Given the repressive nature of the regime of Napoleon III, Bartholdi took no immediate action on the idea except to discuss it with Laboulaye.

Given " mappings " of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of " rules ", each of the form:

Given the need for immediate action was no longer pressing, François once again demanded he be allowed to wait for his artillery supplies.

" Given that declaration, along with seven years of bombings and the wording of their communiques throughout that time that strove to present an image of a powerful organization spread secretly throughout all sectors of society, the authorities took significant action.

Given his standing, he was one of the few officers who might have persuaded Hitler to follow more rational courses of action.

: Given that the particle begins at position x < sub > 1 </ sub > at time t < sub > 1 </ sub > and ends at position x < sub > 2 </ sub > at time t < sub > 2 </ sub >, the physical trajectory that connects these two endpoints is an extremum of the action integral.

* Given the action of a Lie algebra g on a manifold M, the set of g-invariant vector fields on M is a Lie algebroid over the space of orbits of the action.

Given the option, most swimmers choose to use a dolphin kicking action, but there still is a small minority of swimmers who prefer the breaststroke kick, for recreational swimming and even for competition.

For a finite group G, the left regular representation λ ( over a field K ) is a linear representation on the K-vector space V whose basis is the elements of G. Given g ∈ G, λ ( g ) is the linear map determined by its action on the basis by left translation by g, i. e.

Given a fundamental domain for the group action ( for the full, orientation-reversing symmetry group, a ( 2, 3, 7 ) triangle ), the reflection domains ( images of this domain under the group ) give a tiling of the quartic such that the automorphism group of the tiling equals the automorphism group of the surface – reflections in the lines of the tiling correspond to the reflections in the group ( reflections in the lines of a given fundamental triangle give a set of 3 generating reflections ).

Given this closure property for CSAs, they form a monoid under tensor product, compatible with Brauer equivalence, and the Brauer classes are all invertible: the inverse class to that of an algebra A is the one containing the opposite algebra A < sup > op </ sup > ( the opposite ring with the same action by K since the image of K → A is in the center of A ).

Given a set of action names, the set of CCS processes is defined by the following BNF grammar:

Given an action that must be repeated, for instance, five times, different languages ' for loops will be written differently.

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.

Given an action of a group G on a topological space X by homeomorphisms, a fundamental domain ( also called fundamental region ) for this action is a set D of representatives for the orbits.

Given the proposed manner of action of the muscle pump to increase arterial blood flow, it would seem impossible for a muscle contraction and skeletal muscle hyperemia to be uncoupled.

Given a faithful irreducible representation ρ of G, the lattice Yang-Mills action is the sum over all lattice sites of the ( real component of the ) trace over the n links e < sub > 1 </ sub >, ..., e < sub > n </ sub > in the Wilson loop,

Given the popularity of the first-person shooter genre, it was assumed that all tactical-level military gameplay necessarily involved individual combat action.

However, in his Travels With Charley, Steinbeck mentions wearing a naval officer's cap, ' Given me by a British torpedo boat captain, a very gentle gentleman and a murderer ,' which phrase suggests that Steinbeck may well have observed action at first hand.

Given the exacerbated ethnic tensions and the lack of government control in the East, Rwanda was to take action against the security threat posed by the génocidaires that had found refuge in eastern Zaire.

" Given the unprecedented decline in new construction, however, more action is necessary.

Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given that one cannot be motivated by reason alone, requiring the input of the passions, Hume argued that reason cannot be behind morality.

Given the limited success of the Charity School, however, Wheelock intended his new College as one primarily for whites.

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

Given good circumstances one might be able to discern the result of some human activity such as the changing of the Netherlands ' coast or the partial drying out of the Aral Sea, but even that would not be easy.

Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.

Given our formula φ, we group strings of quantifiers of one kind together in blocks:

Given an equilateral triangle, the counterclockwise rotation by 120 ° around the center of the triangle " acts " on the set of vertices of the triangle by mapping every vertex to another one.

Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

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

Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given the above fact, one can ask:

Given a preorder on S one may define an equivalence relation ~ on S such that a ~ b if and only if a b and b a.

# Given any two distinct points, there is exactly one line incident with both of them.

# Given any two distinct lines, there is exactly one point incident with both of them.

# Given an array of values to be sorted, set up an auxiliary array of initially empty " pigeonholes ," one pigeonhole for each key through the range of the original array.

Given the unusual casting and production demands, Pacific Overtures remains one of the least-performed musicals by Stephen Sondheim.

Given the above expression, evidently the result of her ( local ) measurement is that the three-particle state would collapse to one of the following four states ( with equal probability of obtaining each ):