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Given and these
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 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 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 and origins
Given the British origins of the majority of uitlanders and the ongoing influx of new uitlanders into Johannesburg, the Boers recognised that granting full voting rights to the uitlanders would eventually result in the loss of ethnic Boer control in the South African Republic.
Given his generous notion of what constituted an Aryan race ( Evola was convinced of the Hyperborean origins of most Europeans, the indigenous peoples of North and South America, as well as those of the Indian subcontinent ), those candidate races Evola considered to be truly ' alien ' were never explicitly catalogued — except in terms of Semites and the deeply pigmented peoples of sub-Saharan Africa ( see Evola, ' Psicologia criminale ebraica ,' Difesa della Razza 2, no.
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 sport's origins, Irish-bred and trained horses remain a dominant force in national hunt racing today.
Given here are the ethnic origins of Canadian residents ( citizens, landed immigrants, and non-citizen temporary residents ) as recorded by them on their 2006 census form.
Given the English origins of this alternative, it has traditionally been the version used in the Church of England ( including Canterbury Cathedral ) until modern times, and is the version printed in traditional Church of England liturgical sources including the English Hymnal and New English Hymnal.
Given its origins in the Austro-Hungarian Empire, the name has gone through some transformations, mainly through Magyarization.
Given that there was no evidence that either the U. S. or the U. S. S. R. had anything remotely like the UFOs reported, Sign personnel gradually began considering extraterrestrial origins for the objects.

Given and there
: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.
* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.
Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).
Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.
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 its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.
* Given any set X, there is an equivalence relation over the set of all possible functions X → X.
* Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits of G.
Given a left neutral element and for any given then A4 ’ says there exists an such that.
Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force.
Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.
Given that non-violence has priority, all other principles yield to it whenever there is a conflict.
Given this assumption, there are four categories in which a firm's profit may be considered to be.
Given the overall size of trade between Mexico and the United States, there are remarkably few trade disputes, involving relatively small dollar amounts.
Given the above commonalities there appear to be only two string theories: the heterotic string theory ( which is also the type I string theory ) and the type II theory.
Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.
Given the diversity of functions performed by neurons in different parts of the nervous system, there is, as expected, a wide variety in the shape, size, and electrochemical properties of neurons.
: Given any positive number ε, there is a sequence
Given a base for the topology, in order to prove convergence of a net it is necessary and sufficient to prove that there exists some point x, such that ( x < sub > α </ sub >) is eventually in all members of the base containing this putative limit.
Given that both A and not-A are seen to be “ true ,” Kant concludes that it ’ s not that “ God doesn ’ t exist ” but that there is something wrong with how we are asking questions about God and how we have been using our rational faculties to talk about universals ever since Plato got us started on this track!
Given the immense expanse of the entire Universe, it has been argued that there is a higher probability that there exists ( or has existed ) another Earth-like planet that has yielded life ( geogenesis ) than not.
# Given any two distinct points, there is exactly one line incident with both of them.

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