A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables ( Dover: New York, 1972 ), p. 78.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

Formulas in Calligra Words are provided by the Formula plugin.

Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of X can be present:

Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts.

Formulas for the other coefficients are much harder to get ; Todd classes of toric varieties, the Riemann – Roch theorem as well as Fourier analysis have been used for this purpose.

Formulas are quite often interpreted as propositions ( as, for instance, in propositional logic ).

Formulas with the form described above are known as 2-CNF formulas ; the " 2 " in this name stands for the number of terms per clause, and " CNF " stands for conjunctive normal form, a type of Boolean expression in the form of a conjunction of disjunctions.

Formulas for different colors of glass are closely guarded.

Formulas for triose and TP are C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OH and C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OPO < sub > 3 </ sub >< sup > 2 -</ sup > + 2H < sup >+</ sup >.

Formulas are given in SI units and Gaussian-cgs units.

Formulas not involving st ( i. e., formulas of the usual language of set theory ) are called internal, other formulas are called external.

This edition consisted of the following titles ( the three titles marked with an asterix (*) are the volumes that had appeared together as The Arcane Teaching in the previous edition ): The One and the Many * ( hardback ), Cosmic Law * ( hardback ), The Psychic Planes * ( hardback ), The Arcane Formulas, or Mental Alchemy ( binding unknown ), The Mystery of Sex, or Sex Polarity ( binding unknown ), and Vril, or Vital Magnetism ( binding unknown ).

Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers.

Formulas are available to estimate the effective length of a whistle, but an accurate formula to predict sounding frequency would have to incorporate whistle length, scale, gas flow rate, mouth height, and mouth wall area ( see below ).

Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of propositional formulas ( in the language consisting of and 0 ) into A. Formulas mapped to 1 ( or 0 ) for all A-valuations are called A-tautologies.

Formulas such as XLys, XTrp Analog, XLys, XTrp Maxamaid, XLys, XTrp Maxamum or Glutarex 1 are designed to provide amino acids other than lysine and tryptophan, in order to tentatively prevent protein malnutrition.

This engine and its legacy drive the SD Trans Ams and Formulas as one of the more, if not the most, desirable Pontiacs ever produced.

Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.

TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark ’ s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.

Formulas Fatal to the Flesh is the fifth full-length studio album by death metal band Morbid Angel.

For example, a 1901 medical book published for home health use gave the following two " Simple Remedy Formulas " for DYSENTERRY: ( 1 ) Thin boiled starch, 2 ounces ; Laudanum, 20 drops ; " Use as an injection every six to twelve hours "; ( 2 ) Tincture rhubarb, 1 ounce ; Laudanum 4 drachms ; " Dose: One teaspoonful every three hours.

Formulas for expressing the roots of polynomials of degree 2 in terms of square roots have been known since ancient times ( see quadratic equation ), and for polynomials of degree 3 or 4 similar formulas ( using cube roots in addition to square roots ) were found in the 16th century ( see cubic function and quartic function for the formulas and Niccolo Fontana Tartaglia, Lodovico Ferrari, Gerolamo Cardano, and Vieta for historical details ).

*" Basic Concepts and Formulas in Microscopy: Numerical Aperture " by Michael W. Davidson, Nikon MicroscopyU ( website ).

During this period he started supervising Ph. D. students, such as James Halpern ( Contributions to the Study of the Independence of the Axiom of Choice ) and Edgar Lopez-Escobar ( Infinitely Long Formulas with Countable Quantifier Degrees ).

A Complete Collection of Thermodynamic Formulas ( abstract ).

The four titles in this edition were: The Arcane Teaching ( hardback ), The Arcane Formulas, or Mental Alchemy ( pamphlet ), The Mystery of Sex, or Sex Polarity ( pamphlet ), and Vril, or Vital Magnetism ( pamphlet ).

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 ).

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Work-outs for the week are as follows: Plain Scotch, 3 ( by Scotch Victor ), Demon Law, 3 ( by Demon Hanover ), Coffee Royal, p ( by Royal Blackstone ) and Beauty Way, p, 3 ( by Demon Hanover ) in 25 ; ;

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

The natural allegiance and obedience is an incident inseparable to every subject, for as soon as they are born they owe by birthright allegiance and obedience to the Sovereign ( Ex p. Anderson ( 1861 ) 3 E & E 487 ).

It has been maintained that the right to wear mitres was sometimes granted by the popes to abbots before the 11th century, but the documents on which this claim is based are not genuine ( J. Braun, Liturgische Gewandung, p. 453 ).

The exchange's normal trading sessions are from 9: 30 a. m. to 4: 00 p. m. on all days of the week except Saturdays, Sundays and holidays declared by the Exchange in advance.

Trans., 1830, 3, p. 1 ) is fulfilled in all systems which are symmetrical with respect to their diaphragm ( briefly named symmetrical or holosymmetrical objectives ), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it ( hemisymmetrical objectives ); in these systems tan w ' / tan w

In the language of valence bond theory, the carbon atoms in an alkyne bond are sp hybridized: they each have two unhybridized p orbitals and two sp hybrid orbitals.

< p > Flavored malt beverages are brewery products that differ from traditional malt beverages such as beer, ale, lager, porter, stout, or malt liquor in several respects.

At the same time, flavored malt beverages are marketed in traditional beer-type bottles and cans and distributed to the alcohol beverage market through beer and malt beverage wholesalers, and their alcohol content is similar to other malt beverages in the 4-6 % alcohol by volume range .</ p >

< p > Although flavored malt beverages are produced at breweries, their method of production differs significantly from the production of other malt beverages and beer.

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.