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, the client can handle different requests, and commands can be scattered throughout the application.

Thus, in practice, the Council of Ministers cannot be dismissed as long as it commands the support of a majority in the Lok Sabha.

Thus, it was quite easy to write a client, as the incoming messages were very easy to parse, and outgoing commands were easy to generate.

Thus, plinkers do not generally use typical range commands and it is not uncommon for plinkers who do not use prescription lenses to go without eye protection.

Thus the language has commands that deal directly with the reading and writing of databases.

Thus William P. Alston writes, " since the standards of moral goodness are set by divine commands, to say that God is morally good is just to say that he obeys his own commands ... that God practises what he preaches, whatever that might be ", and Hutcheson deems such a view " an insignificant Tautology, amounting to no more than this, ' That God wills what he wills.

Thus, in practice, the Council of Ministers cannot be dismissed as long as it commands the support of a majority in the Lok Sabha.

Thus, screen update commands need only be sent once and this allows the use of a slower data connection, typically serial — a feature very well adapted to computer terminal use in 1960s and 1970s computing.

Thus, every officer or non-commissioned officer is in the land and air forces is generally named after the type of unit he commands, with the suffix-agos ( from agein, " to lead ") or-archos / arches ( from archein, " to rule ").

Thus, the uses are different — popup menus are used to select a single option from a list while pop-down menus are used to issue commands or in cases where multiple options can be selected.

Thus, we might provide limited assistance in such fields as education, essential transport, communications, and agricultural improvement despite the absence of acceptable country programs.

Thus, an enemy would probably use this weapon for attack on static population centers such as large cities.

Thus there are polynomials Af such that Af.

Thus such great American documentaries as The River and The Plow That Broke The Plains were composed as visual stories rather than as illustrated lectures.

Thus an algorithm can be an algebraic equation such as y

The evaluation order does not affect the value of such expressions, and it can be shown that the same holds for expressions containing any number of operations .< ref > Thus, when is associative, the evaluation order can be left unspecified without causing ambiguity, by omitting the parentheses and writing simply:

Thus while among his own colleagues he seemed merely a hypocritical and arrogant priest, in his relations with his brother humanists, such as Cosimo de ' Medici, he appeared as the student of classical antiquities and especially of Greek theological authors ".

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

Thus, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.

Thus, as with other proposed megafauna cryptids, climate and food supply issues would make such a creature's survival in reported habitats unlikely.

Thus, the Big Bang theory cannot and does not provide any explanation for such an initial condition ; rather, it describes and explains the general evolution of the universe going forward from that point on.

Thus permanent building societies quickly became mortgage banks and in such institutions there always existed a conflict of interest between borrowers and savers.

Thus, a number of Allied soldiers received the Bronze Star Medal in World War II, as well as U. N. soldiers in the Korean War, Vietnamese and allied forces in the Vietnam War, and coalition forces in recent military operations such as the Gulf War, Operation Enduring Freedom and the Iraq War.

Thus far, however, most such cases against file sharers have been settled out of court.

Thus linguists must resort to indirect methods to determine what those rules might be, if indeed rules as such exist.

Thus, in an agent-focused account, such as one that Peter Railton outlines, the actor might be concerned with the general welfare, but the actor is more concerned with the immediate welfare of herself and her friends and family.

Thus the castrati came to supplant both boys ( whose voices broke after only a few years ) and falsettists ( whose voices were weaker and less reliable ) from the top line in such choirs.

Thus the set of strings of length k in the domain is exactly the set of such strings already enumerated.

Thus, if ( M, d ) and ( N, d ) are two metric spaces, and, then there is a constant k such that

Thus, despite all of these desirable properties, such engines have not succeeded in production because of costs for the ceramic components and the limited advantages.

Thus, for instance, the Taking Children Seriously movement has criticised pedagogic coercion by adults, including parents, on children, holding that it is possible and desirable to act with a child in such a way that all activities are consensual.

Thus it is unperturbed by complications such as leap years.

Thus, courts will generally allow a class action in such a situation.

Thus, the Debian Project is an independent decentralized organization ; it is not backed by a company like Linux distributions such as Ubuntu, openSUSE, Fedora, and Mandriva.