Given this uncertainty, between April – May 2006 at the JINR, a FLNR – PSI team conducted experiments probing the synthesis of this isotope as a daughter in the nuclear reaction < sup > 242 </ sup > Pu (< sup > 48 </ sup > Ca, 3n )< sup > 287 </ sup > Fl.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

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 field K, the corresponding general linear groupoid GL < sub >*</ sub >( K ) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition.

Given a topological space X, let G < sub > 0 </ sub > be the set X.

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 ( random ) sample the relation between the observations Y < sub > i </ sub > and the independent variables X < sub > ij </ sub > is formulated as

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 m real values t < sub > i </ sub >, called knots, with

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

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 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 the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.

Given two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the rigorous admission process it is not surprising that CUNY BA boasts a 70 % graduation rate within an average of 2. 2 years and that 60 % graduate with academic honors.

Given the need for such fine regulation of Ca < sup > 2 +</ sup > signaling, it is perhaps unsurprising that dysregulated mitochondrial Ca < sup > 2 +</ sup > has been implicated in several neurodegenerative diseases, while the catalogue of tumor suppressors includes a few that are enriched at the MAM.

:( b ) Given player 1's strategy, the best payoff possible for player 2 is − V.

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 two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >), the change in x from one to the other is ( run ), while the change in y is ( rise ).

Given metric spaces ( X, d < sub > 1 </ sub >) and ( Y, d < sub > 2 </ sub >), a function f: X → Y is called uniformly continuous if for every real number ε > 0 there exists δ > 0 such that for every x, y ∈ X with d < sub > 1 </ sub >( x, y ) < δ, we have that d < sub > 2 </ sub >( f ( x ), f ( y )) < ε.

Given a Hilbert space L < sup > 2 </ sup >( m ), m being a finite measure, the inner product < ·, · > gives rise to a positive functional φ by

The quantum circuits used for this algorithm are custom designed for each choice of N and the random a used in f ( x ) = a < sup > x </ sup > mod N. Given N, find Q = 2 < sup > q </ sup > such that < math > N ^ 2

# Given u and v in W, then they can be expressed as u = ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, 0 ) and v = ( v < sub > 1 </ sub >, v < sub > 2 </ sub >, 0 ).

# Given u in W and a scalar c in R, if u = ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, 0 ) again, then cu = ( cu < sub > 1 </ sub >, cu < sub > 2 </ sub >, c0 ) = ( cu < sub > 1 </ sub >, cu < sub > 2 </ sub >, 0 ).

Given a set A of N people, it has 2 < sup > N </ sup > possible subsets.

Given a 5 % male excess birth rate, there appears to be 3. 15 male SIDS cases per 2 female, for a male fraction of 0. 61.

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

Given some " primitive formulas " such as PM's primitives S < sub > 1 </ sub > V S < sub > 2 </ sub > OR, ~ S ( negation ) one is forced to define the axioms in terms of these primitive notions.

Given an adequate supply of food, larvae should pupate and weave a silken cocoon within 1 – 2 weeks after 3 larval stages.

Given f ∈ G ( x * x < sup >- 1 </ sup >, y * y < sup >-1 </ sup >) and g ∈ G ( y * y < sup >-1 </ sup >, z * z < sup >-1 </ sup >), their composite is defined as g * f ∈ G ( x * x < sup >-1 </ sup >, z * z < sup >-1 </ sup >).

Given the longevity of CFC molecules, recovery times are measured in decades.

Given a set M of molecules, chemical reactions can be roughly defined as pairs r =( A, B ) of subsets from M.

Given any x and any y, if all the molecules in y are perfectly elastic and spherical, possess equal masses and volumes, have negligible size, and exert no forces on one another except during collisions, then if x is a gas and y is a given mass of x which is trapped in a vessel of variable size and the temperature of y is kept constant, then any decrease of the volume of y increases the pressure of y proportionally, and vice versa.

Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

Given the magnitude of the disaster, reconstruction and economic recovery will remain the primary focus of the Salvadoran Government for some time to come.

Given that most French supporters of phrenology were liberal, left-wing or socialist, it was an objective of the social elite of France who held a restrained vision of social change that phrenology remain on the fringes.

Given the appropriate rites, she helped the deceased into afterlife as an underworld shade ( Di Manes ), else their spirit might remain to haunt the living, as a wandering, vengeful ghost.

Given that Rothko had known in advance about the luxury decor of the restaurant and the social class of its future patrons, the exact motives for his abrupt repudiation remain mysterious.

Given the borough's small size, as well as the county's small population, the presence of business and government remain limited.

Given a small angular displacement, the vessel may return to its original position ( stable ), move away from its original position ( unstable ), or remain where it is ( neutral ).

Given Orr / Alex's desire to remain within the world of the Bridge, a world where he is well treated and lives a fairly pampered life, his attempts to stonewall and block the doctor's attempts to cure him are understandable.

Given its heritage, MCC continues to participate in the administration of English cricket, and in 2010 offered Lord's as a neutral venue for Pakistan to stage a " home " Test match, as scheduled by the ICC, versus Australia ; although the outcome of that game proved controversial the club's initial offering was made with the intention that Pakistan, whose terrorist-stricken country had rendered it a no-go area for international cricket, could remain within the international cricketing fold.

Given the subversive nature of Lazarillo and its open criticism of the Catholic Church, it is likely that the author chose to remain anonymous out of fear of religious persecution.

Given the current economic climate, this is likely to remain in this state for at least another decade.

Given the editorial style of the books, it is not surprising that they were ( and to some extent remain ) controversial within the numerical analysis community.

The Government believes that it must remain so .” Given the prospect of " incineration without representation ", Canadians seemed to feel that the doctrine which most encouraged restraint was the strategically soundest one to support.

Given the sport's origins, Irish-bred and trained horses remain a dominant force in national hunt racing today.

Given that the only remaining humans ( after Zion's destruction ) remain in the Matrix, failure to enter the door to the Source will lead to an eventual catastrophic system crash of the Matrix, killing its human inhabitants and effectively annihilating humanity as a race.

Given the context of this conversation ( Blackadder is attempting to get transferred into the Royal Flying Corps ), and Darling's character in general, he has presumably pulled some strings to allow him to remain in the army without having to serve in battle.

Given numerous chances to escape antisemitic persecution ( as late as 1944 ), he chose to remain in Hungary, where his last novel, a Pirandellian fantasy about a king staging a coup against himself, then having to impersonate himself, Oliver VII, was published in 1942.

Given the total mass and the scalars r and v at a single point of the orbit, one can compute the specific orbital energy, allowing an object orbiting a larger object to be classified as having not enough energy to remain in orbit, hence being " suborbital " ( a ballistic missile, for example ), having enough energy to be " orbital ", but without the possibility to complete a full orbit anyway because it eventually collides with the other body, or having enough energy to come from and / or go to infinity ( as a meteor, for example ).

Given names that remain in modern use include:

Given the as-yet-undeciphered nature of the script, the precise significance of the post-firing addition of a Cypro-Minoan sign must remain uncertain.

Given the impossibility of sending a bacteria-free human being into space, forward-contamination will remain an issue for as long as manned missions continue.

Given such contradictions, these characters ' actual names and thus identities remain unclear.