But it is apparent that no acceptable formula has been found to prevent such a possibility.

One has a recursive formula for binomial coefficients

For example, if a graph has 17 valid 3-colorings, the SAT formula produced by the reduction will have 17 satisfying assignments.

The problem of how many variable assignments satisfy a formula, not a decision problem, is in # P. UNIQUE-SAT or USAT or Unambiguous SAT is the problem of determining whether a formula known to have either zero or one satisfying assignments has zero or has one.

Propositional satisfiability has various generalisations, including satisfiability for quantified Boolean formula problem, for first-and second-order logic, constraint satisfaction problems, 0-1 integer programming, and maximum satisfiability problem.

After one pair of Bézout coefficients ( x, y ) has been computed ( using extended Euclid or some other algorithm ), all pairs may be found using the formula

It has a formula of C < sub > 12 </ sub > H < sub > 22 </ sub > O < sub > 11 </ sub >.

( Some exceptions exist ; for example, deoxyribose, a component of DNA, has the empirical formula C < sub > 5 </ sub > H < sub > 10 </ sub > O < sub > 4 </ sub >.

The aldohexose D-glucose, for example, has the formula ( C · H < sub > 2 </ sub > O ) < sub > 6 </ sub >, of which all but two of its six carbons atoms are stereogenic, making D-glucose one of 2 < sup > 4 </ sup > = 16 possible stereoisomers.

In this situation, the chain rule represents the fact that the derivative of is the composite of the derivative of f and the derivative of g. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.

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 ").

It has the following formula under cold air standard analysis:

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

Using the DPV formula above ( FV =$ 150, 000, i = 0. 05, n = 3 ), that means that the value of $ 150, 000 received in three years actually has a present value of $ 129, 576 ( rounded off ).

For example the ester hexyl octanoate, also known under the trivial name hexyl caprylate, has the formula CH < sub > 3 </ sub >( CH < sub > 2 </ sub >)< sub > 6 </ sub > CO < sub > 2 </ sub >( CH < sub > 2 </ sub >)< sub > 5 </ sub > CH < sub > 3 </ sub >.

Such a formula for estimating energy typically has relative error of order of 10 %, but can be used to get a rough qualitative idea and understanding of a molecule.

This imbalance has received considerable criticism, and is the subject of 2007 legislative proposals designed to alter the formula.

The Divine Liturgy of St. John Chrysostom, used in the Byzantine Churches, still has a formula of dismissal of catechumens ( not usually followed by any action ) at this point.

For example, the chemical compound n-hexane has the structural formula, which shows that it has 6 carbon atoms arranged in a chain, and 14 hydrogen atoms.

It is called in the Hebrew canon ' Eikhah, meaning " How ," being the formula for the commencement of a song of wailing.

In most of these, the formula remains the same, though the meaning of that formula may be vastly different.

was obtained from the linear time-coefficient in Newcomb's expression for the solar mean longitude ( above ), taken and applied with the same meaning for the time as in formula ( 3 ) above.

The meaning of Logos also is subject to interpretation: " word ", " account ", " plan ", " formula ", " measure ", " proportion ", " reckoning.

A magical formula is generally a name, word, or series of letters whose meaning illustrates principles and degrees of understanding that are often difficult to relay using other forms of speech or writing.

Tantra, literally meaning " formula ", " method, or " way ", ( parallel to the Chinese Tao, which also means " the way " or " the method "), and also having the secondary meaning of " loom ", " thread " or " warp and woof " is the name scholars give to a style of religious ritual and meditation that arose in medieval India no later than the fifth century CE, and which came to influence all forms of Asian religious expression to a greater or lesser degree.

Pyrope ( from the Greek pyrōpós meaning " fire-eyed ") is red in color and chemically a magnesium aluminium silicate with the formula Mg < sub > 3 </ sub > Al < sub > 2 </ sub >( SiO < sub > 4 </ sub >)< sub > 3 </ sub >, though the magnesium can be replaced in part by calcium and ferrous iron.

These are generally adverbs such as " very ", or " somewhat ", which modify the meaning of a set using a mathematical formula.

The full dental formula of dugongs is, meaning they have two incisors, three premolars, and three molars on each side of their upper jaw, and three incisors, one canine, three premolars, and three molars on each side of their lower jaw.

