Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus twenty `` black souls '' were to remain ignorant of their imminent journey to the land of free men.

Thus such great American documentaries as The River and The Plow That Broke The Plains were composed as visual stories rather than as illustrated lectures.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

Thus #, $ and % were placed to correspond to 3, 4, and 5 in the adjacent column.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

Thus, before the modern assembly line took shape, there were prototypical forms in various industries, as outlined below.

Thus Myspace and YouTube were not liable for a dyslexic man's inability to navigate the site regardless of how impressive the " online theater " is.

Thus we were spared the affliction of his absence and the triumph of suffering for his principles.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus while Persian-speakers were concentrated on the lower rungs of the work force, managers tended to be brought in from some distance.

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

Thus a third style, the " curved lip " style was produced, and all official and third-party cartridges during the console's lifespan were released ( or re-released ) using this style.

Thus, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.

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 the farmers were placed in a disadvantageous economic position.

Thus, dark blue jerseys, were introduced with white shorts and the red socks of 1908.

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 in 1880 and 1882, Benedictine teaching monks were effectively exiled ; this was not completed until 1901.

Thus, in 250-1, the Bastarnae were probably involved in the Gothic and Sarmatian invasions which culminated in the Roman defeat at the Battle of Abrittus and the slaying of the emperor Decius ( 251 ).

Thus parliamentary constituencies were derived from the ancient boroughs.

Thus far, the origins of the word remain inconclusive, as the term is not used outside Mexican-American communities, further indicating that the term is primarily self-identifying.

Thus greenhouses work primarily by preventing convective cooling.

Thus, the state required service from both the old and the new nobility, primarily in the military.

Thus, the convention that Sovereigns do not attend Cabinet meetings was established primarily through royal indifference to the everyday tasks of governance.

Expected to make use of devices with which listeners could press a button to indicate whether they liked or disliked a particular piece of music, Adorno bristled with distaste and astonishment: “ I reflected that culture was simply the condition that precluded a mentality that tried to measure it .” Thus Adorno suggested using individual interviews to determine listener reactions and, only three months after meeting Lasarzfeld, completed a 160-page memorandum on the Project ’ s topic, “ Music in Radio .” Adorno was primarily interested in how the musical material was affected by its distribution through the medium of radio and thought it imperative to understand how music was affected by its becoming part of daily life.

Thus, the most meaningful comparison of advantages and disadvantages is with other forms of local transit, primarily the local bus.

Thus, the creation of Turkish hip hop in Germany ( primarily through such groups as Cartel and Islamic Force ) that sought to address Turkish nationalist identities was born.

" Thus, many long-term investors, even those who buy and hold for decades, may be classified as speculators, excepting only the rare few who are primarily motivated by income or safety of principal and not eventually selling at a profit.

Thus, a financial concept of capital should be adopted if the users of financial statements are primarily concerned with the maintenance of nominal invested capital or the purchasing power of invested capital.

Thus, in regard to stress or injury, the function of adenosine is primarily that of cytoprotection preventing tissue damage during instances of hypoxia, ischemia, and seizure activity.

Thus, in present-day ethnomusicology, an electrophone is considered to be only musical instruments which produce sound primarily by electrical means.

Thus, the elastic modulus of the bilayer is primarily determined by how much extra area is exposed to water when the lipid molecules are stretched apart.

Thus, whether or not the destruction of the press was legal depends primarily on the laws of the state of Illinois and the Nauvoo Charter.

Thus, Bellman – Ford is used primarily for graphs with negative edge weights.

Thus the struggle between metaphysics and scientific world-conception is not only a struggle between different kinds of philosophies, but it is also — and perhaps primarily — a struggle between different political, social and economical attitudes.

“ Since timing and levels of sexual activity are quite similar across France, Canada, Great Britain, and the U. S., the high U. S. rates arise primarily because of less, and possibly less-effective, contraceptive use by sexually active teenagers .” Thus, the cause for the discrepancy between rich nations can be traced largely to contraceptive-based issues.

Thus this particular Protestant ( primarily Methodist ) understanding of theosis is substantially different from that of the Roman Catholic, Orthodox, or Anglican Churches.

Thus the network has registered a sevenfold growth since independence, with the focus of the expansion primarily in rural areas.

Thus weights are primarily of interest for abelian Lie algebras, where they reduce to the simple notion of a generalized eigenvalue for space of commuting linear transformations.

Thus syllabic technique does not — in English — convey a metrical rhythm ; rather it is a compositional device: primarily of importance to the author, perhaps noticed by the alert reader, and imperceptible to the hearer.

Thus, the Company remains primarily as a charitable institution.

Thus, it remains primarily as a charitable institution.

Thus, while appearing to honor his pledge to increase suffrage, Louis-Philippe acted primarily to empower his supporters and increase his hold over the French Parliament.

Thus any algorithm that can be expressed primarily as operations on arrays and matrices can run almost as quickly as the equivalent C code.