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, most security researchers set maximum times ( such as 14 days or 30 days ) before fully revealing a vulnerability to the public, since otherwise many vendors would never fix even critical vulnerabilities in their products.

" Thus, in March 2011 a team of researchers assembled 27 male volunteers and analyzed their pre-ejaculate samples within two minutes after producing them.

Thus, researchers have devised methods such as altering the sleep schedule for a span of days following a REM deprivation period and combining sleep-schedule alterations with pharmacotherapy to prolong this effect.

Thus, this experimental setup allows the researchers to look at the gambling behavior of the animals.

Thus, due to the painstaking labour of these musicians and researchers, there now exists a stable and definitive collection of Thyagaraja's music.

Thus, while researchers may know what factors are important to their inquiry, they may have difficulty understanding which methodologies will result in the most informative findings.

Thus, there is no practical purpose or favorable cost / benefit ratio for this, except for people like zoo handlers, researchers, and circus artists who deal closely with venomous animals.

Thus, some researchers have argued that economic development also plays a factor in the establishment of peace.

Thus, this method is empirically feasible and, as a result, it is very popular among researchers.

Thus, the data in eHRAF Archaeology can allow researchers to determine whether evolutionary patterns in one region are repeated in others, and to determine whether the presumed causal factors in one region are important, and antecedent, in other world regions too.

Thus, the Social Animal's explanations of human behavior are largely validated with citations of studies done by researchers of social psychology.

Thus, specialists, researchers, professors and students from all over Europe mix on the site every summer in order to excavate different parts of the site.

Thus, only a neatly composed chronology of rulers may serve as a good basis for researchers.

Thus, urea is typically utilized for gel preparation ; however, researchers need to be aware that the amount of urea used will have an impact on the overall temperature required to separate the DNA ( Biometra, 2000 ).

Thus, the researchers conclude by noting that the p53 mutation may not be the sole indicator of pancreatic carcinoma oncogenesis.

Thus the SSRC frequently acted as an intermediary between researchers and research-supporting foundations, assuming the functions of assessing research priorities and disbursing research funds.

Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus, the avant-garde choreographers have extended the scope of materials available for dance composition.

Thus he complains, with considerable justice, that the Tory writers have resorted to libel instead of answering his arguments.

Thus we will have a society consisting of the planners or conditioners, and the controlled.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus far the advances made have been almost entirely along functional lines.

Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

Thus, we have no part, and want none, in current discussions of the relative importance of science, the social studies, the humanities, the creative arts.

Thus, when you have prepared your foundation and laid the floor, these can be trucked to the site and erected with a small crew of friends in a weekend.

Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus in it's incredible what that boy can eat dominant stress is likely to be on incredible, and eat will have strong stress also.

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus when yes, I have is the response to have you finished reading the paper??

Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.

Thus far, the cases which have come before the courts have involved only the issue of referral where the job is vacant due to a strike -- condition ( 1 ) in the Regulation of the Secretary.

Thus he will be in a position to disabuse the Soviet leader of any notions he may have about grave Allied disunity.

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, in `` The Story Of Ruth '' we have Ruth, Naomi, and Boaz and sets that are meticulously authentic.

Thus we have the De officiis ministrorum, De viduis, De virginitate and De paenitentia.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.