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, the emperor could draw on sources not available to those with less puissant ancestors.

Thus, natural beryllium bombarded either by alphas or gammas from a suitable radioisotope is a key component of most radioisotope-powered nuclear reaction neutron sources for the laboratory production of free neutrons.

Thus, he challenged the arguments of clerical intellectuals who wanted to limit access to classical sources to prevent any moral harm to Christian readers.

Thus different sources give sometimes wildly different accounts of the number of languages within a family.

Thus additional revenue is generated from two sources.

Thus, for instance, forces that act on particles are frequently derived from fields ( electromagnetic or gravitational ), and particles generate fields by acting as sources.

Thus, best educated opinions and available statistics are the primary sources of information.

Thus distant suppliers can be cheaper than local sources ( e. g., New York City buys a lot of electricity from Canada ).

Thus when N is very large, the signal-to-noise ratio is very large as well, and any relative fluctuations in N due to other sources are more likely to dominate over shot noise.

Thus, sources state that Caius was the uncle of Saint Susanna.

Thus, these programs encouraged the development of alternative sources of supply of these essential materials.

Thus, the period of colonialism brought in sources for raw materials and captive markets for exports, while decolonialization brought new opportunities in the form of dependence.

: Thus, in Bergsland & Vogt ( 1962 ), the authors make an impressive demonstration, on the basis of actual language data verifiable by extra-linguistic sources, that the " rate of change " for Icelandic constituted around 4 % per millennium, whereas for closely connected Riksmal ( Literary Norwegian ) it would amount to as much as 20 %.

Thus, OSX 10. 4, Tiger, was never supported except by porting from sources.

Thus the location of Joseon as in these earlier sources is not clear.

Thus some sources attribute the use of the phrase " OK " to Van Buren and his supporters.

Thus a neon lamp can be used to distinguish between AC and DC sources and to ascertain the polarity of DC sources.

Thus the MSE results from pooling all these sources of error, geometrically corresponding to radius of a circle within which 50 % of rounds will land.

Thus slowdowns, speed ups, improvements in the education of the labor force and all sorts of things will appear as ’ technical change ’ ” Since then more specific descriptions of productivity sources have emerged referring to investment, innovations, skills, enterprise and competition ( ONS 3, 20 ).

Thus although he named the infant Ninan Cuyochi as his first heir but sources differ as to whether the boy died first, was unacceptable because of an unfavorable divination, or even if Huayna simply forgot that he had named him when asked to confirm the nomination.

Thus, the surface-supplied diver is much less likely to have an " out-of-air " emergency than a SCUBA diver as there are normally two alternative air sources available.

Thus, multiple sources that come from inside the Nizari Ismaili community strongly indicate that the Aga Khan IV is viewed by Nizari Ismailis as the incarnation of God or manifestation of God, or as having a portion of God inside of him ( and thereby being divine ) – as was the case with his grandfather ( based on available historical information ), the Aga Khan III.

Thus a system of counting money emerged from two different sources: In the Roman Empire 12 denarii were rated equal to 1 gold solidus – a 4th century Roman coin that was rare but which still circulated ; and, since 240 denarii were cut from one Roman libra of silver valued at 1 gold solidus, 240 denarii therefore equalled one pound in Britain ( also livre in France, peso in Spain etc.

Thus Paschen's law is not valid if there are external electron sources.