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

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 the tendency of the legends of different seafarers – Greek, Norse, Irish, Arab and Iberian – to cross-fertilize and influence each other, the exact source of some legendary Atlantic islands – such as the mythical islands of Brasil and the Isle of Mam – are impossible to disentangle.

Given his resemblance to Uncle Sam, Coltrin named his new cereal after the mythical patriotic character.

Given Poseidon's connection with horses as well as the sea, and the landlocked situation of the likely Indo-European homeland, Nobuo Komita has proposed that Poseidon was originally an aristocratic Indo-European horse-god who was then assimilated to Near Eastern aquatic deities when the basis of the Greek livelihood shifted from the land to the sea, or a god of fresh waters who was assigned a secondary role as god of the sea, where he overwhelmed the original Aegean sea deities such as Proteus and Nereus.

Given its lack of a D ' Oyly Carte or Savoy connection, Thespis has a tenuous claim to be a " Savoy Opera.

Given the reputation of oat grain to have invigorating properties and the obvious connection between plant seeds and human " seed ", it is not surprising that the meaning of the phrase shifted towards more or less explicitly referring to the destructive sexual liaisons of an unmarried young male, possibly resulting in unwanted children born out of wedlock.

Given this connection, she suggests the major war should have been called " The Great Cheyenne War ".

Given that the police had no evidence against " Thomas ", either at Leatherslade Farm or connection with either of the two gangs, Butler was prepared to let him go.

Given the conventions of the day, within which journalism was seen as a disreputable profession for a gentleman, Burke was publicly reticent about his connection with The Annual Register.

Given that John the Baptist was executed before the defeat of Herod by Aretas IV of Nabatea in the AD 36, and based on the scholarly estimates for the approximate date of the marriage of Herod Antipas and Herodias AD 28-35, Josephus establishes a key connection between the time frame of the ministry of Jesus and his execution.

Given vector fields and lying in the tangent bundle, the affine connection describes how to differentiate the vector field along the direction.

Let E be a rank k vector bundle over a smooth manifold M and let ∇ be a connection on E. Given a piecewise smooth loop γ: → M based at x in M, the connection defines a parallel transport map P < sub > γ </ sub >: E < sub > x </ sub > → E < sub > x </ sub >.

Given the hydrological connection of the Humboldt River and Sink to the Carson Sink during flood years ( as recently as 1998 ), it is not surprising that beavers were historically extant on eastern Sierra watercourses.

Given an exterior connection D satisfying this compatibility property, there exists a unique extension of D:

Given this historical connection, the Free Democratic Party ( FDP, Freie Demokratische Partei ) was founded on 11 December 1948 in Heppenheim.

Given the village connection with St. Edith it is perhaps surprising that the parish church, Saxon in origin, is however dedicated to St Mary the Virgin.

Given the connection to the Hessische Ludwigsbahn ( railway ) with the Darmstadt-Mainz stretch in 1858 and the Frankfurt am Main-Mannheim stretch in 1879 ( the Riedbahn ), a multifaceted industrial life sprang up.

Given a fertile mind and boundless energy, he pursued other fields of interest: growing vegetables in Puerto Rico ; owning a beautician school, restaurants, lounges, a marina, marine dredging, data processing services, multi-level marketing of vitamins and cosmetics, cement block manufacturing, country-western music publishing and recording studios, telecommunications companies, a high-end boutique shop, general insurance agency, internet connection and data center, a walk-in medical clinic, wholesale gasoline and diesel fuel distribution operation, a travel agency, home security monitoring, mail order medical and diabetic supply company, a Big & Tall men's clothing store, an AM radio station, a mobile medical screening company, a book publishing company, a warehouse fulfillment and distribution company, an advertising media consulting firm, television stations, mobile home parks, a 225 room hotel in Nassau, Bahamas, a 500, 000 square foot commercial warehouse complex in Las Vegas, and a five-star 23 story resort hotel and residences on Ft. Lauderdale Beach.

Given the alpha wave's connection with relaxed mental states, many people have latched onto the idea of utilizing this state through a technique called biofeedback training.

Given its bidirectional connection between the Broca's and Wernicke's speech areas it could have a role in language.

Given his call for a " Black Pythagoras ," however, a connection seems likely.