There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables ( see more at finite state machine, state transition table and control table ), as flowcharts ( see more at state diagram ), or as a form of rudimentary machine code or assembly code called " sets of quadruples " ( see more at Turing machine ).

Particularly in hardware design and verification applications, satisfiability and other logical properties of a given propositional formula are sometimes decided based on a representation of the formula as a binary decision diagram ( BDD ).

Feynman gave a prescription for calculating the amplitude for any given diagram from a field theory Lagrangian-the Feynman rules.

Unlike a bubble chamber picture, only the sum of all the Feynman diagrams represent any given particle interaction ; particles do not choose a particular diagram each time they interact.

For phaneritic felsic rocks, the QAPF diagram should be used, and a name given according to the granite nomenclature.

In the diagram on the right, this is given by the ratio A /( A + B ), where A and B are the indicated areas.

However, the state of matter and phase diagram usages are not commensurate with the formal definition given above and the intended meaning must be determined in part from the context in which the term is used.

An atom in level 2 may decay by spontaneous emission to the ground state, releasing a photon of frequency ν < sub > 12 </ sub > ( given by E < sub > 2 </ sub > – E < sub > 1 </ sub > = hν < sub > 12 </ sub >), which is shown as the transition L, called the laser transition in the diagram.

The basic rule is that if we have the probability amplitude for a given complex process involving more than one electron, then when we include ( as we always must ) the complementary Feynman diagram in which we just exchange two electron events, the resulting amplitude is the reverse – the negative – of the first.

In this diagram is also given the λ-line.

When the curve given by a series of points in a diagram or in a list of the coordinates of points, the slope may be calculated not at a point but between any two given points.

Suppose ( A < sub > 1 </ sub >, φ < sub > 1 </ sub >) is an initial morphism from X < sub > 1 </ sub > to U and ( A < sub > 2 </ sub >, φ < sub > 2 </ sub >) is an initial morphism from X < sub > 2 </ sub > to U. By the initial property, given any morphism h: X < sub > 1 </ sub > → X < sub > 2 </ sub > there exists a unique morphism g: A < sub > 1 </ sub > → A < sub > 2 </ sub > such that the following diagram commutes:

For a given diagram F: J → C and functor G: C → D, if both F and GF have specified limits there is a unique canonical morphism

* Constellation diagram, which shows ( on a graph or 2D oscilloscope image ) how a given signal state ( a symbol ) can represent three or more bits at once.

In the tuning-fork diagram, the regular spirals occupy the upper branch and are denoted by the letter S, while the lower branch contains the barred spirals, given the symbol SB.

That is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is not-null ".

) If the analemma is drawn in a diagram, tilted at the appropriate angle for an observer's latitude ( as described above ), and if a horizontal line is drawn to pass through the position of the Sun on the analemma on any given date ( interpolating between the date markings as necessary ), then at sunrise this line represents the horizon.

In an abelian category ( such as the category of abelian groups or the category of vector spaces over a given field ), consider a commutative diagram:

Consider the following commutative diagram in any abelian category ( such as the category of abelian groups or the category of vector spaces over a given field ) or in the category of groups.

Examples of proofs by diagram chasing include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.

Conversely, given a commutative diagram, it defines a poset category:

* Construction tasks: no diagram is given in construction tasks ; instead, the aim is to construct a game or position with certain features.

The phase transformations that occur while solidifying a given alloy can be understood by drawing a vertical line from the liquid phase to the solid phase on a phase diagram.

When there are only two means to compare, the t-test and the ANOVA F-test are equivalent ; the relation between ANOVA and t is given by F = t < sup > 2 </ sup >.

The tones in between are then given by 16: 9 for D, 8: 5 for E, 3: 2 for F, 4: 3 for G, 6: 5 for A, and 16: 15 for B, in ascending order.

There can only be one copy of the F-plasmid in a given bacterium, either free or integrated, and bacteria that possess a copy are called F-positive or F-plus ( denoted F < sup >+</ sup >).

It measures the amount of " stuff " flowing through a surface per unit time in a " stuff fluid " of density moving with local velocity F. Its exterior derivative is then given by

The unit of capacitance is the farad, named after Michael Faraday, and given the symbol F: one farad is the capacitance that develops a potential difference of one volt when it stores a charge of one coulomb.

( c ) describing the relationship between numbers such as between temperatures on the Fahrenheit scale ( F ) and the Centigrade scale ( C ), given by F = ( 9C ÷ 5 ) + 32.

In the Sanskrit oral tradition, there was much emphasis on how long ( L ) syllables mix with the short ( S ), and counting the different patterns of L and S within a given fixed length results in the Fibonacci numbers ; the number of patterns that are m short syllables long is the Fibonacci number F < sub > m + 1 </ sub >.

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

If E / F is a Galois extension, then Gal ( E / F ) can be given a topology, called the Krull topology, that makes it into a profinite group.

