Given free rein to change the story however he wanted, Aki's version is a violent saga focused primarily on fighting and has Hitomi transforming into a " curvaceous nymph " that is the power source of the mecha Escaflowne.

noted, " Given that the bandwidth for conducting crawls is neither infinite nor free, it is becoming essential to crawl the Web in not only a scalable, but efficient way, if some reasonable measure of quality or freshness is to be maintained.

So, a collection of functions with given signatures generate a free algebra, the term algebra T. Given a set of equational identities ( the axioms ), one may consider their symmetric, transitive closure E. The quotient algebra T / E is then the algebraic structure or variety.

Given the theoretical ' fog ' around this issue, in practice most industry practitioners rely on some form of proxy for the risk free rate, or use other forms of benchmark rate which are presupposed to incorporate the risk free rate plus some risk of default.

Given a total interaction cross section σ ( typically measured in barns ), the mean free path of a prompt neutron is where n is the nuclear number density.

Given the chance to repeat some futile behavior endlessly, people can notice the futility of it, and by an act of free will do something else.

* 7 " Promo ( Given away free with initial copies of Sweaty Handshake album, 27 January 1995 )

Given they target a same group of customers, it is imperative that free and paid versions be effectively differentiated.

Given these rates, Spanish employers who do hire interns often may be taking advantage of unpaid interships in order to get free labor.

Given a set, a free module on is a free module with basis.

Given his major interests were domestic, and that the war interfered with his domestic focus, he was eager to free his programs from the war — if he could find a way that he considered politically acceptable.

Given any unital ring R, the set of singular n-simplices on a topological space can be taken to be the generators of a free R-module.

Given the lack of regulatory standards in the U. S., some public-health researchers have raised the concern that consumers cannot be certain that spirulina and other blue-green algae supplements are free of contamination.

Given essentially free stocks, friends of the Erie Railroad grew rich ; that is, Drew had found a way to transfer Vanderbilt's wealth to his own friends.

Given that the subtext was instrumental and not " value free ", ethical and philosophical considerations arise.

Given a free group on some number of generators, we can consider the von Neumann algebra generated by the group algebra, which is a type II < sub > 1 </ sub > factor.

Given a free hand by Beecham he engaged Richard Tauber, Jussi Björling, Maria Reining, Hilde Konetzni, Julius Patzak and Helge Roswänge in their Covent Garden debuts.

Given these two conditions, one can write down ( in the vicinity of the critical temperature, T < sub > c </ sub >) a phenomenological expression for the free energy as a Taylor expansion in the order parameter.

Given free and public access to computers and the Internet group of children can

Given the conditions of the election, which were limited and not free under the watchful eye of the military-government, the MMA ’ s ascension does not seem as surprising.

Given a scheme X over a base scheme S or a complex manifold, a line bundle ( or in other words an invertible sheaf, that is, a locally free sheaf of rank one ) L on X is said to be very ample, if there is an immersion i: X → P < sup > n </ sup >< sub > S </ sub >, the n-dimensional projective space over S for some n, such that the pullback of the standard twisting sheaf O ( 1 ) on P < sup > n </ sup >< sub > S </ sub > is isomorphic to L:

Given free rein, he set about creating costumes that rivaled the work of his contemporaries, such as Travis Banton and Adrian.

Given initial speed u, one can calculate how high the ball will travel before it begins to fall.

Given the extensive linguistic, religious and ethnic diversity of the Indian population, nationalism in India in general does not fall within the purview of a solitary variant of nationalism.

Given a Hi of 0. 40, if the H_m is assumed to be 0. 25. then from the equation above RCM count is still high and ANH is not necessary, if BLs does not exceed 2303mL, since the hemotocrit will not fall below H_m.

Given this flow rate and the 96 metre fall it is easy to calculate that the Inga Falls alone has a potential to generate ~ 39. 6 GW of mechanical energy and nearly as much electrical energy.

Given that the ZWZ focused on military aspects of the struggle, its civilian dimension was less clearly defined and developed more slowly — a situation exacerbated by the complex political discussions that were then unfolding between politicians in occupied Poland and the government in exile ( first located in Paris, and after the fall of France, in London ).

Given the sequence of events shaped by Chvalkovský, many countries, such as France ( a signatory of Munich Agreement ), initially considered the fall of Czechoslovakia a result of internal forces rather than German aggression.

Given this security, she can proceed to do what she really wants to do — fall in love with men who are weak and irresponsible ,” won him a following across Canada.

Given the wide range of services, such as policing, health care and education, that fall under provincial jurisdiction, these divergences have considerable importance.

Given the replicants ' superhuman abilities, their identity as created beings ( by Tyrell ) and " fall from the heavens " ( off-world ) makes them analogous to fallen angels.

Given the strongly entrenched opposition the Greek Army faced, historian Richard Hall cites the Battle of Bizani and the fall of Ioannina as Greece's greatest military achievement in the First Balkan War.

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

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 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 any two distinct points, there is exactly one line incident with both of them.