Given this preexisting pattern, having a preference for longer and more colorful tails gives an advantage just as having a longer and more colorful tail does.

: Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners.

Given two similar rewards, humans show a preference for one that arrives sooner rather than later.

; Condorcet winner: Given a preference ν on the outcome space, an outcome a is a condorcet winner if all non-dummy players prefer a to all other outcomes.

; Dominated outcome: Given a preference ν on the outcome space, we say that an outcome a is dominated by outcome b ( hence, b is the dominant strategy ) if it is preferred by all players.

Given the preference for German sedans from Audi, BMW and Mercedes-Benz of many executive car buyers, this can be viewed as good marketing tactics, allowing Renault to draw the buyers looking for alternatives, rather than compete head-on.

Given this situation, preference for smarter child-bearing / rearing partners increases the chance that their descendants will inherit the best resistance alleles, not only for immune system resistance to disease, but also smarter brains for learning skills in avoiding disease and selecting nutritious food.

Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given the importance of reason, Clement stresses apatheia as a reasonable ordering of our passions in order to live within God's love, which is seen as a form of truth.

Given an-element array with an ordering relation as an input for the sorting, consider it as a collection of cards, with the ( unknown in the beginning ) statistical ordering of each element serving as its index.

Given this ordering of A, a subset B of A is cofinal in A if for every a ∈ A there is a b ∈ B such that a ⊃ b.

Given x ∈ A, the holomorphic functional calculus allows to define ƒ ( x ) ∈ A for any function ƒ holomorphic in a neighborhood of Furthermore, the spectral mapping theorem holds:

Given a partial derivative, it allows for the partial recovery of the original function.

Given a set of points in the Euclidean plane, selecting any one of them to be called 0 and another to be called 1, together with an arbitrary choice of orientation allows us to consider the points as a set of complex numbers.

Given the design of the language that allows a function to legitimately accept many different types of arguments, compile-time typing would be difficult to implement and its usefulness would be questionable.

Having a measure on G allows us to define integration of bounded functions on G. Given a bounded function, the integral

Given an extensible list of classes, this allows the classification of any individual thing and to specify part-whole relations for any individual object.

Given that all Sarracenia hybrids are fertile and will hybridize further, this characteristic allows cultivators to produce a limitless number of variants through hybridization.

Given this grammar, we can now say that the number of NPs expected while deriving VPs is 0. 7 x 1 + 0. 3 x 2 = 1. 3.

Given the tendency of birds that have become flightless to increase in size markedly in just a few million years, the probability of Hesperornithes deriving from an animal at least superficially similar and not too far related to Gansus is quite high.

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.