Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus he may be referring to some concrete thing, or incident, in his immediate environment by some symbolic-sounding, hyperbolic reference to transcendental events on the global scene.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

Thus, although some things may be certain, they have little to do with Dasein's sense of care and existential anxiety, e. g., in the face of death.

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

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Thus one finds brass instruments made of wood, like the alphorn, the cornett, the serpent and the didgeridoo, while some woodwind instruments are made of brass, like the saxophone.

Thus fines and noncustodial sentences may address the crimes seen as least serious, with lengthy imprisonment or ( in some jurisdictions ) capital punishment reserved for the most serious.

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 literary criticism became highly theoretical and some of those practicing it began referring to the theoretical dimension of their work as " critical theory "-a philosophically inspired theory of literary criticism.

Thus miniatures were no longer required for game play, although some players continued to use them as a visual reference.

Thus, though the former understanding certainly enjoys the greatest popularity, the identification of Plotinus ’ opponents as Gnostic is not without some contention.

Thus, while D-Cinema is a defined standard, though one that is still partly being framed by SMPTE as of 2007, E-Cinema may be anything, ranging from a DVD player connected to a consumer projector to something that approaches the quality of D-Cinema without conforming to some of the standards.

Thus in some cases a single entity can essentially maintain controlling interest with only 33. 4 % of the outstanding shares.

Thus, some individuals and institutions will enter into a derivative contract to speculate on the value of the underlying asset, betting that the party seeking insurance will be wrong about the future value of the underlying asset.

Thus since the landscape is still recovering from the weight of the glaciers and going through post-glacial rebound and the turmoil this created, the landscape is poorly drained creating the numerous lakes and rivers found in Cass County.

Thus, the initial defeat was covered up by his propagandists, by a very heroic ( and Homeric ) charge into the teeth of an extremely poorly deployed enemy.

Thus the claim that circumcision adversely affects penile sensitivity is poorly supported, and this study provides no evidence for the belief that circumcision adversely affects sexual pleasure.

Thus El Centro de la Raza became very multiethnic from the beginning, interpreting its name as " The Center for the People of All Races " ( when poorly translated without context it means " The Center of the Race ").

Thus, slow-start can perform poorly in situations with poor reception, such as wireless networks.

Thus, pain is poorly localized, and the level of pain stemming from pulpitis varies based on severity, quality, duration, onset, trigger.

Thus, when Gregory was selected as a candidate for the bishopric of Constantinople, both Alexandria and Rome opposed him because of his Antiochene background.

Thus " better " memes are selected.

Thus in July 1981 " VME2900 " was launched: although presented to the customer base as a merger of VME / B and VME / K, it was in reality the VME / B base with a few selected features from VME / K grafted on.

Thus, in 2008, the women's foil and sabre events and men's épée were automatically selected.

Thus, when a township name needed to be selected, the Dewalds outnumbered the Churchills two-to-one.

Thus, because the " female template " is the default for humans, the question is not why evolution has not selected against male nipples, but why it would be advantageous to select against male nipples to begin with:

Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in the latter case.

Thus, when a non-monk was selected to replace St-Calais, the monks began a long struggle to secure what they felt had been promised to them, including the forging of charters ascribed to St-Calais that supported their case.

Thus, the basic method of navigation using Guide was the expansion button, in which a section was replaced when selected and in which an expansion would provide additional levels of detail.

Thus, while his son Tokugawa Hidetada was the second shogun, he selected three other sons to establish the gosanke, hereditary houses which would provide a shogun if there were no male heir.

Thus, it would appear that the name of St. Clements was selected by the rhymer simply for its consonance with the word ‘ lemons ’, and it now seems more likely that the melody called ‘ Oranges and Limons ’ predates the rhyme itself.

Thus it may be in an agency's assets interest to switch its focus from its officially-designated consumers to a carefully selected clientele of constituents that will aid the agency in its quest for greater political influence.

Thus if God commanded us " to gratuitously inflict pain on each other " or to engage in " cruelty for its own sake " or to hold an " annual sacrifice of randomly selected ten-year-olds in a particularly gruesome ritual that involves excruciating and prolonged suffering for its victims ", then we would be morally obligated to do so.

Thus, the slots were limited as teams were selected from conferences and regional champions and multiple teams from the same conferences were not allowed.

Thus, he was not drafted until the 13th round of the 1999 Major League Baseball ( MLB ) Draft, when the St. Louis Cardinals selected him with the 402nd overall pick.

Thus, the base rate probability of a randomly selected inhabitant of the city being a terrorist is 0. 0001, and the base rate probability of that same inhabitant being a non-terrorist is 0. 9999.

Thus, a simultaneous chain reaction develops, resulting in exponential amplification of the selected target sequence ( see Vincent et al .., 2004 for a schematic diagram ).

Thus all of the programming was handled by many " soft " buttons and one data slider that controlled the selected parameter.

Thus, men who display this signal of sexual obedience, may gain social benefits, if married men are selected to offer social trust and investment preferentially to peers who are less threatening to their paternity.

Thus, there would be one Constabulary Headquarters for the entire United States Zone, a brigade headquarters at each of the capitals of the three German Länder, and group, squadron, and troop headquarters established at points selected for ease in performing the mission.

Thus, the church selected a group of its most charismatic and devoted priests and sent them on a mission to proselytize the people of the West.

Thus in regions where malaria exerts or has exerted a strong selective pressure, sickle cell anemia has been selected for its conferred partial resistance to the disease.

The motto selected for the obverse of the Virginia seal is Sic semper tyrannis, or in English, Thus always to tyrants.

Thus, due to his strong leadership skills and popularity, Hoang was selected to take command of Viet Cong forces for operations in Ap Bac.