Given the conceptual context within which ancient thought thrived, how could anyone have questioned this principle??

Given the bias of the Victorian age, female students were denied direct study in anatomy and could not attend drawing classes with live models ( who were often prostitutes ) until a decade later.

Given their strategic location in the North Atlantic, the Faroes could have proved useful to Germany in the Battle of the Atlantic, possibly as a submarine base.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that white is the most effective color in terms of facilitating the reflection of ground light, the hypothesis that straight hair could have been adaptively favorable, cannot be fully discounted in this regard.

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.

" Given the elimination of these pernicious influences, Marx allowed that " normal conditions of spontaneous development " of the rural commune could exist.

" Given a memex, a scholar could create her own knowledge tools as connections within reams of information, share these tools, and use complexes of tools to create yet more sophisticated knowledge that could in turn be deployed toward this work.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox.

Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

Given that coconuts are ideally suited for ocean dispersal, it seems possible that individuals from one population could have floated to the other.

Given that Krasnow had effectively poached the band from Buddah there were limitations on what material could be released.

Given the supposed closeness of war, the FI thought that the Communist Parties and social democratic parties would be the only significant force that could defend the workers of the world against the imperialist camp in those countries where there were mass forces.

Given the wide variety of clientele at the club, which includes Willie the Giant and Elliott the Dragon, the amount of seating at the club could vary wildly at times.

Given its great distance, the daytime " guest star " observed by the Chinese could only have been a supernova — a massive, exploding star, having exhausted its supply of energy from nuclear fusion and collapsed in on itself.

Given that " production could be carried on without any organization is, firm at all ", Coase asks, why and under what conditions should we expect firms to emerge?

Given a chance, it is believed that Miss Earhart could have landed her aircraft in this lagoon and swum or waded ashore.

Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.

Given a treaty representing the last position taken by the French, if he could not reach an agreement within eight days, he was to return to London.

Given the discriminator PARTY TYPE ( which could be individual, partnership, C Corporation, Sub Chapter S Association, Association, Governmental Unit, Quasi-governmental agency ) the two subtype entities are PERSON, which contains individual-specific information such as first and last name and date of birth, and ORGANIZATION, which would contain such attributes as the legal name, and organizational hierarchies such as cost centers.

Given that ethnicity was important for the upper classes, they could adopt multiple ethnicities to secure the allegiance of their partners and followers: a phenomenon referred to as " situational ethnicity ".

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 an isolated physical system, the allowed states of this system ( i. e. the states the system could occupy without violating the laws of physics ) are part of a Hilbert space H. Some properties of such a space are

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

Given inefficiencies in the heat transfer, the actual NERVA designs were planned to produce about 5 GW, which would make them the largest nuclear reactors in the world.

Given enough time, a hypothetical monkey typing at random would, as part of its output, almost surely produce all of William Shakespeare | Shakespeare's plays.

Given any energy eigenstate, we can act on it with the lowering operator, a, to produce another eigenstate with-less energy.

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

* Point location: Given a partitioning of the space into cells, produce a data structure that efficiently tells in which cell a query point is located.

* Ray tracing: Given a set of objects in space, produce a data structure that efficiently tells which object a query ray intersects first.

Given a strictly increasing integer sequence / function ( n ≥ 1 ) we can produce a faster growing sequence ( where the superscript n denotes the n < sup > th </ sup > functional power ).

Given a source of white light, they produce a white shine.

Given small differences in policies, the same type of software can produce radically different social outcomes.

Given almost any substance, it is possible to produce monoclonal antibodies that specifically bind to that substance ; they can then serve to detect or purify that substance.

Given the historical associations of the project's name ( see Masada ), the Hebrew titles of the compositions, and the Jewish imagery on the covers of the associated albums, Zorn was clearly exploring his Jewish roots, stating, " The idea with Masada is to produce a sort of radical Jewish music, a new Jewish music which is not the traditional one in a different arrangement, but music for the Jews of today.

Given the complicated legal process and the sheer number of exiting cul-de-sac streets, however, such efforts would be slow to produce results and may only have a marginal impact in changing the landscape of existing districts.

Given good conditions, a bud can produce a shoot with up to ten or more leaves.

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given these approaches, the bowler can hope to both intimidate the batsman somewhat, and possibly have the ball deflect off the bat at an awkward angle and produce a catch for a nearby fielder.

Given a particular input, it will always produce the same output, and the underlying machine will always pass through the same sequence of states.

Given Brittany's rich musical heritage, contemporary performers produce a range of music sung in Gallo ( see Music of Brittany ).

Given WSRP4J's incubator status, the project did not produce formal releases.

Given the high quality of his produce and packaged goods made by its suppliers, the Fauchon Company quickly became very famous internationally.

Given that all Sarracenia hybrids are fertile and will hybridize further, this characteristic allows cultivators to produce a limitless number of variants through hybridization.

* Given the extended recording times of data loggers, they typically feature a mechanism to record the date and time in a timestamp to ensure that each recorded data value is associated with a date and time of acquisition in order to produce a sequence of events.

The optimization attempts to answer the question: " Given our operating constraints, what is the best mix of products and / or services for us to produce and sell in the period, and at what prices, to generate the highest expected revenue?

Given that the Mughals had historically symbolized Indo-Persian culture to one degree or another, the overthrow of Bahadhur Shah Zafar and the institution of the British Raj in 1858 may be considered as marking the end of the Indo-Persian era, even if, after 1857, Persian would still retain an audience and even produce commendable literature such as the philosophical poetry of Muhammad Iqbal ( d. 1938 ).