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formula and expressing
It shows that in any consistent effective theory T containing PA, the formula C < sub > T </ sub > expressing the consistency of T cannot be proven within T.
In the latter case, it provides an alternative formula for expressing local relationships between distances:
which is the analog of the formula in Euclidean geometry expressing the sine of an angle as the opposite side divided by the hypotenuse.
In science, a specific formula is a concise way of expressing information symbolically as in a mathematical or chemical formula.
A formula is said to be satisfied by any object ( s ) such that if it is written in place of the variable ( s ), it will form a sentence expressing a true proposition.
Stories about the bears generally follow a basic formula, so described by the Berenstains: " Papa sets out to instruct Small Bear in some aspect of the art of living and ends up badly the worse for wear, with Small Bear expressing his appreciation for the fine lesson Papa has taught him.
This formula links Lie groups to Lie algebras by expressing the logarithm of the product of two Lie group elements as a Lie algebra element in
The concept of fields was first ( implicitly ) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher.
At a press conference of law school deans in 1998 decrying the annual US News Law School Rankings, New York University School of Law Dean John Sexton quipped, " If they were asked about Princeton Law School, it would appear on the top 20 -- but it doesn't exist " ( Sexton was denouncing the US News usage of reputation survey results from judges, lawyers and law school deans in its ranking formula, expressing doubt over the expertise of some surveyed ).
He is also recognized as the first to describe the rule for multiplying matrices in 1812, and Binet's formula expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier.
It is based on expressing a formula containing the situation in terms of a formula containing the action and the situation, but not the situation.

formula and terms
The only precaution is that all volumes used in the formula be quoted in the same terms.
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.
Substituting this into the definition of the derivative via a difference quotient and taking limits means that the higher order terms – and higher – become negligible, and yields the formula interpreted as
Such a formula is indeed satisfiable if and only if at least one of its terms is satisfiable, and a term is satisfiable if and only if it does not contain both x and NOT x for some variable x.
Instead, these substances are discussed in terms of formula units or unit cells as the smallest repeating structure within the substance.
There is a formula for the derivative of f in terms of the derivative of g. To see this, note that f and g satisfy the formula
However, if the sequence itself is definable in the sense that we can specify a single formula for all its terms, then its limit will necessarily be a definable number.
The Euler – Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives ƒ < sup >( k )</ sup > at the end points of the interval m and n. Explicitly, for any natural number p, we have
Euler computed this sum to 20 decimal places with only a few terms of the Euler – Maclaurin formula in 1735.
Clenshaw – Curtis quadrature is essentially a change of variables to cast an arbitrary integral in terms of integrals of periodic functions where the Euler – Maclaurin approach is very accurate ( in that particular case the Euler – Maclaurin formula takes the form of a discrete cosine transform ).
Clemence's 1948 proposal did not adopt a correction of this kind in terms of mean solar time: instead, the same numbers were used as in Newcomb's original uncorrected formula ( 1 ), but now in a reverse sense, to define the time and time scale implicitly, based on the real position of the Sun:
Alternatively, for an orientable surface the formula can be given in terms of the genus of a surface, g:
Also Meeus's formula uses a fractional variable to allow computation of the four main phases, and uses a second variable for the secular terms.
For the convenience of the reader, the formula given above is based on Chapront's latest parameters and expressed with a single integer variable, and the following additional terms have been added:
In 1824, Niels Henrik Abel proved the striking result that there can be no general ( finite ) formula, involving only arithmetic operations and radicals, that expresses the roots of a polynomial of degree 5 or greater in terms of its coefficients ( see Abel-Ruffini theorem ).
This striking formula is one of the so-called explicit formulas of number theory, and is already suggestive of the result we wish to prove, since the term x ( claimed to be the correct asymptotic order of ) appears on the right-hand side, followed by ( presumably ) lower-order asymptotic terms.
The above formula can also be re-written in terms of a Composite Risk Index, as follows:
Robert Courtney Jr. ( IBM, 1970 ) proposed a formula for presenting risks in financial terms.
The Framework Agreement would have required the parties to agree on the specific terms of a political settlement based on the Autonomy / Sovereignty formula through direct negotiations.
Looking at this solution, which is valid for all choices compatible with the wave equation, it is clear that the first two terms are simply d ' Alembert's formula, as stated above as the solution of the homogeneous wave equation in one dimension.
The Newton series consists of the terms of the Newton forward difference equation, named after Isaac Newton ; in essence, it is the Newton interpolation formula, first published in his Principia Mathematica in 1687, namely the discrete analog of the continuum Taylor expansion,
To illustrate how one may use Newton's formula in actual practice, consider the first few terms of the Fibonacci sequence f = 2, 2, 4 ... One can find a polynomial that reproduces these values, by first computing a difference table, and then substituting the differences which correspond to x < sub > 0 </ sub > ( underlined ) into the formula as follows,

formula and moment
To arrive at the Breit-Rabi formula we will include the hyperfine structure ( interaction between the electron's spin and the magnetic moment of the nucleus ), which is governed by the quantum number, where is the spin angular momentum operator of the nucleus.
An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom ; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes.
This " supercharged " the Legacy cure, simultaneously killing him and stopping the spread of the Legacy virus, instanteously curing even those dying of the virus at that moment ( Although it was later revealed Colossus had been resurrected by alien technology and was being used as a test subject for an experimental formula that would reverse mutations before he was rescued by the X-Men ).
The following formula, obtained by solving the previous equation for, allows one to assess the proportional difference in energy release between earthquakes of two different moment magnitudes, say and:
Since the moment of inertia of a surface is its area multiplied by the square of a length called the radius of gyration, the above formula may be rearranged as follows.
The electron spin magnetic moment is given by the formula:
Genres include the oldest, yukar ( mimicry ), which is a form of epic poetry, and upopo, in which " the second contrapuntal voice had to imitate the musical formula in the first contrapuntal voice ( not heard until the last moment ), at an interval much shorter than that in our western canons, since the second voice attacks the preceding musical formula before the first voice has finished it.
Assume for a moment that in the above formula, w = 12, t = 4, and r = 2000.
For a two-level system with magnetic moment, the formula reduces to
Those familiar with probability theory will recognize the expression given by Dobinski's formula as the nth moment of the Poisson distribution with expected value 1.
Today, Dobinski's formula is sometimes stated by saying the number of partitions of a set of size n equals the nth moment of that distribution.
The offer and acceptance formula, developed in the 19th century, identifies a moment of formation when the parties are of one mind.
A notable moment is the use of a minor triad 1st inversion on ' long time ' ( at 0. 17 secs ) in which in the triad formula 3-5-1, the 1st note ( 3 ) B is heard as the lowest note in the chord, this being described as a Gm / B ' slash ' polychord.
Allmovie wrote, " This Hammer Films production isn't their finest moment but its easy to understand why it has become an enduring cult favorite with horror fans: The Vampire Lovers pushes the ' bloodshed & bosoms ' formula of the Hammer hits to its limit.
As of 2009, the coefficients of the QED formula for the anomalous magnetic moment of the electron have been calculated through order, and are known analytically up to.

1.209 seconds.