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, 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, 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, Abulafia in the 13th century assumed that the language spoken in Paradise had been different from Hebrew, and rejected the claim then current also among Christian authors, that a child left unexposed to linguistic stimulus would automatically begin to speak in Hebrew.

Thus, in the Hindu schools, if a claim was made that could not be substantiated by appeal to the textual canon, it would be considered as ridiculous as a claim that the sky was green and, conversely, a claim which could not be substantiated via conventional means might still be justified through textual reference, differentiating this from the epistemology of modern science.

Thus, similar to the claim put forward by the Provisional IRA after its split from the Official IRA in 1969, the Continuity IRA claims to be the legitimate continuation of the ' Irish Republican Army ' or Óglaigh na hÉireann.

Thus, SETE could not claim copyright on photographs or panoramas of Paris incorporating the lit tower.

Thus in A v United Kingdom, the Court dismissed a claim that a derogation lodged by the British government in response to the September 11 attacks was invalid, but went on to find that measures taken by the United Kingdom under that derogation were disproportionate .< ref >

Thus, there is a good basis for affirming the straightforward and traditional claim that the Epistle to Titus was authentically written by Paul.

Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.

Thus, this system negates the claim that taking away any of the flagellum's parts would render it useless.

Thus literate lay defendants often also claimed the right to benefit of clergy ; furthermore, as the Biblical passage used for the literacy test was always Psalm 51 ( Miserere mei, Deus ...-" O God, have mercy upon me ..."), an illiterate person who had memorized the psalm could also claim benefit of clergy.

Thus if we wish to claim that no-cloning is a uniquely quantum result, some care is necessary in stating the theorem.

Thus, for Rand, the fact that consciousness must itself possess identity implies the rejection of both universal skepticism based on the " limits " of consciousness and any claim to revelation, emotion or faith based belief.

Thus panentheism separates itself from pantheism, positing the extra claim that God exists above and beyond the world as we know it.

Thus, according to Wittgenstein, mental states are intimately connected to a subject's environment, especially their linguistic environment, and conceivability or imaginability arguments that claim otherwise are misguided.

Thus, they claim, to conceive of a particular apple and its redness is not to conceive of applehood or redness-in-general, so they question the source of the concept.

Thus, although they would admit from the problem of pretense, that at no one time can we claim to have access to another's mental state, they are not permanently unavailable to us.

Thus the mathematical formulation of the Alcubierre metric does not contradict the conventional claim that the laws of relativity do not allow a slower-than-light object to accelerate to faster-than-light speeds.

However, scholars agree that these words of Montanus exemplify the general practice of religious prophets to speak as the passive mouthpieces of the divine, and to claim divine inspiration ( similar to modern prophets stating " Thus saith the Lord ").

Thus, though the College lays claim to few examples of neo-classical design, the College Library stands as one of the earliest examples of English neo-Gothic architecture.

Thus Kito's main claim is that he is responsible for the cookie being so strongly associated with Chinese restaurants.