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, despite widely held popular belief outside the Orthodox cultures, there is not one bishop at the head of the Orthodox Church ; references to the Patriarch of Constantinople as a leader equivalent or comparable to a pope in the Roman Catholic Church are mistaken.

Thus the concept of the " Romantic period " may be meaningless outside of Europe and European-influenced cultures.

Thus, they are often interested in instinctive, or intuitive behavior, and in explaining the similarities, rather than the differences, between cultures.

Thus, by 1900, the Qing dynasty, which had ruled China for more than two centuries, was crumbling and Chinese culture was under assault by powerful and unfamiliar religions and secular cultures.

Thus the same words can mean different things to people from different cultures, even when they talk the " same " language.

To understand the full sweep and complexity of cultures across all of human history, anthropology draws and builds upon knowledge from the social and biological sciences as well as the humanities and physical sciences .” Thus, the field is divided into four subareas: Sociocultural Anthropology, Biological ( or Physical ) Anthropology, Archaeology, and Linguistic Anthropology.

Thus the phrase liberal elite suggests that liberals are unpatriotic, because they like other cultures and are disdainful of American life and culture.

Thus, some Mormon scholars view Lamanites as ( 1 ) one small tribe among many in the ancient Americas, the remainder of whom were not discussed in The Book of Mormon although they were implied or, ( 2 ) a tribe that intermarried with indigenous Native American cultures.

Thus, an erudite jurist has both deep, specific knowledge of the law, and broad knowledge in the form of social and historical context of law ; an erudite jurist may additionally know the laws of other cultures.

Thus, although two countries might both be capitalist, being economically based mainly on private enterprise for profit and wage labour, these capitalisms might be very different in social character and functioning, reflecting very different cultures, religions, social rules and histories.

Thus, old and new techniques and cultures might combine in novel and unique admixtures, which cannot be understood other than by tracing out the history of their emergence.

Thus, Kawaida is, in fact, a continuous dialog with African cultures, asking questions and seeking answers to central and enduring concerns of the African and human community.

Thus, the band's compositions were considerably more complex and their lyrics covered a broader range of topics, showcasing Grebenshchikov's notable erudition in Celtic and Indian cultures, among other things.

Thus, " Jewish " foods like bagels, hummus, stuffed cabbage, and blintzes all come from various other cultures.

Thus, the CDHK is able to train junior staff with both leadership qualities and experience in two cultures for the benefit of Chinese and German companies in China.

Thus, Coleman was animated to think about the role of music and the transmission of information in non-western cultures.

Thus he claimed the ancient Ukrainian Steppe cultures from Scythia, through Kievan Rus ' to the Cossacks as part of the Ukrainian heritage.

Thus, cultures can be distinguished by patterns of craftsmanship ; for instance, if one excavated sherd of pottery is decorated with a triangular pattern, and another sherd with a chequered pattern, they likely belong to different cultures.

Thus, they contend, primitivism becomes a process analogous to Exoticism and Orientalism, as conceived by Edward Said, in which European imperialism and monolithic and degrading views of the " East " by the " West " defined colonized peoples and their cultures.

Thus having had 6 centuries of direct cultural exposure to Western Christianity and other African influences, contemporary Itsekiri language and culture has successfully evolved into a hybrid of the many cultures that have influenced its development.