Subsequent formalizations were framed as attempts to define " effective calculability " or " effective method "; those formalizations included the Gödel – Herbrand – Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's " Formulation 1 " of 1936, and Alan Turing's Turing machines of 1936 – 7 and 1939.

Sometimes the monks were directly subject to the lay abbot ; sometimes he appointed a substitute to perform the spiritual functions, known usually as dean ( decanus ), but also as abbot ( abbas legitimas, monasticus, regularis ).

In conventual cathedrals, where the bishop occupied the place of the abbot, the functions usually devolving on the superior of the monastery were performed by a prior.

The arithmetic logic functions were fully electronic, implemented with vacuum tubes.

The control logic functions, which only needed to operate once per drum rotation and therefore did not require electronic speed, were electromechanical, implemented with relays.

Tyrannosaurid teeth were used as holdfasts for pulling meat off a body, rather than knife-like cutting functions.

By the mid-4th century however the assembly's judicial functions were largely curtailed, though it always kept a role in the initiation of various kinds of political trial.

As the system evolved these last two functions were shifted to the law courts.

There were however officials such as the nine archons, who while seemingly a board carried out very different functions from each other.

These were two functions that called machine-language functions stored in memory.

# The bishops were also successors of the apostles in that " the functions they performed of preaching, governing and ordaining were the same as the Apostles had performed ".

In Ancient Greek, there was no ablative case ; its functions were taken by the genitive, so that the genitive had functions belonging to the Proto-Indo-European genitive and ablative cases.

Originally intended as assistants to the tribunes, they exercised certain police functions, were empowered to inflict fines and managed the plebeian and Roman games.

Under Augustus the office lost much of its importance, its judicial functions and the care of the games being transferred to the praetor, while its city responsibilities were limited by the appointment of a praefectus urbi.

The card would indicate which game functions, such as changing the view or vehicle speed, were assigned to each key.

In 1964, the functions of the Admiralty were transferred to a new Admiralty Board, which is a committee of the tri-service Defence Council of the United Kingdom and part of the Ministry of Defence.

In the late 1990s, functions that had been administered separately by the two major leagues ' administrations were united under the rubric of Major League Baseball.

The East India Company and its Governor-General were replaced by a viceroy and the Indian Council, while at Westminster the Board of Control was abolished and its functions assumed by the newly created India Office, under the Secretary of State for India.

Since they were essentially itinerant, they confided to the care of some of the better educated and highly respected converts the fixed necessary functions relating to the daily life of the community.

The GSI team further studied the reaction in 1989 and discovered the new isotope < sup > 261 </ sup > Bh during the measurement of the 1n and 2n excitation functions but were unable to detect an SF branching for < sup > 261 </ sup > Bh.

Such buildings were used to host civic town functions – including dancing, music listening, and gambling.

During the republic, six or eight were generally elected each year to serve judicial functions throughout Rome and other governmental responsibilities.

If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.

* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

There are then three functions: the officeholders organized and saw to the complex protocols ; Ho boulomenos was the initiator and the proposer of content ; and finally the people, massed in assembly or court or convened as lawmakers, made the decisions, either yes or no, or choosing between alternatives.

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

If x is held fixed, then the Bessel functions are entire functions of α.

The Bessel function of the second kind then can be thought to naturally appear as the imaginary part of the Hankel functions.

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.

The cerebral cortex is a group of tight, dense, " gray matter " composed of the nucleus of the neurons whose axons then form the " white matter ", and is responsible for perception, relay of the sensory input ( sensation ) via the thalamic pathway, and most importantly directly or indirectly in charge of all the neurological functions, from simple reflexes to complex thinking.

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

While Eddy's Manual established limited executive functions under the rule of law in place of a traditional hierarchy, the controversial 1991 publication of a book by Bliss Knapp led the then Board of Directors to make the unusual affidavit during a suit over Knapp's estate that neither acts by it violating the Manual, nor acts refraining from required action, constituted violations of the Manual.

Curried functions may be used in any language that supports closures ; however, uncurried functions are generally preferred for efficiency reasons, since the overhead of partial application and closure creation can then be avoided for most function calls.

One of the functions ( in this case g ) is first reflected about and then offset by t, making it.

then used these equations to construct his theory of functions.

If ( 1a ) and ( 1b ) hold for a differentiable pair of functions u and v, then so do

Launched in early 1972 it was unlike the other basic four-function pocket calculators then available in that it was the first pocket calculator with scientific functions that could replace a slide rule.

If X is a set and M is a complete metric space, then the set B ( X, M ) of all bounded functions ƒ from X to M is a complete metric space.

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

However, if the approximation is defined asymptotically, for example by saying that two functions f and g are approximately equal near some point if the limit of f-g is 0 at that point, then this defines an equivalence relation.

The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.

Its functions were then transferred to the recently established FAO.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has