Thus D' and N' commute with any polynomial in T ; ;

Thus, for non-negative changes in the basic wage rate, the industry becomes the active wage-setter, since any increase in the basic wage rate can occur only by reason of industry acquiescence.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus he wired J. P. Lower and Sons of Denver: `` Have you any percussion hand grenades for throwing in a house or across a well loaded with balls or shrapnel shot??

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus he will be in a position to disabuse the Soviet leader of any notions he may have about grave Allied disunity.

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.

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, there was seen a need for a new law that would ensure the continuance of the succession following the death of the last legal heir under the Bill of Rights, being Princess Anne, guaranteeing the line of succession would continue in the Protestant line, and excluding any possible claims by the deposed James II or his son and daughter, James Francis Edward and Louisa Maria Teresa Stuart.

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, anthroposophy considers there to be a being who unifies all religions, and who is not represented by any particular religious faith.

Thus, any transverse velocity of the emitting source plays no part in aberration.

Thus, for example, fumaroles from the Laguna Caliente crater of Poás Volcano create extremely high amounts of acid rain and fog, with acidity as high as a pH of 2, clearing an area of any vegetation and frequently causing irritation to the eyes and lungs of inhabitants in nearby settlements.

Thus, it determines substancehood empirically by the togetherness of properties rather than by a bare particular or by any other non-empirical underlying strata.

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, a PICMG backplane can provide any number and any mix of ISA, PCI, PCI-X, and PCI-e slots, limited only by the ability of the SBC to interface to and drive those slots.

Thus, in any use of biological weapons, it is highly likely that animals will become ill either simultaneously with, or perhaps earlier than humans.

Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus, any error in technology or judgment may have far-reaching consequences ( though the same can also happen through natural reproduction ).

Thus, computing includes designing and building hardware and software systems for a wide range of purposes ; processing, structuring, and managing various kinds of information ; doing scientific studies using computers ; making computer systems behave intelligently ; creating and using communications and entertainment media ; finding and gathering information relevant to any particular purpose, and so on.

Thus, by speaking of ' consciousness ' we end up misleading ourselves by thinking that there is any sort of thing as consciousness separated from behavioral and linguistic understandings.

Thus, any examination of the evolution of consciousness is faced with great difficulties.

Thus, in an agent-neutral theory, an actor's personal goals do not count any more than anyone else's goals in evaluating what action the actor should take.

Thus, to be valid, any law must conform to natural law and coercing people to conform to that law is morally acceptable.

Thus, the beech marten differs from most other European mustelids of the Quaternary, as all other species ( save for the European mink ) appeared during the Middle Pleistocene.

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

Thus, the binding energy to contain or trap a particle in a smaller region of space, increases without bound, as the region of space grows smaller.

Thus while Athens was increasing her navy with the funds they contributed, a revolt always found itself without enough resources or experienced leaders for war.

Thus the week cycle is by itself not a full calendar system ; neither is a system to name the days within a year without a system for identifying the years.

Thus field protection may be the primary mechanism that saved the population, but it is likely that field protection would not have been increased without CITES protection.

) Thus, when Odo returned, he was able to launch a near complete surprise attack on the besieging force, scattering it at the first attack, and slaughtering units caught resting or that fled without weapons or armour.

Thus, only the Logos incarnate suffered and died on the Cross and therefore the Son was able to suffer without suffering.

Thus it can be interpreted without any reference to the zero-point energy ( vacuum energy ) or virtual particles of quantum fields.

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, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

Thus they do not resolve the ambiguities that E-Prime seeks to alleviate without an additional rule, such as that all sentences must contain a verb.

Thus users can recognize the abnormality of a weather situation without having to define specific space-and time-dependent thresholds.

Thus, in contrast to the sharia, fiqh is not regarded as sacred and the schools of thought have differing views on its details, without viewing other conclusions as sacrilegious.

Thus Finland had to face its big neighbour on its own, without any greater power's protection.

Now, all that lasts is the decaying shell of a once thriving dwelling .” Thus, without the decrepit backdrop to initiate the events, the Gothic Novel would not exist.

Thus the encoder can generate 2 < sup > n </ sup > − 2 codes without triggering an increase in code width.

Thus, for example, two objects may be group isomorphic without being ring isomorphic, since the latter isomorphism selects the additional structure of the multiplicative operator.

Thus the Commons can remove such an officer through a motion of no confidence without a long, drawn-out impeachment.

Thus in 1992, the Catechism of the Catholic Church, while affirming that " the Church does not know of any means other than Baptism that assures entry into eternal beatitude ", but also stating that " God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments ", stated: " As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them.

Thus, on April 28, 2006, after the unofficial repeal of the French First Employment Contract ( CPE ), the Longjumeau ( Essonne ) conseil des prud ' hommes ( labour law court ) judged the New Employment Contract ( CNE ) contrary to international law, and therefore " illegitimate " and " without any juridical value ".

Thus the past, present, future, and anything in and of, would simply exists without possible creation of, or deviation from.

Thus making a conscious entity impossible to exist without cause, and a conscious entity impossible to represent first cause, or solve infinite regress.

Thus, " All-In-God " ( see pantheism ) as stated in one of the Sayings of Gospel of Thomas: " Lift Up A Stone And You Will Find Me There ..." This seemingly contradictory interpretation of Gnosticism's theology is not without controversy.