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 cocktail party would appear to be the ideal system, but there is one weakness.

Thus, an enemy would probably use this weapon for attack on static population centers such as large cities.

Thus in independent voting, Af or 0.52 of the couples would agree.

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, for hydrogen chloride, the IUPAC name would be aqueous hydrogen chloride.

Thus, the MCC would not complete road construction.

Thus she, through whom salvation was being prepared for all people, would be the first to receive the promised fruit of salvation.

Thus, there was seen a need for a new law that would ensure the continuance of the succession following the death of the last legal heir under the Bill of Rights, being Princess Anne, guaranteeing the line of succession would continue in the Protestant line, and excluding any possible claims by the deposed James II or his son and daughter, James Francis Edward and Louisa Maria Teresa Stuart.

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 there are alignments in all directions which would suggest there is little of astronomical significance, However, ethnohistorical records show that the various directions do have cosmological and astronomical significance with various points in the landscape being significant at different times of the year.

Thus, " Armageddon " would mean " Mountain of Assembly ," which Jordan says is " a reference to the assembly at Mount Sinai, and to its replacement, Mount Zion.

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, as with other proposed megafauna cryptids, climate and food supply issues would make such a creature's survival in reported habitats unlikely.

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 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 the world would be seen as " what is among the ground and the sky ", and " Blissymbols " would be seen as " the writing tool to express the world ".

Thus, the universe would have been even more special before the thermalization than after .” The problem of specific or “ fine-tuned ” initial conditions would not have been solved ; it would have gotten worse.

Thus, a week of Beetle Bailey would arrive at the Lansing State Journal in two sheets, printed much larger than the final version and ready to be cut apart and fitted into the local comics page.

Thus criminal law grew out what 21st-century lawyers would call torts ; and, in real terms, many acts and omissions classified as crimes actually overlap with civil-law concepts.

Thus, a catalyst that could change the equilibrium would be a perpetual motion machine, a contradiction to the laws of thermodynamics.