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 royal tomb contained a large amount of Greek Geometric pottery and this has been explained as the dowry of a Greek princess who married into the royal family of Salamis.

One year later, Philip of Alsace had his protégé married to his niece, Isabelle of Hainaut, offering the County of Artois and other Flemish territories as dowry, much to the dismay of Baldwin V. In 1180, war broke out between Philip II and his mentor, resulting in the devastation of Picardy and Île-de-France ; King Philip refused to give open battle and gained the upper hand, and Baldwin V, at first allied with his brother-in-law ( Philip of Alsace ), intervened on behalf of his son-in-law in 1184, in support of his daughter's interests.

One set of 27 diamond stars was kept in the Imperial family ; they are seen in a photograph that shows the dowry of Rudolf's daughter, the Archduchess Elisabeth, known as " Erzsi ", on the occasion of her wedding to Otto Prince Windisch-Graetz in 1902.

One way in which he laid the groundwork for this was by marrying Piccarda Bueri, whose family was old and respectable and who brought a dowry.

One legend tells how John Hull, the Master of the Mint in Boston and a wealthy man, determined the dowry for his daughter Hannah's marriage to Samuel Sewall.

One common penalty for the kidnapping and rape of an unmarried woman was that the abductor or rapist had to provide the woman's dowry.

One year later, Philip of Alsace had his protégé married to his niece, Isabelle of Hainaut, offering the County of Artois and other Flemish territories as dowry, much to the dismay of Baldwin V. When Louis VII died, Philip II began to assert his independence.

One can see it as humiliating that an extra hormone casually fed into our chemistry may induce us to lay down our lives for a lover or a friend ; ;

One might, indeed, argue that the history of ideas, in so far as it includes the literatures, must center on characterizations of human nature and that the great periods of literary achievement may be distinguished from one another by reference to the images of human nature that they succeed in fashioning.

One may be exasperatingly aware that if the answer is favorable it will be judged such only by those of one's own age.

One may be sure the present Republican congressional leadership hasn't meant to repeat this error.

One may conclude that most of the detected micrometeoritic material is concentrated in orbital streams which intersect the Earth's orbit.

Justices Frankfurter and Jackson dissented: `` One State may cherish formalities more than another, one State may be more responsive than another to procedural reforms.

One upward-mobile teacher may be a hard taskmaster for lower-class pupils because she wants them to develop the attitudes and skills that will enable them to climb, while another upward-mobile teacher may be a very permissive person with lower-class pupils because he knows their disadvantages and deprivations at home, and he hopes to encourage them by friendly treatment.

One sitter may think `` a leather couch '' identifies a reading as surely directed to him ; ;

One might say, " Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a well-ordering.

One may generalize this to " closed-form numbers ", which may be defined in various ways.

One may also acquire Tasbih and recite the names of Allah in such manner as " SubahannAllah " or Glory be to Allah in Arabic over and over again to acquire good deeds.

One may try to quantize an electron field without mixing the annihilation and creation operators by writing

Such an anagram may be a synonym or antonym of its subject, a parody, a criticism, or praise ; e. g. George Bush = He bugs Gore ; Madonna Louise Ciccone = Occasional nude income or One cool dance musician ; William Shakespeare = I am a weakish speller, Roger Meddows Taylor = Great words or melody.

One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which vary regionally.

One may also encounter chitronchelo or ( in Italian ) citroncello, based on lemon.

* One of the more serious of these side effects is tardive dyskinesia, in which the sufferer may show repetitive, involuntary, purposeless movements ( that are permanent and have no cure ) often of the lips, face, legs, or torso.

One study has suggested that cannabidiol may be as effective as atypical antipsychotics in treating schizophrenia.

One paper has found that alcohol use at an early age may influence the expression of genes which increase the risk of alcohol dependence.

One popular technique is to mock external interfaces or data to mimic other stories which might not be played out during an iteration ( as those stories may have been relatively lower business priority ).

One master may communicate with up to 7 slaves in a piconet ; all devices share the master's clock.

One can also consider partial binary functions, which may be defined only for certain values of the inputs.

One property many proteins have is that they specifically bind to a certain molecule or class of molecules — they may be extremely selective in what they bind.