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, he believed real charity supplied the means for those who wish to help themselves, achieve their goals.

Thus for iconoclasts the only true ( and permitted ) " icon " of Jesus was the Eucharist, which was believed to be his body and blood.

Thus, to say the name of the play inside a theatre is believed to doom the production to failure, and perhaps cause physical injury or death to cast members.

Thus, Rajaratnam believed that maintaining a balance of power, rather than becoming a de-facto vassal of some larger power, would provide Singapore with freedom to pursue an independent foreign policy.

Thus, the mountains that were believed to be the residence of spirits in pre-Buddhist times became the sites of Buddhist temples.

Thus conjunctions are believed to operate with a larger orb than sextiles.

Thus, Han-era physicians prescribed medicine that was believed to counteract this imbalance.

Thus, many believed that tribes organize links between families ( including clans and lineages ), and provide them with a social and ideological basis for solidarity that is in some way more limited than that of an " ethnic group " or of a " nation ".

Thus, they were classified as a single species V. cholera: however, Hugh believed the differing features between the two could be of epidmiological importance, so El Tor vibrios were further classified as V. cholerae biotype eltor ( serogroup O1 ).

Thus, all heterokonts are believed to descend from a single heterotrophic ancestor that became photosynthetic when it acquired plastids through endosymbiosis of another unicellular eukaryote.

Thus it is believed that the name of the site derived from a reference to " Oswald's Tree ".

Thus, many players believed they had no option but to cheat in order to see more than a fraction of it, by asking the first Pygmy to his right about " ten pints ".

Thus the Cyrenaics believed in the hedonistic value of social obligation and altruistic behaviour.

" Thus, Luther believed that restoring the gospel was the first step in renewing the church, rather than restoring biblical forms and patterns.

Thus, the mountains that were believed to be the residence of spirits in pre-Buddhist times became the sites of Buddhist temples.

Thus Magellan believed wrongly that since Rajah Humabon was the " king " of Cebu, he was the king of Mactan as well.

Thus Mold Alexandra were back where they believed they should have been twelve months earlier, rebuilding at level 3 in the pyramid.

Thus, in the inaugural issue of The American Review, Collins praised Benito Mussolini for creating an ethical state which protected workers and small businesses and also wrote favorably of the election of Adolf Hitler to Chancellor of Germany whose new program, Collins believed, heralded the end of the Communist threat.

Thus, by knowing the process and praising it, Koreans believed that the god would eventually solve their problems.

Thus, though hard proof is lacking but given the extent of possible habitat and the precautionary principle, it is believed to be extant for the time being.

Thus, he believes that they are closer to the solution than they previously believed, and notifies Mr. Carter that he believes the pieces of Tuppence's clothing were fakes.

Thus, it was believed to be better prepared for the role than any unit in the police or elsewhere in the armed forces.

Thus Musa al-Kazim who was believed to be poisoned by the Abbasid Caliph Harun was in fact a veil ( hijab ) for his elder brother Ismail.

Thus, the Balts ' culture is believed to have preserved primeval features of Indo-European culture for a longer time.