More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,

Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:

Formally, the outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data, where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to the outcome at hand, but related to the explanatory variables.

Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.

Formally, he says, the piece consists of two parts of nearly equal length, the end of the first section being bars 24 – 28 ( p. 77 ).

Formally, let p ( x, y ) be a complex polynomial in the complex variables x and y.

Formally, a cumulativity predicate CUM can be defined as follows, where capital X is a variable over sets, U is the universe of discourse, p is a mereological part structure on U, and is the mereological sum operation.

Formally, let p and q be two nonzero polynomials, respectively of degree m and n. Thus:

Formally, the theorem is stated as follows: There exist unique integers q and r such that a = qd + r and 0 ≤ r < | d |, where | d | denotes the absolute value of d.

Formally, a deterministic Büchi automaton is a tuple A = ( Q, Σ, δ, q < sub > 0 </ sub >, F ) that consists of the following components:

Formally, an absolute coequalizer of a pair in a category C is a coequalizer as defined above but with the added property that given any functor F ( Q ) together with F ( q ) is the coequalizer of F ( f ) and F ( g ) in the category D. Split coequalizers are examples of absolute coequalizers.

Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):

Formally said, the intersection of each two of them is empty ( the null event ): A and B

Formally, let X be any scheme and S be a sheaf of graded-algebras ( the definition of which is similar to the definition of-modules on a locally ringed space ): that is, a sheaf with a direct sum decomposition

where p is the frequency of one allele and q is the frequency of the alternative allele, which necessarily sum to unity.

Then, p < sup > 2 </ sup > is the fraction of the population homozygous for the first allele, 2pq is the fraction of heterozygotes, and q < sup > 2 </ sup > is the fraction homozygous for the alternative allele.

If the first allele is dominant to the second, then the fraction of the population that will show the dominant phenotype is p < sup > 2 </ sup > + 2pq, and the fraction with the recessive phenotype is q < sup > 2 </ sup >.

where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

* A node p is an ancestor of a node q if it exists on the path from the root to node q.

The node q is then termed as a descendant of p.

where q ' is the heat release rate perturbation and p ' is the pressure fluctuation.

It is the inference that if the proposition p is true, and proposition q is true, then the logical conjunction of the two propositions p and q is true.

Retrieved at < http :// books. google. com / books? id = NztlWQeXf2IC & printsec = frontcover & dq = zhou + enlai & hl = en & ei = wBkuTdKyB4H_8AaJucigAQ & sa = X & oi = book_result & ct = result & resnum = 2 & ved = 0CCsQ6AEwAQ # v = onepage & q & f = false > on March 12, 2011. p. 38 </ ref > More liberal estimates regarding the White Terror in China, estimate it took millions of lives, most of them in the rural areas.

Each chromosome has two arms, labeled p ( the shorter of the two ) and q ( the longer ).

According to Emile Benveniste ( 1954 ), the earliest written occurrence in English of civilisation in its modern sense may be found in Adam Ferguson's An Essay on the History of Civil Society ( Edinburgh, 1767 – p. 2 ): " Not only the individual advances from infancy to manhood, but the species itself from rudeness to civilisation.

London ( UK ): Harvey and Blythe ; 1951. p. 103 – 8.

The proof uses Euclid's lemma ( Elements VII, 30 ): if a prime p divides the product of two natural numbers a and b, then p divides a or p divides b ( or perhaps both ).

While for p equal to 0 we assume that it's equal to the geometric mean ( which is, in fact, the limit of means with exponents approaching zero ):

The following C language fragment is syntactically correct, but performs operations that are not semantically defined ( the operation < tt >* p >> 4 </ tt > has no meaning for a value having a complex type and < tt > p -> im </ tt > is not defined because the value of < tt > p </ tt > is the null pointer ):

As Alex Martelli put it in his Python Cookbook ( 2nd ed., p. 230 ): " To describe something as clever is NOT considered a compliment in the Python culture.

where, by definition, the left hand side is ζ ( s ) and the infinite product on the right hand side extends over all prime numbers p ( such expressions are called Euler products ):

* 1: 25 p. m. EDT ( approx ): Health officials announce that anthrax spores were found in office where the man killed by anthrax worked.

IV, p. 164 ): " The fundamental tenet of the Vedânta school consisted not in denying the existence of matter, that is solidity, impenetrability, and extended figure ( to deny which would be lunacy ), but in correcting the popular notion of it, and in contending that it has no essence independent of mental perception ; that existence and perceptibility are convertible terms.

", p. 90 ):

p ' ai ):

In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature ; he related wavelength ( denoted as λ ), and momentum ( denoted as p ):

* G. Levasseur, Napoléon et l ’ élaboration des codes répressifs ( Mélanges en homme à Jean Imbert, PUF, 1989 p. 371 ): Legal analysis of the Code of Criminal Procedure.

* Sonneveld, H, Loenning, K: ( 1994 ): Introducing terminology, in Terminology, p. 1-6

He does not explicitly acknowledge any anticipation of his demonstration of electrostatic repulsion by the latter but, as he quotes a passage from the same page, could not have been unaware that, in a discussion of the nature of electrical attraction, Cabeo had written ( Philosophia Magnetica p. 192 ): " When we see that small bodies ( corpuscula ) are lifted ( sublevari et attolli ) above the amber and also fall back to the motionless amber, it cannot be said that such erratic behaviour ( talem matum-but if " matum " is taken as a misprint for " motum ", then the translation is simply " such motion ") is an attraction by the gravity of the attracting body.

): Hitlers militärische Elite Band 1: Von der Anfängen des Regimes bis zum Kriegsbeginn ( p. 185-194 ).

The Quarterly Review of Economics and Finance, 50 ( 4 ): p. 456-470.

Stock market bubble effects on mergers and acquisitions, The Quarterly Review of Economics and Finance, 50 ( 4 ): p. 456-470.

CONTENTS ( James Bacque contributions ): “ The High Snow ,” p. 67-72 ; “ A small Film ,” 73-80 ; “ Sun and Earth for a Dollar ,” 81-88 ; “ the truth shall make you wierd ,” 88-97 ; “ On the morning of the death of Colonel Alexander Ramsay, O. B. E .,” 98-114 ; “ The Nancy Poems ,” 115-119 ; “ A Conversation with Milton Wilson ,” 120-146.

Wallis Budge, The Chronography of Gregory Abu ' l-Faraj, vol I, p. 98, APA – Philo Press, Amsterdam, 1932 ): ( After the Arab pillage of Rhodes ) " And a great number of men hauled on strong ropes which were tied round the brass Colossus which was in the city and pulled it down.

The recommendation in Freud ’ s technical papers for analysts to be emotionless, according to Ferenczi and Rank ( 1924 ), had led to " an unnatural elimination of all human factors in the analysis " ( pp. 40 – 41 ), and to " a theorizing of experience " ( p. 41 ): the feeling experience of the intersubjective relationship, two first-person experiences, within the analytic situation.