Given that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

Given limited defense budgets, air forces tended to be conservative in their aircraft purchases, and biplanes remained popular with pilots because of their agility, and remained in service long after they had ceased to be competitive.

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 there's a gulf of 100, 000, 000 light years, he checks his diary to find out what he had been doing that day, and finds out that it was something he wished to hide.

Given civilian status, he recovered his teaching position at Lycée Pasteur near Paris, settled at the Hotel Misgiven a new position at Lycée Condorcet, replacing a Jewish teacher who had been forbidden to teach by Vichy law.

It is described as " the ancient grayhound .. that had been with Lugh of the Mantles, / Given him by the sons of Tuireann Bicreann ;.."

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

Given that by this time it was common for castles to be built in stone, and that many barons had expanded or refortified their castles, this was not an easy task.

Given the use of similar symbols on the Roman standard, this depiction also conveyed another victory, namely that of the Christian faith: the Roman soldiers who had once arrested Jesus and marched him to Calvary now walked under the banner of a resurrected Christ.

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 that starters knew only the target recipient's name and address, they had a seemingly impossible task.

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 a color name to match the name of amber mutants, ochre mutant viruses had a similar property in that they recovered infectious ability within certain suppressor strains of bacteria.

Given his age, the king probably had very powerful advisers, presumably including General Horemheb, the Vizier Ay, and Maya, the " Overseer of the Treasury ".

Given this they would have qualified as Corbett summits had they been under 3, 000 feet.

Given that many businessmen and bankers were terrified of Bryan's populist rhetoric and support for ending the gold standard, Hanna had few problems in raising record amounts of money.

Given to Graham with the working title " Ballet for Martha ," it was named by her for the scenario she had in mind, though Copland often said he was thinking of neither Appalachia nor Spring while he wrote it.

Given the type of warfare that had been carried out in the conflict — wherein highly mobile groups of soldiers and rebels continued to move to and from on the desert terrain, retreating at a time and then suddenly attacking to regain control of small towns and villages in the Eastern rebel held parts of Libya — had led to the technical becoming a vehicle of choice for both sides.

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 the circumstances, the Ghent Altarpiece is a difficult work to use for comparison when assessing other attributions, especially as several other artists from the brothers ' workshops probably worked on it as well.

Given Deja had worked with three villains before, he was first offered Hades, but asked to animate the protagonist instead-" I knew if would be more difficult and more challenging, but I just needed that experience to have that in your repertoire.

# Given an artifact whose performance has been evaluated, it is important to determine why and how the artifact worked or did not work within its environment.

Given all the signs that a very large eruption was imminent, PHIVOLCS – assisted by the U. S. Geological Survey – worked to convince local inhabitants of the severity of the threat.

Given the frenetic pace at which he worked, Offenbach sometimes used the same material in more than one opera.

Given in recognition of individuals who worked on organising the 11th Olympic Games in Berlin and the 4th Olympic Winter Games held in Garmisch-Partenkirchen, 1936.

Given the overriding importance of economic factors in foreign relations, the ministry worked closely with the Ministry of Finance on matters of customs, tariffs, international finance, and foreign aid ; with the Ministry of International Trade and Industry ( MITI ) on exports and imports ; and with the Ministry of Agriculture, Forestry, and Fisheries on questions of foreign agricultural imports and fishing rights.

Given their historical ties, the Rwandan and Ugandan governments were closely allied and thus Museveni worked closely with Kagame throughout the First Congo War.

Given that recorded vocalizations are an effective means to attract owls, and given the similarity of a distant accordion's tune to the call of the Laughing Owl as reported, it is apparent that the method might have worked.

Given the rules from NEC, it was a pretty sensitive subject, so direct references had to be changed ", explained Vic Ireland, who worked closely with the game's localization.

Given the software limitations at the time, to make the sound work correctly required a full live orchestra, the first that Soule had ever worked with ; the orchestral tracks in Evermore had been performed by Soule and his brother by themselves, two instruments at a time.

Previously he had worked alongside Brayshaw on The Sunday Footy Show and in 2005 on Any Given Sunday, as well as being a presenter of the Melbourne Commonwealth Games 2006 coverage on Nine.

Given the importance of these exchanges for ensuring the perpetuation of the republic of letters as a community, Lespinasse, Roland, Mosconi, and Renier Michiel worked to reinforce cohesion through friendship and loyalty.

Given the cost, only a few were produced and many of the engineers who worked on the project in Japan were moved to PlayStation development.

Given our formula φ, we group strings of quantifiers of one kind together in blocks:

Put together: Given an input signal, current state, and stack symbol, the automaton can follow a transition to another state, and optionally manipulate ( push or pop ) the stack.

Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.

A Clifford algebra Cℓ ( V, Q ) is a unital associative algebra over K together with a linear map satisfying for all defined by the following universal property: Given any associative algebra A over K and any linear map such that

* Given a category C with finite coproducts, a cogroup object is an object G of C together with a " comultiplication " m: G → G G, a " coidentity " e: G → 0, and a " coinversion " inv: G → G, which satisfy the dual versions of the axioms for group objects.

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

Given a set of points in the Euclidean plane, selecting any one of them to be called 0 and another to be called 1, together with an arbitrary choice of orientation allows us to consider the points as a set of complex numbers.

: Given two sets, A and T, of equal size, together with a weight function C: A × T → R. Find a bijection f: A → T such that the cost function:

Given the closeness in age of the two royal brothers, they were educated together.

Given this supposition, Evola proceeded to argue that Fascism or National Socialism — with their heroism, their sacrificial and ascetic ethic, their authoritarian and hierarchical order, together with their appeal to myth and ritual — provided an environment compatible with the ' spirit ' of the celestials.

Given a bounded lattice with largest and smallest elements 1 and 0, and a binary operation, these together form a Heyting algebra if and only if the following hold:

Given the arrival of DVDs etc., it is unlikely that any movie ever made will sell as many tickets as DVS Karna sold over 150 million tickets ( currently higher than the next highest ticket selling 19 movies put together!

: Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners.

Given the fortuitous timing ( Kaplan's parting with his Las Vegas team ), he agreed to go in the hopes of putting together a new local team that he could train and manage.

Given four operators ( F, G, U, and V ) together with a product operation (∙) defined for any pair of these four operators, and given that the following four pairs of operators commute:

Given the circumstances under which he operated, he put together an imposing war machine and masterminded a sophisticated strategy that suggest he had a keen grasp of the economic, political, and geographic contexts in which he operated.

Given a sequence of matrices, we want to find the most efficient way to multiply these matrices together.

Given a basis for the complex space, this set, together with these vectors multiplied by i, namely form a basis for the real space.

: Given two sets, P (" facilities ") and L (" locations "), of equal size, together with a weight function w: P × P → R and a distance function d: L × L → R. Find the bijection f: P → L (" assignment ") such that the cost function:

Given a map, the mapping cylinder is a space, together with a cofibration and a surjective homotopy equivalence ( indeed, Y is a deformation retract of ), such that the composition equals f.

Given a real vector space together with a convex, real-valued function

Given a label set with an involution, and a fixed set of words in the elements of the label set, a planar algebra consists of a collection of modules, one for each element in, together with an action of the operad of tangles labelled by.

Given that authors of documents try to formulate sentences which contain a single idea, or cluster of related ideas within neighboring sentences or organized into paragraphs, there is an inherent, relatively high, probability within the document structure that words used together are related.

Given a certain board position, it breaks up the board into independent components, finds out what state each component is in, and combines the bitstrings representing those elements together using bitwise XOR.