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 lack of paved highways in America, this turned out to be a shrewd business move that enlarged Barnum's geographical reach.

Given the global nature of gonococcal and meningococcal diseases, the worldwide distribution of antibiotics, differing social practices in controlling and monitoring antibiotic availability, and geographical differences in treatment regimens, it is likely that the global problem of antibiotic resistance will continue in the foreseeable future.

" As well, he also stated: " Given its extensive geographical coverage and the recent move to integrate it with other means of transportation, the Asian Highway project requires collective effort and close collaboration among the Asian countries.

Given that the virus did not evolve into two separate strains until around 1900, and given how many transfers of fish there were, according to this research, " At present it is therefore not possible to suggest a geographical origin of the ISA virus.

Given the geographical and numerical limitations of the Fijian language, it needed to be given special attention on its own merit.

Given the relatively small geographical area and high population density of the UK, online DVD rentals have some differences from in the US, as a single shipping facility can serve the entire country.

Given State and Local laws, types of weapon can also vary depending on type, size, sex of game and also the geographical layout of that specific hunting area.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given a presheaf, a natural question to ask is to what extent its sections over an open set U are specified by their restrictions to smaller open sets V < sub > i </ sub > of an open cover of U. A presheaf is separated if its sections are " locally determined ": whenever two sections over U coincide when restricted to each of V < sub > i </ sub >, the two sections are identical.

Given his background as a novel / action-scene illustrator, and the close collaboration with Augusta the ' story-teller ', Burian viewed the subjects of his paintings as very real animals ( as would a natural history artist ), and the new restrictions did not sit well with him.

Given that Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given Guatemala's large expatriate community in the United States, it is the top remittance recipient in Central America, with inflows serving as a primary source of foreign income equivalent to nearly two-thirds of exports.

Given that bankruptcies and real estate prices did not fare as negatively in Central Canada as in the rest of Canada and the United States during the NEP, it is possible that the NEP had a positive effect in Central Canada.

Given that the seizure of so much of Central and Eastern Europe, and the accompanying violence directed against various Slavic groups, Jews, Communists, homosexuals, prisoners of war, and so-called partisans, was part and parcel of the Nazi idea of the German nation, and that the forced departure of German settlers and ethnic Germans ( the Volksdeutsche ) living in the extended Reich before the advance of the Red Army was amongst its consequences, the memory of the violence accompanying German occupation and then evacuation of that land is another abiding element of this struggle.

Given the absence of written records, the ethnicities and linguistic affiliations of the groups living in Central and Eastern Europe at that time are speculative — there is considerable disagreement.

Given the experience of state governments in passing practicable legislation, the Central Government appointed a working group under H. D. Shourie and assigned it the task of drafting legislation.

Given this kind of business climate, what competitive marketing problems will your company face in the next 10 yrs.??

Given the magnitude of the disaster, reconstruction and economic recovery will remain the primary focus of the Salvadoran Government for some time to come.

Given the distances between the stars, the great majority of stellar systems in colliding galaxies will be unaffected.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given the same bullet and cartridge, a faster burning powder will generally use a smaller charge of powder than required with a slower powder.

Given these conditions, Lovelock expects human civilization will be hard pressed to survive.

Given that bodhisattvas are known to incarnate at will as living people according to the sutras, the princess Miaoshan is generally viewed as an incarnation of Avalokitesvara.

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

Given enough time and repeated exposure to the antibiotic, a population of antibiotic-resistant bacteria will emerge.

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

Given the poorly understood nature of the endocannabinoid system, it will take many more generations of progress to even scratch the surface of the extraordinarily complex mechanisms that control neurological development / degeneration.

Given sufficient time, oxygen, and water, any iron mass will eventually convert entirely to rust and disintegrate.

Given any two cards from the deck, there will be one and only one other card that forms a set with them.

Given current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given time, the simple mixture of sand, silt, and clay will evolve into a soil profile which consists of two or more layers called horizons that differ in one or more properties such as texture, structure, colour, porosity, consistency, and reaction.

Given this announcement the prisoner can deduce that the hanging will not occur on the last day of the week.

# Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone.

Given the CIA's purposeful destruction of most records, its failure to follow informed consent protocols with thousands of participants, the uncontrolled nature of the experiments, and the lack of follow-up data, the full impact of MKUltra experiments, including deaths, will never be known.

Given sufficient resources for growth, a biofilm will quickly grow to be macroscopic ( visible to the naked eye ).

Given the objectivity and lowered costs of satellite-based land cover analysis, it appears likely that remote sensing technology will be an integral part of assessing the extent and damage of deforestation in the basin.

Given a grammar in GNF and a derivable string in the grammar with length n, any top-down parser will halt at depth n.

Given expectations about returns on fixed investment, every level of the real interest rate ( i ) will generate a certain level of planned fixed investment and other interest-sensitive spending: lower interest rates encourage higher fixed investment and the like.