Given a morphism f: B → A the associated natural transformation is denoted Hom ( f ,–).

Given the ( particularly modern ) prevalence of crowd events, and the potential safety issues associated with such large gatherings of people, the topic is receiving increasing attention from agencies responsible for crowd management and also from governments.

Given that many of the talented young artists had been raised in housing projects and were short on social and dress skills, this Motown department was not only necessary, it created an elegant style of presentation long associated with the label.

Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, ( written X → Y ) if, and only if, each X value is associated with precisely one Y value.

Given the wide variety of symptoms that are associated with whiplash injuries, the Quebec Task Force on Whiplash-Associated Disorders coined the phrase ' Whiplash-Associated Disorders '.

Given *- representations π, π ' each with unit norm cyclic vectors ξ ∈ H, ξ ' ∈ K such that their respective associated states coincide, then π, π ' are unitarily equivalent representations.

Given a state ρ of A, there is a *- representation π of A with distinguished cyclic vector ξ such that its associated state is ρ, i. e.

An open set U in X admits a local trivialization if and only if there exists a local section on U. Given a local trivialization one can define an associated local section by

Given the historical associations of the project's name ( see Masada ), the Hebrew titles of the compositions, and the Jewish imagery on the covers of the associated albums, Zorn was clearly exploring his Jewish roots, stating, " The idea with Masada is to produce a sort of radical Jewish music, a new Jewish music which is not the traditional one in a different arrangement, but music for the Jews of today.

Given that folk psychology represents causal knowledge associated with the mind ’ s categorization processes, it follows that folk psychology is actively employed in aiding the explanation of everyday actions.

Given the physical punishment suffered by catchers, the pieces of equipment associated with the position are often referred to as " the tools of ignorance ".

* Given a frame ƒ and a point A ∈ X, there is associated a point x = ( A, ƒ ) belonging to Σ.

Given what is known of the chronology of the ‘ Gallic Empire ’ his bid for Empire is most probably associated with the period of confusion following the officers ’ coup against the ‘ Gallic Emperor ’, Victorinus, early in 271.

Given an square matrix of real or complex numbers, an eigenvalue and its associated generalized eigenvector are a pair obeying the relation

" Given the risks of toxicity associated with ingesting urine ," he wrote, " the health ministry advises against the consumption of urine and invites those who promote the practice to cease doing so or risk prosecution.

Given the Wyld's inconstant nature, however, concrete locations associated with Flux are few ; more commonly, the energies of Flux pass over an area, causing rapid change and general chaos, then move on.

Given a group G and a filtration G < sub > n </ sub >, there is a natural way to define a topology on G, said to be associated to the filtration.

Given its high price in the West, caviar is associated with luxury and wealth.

Given the fact that the vast majority of SUVs were rarely taken off-pavement by their owners, much less driven under serious off-road conditions, a new type of car-based " crossover SUV " was developed that was hoped would provide all the elements that customers actually wanted from their SUVs such as cargo carrying capacity, elevated seating height and the suggestion of an active outdoor lifestyle with less of the negative attributes typically associated with traditional SUVs such as poor gas mileage, uncomfortable ride, high step-in height, propensity to roll over, etc.

Given the prevalence of crowd events, and the potential safety issues associated with such large gatherings of people, the topic is receiving increasing attention from agencies responsible for crowd management and also from governments.

* Given the extended recording times of data loggers, they typically feature a mechanism to record the date and time in a timestamp to ensure that each recorded data value is associated with a date and time of acquisition in order to produce a sequence of events.

Given the flatter structures associated with n-ary branching, certain phenomena ( e. g. inversion and shifting ) do not result in discontinuities, a fact that reduces the role that the component for discontinuities must play in the theory.

Fix a base field F and a finite-dimensional vector space V over F. Given a polynomial p ( x ) ∈ F, there is associated to it a companion matrix C whose characteristic polynomial is p ( x ).

Given that a preference ordering allows deriving its associated knowledge base but also allows performing a single step of revision, studies on iterated revision have been concentrated on how a preference ordering should be changed in response of a revision.

Given that NASA and USAF ( as well as government programs in other countries ) are the primary customers and sources of development capital, government regulatory requirements for oversight, parwork, quality, safety, and other documentation tend to inflate the operational costs of any such system.

Given the large number of junctions and the intensive use of its system, the LB & SCR maintained a good safety record during the last half century of its existence.

Given the tonal design of the train whistle, the sound level, how often trains pass through a given community, the number of grade crossings in proximity, and the time of day ( night ) of occurrence, community residents residing near crossing sometimes feel that train whistles have a serious detrimental effect on the quality of life despite the gain in safety that sounding the horn provides to motorists.

