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 lack of effective recognition of the responsibilities involved in caring for two babies showed signs of becoming a disabling problem.

Thus it is reasonable to believe that there is a significant difference between the two groups in their performance on this task after a brief `` structuring '' experience.

Thus one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

Thus, the combined efficiency of the elements replaced by the two fiber plates ( with a combined efficiency of 0.25 ) is 0.043 or about six times less than that of the two fiber plates.

Thus, according to the character Pausanias in Plato's Symposium, Aphrodite is two goddesses, one older while the other younger.

Thus, from the human body, the usual form assigned to the Deity, forasmuch as it is written that God created man in his own image, issue the two supporters, Nous and Logos, symbols of the inner sense and the quickening understanding, as typified by the serpents, for the same reason that had induced the old Greeks to assign this reptile for an attribute to Pallas.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

Thus in the classical tradition of later Western art and literature, the mythology of the two figures becomes virtually indistinguishable.

Thus two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array.

Thus they add two equivalents of bromine whereas an alkene adds only one equivalent.

Thus, ocular albinism occurs more frequently in males as they have a single X and Y chromosome, unlike females, whose genetics are characterized by two X chromosomes.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus there were two classes of baccalarii: the baccalarii cursores, theological candidates passed for admission to the divinity course ; and the baccalarii dispositi, who, having completed this course, were entitled to proceed to the higher degrees.

Thus, a Blackwood query by the player holding two quick losers in a side suit is a wild gamble, as it is still possible that the suit is not controlled by an Ace or a King.

Thus, Blackwood will not tell you what you want to know: Are we at risk of losing the first two tricks?

Thus, if two species use the same codon at the same place to specify an amino acid that can be represented by more than one codon, that is evidence for a recent common ancestor.

Thus an understanding of how these two levels relate to each other is needed.

Thus, two versions distributed by rival syndicates graced the comics pages for decades.

Thus, a week of Beetle Bailey would arrive at the Lansing State Journal in two sheets, printed much larger than the final version and ready to be cut apart and fitted into the local comics page.

Thus, covalent bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared between them.

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

Thus, covalent bonding does not necessarily require the two atoms be of the same elements, only that they be of comparable electronegativity.