Given the absolute magnitude, you can also compute apparent magnitude from its parallax:

Given its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.

Given its roughly constant size, the encyclopaedia has needed to reduce or eliminate some topics to accommodate others, resulting in controversial decisions.

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 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 a point ( in terms of its coordinates ) and the direction ( azimuth ) and distance from that point to a second point, determine ( the coordinates of ) that second point.

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 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 a binary operation, an idempotent element ( or simply an idempotent ) for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result.

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

Given that different groups in society have different beliefs, priorities, and interests, to which group would the media tailor its bias?

Given its limitations, however, NAALC has not produced ( and in fact was not intended to achieve ) convergence in employment, productivity and salary trend in North America.

Given that its brightest stars are of fifth magnitude, the constellation is invisible to the naked eye in areas with polluted skies.

In May 2006, the International Methodist-Catholic Dialogue Commission completed its most recent report, entitled " The Grace Given You in Christ: Catholics and Methodists Reflect Further on the Church ," and submitted the text to Methodist and Catholic authorities.

Given the ideals of Juche, North Korea chose to default on its loans and by the late 1980s its industrial output was declining.

Given its small domestic market but favourable location and a superb transport and communications base, Namibia is a leading advocate of regional economic integration.

Given its long stability and isolation, New Caledonia serves as a unique island refugium — a sort of biological ' ark ' — hosting a unique ecosystem and preserving Gondwanan plant and animal lineages no longer found elsewhere.

Given its continental origin as a fragment of Zealandia, unlike many of the islands of the Pacific such as the Hawaiian chain, New Caledonia is not of geographically recent volcanic provenance.

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 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 general rule in British law that a wife automatically takes her husband's rank upon marriage, Mrs Simpson consequently should have been addressed, upon marriage to the duke, as Her Royal Highness.

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 ).

The band's final release was a single for the movie Any Given Sunday ( 1999 ).

Given international pre-release sales had already made a profit, the studio allocated a reduced promotion and advertising budget to avoid the risk of the film becoming a loss-maker ; as a consequence, theatrical release was limited.

** Navajo leap or " navajoing ": Given two loops on one finger, move the lower loop over the upper loop and release it from the finger.

Given certain signals to cells ( such as feedback from neighbors, stress or DNA damage ), mitochondria release caspase activators that trigger the cell-death-inducing biochemical cascade.

* Given the name by the Seleucids after he fought in the region alongside Antiochus VII Sidetes against Phraates II of Parthia in 130 – 129 BCE, a campaign which resulted in the release of Antiochus ' brother Demetrius II Nicator from captivity in Hyrcania

Leveraging the release of Any Given Sunday, Plank purchased an ad in ESPN The Magazine.

Cafferty courted controversy on September 23, 2004 while discussing terrorist demands for the release of two female scientists from an Iraqi prison and remarking: " Given the way these mutants treat women in their societies, the women are probably better off in U. S. custody.

In January 2010, William and Julie Clark asked a judge to order the University of Washington to release records from the 2007 effects of television viewing study, citing, “ Given that other research studies have not shown the same outcomes, we would like the raw data and analytical methods from the Washington studies so we can audit their methodology, and perhaps duplicate the studies, to see if the outcomes are the same.

Coinciding with this concert was the release of an album that returned to Karat's more distinctive style of progressive rock, Die geschenkte Stunde ( The Given Hour ).

Given that the EP format was no longer a viable marketing medium, and the poor performance of Easy Come, Easy Go, it was the final release of new material by Presley in the EP format.

Given Kaoma's clear act of plagiarism and release of their single without Los Kjarkas ' permission, Los Kjarkas successfully sued.

Given Larry ’ s well-established reputation and strengths as a DJ, the release of the album was followed by a deluge of bookings for an album world tour that continued for the rest 2005 ; two U. S. tours, two Australian tours, and countless European dates ensured that the Calyx sound spread far and wide.

Given the size of the Quebec market ( the film saw limited release in English Canada ), a $ 6 million box office is the approximate equivalent of over $ 250 million for a domestic U. S. release.