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.

Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

Now consider the transformation of the lines of a bundle with vertex, P, on **zg which is effected by the involution as a whole.

Moreover, in this involution there is a cone of invariant lines of order Af, namely the cone of secants of **zg which pass through P.

Af is the friction force between chip and knife surfaces, and P is the normal force acting on the face of the knife.

A typical Victorian koala ( formerly P. cinereus victor ) has longer, thicker fur ; is a darker, softer grey, often with chocolate-brown highlights on the back and forearms ; and has a more prominently light-coloured ventral side and fluffy white ear tufts.

The race ( s ) descended from P ' an Hu were often characterized by Chinese writers as monsters who combined human and dog anatomy.

is the Japanese name for edible seaweed species of the red alga genus Porphyra, including most notably P. yezoensis and P. tenera, called laver in Wales and other English-speaking countries and Gim in Korean-though the rampant popularity of sushi in the United States means that the United States is often an exception to this, either referring to the product as " nori " as the Japanese do, or simply " seaweed ".

In linear algebra, the vector from the origin O to the point P is often called the position vector of P.

Another point is that those actions of free beings which bring about evil very often diminish the freedom of those who suffer the evil-for example, the murder of a young child ( e. g. Death of Baby P ) may prevent the child from ever exercising their free will in a significant way.

He is often cited as the King's " P. R.

Compound fertilizers often combine N, P and K fertilizers into easily dissolved pellets.

Author H. P. Lovecraft is alluded to often, with many mentions of characters ( e. g., Robert Harrison Blake, Henry Armitage, Klarkash-Ton ), monsters ( e. g., Tsathoggua, Yog-Sothoth ), books ( Necronomicon, Unaussprechlichen Kulten ) and places ( Miskatonic University ) from his Cthulhu Mythos.

Mayor Daley is a brother of William M. Daley, former White House Chief of Staff and former United States Secretary of Commerce under President Bill Clinton ; John P. Daley, a commissioner on the Cook County Board of Commissioners who also serves as its chairman of the County Board's Finance Committee ; and Micheal Daley, an attorney with Daley & George, a law firm founded by their father Richard J. Daley, that specializes in zoning law and is often hired by developers to help get zoning changes from City Hall.

The Dukes of Hazzard follows the adventures of " The Duke Boys ", cousins Bo and Luke Duke, who live in a rural part of the fictional Hazzard County, Georgia with their attractive cousin Daisy and their wise old Uncle Jesse, as they race around in their customized 1969 Dodge Charger stock car, christened ( The ) General Lee, evading crooked county commissioner Boss Hogg and his inept county sheriff Rosco P. Coltrane, and always managing to get caught in the middle of the various escapades and incidents that often occur in the area.

A music copyright is often notated as ℗, or a letter P ( instead of the letter C ) inside a circle.

In private, Raeder often fumed against the Social Democrats for playing " party politics " with the naval budget as he deemed their opposition to navalism, and which was incensed that the S. P. D were against even building up the Navy to the levels allowed by the Treaty of Versailles.

Mexican Douglas-fir, which ranges as far south as Oaxaca, is often considered part of P. menziesii.

According to Professor Lynda Walsh of the University of Nevada, Reno, some hoaxes — such as the Great Stock Exchange Fraud of 1814, labeled as a hoax by contemporary commentators — are financial in nature, and successful hoaxers — such as P. T. Barnum, whose Fiji mermaid contributed to his wealth — often acquire monetary gain or fame through their fabrications, so the distinction between hoax and fraud is not necessarily clear.

Frequently a critic of US and Soviet foreign policy, he resorted to fierce and often polarizing criticism in pinpointing his resistance towards imperialist ambitions and authoritarian regimes, including those of Francisco Franco of Spain, Gustáv Husák of Czechoslovakia, and B J Vorster and P W Botha of South Africa.

Some versions penalize for abbreviating Point of Order to P of O, which often confuses new players into thinking only the Dealer or Chairman is permitted to call a Point of Order.

The most common variant of discrete cosine transform is the type-II DCT, which is often called simply " the DCT ", ( N. Ahmed, T. Natarajan and K. R. Rao, 1974 ; K. R. Rao and P. Yip, 1990 ); its inverse, the type-III DCT, is correspondingly often called simply " the inverse DCT " or " the IDCT ".

Shub-Niggurath, often associated with the phrase “ The Black Goat of the Woods with a Thousand Young ”, is a deity in the Cthulhu Mythos of H. P. Lovecraft.

It is often convenient to formulate the trajectory of a particle P ( t ) = ( X ( t ), Y ( t ) and Z ( t )) using polar coordinates in the X-Y plane.

Records of Pistacia from pre-classical archaeological sites, and mentions in pre-classical texts, always refer to one of these other species ( often P. terebinthus ).

Pieter Corneliszoon Hooft, often abbreviated to P. C.

Average annual PET is often compared to average annual precipitation, P. The ratio of the two, P / PET, is the aridity index.