" Given its general release in January 1931, City Lights proved to be a popular and financial success — eventually grossing over $ 5 million.

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

Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement.

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 general triangle ABC, the following conditions would need to be fulfilled for the case to be ambiguous:

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given the parallels between visual and musical arts, it is possible that general acceptance of the value of digital art will progress in much the same way as the increased acceptance of electronically produced music over the last three decades.

Given the extensive linguistic, religious and ethnic diversity of the Indian population, nationalism in India in general does not fall within the purview of a solitary variant of nationalism.

Given this outlook, whatever the level of affection Whistler may have felt for his own mother, one finds an even more divergent use of the image in the Victorian era and later, especially in the United States, as an icon for motherhood, affection for parents, and " family values " in general.

De Tactionibus embraced the following general problem: Given three things ( points, straight lines, or circles ) in position, describe a circle passing through the given points and touching the given straight lines or circles.

Given the similarities with readings from people living on loess soils, the general direction of the local movement according to Price et al., is from the northeast to the southwest.

Given Ríos Montt's staunch anticommunism and ties to the United States, the Reagan administration continued to support the general and his regime, paying a visit to Guatemala City in December 1982.

Given the affine group of an affine space A, the stabilizer of a point p is isomorphic to the general linear group of the same dimension ( so the stabilizer of a point in Aff ( 2, R ) is isomorphic to GL ( 2, R )); formally, it is the general linear group of the vector space: recall that if one fixes a point, an affine space becomes a vector space.

Given any subgroup < math > G < GL ( V )</ math > of the general linear group,

Given their general lack of interest in the area, the British decided to abandon the Sudan in December 1883, holding only several northern towns and Red Sea ports, such as Khartoum, Kassala, Sannar, and Sawakin.

Given the widely different national provisions, this " general regime " gives much more power to the European Commission ( compared to the special regimes ) to ensure a harmonized protection across the European Union.

A more general class are flat G-bundles with for a manifold F. Given a representation, the flat-bundle with monodromy is given by, where acts on the universal cover by deck transformations and on F by means of the representation.

Given four points in general linear position ( no three collinear ; in particular, no two coincident ), there are exactly three pairs of lines ( degenerate conics ) passing through them, which will in general be intersecting, unless the points form a trapezoid ( one pair is parallel ) or a parallelogram ( two pairs are parallel ).

The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).

Given where and, determine the value of and using the chain rule.

The Fascist government had direct rule only over the Benadir territory Given the defeat of the Dervish movement in the early 1920s and the rise of fascism in Europe, on 10 July 1925, Mussolini gave the green light to De Vecchi to start the takeover of the north-eastern sultanates.

Given events, and, Bayes ' rule states that the conditional odds of given are equal to the marginal odds of multiplied by the Bayes factor:

Given a precondition, a conclusion, and a rule that the precondition implies the conclusion, they can be explained in the following way:

Given that buying an inventory of G bugles prior to the any-key rule would always be very expensive, the adoption of any-key brass greatly aided the almost explosive increase in the number of all-age corps hitting the field.

Given that the directors can not ensure corporate success, the business judgment rule specifies that the court will not review the business decisions of directors who performed their duties ( 1 ) in good faith ; ( 2 ) with the care that an ordinarily prudent person in a like position would exercise under similar circumstances ; and ( 3 ) in a manner the directors reasonably believe to be in the best interests of the corporation.

Given Planck's quantization rule for the harmonic oscillator, either condition determines the correct classical quantity to quantize in a general system up to an additive constant.

" Given the Rules ' permissive backdrop and their inclusion of a specific rule on expert testimony that does not mention ' general acceptance ,' the assertion that the Rules somehow assimilated Frye is unconvincing.

Given the rule for optimal k, this may also be expressed as

" Given that implies, and given an, use a unifier of and to make and of the same form, then use a standard rule of detachment.

Given that both he and Narciso López were neighbors in Valencia, Venezuela and both were originally members of the Spanish Armies who turned against Spanish rule, it is possible that he conspired with Narciso López in Lopez's failed attempt to throw the Spanish out of Cuba.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

Given the British origins of the majority of uitlanders and the ongoing influx of new uitlanders into Johannesburg, the Boers recognised that granting full voting rights to the uitlanders would eventually result in the loss of ethnic Boer control in the South African Republic.

Given this sense of caution among key members of the British cabinet and of the army, it is even harder to understand why the British government went against the advice of its generals ( such as Wolsely ) to send substantial reinforcements to South Africa before war broke out.

Given as a series of linked short stories, the book is also interspersed with brief commentaries on contemporary British politics.

Given the shared nature of the Canadian monarch, most members of the Canadian Royal Family are also members of the British Royal Family, and thus the House of Windsor.

Given what is known of Cathróe's own background, this probably means that she was of British (" Cumbrian ") or Scottish descent.

Given the lack of concrete historical knowledge about one of the most potent figures in British mythology, it is unlikely that any definitive conclusions about the claims for these places will ever be established ; nevertheless it is both interesting and important to try to evaluate the body of evidence which does exist and examine it critically.

* Santa Cruz ( Indefatigable ) Island ( Galápagos ) – Given the name of the Holy Cross in Spanish, its English name derives from the British vessel HMS Indefatigable.

Given intelligence that the rebels had been stockpiling weapons at Concord, Massachusetts, he ordered a troop of British regulars to march there on the night of 18 April to confiscate them.

Given that it is impossible for civilians to visit the British Indian Ocean Territory, it is not clear whether the flag is actually used.

Given that the archaeological record demonstrates Irish settlement on the Llŷn Peninsula however and possible raids as far west as Wroxeter by the late 4th century, it is difficult to conceive of either Roman or allied British forces having presented an effective defence in Wales.

Given the strategic requirements of winning the war, British Prime Minister Winston Churchill and U. S. President Franklin D. Roosevelt had no option but to accept the demands of their erstwhile ally, Soviet Premier Joseph Stalin, at Tehran, Yalta and Potsdam, argues retired diplomat Charles G. Stefan.

Given its unique cultural and economic development, and linguistic differences ( Greater Sylhet region was a part of Assam and Surma Valley State for much of the British Raj in comparison to the rest of Bangladesh ), and given that Sylhet has, for most of its recent history, been a region of a larger entity.

Given the nickname " Raging Bull ", he played in three Rugby World Cups, including as England captain in the 2007 tournament, and toured Australia and South Africa with the British and Irish Lions.

Given the British Railways power classification 9F, the locomotives were numbered in the 92xxx series, between 92000 and 92250.

Given that other Latin American countries and also Portugal were becoming easy prey to European ( mainly British ) greed, maintaining the monarchy with a monarch of European origin acted as a deterrent and allowed Brazil to ensure the predominance of its international interests.

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 these problems, Percy resigned his command of the British Italian Legion in October 1855 in a state of total exasperation.

Given U. S. usage of the word ' joint ' meaning such activities, the British usage faded relatively quickly.

Given the tide of militant nationalism that swept through India and the resentment and revolts it inspired, it is arguable that its overarching aim: to germinate public resentment and revolts within the Indian forces of the British Indian Army to overthrow the Raj was ultimately successful.

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 ).

Given the structure of the Canadian infantry platoon, the MCpl is roughly equivalent to the British rank of corporal, second in command of an infantry section.