, P. Carroll, J. and Goldberg, S. ( 1981 ) A general approach to product design optimization via conjoint analysis, Journal of Marketing, vol 43, summer 1981, pp 17-35.

Daniel P. Miranker later improved on Rete with another algorithm, TREAT, which combined it with optimization techniques derived from relational database systems.

However, complexity classes can be defined based on function problems ( an example is FP ), counting problems ( e. g. # P ), optimization problems, promise problems, etc.

This optimization wins for common simple expressions ( e. g. loading variable X or pointer P ) as well as less-common complex expressions.

Any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have an FPTAS unless P = NP.

Several important graph optimization problems are APX hard, meaning that, although they have approximation algorithms whose approximation ratio is bounded by a constant, they do not have polynomial time approximation schemes whose approximation ratio tends to 1 unless P = NP.

However, David Zuckerman showed in 1996 that every one of these 21 problems has a constrained optimization version that is impossible to approximate within any constant factor unless P