Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

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 we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus the multiplicity of Af for a given T must be an even number.

Thus, casework involving a limited number of interviews is still to be regarded in terms of the quality of service rendered rather than of the quantity of time expended.

Thus a number of operations of the order of Af are required.

Thus the middle number, 5, represented Sung-Shan in Honan, Central China ; ;

Thus a simple count of the number of distinct symbols is an important clue to the nature of an unknown script.

Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

Thus, almost all positive integers are composite ( not prime ), however there are still an infinite number of primes.

The evaluation order does not affect the value of such expressions, and it can be shown that the same holds for expressions containing any number of operations .< ref > Thus, when is associative, the evaluation order can be left unspecified without causing ambiguity, by omitting the parentheses and writing simply:

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

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, when the fluid finally does strike the object, it is forced to change its properties -- temperature, density, pressure, and Mach number -- in an extremely violent and irreversible fashion called a shock wave.

Thus, in the mid-1990s the army sought to reduce the number of active-duty generals.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

Thus, a PICMG backplane can provide any number and any mix of ISA, PCI, PCI-X, and PCI-e slots, limited only by the ability of the SBC to interface to and drive those slots.

Thus, a number of Allied soldiers received the Bronze Star Medal in World War II, as well as U. N. soldiers in the Korean War, Vietnamese and allied forces in the Vietnam War, and coalition forces in recent military operations such as the Gulf War, Operation Enduring Freedom and the Iraq War.

Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may differ in number of neutrons.

Thus, a poison that covers surface randomly will tend to reduce the number of uncontaminated large planes but leave proportionally more smaller sites free, thus changing the hydrogenation vs. hydrogenolysis selectivity.

Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.

Thus on 28 December 1852, the Earl of Aberdeen appointed Palmerston as Home Secretary and appointed John Russell as Foreign Minister.

Thus from October 1, 1814, to February 28, 1815, Monroe effectively held both cabinet posts.

Thus, on April 28, 2006, after the unofficial repeal of the French First Employment Contract ( CPE ), the Longjumeau ( Essonne ) conseil des prud ' hommes ( labour law court ) judged the New Employment Contract ( CNE ) contrary to international law, and therefore " illegitimate " and " without any juridical value ".

Thus, on November 28, 1821, the national assembly was convened and it was officially declared ( through Fábrega, who was invested with the title of Head of State of Panama ) that the isthmus of Panama had severed its ties with the Spanish Empire and its decision to join New Granada and Venezuela in Bolivar's recently founded Republic of Colombia.

Thus, on July 28, Seward was able to certify unconditionally that the amendment was part of the Constitution without having to endorse the Congress's assertion that the withdrawals were ineffective.

Thus, the ARP packet size in this case is 28 bytes.

Thus, SPIN explored all of these approaches, and eventually it delivered a very large 28 " diameter fixed disk and also a smaller multi-platter 14 " removable disk-pack system.

Thus Hopkins could not have been born before 1619, and could not have been older than 28 when he died, but he may have been as young as 25.

Thus we find him at the head of the right wing at Monmouth on June 28, 1778.

Thus, the mass of an imperial fluid ounce of water is one avoirdupois ounce ( 28. 4 g ).

Thus from October 1, 1814, to February 28, 1815, Monroe effectively held both cabinet posts.

Thus, sympathy is never enough, as the " sole consolation " for the sufferer is " to see the emotions of their hearts, in every respect, beat time to his own, in the violent and disagreeable passions " ( p. 28 ).

Thus he began his career as a radio disc jockey on June 28, 1968 at radio station KUTY in Palmdale, California.

* November 28 – Thus far in the Spanish Civil War, Italy has sent about 24 Fiat CR. 32 fighters, 19 Savoia-Marchetti SM. 81 bombers, and some IMAM Ro. 37 reconnaissance aircraft to support the Nationalists.

Thus Stenton concluded that Deusdedit died on 28 October 663.

Thus, there are 16 wind tiles and 12 Dragon tiles for 28 honor tiles.

Thus, z words disappear in chapter 28, y in chapter 29, etc ...

Thus, they claim that the throne of David was transplanted by Jeremiah, via a daughter of King Zedekiah, the last king of Judah, to Ireland ( Jeremiah 43: 6 ), along with the stone of Jacob, which was named " The House of God " ( Genesis 28: 22 ), to Scotland and then to England, where the descendants of David, via the daughter of Zedekiah, are sitting on David ’ s throne today over the " House of Israel " who migrated there after having been transplanted by the Assyrians into northern Europe, then into Great Britain.

Thus, for example, a recent study observed that in 89 marriages contracted by men of the Dhulbahante clan, 55 ( 62 %) were with women of Dhulbahante sub-clans other than those of their husbands ; 30 ( 33. 7 %) were with women of surrounding clans of other clan families ( Isaaq, 28 ; Hawiye, 3 ); and 3 ( 4. 3 %) were with women of other clans of the Darod clan family ( Majerteen 2, Ogaden 1 ).

Thus, with three-quarters of the season gone, Prost was a full 28 points ahead and could sense the championship, having 81 points to Senna's 53.

Thus, with three-quarters of the season gone, Prost was a full 28 points ahead and could sense the championship, having 81 points to Senna's 53.

Thus, on June 28, 1975, Espada became the WBA's world Welterweight champion, and Puerto Rico's fourth world boxing champion in history, by outpointing the well known | Canadian, Clyde Gray, over fifteen rounds in San Juan.

Thus, for example, a recent study observed that in 89 marriages contracted by men of the Dhulbahante clan, 55 ( 62 %) were with women of Dhulbahante sub-clans other than those of their husbands ; 30 ( 33. 7 %) were with women of surrounding clans of other clan families ( Isaaq, 28 ; Hawiye, 3 ); and 3 ( 4. 3 %) were with women of other clans of the Darod clan family ( Majerteen 2, Ogaden 1 ).

Thus, a corrected table includes their 14 unique cases, plus 14 correct sign changed cases, so 28 cases in total.