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 an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

Given a hierarchical netlist, the list of instance names in a path from the root definition to a primitive instance specifies the single unique path to that primitive.

Given a class function G: V → V, there exists a unique transfinite sequence F: Ord → V ( where Ord is the class of all ordinals ) such that

Given a functor U and an object X as above, there may or may not exist an initial morphism from X to U. If, however, an initial morphism ( A, φ ) does exist then it is essentially unique.

Given any curve C and a point P on it, there is a unique circle or line which most closely approximates the curve near P, the osculating circle at P. The curvature of C at P is then defined to be the curvature of that circle or line.

Given these unique characteristics, for statistical purposes the county is included as a municipality within the Washington Metropolitan Area by the United States Census Bureau.

* Given any morphism k ′: K ′ → X such that f k ′ is the zero morphism, there is a unique morphism u: K ′ → K such that k u

Given two column vectors, their dot product can also be obtained by multiplying the transpose of one vector with the other vector and extracting the unique coefficient of the resulting 1 × 1 matrix.

Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is automatic.

Given a basis f = ( X < sub > 1 </ sub >,..., X < sub > n </ sub >) of V, there is a unique reciprocal basis f < sup >#</ sup > = ( Y < sup > 1 </ sup >,..., Y < sup > n </ sup >) of V determined by requiring that

# Given two points p < sub > 1 </ sub > and p < sub > 2 </ sub >, there is a unique fold that passes through both of them.

# Given two points p < sub > 1 </ sub > and p < sub > 2 </ sub >, there is a unique fold that places p < sub > 1 </ sub > onto p < sub > 2 </ sub >.

# Given a point p < sub > 1 </ sub > and a line l < sub > 1 </ sub >, there is a unique fold perpendicular to l < sub > 1 </ sub > that passes through point p < sub > 1 </ sub >.

Given two points p < sub > 1 </ sub > and p < sub > 2 </ sub >, there is a unique fold that passes through both of them.

Given two points p < sub > 1 </ sub > and p < sub > 2 </ sub >, there is a unique fold that places p < sub > 1 </ sub > onto p < sub > 2 </ sub >.

Given a point p < sub > 1 </ sub > and a line l < sub > 1 </ sub >, there is a unique fold perpendicular to l < sub > 1 </ sub > that passes through point p < sub > 1 </ sub >.

* Darkness Given Hunger-A unique colossal black pudding / hezrou fusion.

Heterogeneity / Variability: Given the very nature of services, each service offering is unique and cannot be exactly repeated even by the same service provider.

* Given a point and line there is a unique line which contains the point and is parallel to the line

Let X be any Lie algebra over K. Given a unital associative K-algebra U and a Lie algebra homomorphism: h: X → U < sub > L </ sub >, ( notation as above ) we say that U is the universal enveloping algebra of X if it satisfies the following universal property: for any unital associative K-algebra A and Lie algebra homomorphism f: X → A < sub > L </ sub > there exists a unique unital algebra homomorphism g: U → A such that: f (-) = g < sub > L </ sub > ( h (-)).

Given two distinct points, there is a unique double line through them.

: Given a function f that has values everywhere on the boundary of a region in R < sup > n </ sup >, is there a unique continuous function u twice continuously differentiable in the interior and continuous on the boundary, such that u is harmonic in the interior and u = f on the boundary?

Given his considerable martial ability, a result of hard and dedicated training, he was able to develop a unique and outstanding version of lion dance.