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 with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.

Thus the member of an industrial union comes to regard his officers as business agents who may proceed without interference or recall ; ;

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus, Henri's own short-sightedness in this regard jeopardized the alliance between Legitimists ( Bourbons ) and Orleanists.

Thus, theoretical physicists tend to regard these dimensionless quantities as fundamental physical constants.

Thus, in regard to this matter and this document, either one of two explanations is commonly held:

Thus the standard was created by taking a union of the features in all proposals with no regard to their coherence.

Thus, one might regard it as a " new political economy.

Thus, according to Paul L. Maier, the majority of Herod biographers and theologians hold that the Massacre of the Innocents is " legend and not historical ": Geza Vermes and E. P. Sanders, for example, regard the story as part of a creative hagiography.

Thus, owing to an argument between the two in regard to the source or cause of the electricity, Volta built the first battery in order to specifically disprove his associate's theory.

Thus, in regard to stress or injury, the function of adenosine is primarily that of cytoprotection preventing tissue damage during instances of hypoxia, ischemia, and seizure activity.

Thus, the formal organization is expected to behave impersonally in regard to relationships with clients or with its members.

Thus, the formal organization is expected to behave impersonally in regard to relationships with clients or with its members.

Thus, these attorneys may freely advise clients as to these matters anywhere in the jurisdiction of the United States without regard to state court or bar association rules.

Thus 1 Corinthians 4: 1: " No one should regard us as anything else than ministers of Christ and dispensers of the mysteries of God.

Thus, many now regard them as Christian anarchists.

for any p in M and smooth function f. Thus we can regard covector fields not just as sections of the cotangent bundle, but also linear mappings of vector fields into functions.

Fatherhood was therefore recognised as a social role ; the woman's husband is the " man whose role and duty it is to take the child in his arms and to help her in nursing and bringing it up "; " Thus, though the natives are ignorant of any physiological need for a male in the constitution of the family, they regard him as indispensable socially ".

Thus, poems such as Tang Dynasty poems and other Chinese poetry may be read as either heterosexual or homosexual, or neutral in that regard, depending on the reader's desire.

Thus editor Horace Greeley in 1838 started a magazine, The Jeffersonian, that he said " would exhibit a practical regard for that cardinal principle of Jeffersonian Democracy, and the People are the sole and safe depository of all power, principles and opinions which are to direct the Government.

Thus UK courts refused to regard sales and repurchases ( known as bed-and-breakfast transactions ) or back-to-back loans as tax avoidance.

Although there is still ongoing debate about the Jewish Christian Gospels and " only the very daring, nowadays, venture on speculations in regard to the Gospel of the Hebrews ", most scholars agree with Schneemelcher when he says, " Thus the number of Jewish Gospels -- whether there be one, two or three such gospels -- is uncertain, the identification of the several fragments is also uncertain and, finally the character and the relationship to one another of the several Jewish gospels is uncertain.

Thus it permits Eastern Christians who are not in full communion with the Roman Catholic Church ( Eastern Orthodox Church, Oriental Orthodoxy and Assyrian Church of the East ) to receive Communion from Roman Catholic ministers, if they request it of their own accord and are properly disposed, and it applies the same rule also to some Western Churches that the Holy See judges to be in a situation similar to that of Eastern Christians with regard to the sacraments.

Thus, the Chief Justice's role in this regard is a limited one.