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 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 any family of nonempty sets, their Cartesian product is a nonempty set.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

Given that the bulk of family chores fell to women, and that they were five times more likely than men to head a single-parent family, the shortcomings of Finland's child day-care system affected women more than it did men.

Given our political differences, people are sometimes surprised how close Ronnie and I have been to the Kennedy family.

Given the fact that many of the royal depictions of Akhenaten often featured such an elongated head, it is likely an exaggeration of a family trait, rather than a distinct abnormality.

Given two affine spaces and, over the same field, a function is an affine map if and only if for every family of weighted points in such that

Given a parameterized family of probability density functions ( or probability mass functions in the case of discrete distributions )

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 a topological space X, a base for the closed sets of X is a family of closed sets F such that any closed set A is an intersection of members of F.

Given the broad expanse of the Malvasia family, generalizations about the Malvasia wine are difficult to pin point.

Given Harry Evans Sr .' s destructive character, Mary Evans would often leave home with her sons to nearby Somerville, to stay with her sister Justine and the Epps family.

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given the sheer power of leverage the Rothschild family had at its disposal, this profit was an enormous sum.

* Given a family of continuous functions f < sub > n </ sub >: X → Y with pointwise limit f: X → Y.

Given his father's naval career, where the family was domiciled is uncertain.

Given this situation, Jose Antonio del Valle had to move his family to Guatemala City, where he hoped young Jose would be better formed.

Given this outlook, whatever the level of affection Whistler may have felt for his own mother, one finds an even more divergent use of the image in the Victorian era and later, especially in the United States, as an icon for motherhood, affection for parents, and " family values " in general.

Given a family of sets X < sub > i </ sub > the product is defined as

Given any set Y with a family of functions

Given the difficulties faced in Berlin, he decided to accept the offer and immediately moved to Göttingen with his family.

Given a manifold and a Lie algebra valued 1-form, over it, we can define a family of p-forms:

Given her mother's ambitions for her and the fact that Rudolf was married to Princess Stephanie of Belgium, her family and friends found this liaison to be not only foolish, but potentially socially compromising for the family as well.

* Given names often turned into family names when people were identified by their father's name.