Given the guaranteed low prices during contract days and the continued high cost of logging in Southeast Alaska today, one analysis concludes that, since 1980, the forest service has lost over a billion dollars in Tongass timber sales.

# Given that the system is in a correct state, it is guaranteed to stay in a correct state, provided that no fault happens ( closure ).

Given a description of the possible initial states of the world, a description of the desired goals, and a description of a set of possible actions, the planning problem is to find a plan that is guaranteed ( from any of the initial states ) to generate a sequence of actions that leads to one of the goal states.

Given the large number of articles transferred between servers and the large size of individual articles, their complete propagation to any one server farm is not guaranteed.

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given the tendency for real negotiations in Japan to be conducted privately ( in the nemawashi, or root binding, process of consensus building ), the shingikai often represented a fairly advanced stage in policy formulation in which relatively minor differences could be thrashed out and the resulting decisions couched in language acceptable to all.

An analytic philosopher, Rorty believed that combining Willard Van Orman Quine's criticism of the analytic-synthetic distinction with Wilfrid Sellars's critique of the " Myth of the Given " allowed for an abandonment of the view of the thought or language as a mirror of a reality or external world.

Category: Given names of Greek language origin

Given a programming or specification language, abstract interpretation consists of giving several semantics linked by relations of abstraction.

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Category: Given names of Greek language origin

Given the more widespread social use, in the English language, of the word condom, it is interesting to note that the town is located on the river Baïse ; baise, without the diaeresis, is a French vulgarism for a sexual act.

Category: Given names of Greek language origin

Given the focus on intramodal competition and the lack of intermodal competition, there was little concern about statutory or regulatory language that set different regulatory burdens for different technology modes.

Given the prevalence of-assa place-names and words scattered around all sides of the Aegean Sea, this possessive suffix was sometimes considered evidence of a shared non-Indo-European language or an Aegean Sprachbund preceding the arrivals of Luwians and Greeks.

Category: Given names of Greek language origin

Given a language L, and a pair of strings x and y, define a distinguishing extension to be a string z such that

Category: Given names of Greek language origin

Solomonoff's universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs ( for a universal computer ) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes ' theorem can be used to predict the yet unseen parts of x in optimal fashion.

Given a natural number x, h outputs the index of the partial computable function that performs the following computation:

Given a precomplete numbering then for any partial computable function with two parameters there exists a total computable function with one parameter such that

* Given a Gödel numbering of the computable functions, the set ( where is the Cantor pairing function and indicates is defined ) is recursively enumerable.

* Given a Gödel numbering of the computable functions, the set is recursively enumerable.

The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs ( for a universal computer ) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes ' theorem can be used to predict the yet unseen parts of x in optimal fashion.

The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).

Given a Gödel numbering of recursive functions, there is a primitive recursive function s of two arguments with the following property: for every Gödel number p of a partial computable function f with two arguments, the expressions and are defined for the same combinations of natural numbers x and y, and their values are equal for any such combination.

Given a Blum complexity measure and a total computable function with two parameters, then there exists a total computable predicate ( a boolean valued computable function ) so that for every program for, there exists a program for so that for almost all

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given x ∈ A, the holomorphic functional calculus allows to define ƒ ( x ) ∈ A for any function ƒ holomorphic in a neighborhood of Furthermore, the spectral mapping theorem holds:

Given a function f of type, currying it makes a function.

Given a function of type, currying produces.

Given the definition of above, we might fix ( or ' bind ') the first argument, producing a function of type.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given a vector space V over the field R of real numbers, a function is called sublinear if

Given a complex-valued function ƒ of a single complex variable, the derivative of ƒ at a point z < sub > 0 </ sub > in its domain is defined by the limit

Given a function f of a real variable x and an interval of the real line, the definite integral

Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function

Given a set of training examples of the form, a learning algorithm seeks a function, where is the input space and

Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.

Given a function ƒ defined over the reals x, and its derivative ƒ < nowiki > '</ nowiki >, we begin with a first guess x < sub > 0 </ sub > for a root of the function f. Provided the function is reasonably well-behaved a better approximation x < sub > 1 </ sub > is

Given a relation, scaling the argument by a constant factor causes only a proportionate scaling of the function itself.

# Composition operator ( also called the substitution operator ): Given an m-ary function and m k-ary functions:

# Primitive recursion operator: Given the k-ary function and k + 2-ary function:

# Minimisation operator: Given a ( k + 1 )- ary total function:

Given a class function G: V → V, there exists a unique transfinite sequence F: Ord → V ( where Ord is the class of all ordinals ) such that