Given these changes, the classical terms " system ", " expansion " and " peripheral " no longer have the same connotations.

Given the military strength of the Great Powers, these interventions were nearly always decisive and quickly ended the civil wars.

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given these origins, there have been various suggestions over the years to rename the town ( for example, to " Invernevis ").

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

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 these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

We have seen a few cavities of the appropriate size and shape for ivory-bills, but these can be old, or exceptionally large Pileated Woodpecker cavities, or mammal-enlarged Pileated Woodpecker cavities .… Given the results, it is unlikely a population of any meaningful size of Ivory-billed Woodpeckers exists in south Florida.

Given that the Qur ' an is vague regarding the punishment of homosexual sodomy, Islamic jurists turned to the collections of the hadith and seerah ( accounts of Muhammad's life ) to support their argument for Hudud punishment ; these are perfectly clear but particularly harsh.

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

" Given the elimination of these pernicious influences, Marx allowed that " normal conditions of spontaneous development " of the rural commune could exist.

Given the properties of a concept, these are necessary and sufficient conditions to classify the concept.

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 a memex, a scholar could create her own knowledge tools as connections within reams of information, share these tools, and use complexes of tools to create yet more sophisticated knowledge that could in turn be deployed toward this work.

Given these issues, Microsoft started to work in parallel on a version of Windows which was more future-oriented and more portable.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).

Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these.

Given that the validity of conclusions drawn from a statistical analysis depend on the validity of any assumptions made, it is clearly important that these assumptions should be reviewed at some stage.

" Given enough time, these formations can meet and fuse to create columns of calcium carbonate.

Given India's historic position that the original intent of the line was to separate the two nations by the highest mountains in the world, in these locations India extended its forward posts northward to the ridges, regarding this move as compliant with the original border proposal, although the Simla Convention did not explicitly state this intention.

Given Jerome's conservative methods, and that manuscript evidence from outside Egypt at this early date is very rare ; these Vulgate readings have considerable critical interest.

Given these facts, algorithm defined by the following pseudocode:

Given a model of some atomic positions, these positions and their respective Debye-Waller factors ( or B-factors, accounting for the thermal motion of the atom ) can be refined to fit the observed diffraction data, ideally yielding a better set of phases.

Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide.

Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion.

Given these assumptions, the following forces should be taken into account:

Given that the four trials under consideration can indeed be consistently considered and experimentally realized, the assumptions concerning hidden variables which lead to the indicated mathematical contradiction are therefore collectively unsuitable to represent all experimental results ; namely the assumption of local hidden variables which occur equally in distinct trials.

Given that a dichotomous criterion violates these assumptions of linear regression, conducting linear regression with a dichotomous criterion may lead to errors in inference and at the very least, interpretation of the outcome will not be straightforward.

Given the assumptions of the model ( for example, that the profits are reinvested and that capital accumulation does not substitute for skilled labor in production ), the process becomes self-sustaining and leads to modernization and economic development.

Given certain assumptions about how to treat the gravitational force, he argued that the bullet sinks with acceleration, where g is the acceleration due to gravity ( assumed to be uniform over the scale of the thought experiment ) and is the factor mentioned above.

Given the assumptions of biological positivism, the only reasonable rationale for punishing offenders is to incapacitate them for as long as possible so that they no longer posed a threat to the peace and security of society.

Given the assumptions of the Hotelling model, consumers will choose either firm as long as the combined price and transportation cost of the product is less than the competitive firm.

Given two candidates, A and B, A is better than B on a constraint if A incurs fewer violations than B.

# Given a maximum distortion constraint, minimize the bit rate

# Given a maximum bit rate constraint, minimize the distortion

Given this constraint, we can write in the following representation:

Given a point in the feasible region, a constraint

Given more time to prepare for trial, Kidd likely would have been able to find the deposition Palmer gave when he was captured in Rhode Island two years earlier.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

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 limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

Given sufficient travel time and engineering work, both unmanned and generational interstellar travel seem possible, though present considerable technological and economic challenges are unlikely to be met in the near future, particularly for manned probes.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

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 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 fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.

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

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

Given time t, the source produces ωt oscillations.

Given prevailing views on homosexuality at the time, circulation of the diaries helped undermine support for clemency for Casement.

Given their wide historical distribution, red wolves probably utilized a large suite of habitat types at one time.

Given that by this time it was common for castles to be built in stone, and that many barons had expanded or refortified their castles, this was not an easy task.

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

Given the medieval medicine's main theory of humorism, spices and herbs were indispensable to balance " humors " in food, a daily basis for good health at a time of recurrent pandemics.

Given the number of homes, it seems likely that no more than fifty people lived in Skara Brae at any given time.