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Thus and over
Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).
Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.
" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.
Thus in 1285 he declared war on his uncle, James II of Majorca, and conquered both Majorca ( 1285 ) and Ibiza ( 1286 ), effectively reassuming suzerainty over the Kingdom of Majorca.
Thus, the Hungarian supremacy over Halych disappeared.
In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.
Thus, over time, the expression " a cappella " ( Italian for " in the manner of the chapel ") came to mean exclusively vocal music in contradistinction to the spreading use of the organ in cathedrals.
Thus, if the score was 3 – 2 with the bases loaded in the bottom of the ninth, and the batter smacked an " over the fence home run ", the game would end at 4 – 3, with the batter only allowed a double, and the runners officially stopped on 2nd and 3rd ( since they were not needed to win the game ).
Thus, if a ball went over the fence fair, and curved behind the foul pole, it was ruled foul.
Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.
Thus the CSF turns over about 3. 7 times a day.
Thus a spacecraft can determine its relative position by tracking such asteroids across the star background, which appears fixed over such timescales.
Thus, we should prioritize social reform over attempts to account for consequences, individual virtue or duty ( although these may be worthwhile attempts, provided social reform is provided for ).
Thus an equivalence relation over X, a partition of X, and a projection whose domain is X, are three equivalent ways of specifying the same thing.
Thus, before the Aswan High Dam was completed in 1971, the White Nile watered the Egyptian stretch of the river throughout the year, whereas the Blue Nile, carrying seasonal rain from Ethiopia, caused the Nile to overflow its banks and deposit a layer of fertile mud over adjacent fields.
Thus, over time we would expect each traditional song to become aesthetically ever more appealing — it would be collectively composed to perfection, as it were, by the community.
Thus John asserts Jesus ' innate superiority over all divine messengers, whether angels or prophets.
Thus methane has a potential of 25 over 100 years but 72 over 20 years ; conversely sulfur hexafluoride has a GWP of 22, 800 over 100 years but 16, 300 over 20 years ( IPCC TAR ).
Thus, if Adar was over and Spring had not yet arrived, an additional month was observed.
Thus they were involved in the struggle for power within France as princes but they also had a religious authority over Roman Catholicism in France as King.

Thus and past
Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).
This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.
Thus, current expected inflation reflects a weighted average of all past inflation, where the weights get smaller and smaller as we move further in the past.
Thus, as a simple instance posed by Hume, we cannot know with certainty by inductive reasoning that the sun will continue to rise in the East, but instead come to expect it to do so because it has repeatedly done so in the past.
Thus the past, present, future, and anything in and of, would simply exists without possible creation of, or deviation from.
Thus, inherited behavioral mechanisms that allowed an organism a greater chance of surviving and / or reproducing in the past are more likely to survive in present organisms.
Thus, the major threat in these areas is fire management ( protection of private assets is a key objective and so past fire regimes may not reflect environmental needs ), weed invasion and lack of connectivity between patches.
Thus the Báb taught that with his revelation the end times ended and the age of resurrection had started, and that the end-times were symbolic as the end of the past prophetic cycle.
Thus, '... his nutrition has been deficient in the past several weeks, as he is showing signs of scurvy, the deficiency disease associated with inadequate levels of vitamin C '.
Thus, in the study of historical Chinese culture, many of the stories that have been told regarding characters and events which have been written or told of the distant past have a double tradition: one which tradition which presents a more historicized and one which presents a more mythological version.
Thus, in classical physics, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace's claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past ( see Laplace's demon ).
Thus, Ellwood believes that the later Eliade probably thought modern man should preserve elements of the past, but should not try to restore their original form through reactionary politics.
" Thus the dispensation was not a posteriori, and concerned with unfulfilled obligations of the past year, but a priori and having reference to vows one might not be able to fulfill or might forget to observe during the ensuing year.
Thus, successfully eliminating a thousand years worth of culture that even surpassed the Spanish's barbaric past as Vandals.
Thus, in Descartes work, we can see some of the fundamental assumptions of modern cosmology in evidence-the project of examing the historical construction of the universe through a set of quantitative laws describing interactions which would allow the ordered present to be constructed from a chaotic past.
Thus, whoever heeds this commandment from his Lord, and refrains from usury, he may keep his past earnings, and his judgment rests with God.
Thus, the party has held power for 24 of the past 38 years ( to 2009 ).
Thus, after this time, the time-out calculation overflowed and returned a date that was actually in the past, causing the software to crash.
Thus, the rivalry has decreased over the past years.
Thus, a guarantee may only be given or a loan raised by the Government if the President concurs, and his approval is also needed for budgets of specified statutory boards and Government companies that draw on their past reserves.
Thus, an archaeological in-situ-find may be an object that was historically looted from another place, an item of " booty " of a past war, a traded item, or otherwise of foreign origin.
Thus, as illustrated by the pre / trans fallacy, religious and spiritual experiences have in the past been seen as either regressive or pathological and treated as such.
Thus the degree of " tuning " necessary for intervention in otherwise " perfect " market mechanisms becomes more and more extreme as the time in which the capitalist order is a progressive factor in the development of productive forces recedes further and further into the past.

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