They'd peddled the soap virtually alone, and without much success, until about a year ago, when -- with the addition of `` SX-21 '' to their secret formula and the inauguration of a high-powered advertising campaign -- sales had soared practically into orbit.

As is the case with the allotment provisions for support of vocational rehabilitation services, the matching requirements are also based on a statutory formula.

Actually, the engine displacement formula is the standard formula for computing the volume of a cylinder of any type with an added factor that represents the number of cylinders in the engine.

The formula, with the fractions converted to decimals, becomes Af.

The compression ratio arrived at with the formula will be the same regardless of whether cubic inches or cubic centimeters are used.

The Giants who had been anemic with the bat in their windy Candlestick Park suddenly found the formula in Milwaukee's park.

# for any formula with one free variable.

As debates raged in an attempt to come up with a new formula, three camps evolved among the opponents of the Nicene creed.

Closely related and even more numerous are amides derived from primary amines ( R ' NH < sub > 2 </ sub >) with the formula RC ( O ) NHR '.

Amides are also commonly derived from secondary amines ( R ' RNH ) with the formula RC ( O ) NR ' R.

Model theory generalizes the notion of algebraic extension to arbitrary theories: an embedding of M into N is called an algebraic extension if for every x in N there is a formula p with parameters in M, such that p ( x ) is true and the set

Similarly, the angle that a line makes with the horizontal can be defined by the formula

Initial approaches relied on the results of Herbrand and Skolem to convert a first-order formula into successively larger sets of propositional formulae by instantiating variables with terms from the Herbrand universe.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

The simplest acyclic alkenes, with only one double bond and no other functional groups, form an homologous series of hydrocarbons with the general formula C < sub > n </ sub > H < sub > 2n </ sub >.

Alkynes are hydrocarbons that have a triple bond between two carbon atoms, with the formula C < sub > n </ sub > H < sub > 2n-2 </ sub >.

An amyl alcohol is any of 8 alcohols with the formula C < sub > 5 </ sub > H < sub > 11 </ sub > OH.

Eight structural isomers with molecular formula C < sub > 5 </ sub > H < sub > 12 </ sub > O and all alcohols are known:

This formula is useful especially when working with Fourier transforms.

A number of variants deal with the number of variable assignments making the formula true.

Starting again with a slightly more general formula

Hedonism, for example, teaches that this feeling is pleasure — either one's own, as in egoism ( the 17th-century English philosopher Thomas Hobbes ), or everyone's, as in universalistic hedonism, or utilitarianism ( the 19th-century English philosophers Jeremy Bentham, John Stuart Mill, and Henry Sidgwick ), with its formula of the " greatest pleasure of the greatest number.

A carbohydrate is an organic compound that consists only of carbon, hydrogen, and oxygen, usually with a hydrogen: oxygen atom ratio of 2: 1 ( as in water ); in other words, with the empirical formula.

A more dangerous formula for national frustration cannot be imagined.

A mathematical formula is nothing more than a pattern for solving a specific problem.

A patient could receive up to 300 days paid-for nursing home care under a `` unit formula '' allowing more of such care for those who use none or only part of the hospital-care credit.

* branched ( general formula, n > 3 ) wherein the carbon backbone splits off in one or more directions

The Newton formula can lead one to believe that flight is more difficult than it actually is, due to this overprediction of drag and thus required thrust, and it may have contributed to a delay in human flight.

Some argue that the OPS formula is flawed and that more weight should be shifted towards OBP ( on base percentage ).

", while focusing on a Hi-NRG musical formula, was more lyrically focused on anti-homosexual prejudice.

* The sequential use of the Bayes ' formula: when more data become available after calculating a posterior distribution, the posterior becomes the next prior.

Natural saccharides are generally built of simple carbohydrates called monosaccharides with general formula ( CH < sub > 2 </ sub > O )< sub > n </ sub > where n is three or more.

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.

A strong indication of the reliability of Chandrasekhar's formula is that the absolute magnitudes of supernovae of Type Ia are all approximately the same ; at maximum luminosity, M < sub > V </ sub > is approximately-19. 3, with a standard deviation of no more than 0. 3 .< sup >, ( 1 )</ sup > A 1-sigma interval therefore represents a factor of less than 2 in luminosity.

Church subsequently modified his methods to include use of Herbrand – Gödel recursion and then proved ( 1936 ) that the Entscheidungsproblem is unsolvable: There is no generalized " effective calculation " ( method, algorithm ) that can determine whether or not a formula in either the recursive-or λ-calculus is " valid " ( more precisely: no method to show that a well formed formula has a " normal form ").

Part V of this act established an amending formula for the Canadian constitution, the lack of which ( due to more than 50 years of disagreement between the federal and provincial governments ) was the only reason Canada's constitutional amendments still required approval by the British parliament after ratification of the Statute of Westminster in 1931.

In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas ( such as the Pythagorean formula for the distance ) do not hold.

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

More generally a disjunction is a logical formula that can have one or more literals separated only by ORs.

The formula is more complex than the Otto cycle ( petrol / gasoline engine ) relation that has the following formula ;

This complex exponential function is sometimes denoted The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.

In electronic engineering and other fields, signals that vary periodically over time are often described as a combination of sine and cosine functions ( see Fourier analysis ), and these are more conveniently expressed as the real part of exponential functions with imaginary exponents, using Euler's formula.

The covalent energy of a bond is approximately, by quantum mechanical calculations, the geometric mean of the two energies of covalent bonds of the same molecules ( which is approximately equal to the arithmetic mean-which is applied in the first formula above-as the energies are of the similar value, except for the highly electropositive elements i. e. when there is a larger difference of two dissociation energies, but the geometric mean is more accurate and almost always gives a positive excess energy, due to ionic bonding ), and there is an additional energy that comes from ionic factors, i. e. polar character of the bond.