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 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 these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox.

Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.

Given good viewing conditions, Thuban is relatively easy to spot in the night sky, due to its location in relation to the Big Dipper asterism of Ursa Major.

Given a ring R and a proper ideal I of R ( that is I ≠ R ), I is a maximal ideal of R if any of the following equivalent conditions hold:

Given the harsh conditions of the retreat, the infant was left with a local family ( Two Europeans retracing the Long March route in 2003 met a woman in rural Yunnan province, said by local officials to be Mao and He Zizhen's long-lost daughter ).

Given the many presentations and the relatively low occurrence of porphyria, the patient may initially be suspected to have other, unrelated conditions.

Given that " production could be carried on without any organization is, firm at all ", Coase asks, why and under what conditions should we expect firms to emerge?

Given a general triangle ABC, the following conditions would need to be fulfilled for the case to be ambiguous:

Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

Given the weather conditions close to the summit, cold weather injuries are very common.

Given the desperate economic conditions in Switzerland, 193 volunteers decided to leave their homeland to start anew in America.

Given a manifold M representing ( continuous / smooth / with certain boundary conditions / etc.

Given the landscape changes ( e. g., land development, urbanization, clearcutting in forested areas ) in the watersheds of many freshwater bodies, returning to pristine conditions would be a significant challenge.

Given the right reaction conditions ring-opening metathesis polymerization ( ROMP ) can be rendered living.

Given a set with three binary operations and, and two distinguished elements 0 and 1, then is a Heyting algebra for these operations ( and the relation defined by the condition that when ) if and only if the following conditions hold for any elements and of:

Given the right overall conditions of the compressed fuel — high enough density and temperature — this heating process will result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given the conditions of the experiment, the Canterbury group conclude that if any such ' Tajmar ' effect exists, it is at least 22 times smaller than predicted by Tajmar in 2006.

Given good conditions, a bud can produce a shoot with up to ten or more leaves.

Given sufficient time under fire or heat conditions, these products char away, crumble, and disappear.

Given the origins of the cardinal tetra, namely blackwater rivers whose chemistry is characterised by an acidic pH, low mineral content and the presence of humic acids, the species is adaptable to a wide range of conditions in captivity, though deviation from the soft, acidic water chemistry of their native range will impact severely upon breeding and fecundity.

Given the same energy source and operating conditions, a higher COP heat pump will consume less purchased energy than one with a lower COP.

Given such conditions, the chances are good that the whales can be driven fully ashore or close enough to the shore that they can be killed from land.

Given the difficult topographic and climatic conditions, construction units were prefabricated.