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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, over the past 1, 500 years, some Christians have used the term Arian to refer to those groups that see themselves as worshiping Jesus Christ or respecting his teachings, but do not hold to the Nicene creed.
" 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 period
Thus the student of literature may sometimes find it helpful to classify a poem or an essay as being in idea or in ideal content or subject matter typical or atypical of its period.
According to the Christian doctrine of Universal Reconciliation, the Greek New Testament scriptures use the word " eon " to mean a long period ( perhaps 1000 years ) and the word " eonian " to mean " during a long period "; Thus there was a time before the eons, and the eonian period is finite.
Thus, Confucius could not achieve the idealistic reform that he wanted and restore the legitimate rule of the duke, returning to the period of the Duke of Zhou.
Thus use of the term " period " is somewhat deceptive.
Thus, for a period, economics worked in favour of cable cars even in relatively flat cities.
Thus the discounted present value ( for one cash flow in one future period ) is expressed as:
Thus began what is now often called " The Golden Age of Hollywood ", which refers roughly to the period beginning with the introduction of sound until the late 1940s.
Thus, in Chile, Argentina and the Canary Islands, godo was an ethnic slur used against European Spaniards, who in the early colony period often felt superior to the people born locally ( criollos ).
Thus it was at Naples that Anatoli passed his most fertile period of literary production, and from that city were issued the numerous translations bearing his name.
Thus, Peter Wimsey remained forever fixed on the background of inter-war England, and the books are nowadays often read for their evocation of that period as much as for the intrinsic detective mysteries.
Thus a 3D display must display twice as many images in the same period of time as a conventional display, and consequently the response time of the LCD is more important.
Thus the concept of the " Romantic period " may be meaningless outside of Europe and European-influenced cultures.
Thus, the aggregate term Third World was challenged as misleading even during the Cold War period because it had no consistent or collective identity among the countries it supposedly encompassed.
Thus, instead of expecting a single Antichrist to rule the earth during a future Tribulation period, Martin Luther, John Calvin and the other Protestant Reformers saw the Antichrist as a present feature in the world of their time, fulfilled in the papacy.
Thus it follows the path starting from the more modern period of the 15th century onward ( e. g. neo-Alexandrian, hermeticism, Christian Kaballah, Rosicrucianism, Alchemy etc .).
Thus began the Hellenistic age, a period characterized by a more absolute approach to rule, with Greek kings taking on royal trappings and setting up hereditary successions.
Thus a new period in Belarusian history started, with all its lands annexed by the Russian Empire, in a continuing endeavor of Russian tsars of " gathering the Rus lands " started after the liberation from the Tatar yoke by Grand Duke Ivan III of Russia.
Thus, the early 20th century is a period often referred to as the " nadir of American race relations ".
Thus postmenopause is all of the time in a woman's life that take place after her last period, or more accurately, all of the time that follows the point when her ovaries become inactive.
Thus Norman came into use as a language of polite discourse and literature, and this fundamentally altered the role of Old English in education and administration, even though many Normans of the early period were illiterate and depended on the clergy for written communication and record-keeping.
Thus the transitional period in post-Soviet Russian politics came to an end.
Thus, if a metal is subject to lending guidance, dominant position holders may be required to lend tom-next, that is sell a tom-position and buy a cash-position, should the backwardation for that period exceed a certain exchange-set percentage.
Thus, the oldest pottery fragments found come from hillside settlements of the period between 7500 BC and 5000 BC.

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