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 an equivalence relation over X, a partition of X, and a projection whose domain is X, are three equivalent ways of specifying the same thing.

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.

As Bush writes, " Thus science may implement the ways in which man produces, stores, and consults the record of the race " ( 8 ).

The absolute number of cancer cases attributed to exposure to gasoline, however, is low, estimated a few cases per year in the U. S. Thus, the decision to require fewer aromatics has been criticized on the grounds of opportunity cost: the hundreds of millions of dollars spent on process redesign could have been spent on other, more fruitful ways of reducing deaths caused by cancer or automobiles.

Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match.

Thus, although all people perceive visible radiation the same way, in terms of a continuum of color, people who speak different languages slice up this continuum into discrete colors in different ways.

Thus, cultural studies seeks to understand the ways in which meaning is generated, disseminated, and produced through various practices, beliefs and institutions.

Thus it would be irrational to act in ways that we know we would prefer later to undo.

Thus the study of racism can be seen, at least superficially, as the study of the ways that people with a certain skin color and cultural background are systematically mistreated by society at large.

Thus, by taking Scott to this territory and keeping him there for two and a half years, Emerson was breaking the law in three distinct ways.

Thus we have an incomparable clarity about the ways of thinking of a 13th century man.

Thus, for example,, which is just the statement that and are the only two ways of pairing three elements of a magma with two operations.

Thus, it appears that people's feelings and creative cognitions are interwoven in several distinct ways within the complex fabric of their daily work lives.

Thus, new world records for straitjacket escape are constantly being attempted, in various ways and with various degrees of difficulty added.

Thus, under English common law, there were two main ways an escheat could happen:

Thus, conscience can be viewed as an outcome of those biological drives that prompt humans to avoid provoking fear or contempt in others ; being experienced as guilt and shame in differing ways from society to society and person to person.

Thus in many ways it can be considered that " Harrison Bergeron " is a later version of the society seen in The Sirens of Titan, an idea supported by the later date, 2081, in which " Harrison Bergeron " is set.

Thus, DLB is similar in some ways to both the dementia resulting from Alzheimer's disease and the movement problems of Parkinson's disease.

Thus, one can know both the names Mark Twain and Samuel Clemens without realizing that they are about the same object, because they present that object in different ways, that is, they have different senses.

Thus, much like Ralph, Fred tends to be loud-mouthed, aggressive, and constantly scheming ways to improve his family's working class lot in life, often with unintended results.

Thus there are four possible ways of imprinting the first two circuits:

Thus the convergence of new methods of communication with new technologies shifts the model of mass communication, and radically reshapes the ways we interact and communicate with one another.

Thus, M is a space which has a point for every object that could appear in a family, and whose geometry reflects the ways objects can vary in families.

Thus, for example, Euclidean space, affine space and projective space are all in natural ways homogeneous spaces for their respective symmetry groups.

Thus, in many ways, structuration was "... an exercise in clarification of logical issues.