The wide bandwidth makes it possible to send with a very poor signal-to-noise ratio of much less than 1 ( less than 0 dB ) according to the Shannon-Heartly formula, meaning that the transmission power can be reduced to a level below the level of the noise and co-channel interference ( cross talk ) from other message signals sharing the same frequency.

: This and several other similar examples effectively proved that Swadesh's formula would not work on all available material — a serious accusation considering that evidence that can be used to " calibrate " the meaning of L ( i. e. language history recorded during prolonged periods of time ) is not overwhelmingly large in the first place.

In this formula, − Lc reflects the gradual slowing down of the replacement process due to different individual rates ( the less stable elements are the first and the quickest to be replaced ), whereas the square root represents the reverse trend – acceleration of replacement as items in the original wordlist " age " and become more prone to shifting their meaning.

) has a specific meaning when used in the context of DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has its molecular weight quoted including these groups, the amount of molecular weight that is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's formula weight ( i. e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups ).

Since the meaning and the words never vary, except for the spelling and inflection of populus in literature, Latin dictionaries classify it as a formula.

Whether the old text was already too deeply rooted, or whether Rabbenu Tam did not correct these verbal forms consistently and grammatically, the old perfects are still retained at the beginning of the formula, although a future meaning is given to them.

It relies on the simple if " x " then " y " formula of establishing meaning.

A necessary condition for a formula to be valid is that all terms have the same dimension, meaning every term in the formula could be potentially converted to contain the identical unit ( or product of identical units ).

This requires that the universal formula be converted to a formula that is intended to be used only with prescribed units, meaning the numerical quantity is implicitly assumed to be multiplying a particular unit.

* A course in happiness An authentic happiness formula for well-being, meaning and flourishing-ISBN 978-1-4563-7413-6

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

Saturated hydrocarbons can also combine any of the linear, cyclic ( e. g., polycyclic ) and branching structures, and they are still alkanes ( no general formula ) as long as they are acyclic ( i. e., having no loops ). They also have single covalent bonds between their carbons.

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

All other companies offer also fixed telephony in a duo play formula.

An identical expression to Einstein's formula for the diffusion coefficient was also found by Walther Nernst in 1888 in which he expressed the diffusion coefficient as the ratio of the osmotic pressure to the ratio of the frictional force and the velocity to which it gives rise.

The same coefficient also occurs ( if ) in the binomial formula

This formula is also referred to as the Binomial Formula or the Binomial Identity.

There is also a corresponding integral formula ( for ),

Bernoulli's formula is sometimes called Faulhaber's formula after Johann Faulhaber who also found remarkable ways to calculate sum of powers.

He was also hesitant to change the formula that had brought him such success, and feared that giving the Tramp a voice would limit his international appeal.

These compounds are also known as organocarbonates or carbonate esters, and have the general formula ROCOOR ′, or RR ′ CO < sub > 3 </ sub >.

This formula is true whenever g is differentiable and its inverse f is also differentiable.

The term carotene ( also carotin, from the Latin carota, or carrot ) is used for several related unsaturated hydrocarbon substances having the formula C < sub > 40 </ sub > H < sub > x </ sub >, which are synthesized by plants but cannot be made by animals.

Lanthanoids also form carbides ( sesquicarbides, see below ) with formula M < sub > 2 </ sub > C < sub > 3 </ sub >.

The term " deed ", also known in this context as a " specialty ", is common to signed written undertakings not supported by consideration: the seal ( even if not a literal wax seal but only a notional one referred to by the execution formula, " signed, sealed and delivered ", or even merely " executed as a deed ") is deemed to be the consideration necessary to support the obligation.

One may also wish to talk about definable complex numbers: complex numbers which are uniquely defined by a logical formula.

Hence, we may also write the formula as follows:

The Euler – Maclaurin formula is also used for detailed error analysis in numerical quadrature.

In contrast, the molecular formula identifies the number of each type of atom in a molecule, and the structural formula also shows the structure of the molecule.

Erlang-B ( sometimes also written without the hyphen Erlang B ), also known as the Erlang loss formula, is a formula for the blocking probability derived from the Erlang distribution to describe the probability of call loss on a group of circuits ( in a circuit switched network, or equivalent ).