** ( Actual approximately − 11. 0 ) The diffuse reflector formula does for smaller phases.

This formula requires only k multiplications and k − 1 additions, for any array that can fit in memory.

The coefficient of x < sup > n − k </ sup > y < sup > k </ sup > is given by the formula

Some authors use the convention B < sub > 1 </ sub > = − 1 / 2 and state Bernoulli's formula in this way:

The sequence of N complex numbers x < sub > 0 </ sub >, ..., x < sub > N − 1 </ sub > is transformed into another sequence of N complex numbers according to the DFT formula:

− 1 / 30, … are the Bernoulli numbers, and R is an error term which is normally small for suitable values of p and depends on n, m, p and f. ( The formula is often written with the subscript taking only even values, since the odd Bernoulli numbers are zero except for B < sub > 1 </ sub >.

It follows from Euler's polyhedron formula, V − E + F = 2 ( where V, E, F are the numbers of vertices, edges, and faces ), that there are exactly 12 pentagons in a fullerene and V / 2 − 10 hexagons.

Parmanand Singh cites Pingala's cryptic formula misrau cha (" the two are mixed ") and cites scholars who interpret it in context as saying that the cases for m beats ( F < sub > m + 1 </ sub >) is obtained by adding a to F < sub > m </ sub > cases and to the F < sub > m − 1 </ sub > cases.

This together with Euler's formula v − e + f

For example, the first four perfect numbers are generated by the formula 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ), with p a prime number, as follows:

It was not until the 18th century that Leonhard Euler proved that the formula 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ) will yield all the even perfect numbers.

* Group intercommunication formula: n ( n − 1 ) / 2

A vinyl compound ( formula − CH = CH < sub > 2 </ sub >) is any organic compound that contains a vinyl group ( Preferred IUPAC name ethenyl ),

The form or shape of F in d ' Alembert's formula involves the argument x − vt.

For example for three structural isomers with molecular formula C < sub > 5 </ sub > H < sub > 12 </ sub > the melting point increases in the series isopentane − 160 ° C ( 113 K ) n-pentane − 129. 8 ° C ( 143 K ) and neopentane − 18 ° C ( 255 K ).

Cayley's formula states that there are n < sup > n − 2 </ sup > trees on n labeled vertices.

Otto Nordenskiöld theorized that winter conditions also play a role: His formula is W = 9 − 0. 1 C, where W is the average temperature in the warmest month and C the average of the coldest month, both in degrees Celsius ( this would mean, for example, that if a particular location had an average temperature of in its coldest month, the warmest month would need to average or higher for trees to be able to survive there ).

The sequence 0, 3, 8, 15, … is formed according to the formula n < sup > 2 </ sup > − 1 for the nth term: an explicit definition.

The formula is important because it connects complex numbers ( i stands for the imaginary unit ( i < sup > 2 </ sup > = − 1.

: For x = 2π the formula gives 1 < sup > ½ </ sup > = − 1.

The Golden Ratio is an irrational number approximating 1. 6180 < ref > The golden ratio can be derived by the quadratic formula, by starting with the first number as 1, then solving for 2nd number x, where the ratios = x / 1 or ( multiplying by x ) yields: = x < sup > 2 </ sup >, or thus a quadratic equation: x < sup > 2 </ sup > − x − 1

This formula describes the central tendency, but every family of mammals departs from it to some degree, in a way that reflects in part the complexity of their behavior.

The molecular formula reflects the exact number of atoms that compose the molecule and so characterizes different molecules.

After the first year of implementation, this tax rate would be automatically adjusted annually using a formula specified in the legislation that reflects actual federal receipts in the previous fiscal year.

In 2009, a movement began within the churches to declare the episcopal orders of the Roman Catholic Church invalid by the use of the 1968 formula due to a substantial change in form which no longer reflects the effect of the sacrament.

The Canadian formula has a different taste which reflects the " Canadian taste preference " ( according to the Consumer Relations department of Kellogg's in Canada ) while the American formula is similar to that used in other related products but without nuts or dried fruits.

