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.

Ab initio methods need to define a level of theory ( the method ) and a basis set.

An alternative method is to define the region based on ethnicity, and in particular, areas populated by Eastern Turkic, Eastern Iranian, or Mongolian peoples.

define method factorial ( n :: < integer >)

The precise level of glucose considered low enough to define hypoglycemia is dependent on ( 1 ) the measurement method, ( 2 ) the age of the person, ( 3 ) presence or absence of effects, and ( 4 ) the purpose of the definition.

If the situation requires it, it is also possible to define a method to execute before ( or after ) each ( or all ) of the test methods with the ( or ) and ( or ) annotations.

But Jean Piaget, who would better define himself as constructivist, considers structuralism as " a method and not a doctrine " because for him " there exists no structure without a construction, abstract or genetic "

Therefore, remote method call architectures such as CORBA define their serialization formats in detail.

To modify the default deserialization ( for example, to automatically initialize a member marked ), the class must implement the interface and define the method.

While real-world sound changes often admit exceptions ( for a variety of known reasons, and sometimes without one ), the expectation of their regularity or " exceptionlessness " is of great heuristic value, since it allows historical linguists to define the notion of regular correspondence ( see: comparative method ).

There are several ways to define the result of a rule, but one of the most common and simplest is the " max-min " inference method, in which the output membership function is given the truth value generated by the premise.

These standards define common features such as physical videocassettes, recording modulation method, magnetization, and basic system data in part 1.

Another method is to define neighbourhoods differently for these cells.

Since nematodes have such a seemingly erratic distribution in cassava agricultural fields, it is not easy to clearly define the level of direct damage attributed to nematodes and thereafter quantify the success of a chosen management method.

No definitive answers were ever forthcoming by this method ; rather, it served to define the problems better.

His View of Positivism would therefore set out to define, in more detail, the empirical goals of sociological method.

The plan can be used to measure the impact that new growth will have on the community and define the method by which that impact is mitigated.

Following Frege and Russell, Hilbert sought to define mathematics logically using the method of formal systems, i. e., finitistic proofs from an agreed-upon set of axioms.

Here we define a method for the generic function collide which is specialized for the classes asteroid ( first parameter object-1 ) and spaceship ( second parameter object-2 ).

Programmers may define a special method in an object to provide custom copying implementation.

At first glance it might appear reasonable to define brakes as " a method to quickly stop a vehicle ", however this permits all vehicles to be described as having brakes.

It is common to define a buoyancy mass m < sub > b </ sub > that represents the effective mass of the object as can be measured by a gravitational method.

During the late 19th century, English psychometrician Sir Francis Galton attempted to define physiognomic characteristics of health, disease, beauty, and criminality, via a method of composite photography.

The first step was to define the problem: a method of identifiably duplicating colonies.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

T is valid in any reflexive frame: if, then since w R w. On the other hand, a frame which validates T has to be reflexive: fix w ∈ W, and define satisfaction of a propositional variable p as follows: if and only if w R u.

Let x = x ( u, v, w ), y = y ( u, v, w ), z = z ( u, v, w ) be defined and smooth in a domain containing, and let these equations define the mapping of into.

The Minkowski inner product is a map ( i. e. given any two vectors v, w in M we define η ( v, w ) as a real number ) which satisfies properties ( 1 ), ( 2 ), and ( 3 ) listed here, as well as property ( 4 ) given below:

Thus we define the representations of G on an Hilbert space H to be those group homomorphisms, ρ, which arise from continuous actions of G on H. We say that a representation ρ is unitary if ρ ( g ) is a unitary operator for all g ∈ G ; i. e., for all v, w ∈ H. ( I. e.

Starting with w < sub > 1 </ sub > = 0, define w < sub > 2 </ sub >, w < sub > 3 </ sub >, ..., w < sub > 12 </ sub > by the rule that w < sub > n </ sub > is the smallest integer which differs from all linear combinations of previous elements in at least eight coordinates.

) Suppose additionally that a < sub > n </ sub > is the number of elements of A with weight n. Then we define the formal Dirichlet generating series for A with respect to w as follows:

Moreover, and perhaps a bit more interestingly, if ( A, u ) and ( B, v ) are two weighted sets, and we define a weight function w: A × B → N by

Given input M and w ( a Turing machine and some input string ), define S ( M, w ) with the following behavior: S creates a Turing machine N that accepts only if the input string to N is w and M halts on input w, and does not halt otherwise.

Similarly, one may define the weak space as the space of all functions f such that belong to L < sup > 1, w </ sup >, and the weak norm using

:: "... prose used to define the way the Turing machine uses its head and the way that it stores data on its tape.

In short MOF uses the notion of MOF :: Classes ( not to be confused with UML :: Classes ), as known from object orientation, to define concepts ( model elements ) on a metalayer.

:: The Department of Treasury found that Mr. Banister provided erroneous advice to taxpayers, including improperly advising them that tax returns were not required because IRS Code sections 861 through 856 define " source of income " in a manner that excluded the income of United States citizens residing in the United States from United States tax.

:: Use protocol classes to define public interfaces.

The number of carbon atoms is used to define the size of the alkane ( e. g., C < sub > 2 </ sub >- alkane ).

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

Four points P < sub > 0 </ sub >, P < sub > 1 </ sub >, P < sub > 2 </ sub > and P < sub > 3 </ sub > in the plane or in higher-dimensional space define a cubic Bézier curve.

An alternate form of ( 2 ) – the machine successively prints all n of the digits on its tape, halting after printing the n < sup > th </ sup > – emphasizes Minsky's observation: ( 3 ) That by use of a Turing machine, a finite definition – in the form of the machine's table – is being used to define what is a potentially-infinite string of decimal digits.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

Many other group theorists define the conjugate of a by x as xax < sup >− 1 </ sup >.

If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.

The completion of M can be constructed as a set of equivalence classes of Cauchy sequences in M. For any two Cauchy sequences ( x < sub > n </ sub >)< sub > n </ sub > and ( y < sub > n </ sub >)< sub > n </ sub > in M, we may define their distance as

define class < window > (< view >)

We define the periodic Bernoulli functions P < sub > n </ sub > by