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, giving grades and promotions based only on an individual's performance relative to a small local group, as is common, may reduce cooperative behaviors in the group.

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, even when reception was effected by a constitution, the common law was still subject to alteration by a legislature's statute.

Thus, if two species use the same codon at the same place to specify an amino acid that can be represented by more than one codon, that is evidence for a recent common ancestor.

Thus was born a new type of beef cattle for Central Brazil, with the name CANCHIM, derived from the name of a tree very common in the region where the breed was developed.

Thus, while values above one are common for newborns, the ratio dwindles until it is well below one for the older population.

Thus, a 7A is a common jazz stick with a wooden tip, while a 7N is the same weight of stick with a nylon tip, and a 7B is a wooden tip but with a different tip profile, shorter and rounder than a 7A.

Thus, in Alaska, Eskimo is in common usage, and is the preferred term when speaking collectively of all Inupiat and Yupik people, or of all Inuit and Yupik people throughout the world.

Thus, Kraepelin's system is a method for pattern recognition, not grouping by common symptoms.

Thus, any other number c that divides both a and b must also divide g. The greatest common divisor g of a and b is the unique ( positive ) common divisor of a and b that is divisible by any other common divisor c.

Thus, g is the greatest common divisor of all the succeeding pairs:

Thus, 21 is the greatest common divisor of 1071 and 462.

The media, in an attempt to explain the ideology of Ayatollah Khomeini and the Iranian Revolution to a Western audience described it as a " fundamentalist version of Islam " by way of analogy to the Christian fundamentalist movement in the U. S. Thus was born the term " Islamic fundamentalist ", which would come to be one of the most common usages of the term in the following years.

Thus, although there is an esoteric tradition in Judaism ( Kabbalah ), Rabbinic scholar Max Kadushin has characterized normative Judaism as " normal mysticism ", because it involves everyday personal experiences of God through ways or modes that are common to all Jews.

Thus in common colloquy the drinking cup is referred to as yunomi-jawan or yunomi for the purpose of distinction.

Thus a leader or important man will be characterised as generous, according to one common convention, and called an " enemy of gold ", " attacker of treasure ", " destroyer of arm-rings ", etc.

Thus, the " pencil beam " directly generated by a common helium-neon laser would spread out to a size of perhaps 500 kilometers when shone on the Moon ( from the distance of the earth ).

Thus, the most common letter in English, the letter " E ," has the shortest code, a single dot.

Thus, any system of policies that benefited one group would by definition harm the other, and there was no possibility of economics being used to maximize the " commonwealth ", or common good.

Thus, in several languages of the Banks Islands, including Mwotlap, the simple m stands for, but an m with a macron ( m ̄) is a labial-velar nasal ; while the simple n stands for the common alveolar nasal, an n with macron ( n ̄) represents the velar nasal ; the vowel ē stands for a ( short ) higher by contrast with plain e ; likewise ō contrasts with plain o.

Thus, the term is more one of common application to macroscopic fungal fruiting bodies than one having precise taxonomic meaning.

Thus the court accepted that a modified doctrine of tenure operated in Australia, and that the law of tenure ( as a product of the common law ) could co-exist with the law of native title ( as a product of customary laws and traditions ), though where there had been a valid grant of fee simple by the Crown the latter title would be extinguished.

Thus the term nucleon number may be used in place of the more common terms mass number or atomic mass number.