One variation avoids the use of choice functions by, in effect, replacing each choice function with its range.

One common version, the two-argument Ackermann – Péter function, is defined as follows for nonnegative integers m and n:

One interesting aspect of the Ackermann function is that the only arithmetic operations it ever uses are addition and subtraction of 1.

One can also define an A-ary function where A is any set ; there is one input for each element of A.

One of the reasons why this computation is possible is because f ′ is a constant function.

One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

One function of CRM is to collect information about clients.

One technique enforces the principle of least privilege to great extent, where an entity has only the privileges that are needed for its function.

One of the next milestones came in 1904, when Helge von Koch, extending ideas of Poincaré and dissatisfied with Weierstrass's abstract and analytic definition, gave a more geometric definition including hand drawn images of a similar function, which is now called the Koch curve ( see Figure 2 ).

One function is transformed into another, and the operation is reversible.

One way of expressing the Lie bracket is through the formalism of Lie derivatives, which identifies a vector field X with a first order partial differential operator L < sub > X </ sub > acting on smooth functions by letting L < sub > X </ sub >( f ) be the directional derivative of the function f in the direction of X.

One obtains the value f ( r ) by substitution of the value r for the symbol X in P. One reason to distinguish between polynomials and polynomial functions is that over some rings different polynomials may give rise to the same polynomial function ( see Fermat's little theorem for an example where R is the integers modulo p ).

One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset.

One writes for the function precisely when for the relation.

One patient regained some cognitive function lost as a result of PML.

One of these active processes is protein synthesis, a universal function whereby mRNA molecules direct the assembly of proteins on ribosomes.

One of the six functions is always the dominant function in a text and usually related to the type of text.

One of the most important equations in Statistical mechanics ( analogous to in mechanics, or the Schroedinger equation in quantum mechanics ) is the definition of the partition function, which is essentially a weighted sum of all possible states available to a system.

One way to rigorously define the delta function is as a measure, which accepts as an argument a subset A of the real line R, and returns δ ( A )

One may then define the integral against δ as the integral of a function against this mass distribution.

One of the most recently proposed drivers of the evolution of skin pigmentation in humans is based on research that shows a superior barrier function in darkly pigmented skin.

One of the ways mechanical and organic societies differ is the function of law: in mechanical society the law is focused on its punitive aspect, and aims to reinforce the cohesion of the community, often by making the punishment public and extreme ; whereas in the organic society the law focuses on repairing the damage done and is more focused on individuals than the community.

One of the meanings of the terms similarity and similarity transformation ( also called dilation ) of a Euclidean space is a function f from the space into itself that multiplies all distances by the same positive scalar r, so that for any two points x and y we have

One young man, exhilarated to the point of insanity by liquor and the excitement of the moment, performed a perfect swan dive out of the stands at the Yale Bowl during the Yale-Army football game, landed squarely on his head on the concrete ramp below, and died at once.

One final act had to be performed, however: al-Fihri's general, al-Sumayl, had to be dealt with, and he was garroted in Córdoba's jail.

One composer who was influential in spreading the more serious style that Mozart and Haydn had formed is Muzio Clementi, a gifted virtuoso pianist who tied with Mozart in a musical " duel " before the emperor in which they each improvised and performed their compositions.

One song from that record, " Producer's Medley ", featured Wariner's recreation of several very famous songs which Chet Atkins both produced and performed on.

One meaning often given is that of old songs, with no known composers ; another is music that has been transmitted and evolved by a process of oral transmission or performed by custom over a long period of time.

Semi-spoken music has long been especially popular in British entertainment, and such examples as David Croft's theme to the 1970s ' sitcom Are You Being Served ?, the 1979 song Mickey as performed by Toni Basil in 1982, and the 1984 title song, " One Night in Bangkok " for the musical Chess have elements indistinguishable from modern rap.

One of the reasons for ragga's swift propagation is that it is generally easier and less expensive to produce than reggae performed on traditional musical instruments.

One 1999 study by Walter and Waterhouse reviewed the previous data on the level of reincarnation belief and performed a set of thirty in-depth interviews in Britain among people who did not belong to a religion advocating reincarnation.

One form is the appropriation of the ideas and results of others, and publishing as to make it appear the author had performed all the work under which the data was obtained.

One such is " Anti-Trauma Inc ." who are hired to " normalize " children, although what they do is more akin to " deprogramming ", as performed on children retrieved from cults.

One of these works was The Authoritarian Personality ( 1950 ), published as a contribution to the Studies in Prejudice performed by multiple research institutes in the US, and consisted on a ' qualitative interpretations ' that uncovered the authoritarian character of test persons through indirect questions.

MacKenzie wrote the lyrics of the song " The Rhythm Divine " performed by Shirley Bassey on the album One Second, with MacKenzie singing backing vocals.

In 1996 a tribute album titled A Small Circle of Friends appeared that featured tracks by Mike Watt, Free Kitten, The Melvins, Meat Puppets, that dog., L7, The Posies, NOFX, Flea, Gumball, and others along with a version of " Circle One " performed by Pat Smear with Hole under the name " The Holez ".

Whereas the golden rule states that " One should treat others as one would like others to treat oneself ", Kant asks us analyze whether an act can be performed simultaneously by everyone without exception.

In November 1995, Wakeman and Howe returned to the line-up and performed on two new tracks, " Be the One " and " That, That Is ".

One of these is the debut of " Singin ' in the Rain ," performed initially by Cliff Edwards as " Ukelele Ike ,'" and later performed at the end of the film by the entire cast.

In 1990, Hicks released his first album, Dangerous, performed on the HBO special One Night Stand, and performed at Montreal's Just for Laughs festival.

One of the first works Ravel performed for the Apaches was Jeux d ' eau, his first piano masterpiece and clearly a pathfinding impressionistic work.

One of his last compositions, the Brook Green Suite, named after the land on which St Paul ’ s Girls ’ School was built, was performed for the first time a few months before his death.

One such dancer was Paul Taylor, who, in 1959, performed in Balanchine's Episodes.

One of his most enduring pieces followed Benvenuto Cellini — the Grande messe des morts, first performed at Les Invalides in December of that year.

One of the pieces he performed was his Op. 11 toccata, a display piece full of parallel thirds.

One of the longer-lived of these was a band called The Craze, which performed a few times around Northampton in 1978.