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Finally, a separated presheaf is a sheaf if compatible sections can be glued together, i. e., whenever there is a section of the presheaf over each of the covering sets V < sub > i </ sub >, chosen so that they match on the overlaps of the covering sets, these sections correspond to a ( unique ) section on U, of which they are restrictions.
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Finally and separated
Finally, the oxidized form of the metal to be reduced at the cathode, is written, separated from its reduced form by the vertical line.
Finally, in 1642 Tasman showed that even New Holland ( Australia ) was separated by sea from any continuous southern continent.
Finally, a day's journey from the Huron camp, Father Menard separated from his travelling companion at a rapids to carry some supplies.
Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air.
" Finally the south side is separated from the east side by the Furggen ridge ( Furggengrat ), according to Collomb " the hardest of the ridges [...] the ridge still has an awesome reputation but is not too difficult in good conditions by the indirect finish ".
Finally, the coal-producing valley of the Saarland, which had been provisionally separated from Germany, was to be the subject of a referendum after the lapse of fifteen years.
Finally, this question of the authenticity of individual Dasein cannot be separated from the " historicality " of Dasein.
Finally, although he believed in a soul, he believed that it resided in the blood, and that upon a human's death it separated from the body and transformed into a bird, until the body was cremated or degenerated into the soil.
Finally cognitivists use a post-positivist methodology which does not believe that social institutions or actors can be separated out of their surrounding socio-political context for analytical purposes.
Finally, on 1 April 1867 the Straits Settlements were separated from the Government of India and became a Crown colony.
Finally on March 12, 1875, the Governor General Don Jose de Malcampoy y Monje issued the decree creating the new town of Anda and it being separated from the town of Guindulman in the civil aspect only in consonance with the desire of the religious authorities.
Finally, in 1929, Sangirin was separated from Aiabat and christened Municipality of Perez in honor of Governor Filemon Perez.
Finally, in 1929 Mansalay was officially separated from Bulalacao.
Finally, in 2003, as Moore approached graduation, the group separated officially from the school, and all but Moore, Brown, Cregger and Williams left the troupe.
Finally and is
Finally, in The Maltese Falcon among others, the clash between detective and police is carried to its logical conclusion: Sam Spade becomes the chief murder suspect.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.
Finally, there is the undeniable fact that some of the finest American fiction is being written by Jews, but it is not Jewish fiction ; ;
Finally come those little flicks of a rigger brush and the job is done.
Finally, it is suggested that in many respects the horse lung may be anatomically more comparable to that of the human than any other presently known species.
Finally, the image of a general bundle of lines is a congruence whose order is the order of the congruence of invariant lines, namely Af and whose class is the order of the image congruence of a general plane field of lines, namely Af.
Finally, whatever the techniques used, a twin goal is common to all preventive casework service: to cushion or reduce the force of the stress impact while at the same time to encourage and support family members to mobilize and use their ego capacities.
Finally, information is retrieved from the dictionary as required by stages of the translation process -- the grammatical description for sentence-structure determination, equivalent-choice information for semantic analysis, and target-language equivalents for output construction.
Finally, there is the question of how strongly an expressed opinion is held -- whether it is a firm opinion or one that the respondent favors only slightly over the alternatives.
Finally, when the accelerometer output is zero, the entire system remains stationary, and the platform is, by definition, leveled.
Finally, the gyro-stabilized platform characteristic is represented by Af.
Finally, we may also mention the several members of the self-consciously `` neoliberal '' movement that developed at the University of Chicago and is heavily indebted philosophically to the creative work of Alfred North Whitehead.
Finally, the staïfi music is born in Sétif and remains a unique style of its kind.
Finally, this is the germ from which the art of Polykleitos was to grow two or three generations later.
Finally, while Armenia is not the only ex-Soviet state that has incurred multimillion-dollar debts to Russia over the past decade, it is the only state to have so far given up such a large share of its economic infrastructure to Russia.
