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 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 then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

Given this information, a timeline of roughly the years 15 – 98 CE can be established for his adult life.

Given a codeword, there are roughly 2 < sup > n H ( p )</ sup > typical output sequences.

The East border is now 24th Avenue E. jogging over at 96th to Swan creek, and south to 104th Street E. The South border is now 104th Street E. jogging over at 14th Avenue E to roughly 109th Street E. and west to Golden Given Road E. The West border is now Golden Given Road E. Golden Given Road E is also the east border of the Jessie Dunlap Donation Land Claim with the north and south borders roughly the same as the combined Meeker claims.

Given a set M of molecules, chemical reactions can be roughly defined as pairs r =( A, B ) of subsets from M.

Given a more realistic yield of 36 tonnes / hectare ( 3834 US gal / acre ) the area required is about 152, 000 square kilometers, or roughly equal to that of the state of Georgia or of England and Wales.

Given a condition number, the relative error of compensated summation is effectively independent of n. In principle, there is the O ( nε < sup > 2 </ sup >) that grows linearly with n, but in practice this term is effectively zero: since the final result is rounded to a precision ε, the nε < sup > 2 </ sup > term rounds to zero unless n is roughly 1 / ε or larger.

Given that both companies have a work force of approximately 100, 000 employees, and a U. S. employment base of roughly 20, 000 H-1B holders, this indicates that roughly 1 / 5 of the Indian workforce of Infosys & Wipro applied for a visa in 2006.

Given its small staff of only 24 men, the Einsatzgrupppe Ägypten would have needed as much help as possible from the local Arabs and from the Afrika Korps to kill the roughly 50, 000 Jews of Egypt, to say nothing of the half million or so Jews of the Yishuv.

The Alaska Time Zone applies to the territory of the state of Alaska east of 169 ° 30 ′ W. Given that the UTC − 9 time corresponds to the solar time at 9 × 15 ° = 135 ° W ( roughly, Juneau ), the westernmost locales of the Alaska Time Zone are off by up to 169 ° 30 ′ − 135 ° = 34 ° 30 ′ from local solar time.

Given a mean AGB lifetime of one Myr and an outer velocity of, its maximum radius can be estimated to be roughly ( 30 light years ).

Given the structure of the Canadian infantry platoon, the MCpl is roughly equivalent to the British rank of corporal, second in command of an infantry section.

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.

Given an n × n matrix A and an eigenvalue λ < sub > i </ sub > of this matrix, there are two numbers measuring, roughly speaking, the number of eigenvectors belonging to λ < sub > i </ sub >.

Given r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.

Given a relation, scaling the argument by a constant factor causes only a proportionate scaling of the function itself.

Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant.

* Aggregate signature-a signature scheme that supports aggregation: Given n signatures on n messages from n users, it is possible to aggregate all these signatures into a single signature whose size is constant in the number of users.

Given a constant density and volume the self-potential of such body depends only on the eccentricity ε of the ellipsoid:

Given two variables x and y, y is directly proportional to x ( x and y vary directly, or x and y are in direct variation ) if there is a non-zero constant k such that

Given the early and constant association of Nekhbet with being a good mother, in later myths she was said to have adopted children.

Given constant migrations, changing allegiances, and new cultural appropriations, all that remained constant was their Gothic name.

Given a linear homogeneous recurrence relation with constant coefficients of order d, let p ( t ) be the characteristic polynomial ( also " auxiliary polynomial ")

Given that all the off diagonal elements have a nonzero frequency ; H being constant implies that H is diagonal.

* Given a group G, one can form the constant group scheme G < sub > S </ sub >.

Given a QTFR defined on, define a constant and a set.

Given its close proximity to Asia and constant flow of Asian immigrants, Asian food has the largest foothold in Los Angeles after Mexican cuisine.

Given full employment, ( a constant Y ) and payments structure ( constant V ), then in terms of the equation of exchange, MV = PY, a rise in M leads only to a rise in P. Thus, the story of the Quantity Theory of Money, the long-run relationship between money and inflation, is kept in Wicksell.

Given Planck's quantization rule for the harmonic oscillator, either condition determines the correct classical quantity to quantize in a general system up to an additive constant.

The invariance theorem follows: Given any description language, our optimal description language is at least as efficient as, with some constant overhead.

Given the constant volume of muscular hydrostats, these contractions cause an elongation of the longitudinal muscles.

Case: Given positive ( or more generally irreducible non-negative matrix ) A, the Perron-Frobenius eigenvector is the only ( up to multiplication by constant ) non-negative eigenvector for A.

Given a constant a function is called-convex if,

Given the continuing and constant US presence in Antarctica since that date, " Operation Deep Freeze " has come to be used as a general term for US operations in that continent, and in particular for the regular missions to resupply US Antarctic bases, coordinated by the United States military.

Given any x and any y, if all the molecules in y are perfectly elastic and spherical, possess equal masses and volumes, have negligible size, and exert no forces on one another except during collisions, then if x is a gas and y is a given mass of x which is trapped in a vessel of variable size and the temperature of y is kept constant, then any decrease of the volume of y increases the pressure of y proportionally, and vice versa.

Given the constant bizarre dangers and her own madness, her crew is soon decimated and Bêlit herself is hanged by the winged monster.