Given the severity of punishment for the offense of zina, the Qur ' an requires solid proof beyond the shadow of doubt before convicting an individual, be it a man or a woman, of zina.

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* 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 the other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.

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 its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

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 this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is

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

Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.

" Given the bill's vague criteria, some critics alleged that this requirement could be used to force faculty to cover implausible theories in their classes.

Given India's historic position that the original intent of the line was to separate the two nations by the highest mountains in the world, in these locations India extended its forward posts northward to the ridges, regarding this move as compliant with the original border proposal, although the Simla Convention did not explicitly state this intention.

" Given the situation in Spain for several years regarding terrorist attacks, these ties can be considered objectively as a threat to democracy ," the court said, also adding that these parties " contradicted the concept of a ' democratic society ' and presented a major danger to Spain's democracy ".

Given what we knew regarding terrorists ’ interest in acquiring and using chemical weapons against Americans, and given the intelligence assessment provided us regarding the al-Shifa facility, I continue to believe that destroying it was the right decision.

Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite category C < sup > op </ sup >.

Given the preceding jurisprudence regarding due process, Chief Justice Taney was not entirely breaking ground in his Dred Scott opinion when, without elaboration, he pronounced the Missouri Compromise unconstitutional because an " act of Congress that deprived a citizen of his liberty or property merely because he came himself or brought his property into a particular territory of the United States, and who had committed no offence against the laws, could hardly be dignified with the name of due process of law.

Given the narrow federalist victory in 1995, a reference was made by the Chrétien government to the Supreme Court of Canada in 1996 regarding the legality of a unilateral secession of Quebec.

Given that field experiments necessarily take place in a specific geographic and political setting, the extent to which findings can be extrapolated to formulate a general theory regarding economic behavior is a concern.

Given their relative isolation, several mistaken rumours regarding the Torres Islands and their people have become widespread by way of travel guides, inter-island gossip and the mass media.

Given the success of the earlier DVDs, it was hoped that the sales would encourage Sony to produce a final direct-to-DVD movie to complete the original Homefront Campaign story arc, but there have been no new announcements regarding the Roughneck series.

Given the passionate nature of most Singaporeans regarding food, and Singaporean cuisine, a constantly updated food guide, Makansutra, has been developed, which focuses on the hawker scene in Singapore, and identifies popular stalls in Singapore.

Given that libraries in Milwaukee, Wisconsin were just connecting to the World Wide Web, Flessas gathered and placed information regarding all the services available to the homeless in Milwaukee on the web so service providers to the homeless and the homeless themselves ( who often sought shelter in local libraries ) had equal and rapid access to information about resources available in Milwaukee via the Milwaukee County library system computer network " OMNINET ".

Given this, Spinoza's views regarding causality and modality begin to make much more sense.

Given that convicts in Australia were already " imprisoned ", punishments for offenses committed in the colonies could not usually result in imprisonment and thus usually consisted of corporal punishment such as hard labour or flagellation.

Given the physical punishment suffered by catchers, the pieces of equipment associated with the position are often referred to as " the tools of ignorance ".

Given Pasolini's well-known reputation as an atheist, a homosexual, and a Marxist, the reverential nature of his film was surprising, especially after the controversy of " La ricotta ".

Given his leader's power of mental persuasion, it is difficult to tell whether or not Off-Ramp actually had a homosexual desire for him, or if he was just being manipulated.

Given that practices similar to courtly love were already prevalent in Al-Andalus and elsewhere in the Islamic world, it is very likely that Islamic practices influenced the Christian Europeans.

Given their perceived piety, The Times noted the irony when a major investigation by their reporters uncovered a link between Islamic Jihadis and child pornography ; a discovery that, according to the London paper, " is expected to improve understanding of the mindsets of both types of criminals and has been hailed as a potentially vital intelligence tool to undermine future terrorist plots .".

Critique by Fritz Lehman: Given that this book is intended as a textbook for Pakistani undergraduates, Shaikh Ahmed Sarhindi predictably appears as the chief preserver of separate Islamic identity in India, yet only a very general and most inadequate description of his ideas and his influence is given.