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 absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given the distance from the main body, our problem is to determine the form of the surface that satisfies the equipotential condition.

Given its great distance, the daytime " guest star " observed by the Chinese could only have been a supernova — a massive, exploding star, having exhausted its supply of energy from nuclear fusion and collapsed in on itself.

Given that their favorite prey are often mammals or birds that hesitate to fly, unsurprisingly most of their prey is killed on the ground and some prey may even pursued on foot for a short distance by the eagle.

Given the distance that these troops had to march in order to make contact with the enemy, it was clear to the two Corps commanders that they would be unable to attack at 4: 00 as ordered.

Given the above, for every point in this ball there is a rotation, with axis through the point and the origin, and rotation angle equal to the distance of the point from the origin.

* Given n points in the plane, find the two with the smallest distance from each other.

* Closest pair of points: Given a set of points, find the two with the smallest distance from each other.

Given Milan's notoriously damp and foggy climate, the Milanese consider it a fair-weather day when the Madonnina is visible from a distance, as it is so often covered by mist.

: Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance.

Given the short distance ( 90 miles ) between Axis airfields on Sicily and the planned drop zones over Malta, it was possible for the motorized transports to make four round-trips per day.

Given the differences in facilities and intangibles such as the distance of the new school from Austin and other law students, the Supreme Court ruled it did not satisfy " separate but equal " provisions, and that African Americans must also be admitted to the University of Texas Law School at Austin.

Given the difficulty of scoring directly from the point due to the distance to the goal, goals scored from the point are typically either on screens, or are tipped goals.

Given a square texture mapped on to a square surface in the world, at some viewing distance the size of one screen pixel is exactly the same as one texel.

Given a connected graph G =( V, E ) with V the set of vertices and E the set of edges, and with a root vertex r, the level structure is a partition of the vertices into subsets L < sub > i </ sub > called levels, consisting of the vertices at distance i from r. Equivalently, this set may be defined by setting L < sub > 0 </ sub > =

Given little chance of winning, Tarver took a weight-drained Jones the distance and lost the fight and WBC title by a majority decision on November 8, 2003, in Las Vegas ( Tarver had relinquished the IBF title a few days earlier in anticipation of being unable to make a mandatory defense.

Given a point off of a line, if we drop a perpendicular to the line from the point, then a is the distance along this perpendicular segment, and φ is the least angle such that the line drawn through the point at that angle does not intersect the given line.

Given the orbital eccentricity of this object, different epochs can generate quite different heliocentric unperturbed two-body best-fit solutions to the aphelion distance ( maximum distance ) of this object.

Given the long distance nature of the fighting the estimate of Indian casualties can only be a guess.

: 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 the distance to the epicenter of the Loma Prieta ( roughly 70 miles or 113 kilometers south of San Francisco ), there was great surprise at the localized destruction around the Bay Area.