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.

Given its proximity to some Portuguese colonies in Brazil, the " Melo Village " ( in Spanish, " Villa de Melo "), as it was once named, it was invaded by Portuguese forces in 1801, 1811, and 1816.

Given that the Mother of God outranks St. Peter of Alcantara in the hierarchy of the saints, with the proclamation of the Virgin of Aparecida as Queen and Patroness of Brazil, the blessed Virgin Mary became the Nation's principal heavenly patron, and the Franciscan saint became the secondary patron.

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.

Given that drug poisoning causes a large portion of patients in a coma, hospitals first test all comatose patients by observing pupil size and eye movement, through the vestibular-ocular reflex.

Given the rugged terrain of Ngazidja and Nzwani, and the dedication of extensive tracts to agriculture on all three islands, population pressures on Comoros are becoming increasingly critical.

Given the central role under the Constitution of the Soviet Union, the party controlled all tiers of government and social institutions in the Soviet Union.

Given any vector space V over a field F, the dual space V * is defined as the set of all linear maps ( linear functionals ).

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

* Given any set X, there is an equivalence relation over the set of all possible functions X → X.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given Mountbatten's determination, Nehru and Patel's inability to deal with the Muslim League and lastly Jinnah's obstinacy, all Indian party leaders ( except Gandhi ) acquiesced to Jinnah's plan to divide India, which in turn eased Mountbatten's task.

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G ( x, y ) ( i. e. the sets of morphisms from x to y ).

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 set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.

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 that non-violence has priority, all other principles yield to it whenever there is a conflict.

Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.

Given that spinning a Dyson Sphere would result in the atmosphere pooling around the equator, the Ringworld removes all the extraneous parts of the structure, leaving a spinning band landscaped on the sun-facing side, with the atmosphere and inhabitants kept in place through centrifugal force and 1000 mile high perimeter walls ( rim walls ).

Given the increasing number of scientists who study the nervous system, several prominent neuroscience organizations have been formed to provide a forum to all neuroscientists and educators.

Given a point x in a topological space, let N < sub > x </ sub > denote the set of all neighbourhoods containing x.

Given a base for the topology, in order to prove convergence of a net it is necessary and sufficient to prove that there exists some point x, such that ( x < sub > α </ sub >) is eventually in all members of the base containing this putative limit.

Given a class function G: V → V, there exists a unique transfinite sequence F: Ord → V ( where Ord is the class of all ordinals ) such that

Given the apparent magnitude (> 20 ) of all but the biggest trans-Neptunian objects, the physical studies are limited to the following:

Given a guaranteed halting language, the computable function which is produced by Cantor's diagonal argument on all computable functions in that language is not computable in that language.

Given a supervaluationist semantics, one can define the predicate ' supertrue ' as meaning " true on all precisifications ".

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given a set of parameters, the second phase computes private and public keys for a single user:

Given a list of public, civil, and private areas to record for evaluation, Perry enters the simulation to find a revitalized Rockvil in 2041.

Given the large number of casualties, since the ambulances and emergency vehicles were not sufficient for the transport of the injured to the city's hospitals, firefighters employed also buses, in particular the line 37, private cars and taxis.

Given that each sigil-in-a-bubble seen on Solusandra's private world ( see Solus # 1 ) is a link to a different sigil-bearer there are at least forty Sigil-Bearers and likely many more.

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given the role that many social groups have in the development of public policy and the extensive connections between state bureaucracies and other institutions, it has become increasingly difficult to identify the boundaries of the state.

Given this relationship of public capital and productivity, public capital becomes a third input in the standard, neoclassical production function:

Given that the U. S. is still home to the world's largest economy, there's no reason it shouldn't have the most vibrant equity markets — unless regulation is holding back the creation of new public companies.

Given the existence as uttered forth in the public works of Puncher and Wattmann of a personal God quaquaquaqua with white beard quaquaquaqua outside time without extension who from the heights of divine apathia divine athambia divine aphasia loves us dearly with some exceptions for reasons unknown but time will tell and suffers like the divine Miranda with those who for reasons unknown but time will tell are plunged in torment ...

** Masterclasses – Given in public by world renowned filmmakers.

Given the associated safety risks, the TGA concluded " efforts should be made to curb the illegal availability of colloidal silver products, which is a significant public health issue.

Given that there was no tradition of writing poetry in the vernacular, these experiments were more radical than those in fiction writing and also less easily accepted by the reading public.

When the measure was sent in May to the parliament they said " Given the damage it produces on those rules which allow the life in community, ensure the dignity of the person and equality between sexes, this practice, even if it is voluntary, cannot be tolerated in any public place ".

Given full freedom to design it as he sees fit, Roark incorporates into it a statue of Dominique, nude, which creates a public outcry.

Given Klein's aggressive spending cuts, which shaped the political climate of Alberta for much of the 1990s, Getty's legacy with respect to public finances has been criticized.

Given the high premium placed by Novo Ecijanos on education, a legislator from Nueva Ecija took the crucial step to compel the American colonial government to allot funding for public education via a legislative act.

Given this and high public expectations of quality, the budget in developing the car reportedly exceeded A $ 1 billion.

Given that most university study is subsidized ( either because it takes place at a state or public university, or because the student receives government loans or grants ), this type of underemployment may also be an ineffective use of public resources.

* 1957 Given the status of a ‘ public legal body ’.

Given the master public key, any party can compute a public key corresponding to the identity ID by combining the master public key with the identity value.

Given the existence of important public policy goals on both sides, a city seeking to maximize walkability should not favor cul-de-sacs over grids, but should also allow some cul-de-sacs as a legitimate residential option ’ ... ‘ In addition, there are “ middle ground ” alternatives between prohibiting cul-de-sacs and mandating them.

Given these improvements dating back to 1728, a case could be made that Boston Common is in fact the world's first public urban park, since these developments precede the establishment of the earliest public urban parks in England — Derby Arboretum ( 1840 ), Peel Park, Salford ( 1846 ), and Birkenhead Park ( 1847 )— which are often considered the first.