: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

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 a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

Given the age of the Rig Veda being at least 1500 BC or before, this must rank as the earliest practice of beating of the war drum in the history of mankind.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

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.

* Frederick Douglass lecture on Haiti – Given at the World's Fair in Chicago, January 1893.

Given away at theatrical showings was a comic herald that told a simplified version of the film.

Given a complex-valued function ƒ of a single complex variable, the derivative of ƒ at a point z < sub > 0 </ sub > in its domain is defined by the limit

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

Along with a hand-picked escort led by Given Campbell, Davis and his wife were captured on May 10, 1865, at Irwinville in Irwin County, Georgia.

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.

Given that bodhisattvas are known to incarnate at will as living people according to the sutras, the princess Miaoshan is generally viewed as an incarnation of Avalokitesvara.

Given the choice between nylon and gut, many luthiers prefer to use gut, as it conforms more readily to the sharp angle at the edge of the fingerboard.

Given the need for such fine regulation of Ca < sup > 2 +</ sup > signaling, it is perhaps unsurprising that dysregulated mitochondrial Ca < sup > 2 +</ sup > has been implicated in several neurodegenerative diseases, while the catalogue of tumor suppressors includes a few that are enriched at the MAM.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given the task of overhauling the Cardinals by owner Gussie Busch, Herzog was looking to trade Templeton when he was approached by Padres General Manager Jack McKeon at the 1981 baseball winter meetings.

Given prevailing views on homosexuality at the time, circulation of the diaries helped undermine support for clemency for Casement.

Given their wide historical distribution, red wolves probably utilized a large suite of habitat types at one time.

Given that the ESCP is a regulation and not a directive, it is arguable whether it has left too many aspects to the discretion of member states, which could call into question the legal certainty expected from a European regulation.

Given that the characterisation system and the choice of law rules were operating in an inflexible way, the solution has been to allow the growth of judicial discretion within both parts of the system.

Given that the leadership of the EU is subject to a particularly low voter turnout, it may be termed an oligarchy of the European Council members.

Given the wide breadth of its mission there was plenty of room for the CCLRC staff to promote different activities of the Council.

The day after the resignation of Cllr Colin Barrow's resignation as Leader of Westminster City Council in January 2012 on the BBC's inaugural Sunday Politics, Field said about the West End parking charges plan: " Given the furore, given the strength of the campaign by the Evening Standard, I would be very surprised if his successor runs along with this.

Given the military-industrial requirements of the Cold War, the authors of the then secret National Security Council Report 68 ( NSC-68 ) proposed the US government undertake a massive permanent national economic expansion that would let it “ siphon off ” a part of the economic activity produced to support an ongoing military buildup to contain the Soviet Union.

Given his Macedonian heritage, Kotcheff serves on the Board of Directors of the Macedonian Arts Council.

Given this, the Council of War decided to march on Gloucester-not to besiege it or capture it by force, but to capture it by having the governor betray the city beforehand.

Given a different uncertainty about the role of the Privy Council at that time, indeed whether it had a role in such appeal cases, this case may be interpreted as significant in the history of that Court as an institution too.

" Given that there was no mechanism in the Victorian Constitution to override the Council, this was taken by conservatives to be a threat of revolutionary violence.

Given the well-publicized hoopla, some sources still consider this as a nomination for Davis ; however, the Academy does not officially record this as a nomination.

Given Dirichlet's young age ( he was 23 years old at the time ), Humboldt was only able to get him a trial position at the Prussian Military Academy in Berlin while remaining nominally employed by the University of Breslau.

Given that Ruggles had no experience with the genre – his best-known films at that point were the Academy Award-winning Western epic Cimarron ( 1931 ) and the Mae West comedy I'm No Angel ( 1933 ), both more than a decade old – and his Hollywood career was on a downslide, he was an odd choice indeed.

Logan wrote Any Given Sunday and the television movie RKO 281, before gaining an Academy Award nomination for co-writing the Best Picture-winner, Gladiator in 2000.

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

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 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 an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given an equilateral triangle, the counterclockwise rotation by 120 ° around the center of the triangle " acts " on the set of vertices of the triangle by mapping every vertex to another one.

Given these, a new term Anthropocene, is specifically proposed and used informally for the latest part of this epoch since approximately synchronous lithospheric evidence, or more recently atmospheric evidence, of human impacts have been found on the Earth and its ecosystems ; these impacts may be considered of global significance for future evolution of living species.

Given that this etymology does not appear in the usual scholarly works on etymology, this claim is usually dismissed as a false etymology.

Given the dual status of science as objective knowledge and as a human construct, good historiography of science draws on the historical methods of both intellectual history and social history.

Given a binary operation ★ on a set S, an element x is said to be idempotent ( with respect to ★) if

Given its heavy dependence on imported energy, Japan has aimed to diversify its sources.

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 that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function

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 ).