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Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.
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Thus and three
Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.
Thus, the three main categories of antisubmarine warfare operations are defense of shipping, defense of naval forces, and area defense.
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 two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array.
Thus, three eclipse calculations may be evidence for the suggestion that Romulus reigned from 746 BC to 709 BC, and Rome was founded during 745 BC.
Thus, negotiation generally features only in games for three or more people.
Thus, an outdoors utility knife suited for camping or hunting might use a broad three to five-inch fixed blade, while a utility knife designed for the construction industry might feature a replaceable utility or razor blade for cutting packaging, cutting shingles, marking cut lines, or scraping paint.
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, for example, there are three main isotopes of carbon.
Thus the overall ratios of the three coinages remained roughly equivalent.
Thus the first two games were played at Wrigley Field and the next three at the home of their opponents, San Diego.
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 every proposition has three components: the two terms, and the " copula " that connects or separates them.
Thus, all three models for paramagnetic Hb-O < sub > 2 </ sub > may contribute to some small degree ( by resonance ) to the actual electronic configuration of Hb-O < sub > 2 </ sub >.
Thus as a result of the three Carnatic Wars, the British East India Company gained exclusive control over the entire Carnatic region of India.
Thus it happened that, with Hermes as their guide, the three candidates bathed in the spring of Ida, then confronted Paris on Mount Ida in the climactic moment that is the crux of the tale.
Thus, every MUMPS command or function name could be abbreviated from one to three letters in length, e. g. Quit ( exit program ) as Q, $ P
Thus the Arabic word ثلاثة ( three ) is transliterated ṯalāṯah.
Thus, for example, the term " glucose " may signify glucofuranose, glucopyranose, the open-chain form, or a mixture of the three.
Thus Antony, as Caesar's key adherent and one of the two men around whom power coalesced following his assassination, was one of the three men chiefly responsible for the fall of the Roman Republic.
Thus, a player who bids three and takes either two or four tricks will lose one point.
Thus a collection of two lines is a couplet ( or distich ), three lines a triplet ( or tercet ), four lines a quatrain, and so on.
Thus represents a sequence of three phonemes,, ( the word push in standard English ), while represents the phonetic sequence of sounds ( aspirated " p "),, ( the usual pronunciation of push ).
Thus and major
Thus, mD represents a case with hypomania and major depression.
Thus far, pyrethroid resistance in Anopheles has not been a major problem.
Thus, there is the idea that in the capitalist mode of production the behaviour of actors in the market economy ( means of production, distribution and exchange, the relations of production ) plays the major role in configuring society.
Thus, it has been suggested that Adams is the only major figure in American history who knew both the Founding Fathers and Abraham Lincoln, though Martin Van Buren knew Founding Fathers Thomas Jefferson and his mentor Aaron Burr and met the young Lincoln while on a campaign trip through Illinois.
" Thus, one does not find in his work a theoretical attempt to discern what constitutes a major work or a work of art, or even handicraft.
Thus, while there was a good measure of debate in the Early Church over the New Testament canon, the major writings are claimed to have been accepted by almost all Christians by the middle of the 3rd century.
Thus, the Phillies became the last of the 16 teams that made up the major leagues from 1901 to 1961 to win a World Series.
Thus, Adobe Photoshop CS6 is the 13th major release of Adobe Photoshop.
Thus at the Battle of Lake Khasan, in 1938, and the Battle of Khalkhin Gol, in 1939, major border clashes with the Imperial Japanese Army, the doctrine was not used.
Thus, sexual selection takes two major forms: intersexual selection ( also known as ' mate choice ' or ' female choice ') in which males compete with each other to be chosen by females ; and intrasexual selection ( also known as ' male – male competition ') in which members of the less limited sex ( typically males ) compete aggressively among themselves for access to the limiting sex.
Thus, there are three major families of superoxide dismutase, depending on the metal cofactor: Cu / Zn ( which binds both copper and zinc ), Fe and Mn types ( which bind either iron or manganese ), and the Ni type, which binds nickel.
Thus, a notrump opener who holds at least four cards in each major suit should " correct " by bidding the other major suit at the lowest level.
Thus, those carrying out the traditions will not be consciously aware of the change, and even if a tradition undergoes major changes over many generations, it will be seen as unchanged.
Thus, planets are allowed to fight out internal wars, and capitalism is the major driving force of civilization.
Thus modern political theorists typically legitimize the state with two major ideas: redistribution and the provision of public goods.
Thus the United States would have to make several major modifications to its copyright law in order to become a party to it.
Thus, evidence of major changes in religious concepts may be recorded only in fragments of myths that supersede and later, obscure the originals.
Thus, a major shift in focus, from concern for the individual ’ s moral behavior to concern for the individuals theological practices, occurred with the post-Reformation morality plays.
Thus, there are depressive disorders, of which the best-known and most researched is major depressive disorder ( MDD ) commonly called clinical depression or major depression, and bipolar disorder ( BD ), formerly known as manic depression and characterized by intermittent episodes of mania or hypomania, usually interlaced with depressive episodes.
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 major peculiarities of the ancient Greek political system were ; firstly, its fragmentary nature, and that this does not particularly seem to have tribal origin ; and secondly the particular focus on urban centres within otherwise tiny states.
Thus the major modern Israeli city of Tel Aviv means " Spring Hill ".
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