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, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

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 ).

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus he prohibited the application of torture to children under fourteen years, though this rule had exceptions.

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, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers.

Thus it was the Aeginetans who, within 30 or 40 years of the invention of coinage in Asia Minor by the Ionian Greeks or the Lydians ( c. 630 BC ), introduced coinage to the Western world.

Thus, it has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations with interparticle separation distances, often being considerably greater than the individual particle diameter.

Thus the week cycle is by itself not a full calendar system ; neither is a system to name the days within a year without a system for identifying the years.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus the castrati came to supplant both boys ( whose voices broke after only a few years ) and falsettists ( whose voices were weaker and less reliable ) from the top line in such choirs.

Thus, southern Germany once more became part of the Frankish kingdom, as had northern Germany during the first years of the reign.

Thus it is unperturbed by complications such as leap years.

Thus, a multitude of Japanese emperors have ascended as children, as young as 6 or 8 years old.

Thus, in England and Wales or in Hong Kong, a person born on February 29, 1996, will have legally reached 18 years old on March 1, 2014.

Thus, despite Gemma's intimate connection with a powerful American politician, who was then director of the United Nations Relief and Rehabilitation Administration ( UNRRA ), it took two years to be cleared and sent to the United States.

The media, in an attempt to explain the ideology of Ayatollah Khomeini and the Iranian Revolution to a Western audience described it as a " fundamentalist version of Islam " by way of analogy to the Christian fundamentalist movement in the U. S. Thus was born the term " Islamic fundamentalist ", which would come to be one of the most common usages of the term in the following years.

Thus in March 1979 Colonel Muammar Gaddafi, who kept absolute power ( until his overthrow in 2011 referred to as " Guide of the Revolution "), after ten years as combined Head of State and Head of government of the Libyan Jamahiriya (" state of the masses "), styled Chairman of the Revolutionary Command Council, formally transferred both qualities to the General secretaries of the General People's Congress ( comparable to a Speaker ) respectively to a Prime Minister, in political reality both were his creatures.

Thus, Hannibal took the Romans by surprise a scant two years later in 218 BC by merely reviving and adapting the original Gaulish-Carthaginian invasion plan of his brother-in-law.

thumbThe backs of Series 14 and 15 100-baht banknotes first announced 20 October 2537 BE / AD 1994 and continued unchanged on the Series 15 of 22 October 2547 BE / AD 2004, depicted boys receiving instruction at a Buddhist wat in days of old ; pupils at a modern school flying the national flag ; and the inscription ( in translation ) " Education in our nation is of the first importance / therefore I shall diligently improve it ./ Thus remarked Rama V ." These were replaced without fanfare by Series 15 ( Revised ) 19 September 2548 BE / AD 2005, to depict Rama V freeing the slaves.

Thus the procedures of the Church tribunal were covered by papal secrecy ( called at that time secrecy of the Holy Office ), but the crime of the priest was not: " These matters are confidential only to the procedures within the Church, but do not preclude in any way for these matters to be brought to civil authorities for proper legal adjudication.