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, infection rates in small-world networks can be reduced somewhat if interactions between individuals within infected hubs are eliminated ( Figure 1 ).

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus, in Bakunin ’ s words: “ All that individuals can do is to clarify, propagate, and work out ideas corresponding to the popular instinct ”.

Thus, only a limited number of individuals were hired as scribes to be trained in its use.

Thus, parents may receive inspiration from God in raising their families, individuals can receive divine inspiration to help them meet personal challenges, church officers may receive revelation for those whom they serve.

Thus prosecutions have been possible of such individuals as Nazi war criminals and officials of the German Democratic Republic responsible for the Berlin Wall, even though their deeds may have been allowed or even ordered by domestic law.

Thus, engaging in the commercial world is a legitimate means to achieving a livelihood, but individuals should participate in modern society as little as possible.

Thus other than the prophets mentioned in the Quran, Ahmadis, with support from theological study also recognize Buddha, Krishna, founders of Chinese religions to be divinely appointed individuals.

Thus, to propagate freedom means to present individuals with the truth and give them a choice to accept or deny it.

Thus in the graph of the demand curve, individuals ' demand curves are added horizontally to obtain the market demand curve.

A person ’ s satisfaction is not part of any greater satisfaction .’ Thus the aggregation of utility becomes futile as both pain and happiness are intrinsic to and inseparable from the consciousness in which they are felt, rendering impossible the task of adding up the various pleasures of multiple individuals.

Thus, individuals with 5-ARD are not able to carry a pregnancy, and, since they have testes and not ovaries, they are unable to create ova, which precludes such infertility treatments as surrogate motherhood.

Thus rather than " nurture ", behavior geneticists distinguish shared family factors ( i. e., those shared by siblings, making them more similar ) and nonshared factors ( i. e., those that uniquely affect individuals, making siblings different ).

Thus, a major shift in focus, from concern for the individual ’ s moral behavior to concern for the individuals theological practices, occurred with the post-Reformation morality plays.

Thus, the carrying capacity is the number of individuals an environment can support without significant negative impacts to the given organism and its environment.

Thus, as individuals develop, morphogens activate or silence genes in an epigenetically heritable fashion, giving cells a " memory ".

Thus, Burgess concludes his argument that Nepotianus father of Nepos, and the military commander Nepotianus, should be considered as two different individuals.

Thus, written records tend to reflect the biases, assumptions, cultural values and possibly deceptions of a limited range of individuals, usually only a fraction of the larger population.

Thus far, global efforts to curb and stymie the growing tide of smuggled individuals have been largely focused on the apprehension and deportation of individual migrants.

Thus, even the open or waiting worship of Quakers is liturgical, since the waiting itself until the Holy Spirit moves individuals to speak is a prescribed form of Quaker worship, sometimes referred to as " the liturgy of silence.

Thus a swarm of automated, self-directing drones can automatically patrol a city and track suspicious individuals, reporting their activities back to a centralized monitoring station.

Thus its view is called conditional predestination, since the predetermination of the destiny of individuals is based on God's foreknowledge of the way in which they will either freely reject Christ or freely accept him.

Thus, defamiliarization serves as a means to force individuals to recognize artistic language:

Thus cast appropriately, the parable regains its message to modern listeners: namely, that an individual of a social group they disapprove of can exhibit moral behavior that is superior to individuals of the groups they approve.