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, a new airport was planned to alleviate congestion.

Thus traffic congestion is rare in the town and usually only experienced in the town centre locally known as The Village.

Thus, to avoid network congestion, the protocol must include session bandwidth management.

Thus, by charging a higher per unit price and a lower lump-sum fee, the firm has generated area E more profit than if it had charged a lower per-unit price and a higher lump-sum fee.

Thus, the charging documents for a suspect charged with murder would be inscribed with " PC 187 ( a )" or just " PC 187 ".

Thus, " charging " the algorithm for the size of the input, or for the size of the output, would not truly capture the memory space used.

Thus, activists have collected more than 50, 000 signatures supporting their demands that the local government stop charging women to urinate, build more toilets, keep them clean, provide sanitary napkins and a trash can, and hire female attendants.

Thus, barrier options were created to provide the insurance value of an option without charging as much premium.

Thus 8-PSK is often omitted from standards and, as seen above, schemes tend to ' jump ' from QPSK to 16-QAM ( 8-QAM is possible but difficult to implement ).

Thus Bernard Madoff and Allen Stanford ran immense schemes for decades, raking in billions of dollars.

Thus the two enemies resumed their war, with Captain America, among other opponents, frustrating the Skull's schemes.

Thus, the pusher is required to be of high accuracy and speed and much effort is spent on optimizing the different schemes.

Thus, schemes were developed to inject pre-accelerated particle beams into a synchrotron.

Thus, in these situations, Exec Shield's schemes fails.

Thus the term has nothing to do with the biological aspects of carrying capacity, but is an economic term employed to imply that the transfer payment schemes of some developed countries might fail once the population declines to a certain point.

Thus, much like Alice, Wilma plays the strong-willed, level-headed person in her marriage, often criticizing Fred for pursuing his various ill-fated schemes.

Thus they would come up with an endless number of " get-poor-quick schemes ", much to the distress of their long-suffering bank manager.

" Thus, adopting a ' rejection for rejection's sake ' attitude, he entered tunnels of utter pessimism without any light at the end of them, with pictures of outrage, dirt and amorality working to convince the reader: no other, better life here would be possible anyway, for man-a scoundrel by nature, worshipping only the needs of his own flesh-is always ready to betray all things sacred for his egotistic schemes and lowly instincts ," Skabichevsky wrote.

Thus, the scheme serves mainly as a proof of concept, and more efficient provably-secure schemes such as Elgamal have been developed since.

Thus was born one of the most famous paint schemes in racing history.