After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

Given that drug poisoning causes a large portion of patients in a coma, hospitals first test all comatose patients by observing pupil size and eye movement, through the vestibular-ocular reflex.

Given their great antiquity, where and when they first existed is not known and perhaps unknowable.

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

Given Chrétien's known tendency to create new stories and characters, being the first to mention the hero Lancelot and his love affair with Queen Guinevere for example, the name might also be entirely invented.

Given is each element's name, atomic number, year of first report, name of the discoverer, and some notes related to the discovery.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given Pauling's recent success in discovering the Alpha helix, they feared that Pauling might also be the first to determine the structure of DNA.

Given the first four rolls turn up heads, the probability that the next toss is a head is in fact,

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 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 that premise, the notion of absolute knowledge ( as described by Plato and the rationalists ) is seen as mere illusion, and this is what he set out to demonstrate in the first part of his magnum opus " The Critique of Pure Reason " ( 1781 ).

The functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place.

Given Cerion's extensive geographic diversity, Gould later lamented that if Christopher Columbus had only cataloged a single Cerion it would have ended the scholarly debate about which island Columbus had first set foot on in America.

Given that the pattern for the first stanza is 123456, this produces 615243 in the second stanza.

Given an object X, a functor G ( taking for simplicity the first functor to be the identity ) and an isomorphism proof of unnaturality is most easily shown by giving an automorphism that does not commute with this isomorphism ( so ).

Given their long range, high survivability and ability to carry many medium-and long-range nuclear missiles, submarines were credible and effective means for full-scale retaliation even after a massive first strike.

Given an embedding of a rooted tree in the plane, if one fixes a direction of children ( starting from root, then first child, second child, etc.

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given its location, Perth was perfectly placed to become a key transport centre with the coming of the railways, and its first station was built in 1848.

Given his role in the usurpation of Benedict IX, and his attitude towards Henry III, it is unsurprising that Boniface at first refused, advising Poppo when he entered Tuscany, " I cannot go to Rome with you.

Given the tense nature of racial tension in America during the time of the film's production, Poitier felt he was " under close observation by both " Tracy and Hepburn during their first dinner meetings prior to production.

Given Henry's marital history – banishing his first wife and beheading the second – Mary refused the offer.

Given a set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.

Given a vector v in R < sup > n </ sup > one defines the directional derivative of a smooth map ƒ: R < sup > n </ sup >→ R at a point x by

* Given a recursively enumerable set A of positive integers that has insoluble membership problem, ⟨ a, b, c, d | a < sup > n </ sup > ba < sup > n </ sup > = c < sup > n </ sup > dc < sup > n </ sup >: n ∈ A ⟩ is a finitely generated group with a recursively enumerable presentation whose word problem is insoluble

Given a normalized light vector l ( pointing from the light source toward the surface ) and a normalized plane normal vector n, one can work out the normalized reflected and refracted rays:

Given a grammar in GNF and a derivable string in the grammar with length n, any top-down parser will halt at depth n.

Given objects A < sub > 1 </ sub >,..., A < sub > n </ sub > in C, their biproduct is an object A < sub > 1 </ sub > ⊕ ··· ⊕ A < sub > n </ sub > together with morphisms

* Aggregate signature-a signature scheme that supports aggregation: Given n signatures on n messages from n users, it is possible to aggregate all these signatures into a single signature whose size is constant in the number of users.

Given this, it is quite natural and convenient to designate a general sequence a < sub > n </ sub > by by the formal expression, even though the latter is not an expression formed by the operations of addition and multiplication defined above ( from which only finite sums can be constructed ).

Given a subset S in R < sup > n </ sup >, a vector field is represented by a vector-valued function V: S → R < sup > n </ sup > in standard Cartesian coordinates ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >).

Given some training data, a set of n points of the form

Given a codeword, there are roughly 2 < sup > n H ( p )</ sup > typical output sequences.

Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A

Given first 12 digits 979-0-9016791-7, the ISMN algorithm evaluates

Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1 / Ω.

Given two groups A and H there exist two variations of the wreath product: the unrestricted wreath product A Wr H ( also written A ≀ H ) and the restricted wreath product A wr H. Given a set Ω with an H-action there exists a generalisation of the wreath product which is denoted by A Wr < sub > Ω </ sub > H or A wr < sub > Ω </ sub > H respectively.

Given a hermitian structure on a vector space, J and Ω are related via

Given a function f belonging to L ^< sup > 1 </ sup >( Ω ), the total variation of f in Ω is defined as

Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic ; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω < sup > 1 </ sup > of Kähler differentials.