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.

Each stage of development in the diagram is paired with a photomicrograph of a developing P. aeruginosa biofilm.

In this context the elucidation of the molecular mechanisms responsible for the switch from planktonic growth to a biofilm phenotype and the role of inter-bacterial communication in persistent disease should provide new insights in P. aeruginosa pathogenicity, contribute to a better clinical management of chronically infected patients and should lead to the identification of new drug targets for the development of alternative anti-infective treatment strategies.

By 18 years of age, 80 % of patients with classic CF harbor P. aeruginosa, and 3. 5 % harbor B. cepacia.

Their ease of culture in vitro and availability of an increasing number of Pseudomonas strain genome sequences has made the genus an excellent focus for scientific research ; the best studied species include P. aeruginosa in its role as an opportunistic human pathogen, the plant pathogen P. syringae, the soil bacterium P. putida, and the plant growth promoting P. fluorescens.

In the year 2000, the complete genome sequence of a Pseudomonas species was determined ; more recently, the sequence of other strains have been determined, including P. aeruginosa strains PAO1 ( 2000 ), P. putida KT2440 ( 2002 ), P. fluorescens Pf-5 ( 2005 ), P. syringae pathovar tomato DC3000 ( 2003 ), P. syringae pathovar syringae B728a ( 2005 ), P. syringae pathovar phaseolica 1448A ( 2005 ), P. fluorescens PfO-1 and P. entomophila L48.

P. aeruginosa can infect a child through foot punctures, and can cause both endocarditis and septic arthritis.

Use of P. putida is preferable to some other Pseudomonas species capable of such degradation as it is a safe species of bacteria, unlike P. aeruginosa for example, which is an opportunistic human pathogen.

The bacterial genus Pseudomonas includes the opportunistic human pathogen P. aeruginosa, plant pathogenic bacteria, plant beneficial bacteria, ubiquitous soil bacteria with bioremediation capabilities and other species that cause spoilage of milk and dairy products.

P. aeruginosa can cause chronic opportunistic infections that have become increasingly apparent in immunocompromised patients and the ageing population of industrialised societies.

Studies also suggest the emergence of antibiotic resistance in P. aeruginosa.

In the year 2000, the complete genome sequence of a Pseudomonas species was determined ; more recently the sequence of other strains have been determined including P. aeruginosa strains PAO1 ( 2000 ), P. putida KT2440 ( 2002 ), P. fluorescens Pf-5 ( 2005 ), P. fluorescens PfO-1 and P. entomophila L48.

On the eve of World War II, Soviet archives indicate a combined camp and colony population upwards of 1. 6 million in 1939, according to V. P. Kozlov.

In its public pronouncements, P ' yongyang has called for accelerated population growth and encouraged large families.

The largest concentrations of population are in North P ' yŏngan and South P ' yŏngan provinces, in the municipal district of P ' yongyang, and in South Hamgyŏng Province, which includes the Hamhŭng-Hŭngnam urban area.

Eberstadt and Banister calculate the average population density at 167 persons per square kilometer, ranging from 1, 178 persons per square kilometer in P ' yongyang Municipality to 44 persons per square kilometer in Yanggang Province.

In 1987 the total national population living in P ' yongyang was 11. 5 percent.

The government also restricts and monitors migration to cities and ensures a relatively balanced distribution of population in provincial centers in relation to P ' yongyang.

* A new population of extended, luminous star clusters in the halo of M31, A. P.

: P is the population number

A generalized logistic curve can model the " S-shaped " behaviour ( abbreviated S-curve ) of growth of some population P. The initial stage of growth is approximately exponential ; then, as saturation begins, the growth slows, and at maturity, growth stops.

Employment at the facility sustained a population of 27, 023 in 1940. Aliquippa Station | P & LE Station The mill closed during the collapse of the steel industry during the 1980s.

The civil war era saw a population boom, and many young men of Mountain City served in the 32nd Cavalry regiment under Col. P. C.

First settled in 1873 by Thomas P. Jones and Charles Villeneuves, its population was 91 at the 2010 census.

In the I = PAT equation, the variable P represents the population of an area, such as the world.

However, with P increasing exponentially, T would have to decrease drastically ( doubling efficiency each time the population doubles ) just to maintain the same impact with the same affluence.

Bacalar is the municipal seat and largest city in Bacalar Municipality ( until 2011 a part of Othón P. Blanco Municipality ) in the Mexican state of Quintana Roo, about north of Chetumal, at 18 ° 40 ' 37 " N, 88 ° 23 ' 43 " W. In the 2010 census the city had a population of 11, 084 people.

Moravian palaeontologist Ferdinand Stoliczka separated the Himalayan population as a third subspecies, P. g. forsythi, but this has not been widely accepted and is usually treated as synonymous with digitatus.

g. grisegena found in Europe and western Asia, and the larger P. g. holboelii in North America and eastern Siberia — is evaluated as Least Concern, and the global population is stable or growing.

The Red-necked grebe has a large range, estimated at 1 – 10 million square kilometres ( 0. 4 – 3. 8 million square miles ), and a global population of 150, 000 – 370, 000 individuals, with P. g. holboellii about twice as numerous as the nominate race.

The challenge of a complete theory of population genetics is to provide a set of laws that predictably map a population of genotypes ( G < sub > 1 </ sub >) to a phenotype space ( P < sub > 1 </ sub >), where selection takes place, and another set of laws that map the resulting population ( P < sub > 2 </ sub >) back to genotype space ( G < sub > 2 </ sub >) where Mendelian genetics can predict the next generation of genotypes, thus completing the cycle.