The company already owned a stake in PT Indonesia Air Transport Tbk, a subsidiary of Pt Media Nusantara Citra Tbk, and president Hary Djaja says that " Given our experience with IAT, which has an excellent safety record, we're certain that we will be able to create positive synergies and improve the way Adam Air is run ,".

Given the violent nature of robot fighting, safety is always the most important issue at robot events.

“ Given the high incidence of craniofacial injury, appropriate safety standards for taxicabs must be initiated, including the reevaluation of the utility of the safety divider ”

Given the unique nature of model aviation insofar as it requires both airspace as well as frequency allocation for radio control, the AMA serves as a liaison with the Federal Aviation Administration concerning aeromodeling safety and operation of model aircraft as it relates to full-scale aviation, most recently with the upcoming likelihood of the start of non-military, commercial and public-use UAV deployment in the National Airspace System over the United States, and how the FAA will regulate such commercial and public use of UAVs, simultaneous with accommodating the needs of recreational and sport flying of radio control model aircraft, with the AMA as an advocate for the aeromodeler.

In a critical statement published in 1955, he asserted that " Given the modern conceptions of the beautiful in literature, given at the very least these essential conceptions, if a work is realistic it has many chances of being good ; if not, supposing even that it has formal qualities, it risks lacking resonance, profundity, that of which all literature has the greatest need -- the human ; from which it follows that it has much less chance of being good -- if only it had some -- than a realistic work.

Given the history and the large number of birds hatched in Basel since 1959, it may be concluded that most of the Greater Flamingo zoo colonies around the world are related to the one at Basel.

Given the small number of NAION events with PDE5 use ( less than 1 in 1 million ), the large number of users of PDE5 inhibitors ( millions ) and the fact that this event occurs in a similar population to those who do not take these medicines, the FDA concluded that they were not able to draw a cause and effect relationship, given these patients underlying vascular risk factors or anatomical defects.

On the issue of the second home he wrote: " I have concluded that Mr MacKay was wrong to designate the Bromsgrove property as his main home Given that, it would be unreasonable to hold that Ms Kirkbride could not make legitimate claims from parliamentary resources for the home in her constituency which she had identified as her second home ".

The study concluded that " Given their frequent and widespread occurrence, especially during storms, pesticides have the potential to affect aquatic life and the quality of drinking water derived from the lower river ," and laid out areas for further study.

Given the evidence presented to the Percé jurors in 1954, Fortin concluded that they were justified to render a verdict of guilty as charged.

Given that the Badlands are some 350 miles away from Alice, Steigerwald concluded that the conversation with the actor was unlikely to have occurred.

They concluded: " Given its hostility to such pluralistic notions of participation and democracy, RC has the potential to become a fully fledged and harmful cult, despite its original humanistic aims.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given the union's commitment to international solidarity, its efforts and success in the field come as no surprise.

Given wide praise for his efforts, the Flyers gave Holmgren a two-year contract and removed the interim label from his title.

Given the weakness of the League of Nations vis-à-vis Germany and the successful efforts by the Nazi regime to stave off an economic boycott of German products, neither track proved not very effective.

Given the complicated legal process and the sheer number of exiting cul-de-sac streets, however, such efforts would be slow to produce results and may only have a marginal impact in changing the landscape of existing districts.

Given the already heavy load on students, efforts must be made to avoid curriculum overload.

Given Zemlya i Volya's failures in its propaganda efforts among the peasants in the movements " to the people " in the early 1870s, Narodnaya Volya turned its energies against the central government.

Given that many of those most actively involved in early efforts were academics ( drawn from a variety of disciplines including Anthropology, Computing Science, Development Studies, Information Science and Systems, Management, Planning, Sociology, and Social Work among others ) it is only inevitable that a process of " sense-making " with respect to these efforts would follow on quite quickly from the flurry of " tool-making " efforts.

Given responsibility for Iraq's second city, Basra, it gained much praise for its efforts to restore security and civil order, but also suffered casualties of one dead and 32 injured sufficiently seriously to require medical evacuation to the United Kingdom.

Given that data dredging efforts typically examine large datasets with many variables, and hence even larger numbers of pairs of variables, spurious but apparently statistically significant results are almost certain to be found by any such study.

* Roland Burris: Given on January 9, 2009, for his efforts to retain his seat, which was appointed controversially by Rod Blagojevich.

Given that labor is the individual's primary commodity in the market, decommodification refers to activities and efforts ( generally by the government ) that reduce individuals ' reliance on the market ( and their labor ) for their well-being.

Given the biological and pharmaceutical significance of molecular docking, considerable efforts have been directed towards improving the methods used to predict docking.

Given the diversity of CNN processors and the momentum that CNN research has gained, it is plausible that these unique analog CNN development efforts will be fairly common in the near future.