Finally, a Registration Examination or a series of exams is required prior to licensure.
Finally, above the central part of the facade is a smaller balcony, also iron, with a different exterior aesthetic, closer to a local type of lily.
Finally and if
Finally, since the public requires some restraint on the part of the companies, larger wage increases call for less than proportionately larger price increases ( e.g., if a wage increase of 5% allows a price increase of 7%, a wage increase of 10% allows a price increase of something less than 14% ).
Finally, if the mission of the Trial was to convict anti-Semitism, how could it have failed to post before the world the contrasting fates of the countries in which the Final Solution was aided by native Jew-haters -- i.e., Germany, Poland, Hungary, Czechoslovakia -- and those in which it met the obstacle of human solidarity -- Denmark, Holland, Italy, Bulgaria, France??
Finally, batters were credited with a stolen base if they were tagged out after over running the base.
Finally, for 1950 only, runners would be credited with a stolen base if they were " well advanced " toward the base they were attempting to steal ", and the pitcher is charged with a balk, with the further exception of a player attempting to steal, who would otherwise have been forced to advance on the balk by a runner behind them.
Finally, in Chapter 3, Habakkuk expresses his ultimate faith in God, even if he doesn't fully understand.
Finally, if the Triangle is assumed to cross land, such as parts of Puerto Rico, the Bahamas, or Bermuda itself, there is no evidence for the disappearance of any land-based vehicles or persons.
Finally, if light pressure were the motive force, the radiometer would spin in the opposite direction, as the photons on the shiny side being reflected would deposit more momentum than on the black side where the photons are absorbed.
Finally, note that even if all arrows grossly miss the target, if they nevertheless all hit the same point, the variance is zero.
Finally, if long-term average cost is constantly decreasing, the least cost method to provide a good or service is by a single company.
Finally, any phenomenon involving individual photons, such as the photoelectric effect, Planck's law, the Duane – Hunt law, single-photon light detectors, etc., would be difficult or impossible to explain if Maxwell's equations were exactly true, as Maxwell's equations do not involve photons.
Also, thick insulators are required to prevent electron leakage, and if high conductivity of the in vivo medium occurs there is a risk of sudden power loss and “ shorting out .” Finally, thick wires are also needed to conduct substantial power levels without overheating.
Finally, if a swing player fails for half the pot, the half that he would have otherwise won can be awarded either to the second-best hand in that direction, or to the player who defeated him in the other.
Finally, some American courts have held that local law will be applied if the injury occurred in an " uncivilized place that has no law or legal system.
Finally, if both S and T are normal in ST, then ST is called a direct product.
Finally, if all possible rightful orders of primogeniture and representation have been exhausted, then the General Courts will select a successor in the way that best suits the interest of Spain.
Finally, if an opponent is deep in his court, a player may suddenly employ an unexpected drop shot, by softly tapping the ball just over the net so that the opponent is unable to run in fast enough to retrieve it.
Finally, if the state objects and opposes, there are no legal obligations under that treaty between those two state parties whatsoever.
Finally, the question has recently been raised as to whether Thucydides was not greatly, if not fundamentally, concerned with the matter of religion.
Finally, in 431 BC, this tension erupted into the Peloponnesian War, the first of a series of conflicts which would tear Greece apart for the next century ; an unforeseen, if indirect, legacy of Themistocles's.
Finally, if the mobile is beyond the 35 km cell range in GSM, then the RACH will arrive in a neighbouring time slot and be ignored.
Finally, whilst motives may not play a role in determining the morality of an action this does not preclude utilitarians from fostering particular motives if doing so will increase overall happiness.
Finally, Butterfly tells Kate, " I will give my child to her only if he comes himself.
Finally, in cases where many people will take an action without an offer, " uplift modeling " can be used to determine which people have the greatest increase in response if given an offer.
* Finally, a preabelian category is abelian if every monomorphism and every epimorphism is normal.
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