The PCE chain-type index is constructed from a formula that reflects the changing composition of spending and thereby avoids some of the upward bias associated with the fixed-weight nature of the CPI.

* The salt lead acetate ( the active ingredient in gradual darkening products such as Grecian formula ) is toxic if ingested.

In Australia there was a formula that was quite similar to NASCAR, but it has now closed down, and a form of touring cars has taken its place.

# With reference to the ' rule of faith ', it may be said that Tertullian is constantly using this expression, and by it means now the authoritative tradition handed down in the Church, now the Scriptures themselves, and, perhaps, a definite doctrinal formula.

This is so that the formula for the longevity drug, which is known only to Devereaux and not written down, can be preserved and kept secret.

Machiavelli wrote The Prince during a time of political chaos in Italy, and writes down a formula by which a leader can lead the country out of turmoil and return it to prosperity.

Due to the chemical composition of the skunk spray, most of these household remedies are ineffective, with the exception of a peroxide formula or other remedies that break down the thiols.

* Numerical analysis is a branch of mathematics, pioneered by celestial mechanicians, for calculating approximate numerical answers ( such as the position of a planet in the sky ) which are too difficult to solve down to a general, exact formula.

In 2008 however, as he was stepping down as editor, he stated that it was possible to " overdo the formula " and that the style of the paper's front pages perhaps needed " reinvention ".

Abbott Laboratories has a manufacturing plant in Brockville, making infant formula and adult nutritionals for the domestic and overseas markets, although it is closing down in 2012, a loss of 150 jobs.

After Dr. John S. Pemberton invented Coca-Cola in 1886, the formula was kept a close secret, only shared with a small group and not written down.

It's a common misconception the rules were " dumbed down " to what was called the " junkyard formula " to allow more entries during the depression.

Cade patented the formula and offered all of the rights to the drink to the University of Florida in exchange for the university's backing of the production and marketing of the drink, but the university turned down his proposal.

He built poems: he didn't put in the seed, and water the seed, and send down his sun — letting the rest take care of itself: he measured his poems — kept them within formula.

Donovan's " The Devil's Due ," about criminals haunted by a mysterious stranger, is in keeping with the formula laid down by Cooper.

The talks bogged down, but U Thant proposed a formula for their reactivation under the auspices of his special representative, B. F. Osorio-Tafall, and they were resumed in 1972, after Thant had left office.

' So the supply-side formula was the only way to get a tax policy that was really ' trickle down.

in which the similarity transformed Hamiltonian ( defined as ) can be explicitly written down with the BCH formula:

Apart from that, Sultan Abdul Aziz Shah Airport was to be a hub for Global Flying Hospitals, but the humanitarian medical charity made the decision to close down Malaysian Operations, stating that the elements to make the correct formula for the GFH model were not present.

) Also, since the height h of the fluid column between z and z < sub > 0 </ sub > is often reasonably small compared to the radius of the Earth, one can neglect the variation of g. Under these circumstances, the integral boils down to the simple formula:

Jimmy climbed up the ivy to Sir Stanley Digby's room, threw the formula down to Loraine, climbed back down the ivy and into the library where he staged the fight, shot himself in his right arm and threw the second pistol onto the lawn.

According to the formula above, at 85 % efficiency air may be cooled only down to which makes it quite impractical.

On 1 December 2005 the Constitutional Court handed down its decision: the nine justices agreed unanimously that the common-law definition of marriage and the marriage formula in the Marriage Act, to the extent that they excluded same-sex partners from marriage, were unfairly discriminatory, unjustifiable, and therefore unconstitutional and invalid.

The Doctor has indeed found one, and as he writes down the formula, the Silurians attack the centre and stun him with their third eyes, taking him away.

Since heat transfer through the ground is slow, temperature measurements at a series of different depths down the borehole, adjusted for the effect of rising heat from inside the Earth, can be " inverted " ( a mathematical formula to solve matrix equations ) to produce a non-unique series of surface temperature values.