The term integral may also refer to the notion of the antiderivative, a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written:

Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if f is a continuous real-valued function defined on a closed interval, then, once an antiderivative F of f is known, the definite integral of f over that interval is given by

The Kolmogorov – Smirnov statistic for a given cumulative distribution function F ( x ) is

While the Kolmogorov – Smirnov test is usually used to test whether a given F ( x ) is the underlying probability distribution of F < sub > n </ sub >( x ), the procedure may be inverted to give confidence limits on F ( x ) itself.

For a probability density function f ( x ) with the cumulative distribution function F ( x ), the Lorenz curve L ( F ( x )) is given by:

For a cumulative distribution function F ( x ) with inverse x ( F ), the Lorenz curve L ( F ) is given by:

According to the principle of relativity, there is no privileged frame of reference, so the inverse transformations frame F ′ to frame F must be given by simply negating v.

A map of Cyprus in the later Bronze Age ( such as is given by J. L. Myres and M. O. Richter in Catalogue of the Cyprus Museum ) shows more than 25 settlements in and about the Mesaorea district alone, of which one, that at Enkomi, near the site of Salamis, has yielded the richest Aegean treasure in precious metal found outside Mycenae.

It had been pointed out previously by J. J. Thomson in his series of lectures at Yale University in May 1903 that the dynamic equilibrium between the velocity generated by a concentration gradient given by Fick's law and the velocity due to the variation of the partial pressure caused when ions are set in motion " gives us a method of determining Avogadro's Constant which is independent of any hypothesis as to the shape or size of molecules, or of the way in which they act upon each other ".

J. P. Harris states that most Luftwaffe leaders from Goering through the general staff believed as did their counterparts in Britain and the United States that strategic bombing was the chief mission of the air force and that given such a role, the Luftwaffe would win the next war and that:

In March 1961 Singer and another University of Maryland physicist, E. J. Opik, were given a $ 97, 000 grant by NASA to conduct a three-year study of interplanetary gas and dust.

The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a, and the eccentricity, e. The forms given are, apart from notational variants, those in the standard reference for map projections, namely " Map projections — a working manual " by J. P. Snyder.

Even after June 1940, official connections between Opel and America were not broken and monetary gain continued throughout the war which was controlled by the J. P Morgan firm, the Rüsselsheim plant was never given a major role in Germany's war preparations.

The following are given by the Chevalier J Y W Lloyd:

Premiums of £ 500 each were given to David Hamilton, J. C. Buckler and William Railton.

The literary historian E. J. W. Gibb observed that " at no time, even in Turkey, was greater encouragement given to poetry than during the reign of this Sultan ".

Robert J. Graham, a Renaissance literary scholar, notes that “ questions of whose language is privileged at any given historical moment are deeply implicated in matters of personal, social and cultural significance ”, which he states is the primary reason for Castiglione ’ s usage of the native vernacular.

A classic version of this criticism was given by H. J. McCloskey:

* During the Spanish – American War US Army General John J. Pershing's original nickname, Nigger Jack, given to him as an instructor at West Point because of his service with " Buffalo Soldier " units, was euphemized to Black Jack by reporters.

In April, 1881 President Garfield was given information from Attorney General Wayne MacVeagh and Postmaster Thomas L. James of postal corruption by an alleged " star route " ringleader, Second Assistant Postmaster-General, Thomas J. Brady.

* On Oct. 2, 2010, Perot was given the William J. Donovan Award from the OSS Society at the Mandarin Oriental Hotel in Washington, D. C.

More recent authors who have used damnatio memoriae as a plot device include Milan Kundera in his 1979 novel The Book of Laughter and Forgetting, R. A. Salvatore in the 1990 novel Homeland, Lois Lowry in her 1993 novel The Giver ( a version in which the damned name is never given to any new baby ever again ), and Brian Herbert and Kevin J. Anderson in their 1999 Prelude to Dune trilogy.

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity.

Walker is a member of the International Boxing Hall of Fame and was given the Edward J. Neil Trophy in 1945 for his service to the sport.

An exact use of this term was given in a lecture " Atomic Energy as an Atomic Problem " by J. Robert Oppenheimer.

Wuthering Heights has also given rise to many adaptations and inspired works, including films, radio, television dramatisations, a musical by Bernard J. Taylor, a ballet, three operas ( by Bernard Herrmann, Carlisle Floyd, and Frédéric Chaslin ), a role-playing game, and the 1978 chart-topping song by Kate Bush.

In J. R. R. Tolkien's legendarium, Arda is the name given to the Earth in a period of prehistory, wherein the places mentioned in The Lord of the Rings and related material once existed.

The order was ostensibly given because of borderline weather conditions in Washington, but according to First Lieutenant Ivan J. Potts who was on board, the order came because LeMay had one fewer general's stars and should not be seen to outperform his superior.

Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is known to the same precision as the gas constant: R = 8. 314 4621 ( 75 ) J mol < sup >− 1 </ sup > K < sup >− 1 </ sup >, that is a relative standard uncertainty of 9. 1 × 10 < sup >− 7 </ sup >, according to the 2010 CODATA recommended value.