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 if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus such a gain medium must have a gain bandwidth sufficiently broad to amplify those frequencies.

Thus, the Eighth Amendment has been interpreted to mean that bail may be denied if the charges are sufficiently serious.

Thus the heater did not function as an electrode, but simply served to heat the cathode sufficiently for it to emit electrons by thermionic emission.

where D denotes the continuum derivative operator, mapping f to its derivative f. The expansion is valid when both sides act on analytic functions, for sufficiently small h. Thus, T < sub > h </ sub >= e < sup > D </ sup >, and formally inverting the exponential yields

Thus there is disagreement among botanists as to whether the genera Chionodoxa and Scilla are sufficiently different to be kept separate.

Thus, Euthyphro is brought to a realization by this dialectical method that his definition of piety is not sufficiently meaningful.

Thus the consistency of a sufficiently strong, effective, consistent theory of arithmetic can never be proven in that system itself.

Thus the key technique here — which characterises a program as a chatbot rather than as a serious natural language processing system — is the production of responses that are sufficiently vague and non-specific that they can be understood as " intelligent " in a wide range of conversational contexts.

Thus, one must be sufficiently knowledgeable of the wants and needs of others to properly conduct business.

Thus, the court found that the statute is not sufficiently ambiguous to raise constitutional concerns.

Thus, for example, many library implementations of quicksort will switch to a simple loop-based insertion sort ( or similar ) algorithm once the number of items to be sorted is sufficiently small.

Thus, for example, in many states, the blood alcohol level for the commission of the offence of driving under the influence is set sufficiently low that people might exceed the limit without realising that they had consumed enough alcohol to do so.

Thus, fog and mist ( except when the terms are used to mean " drizzle ") are not precipitation but suspensions, because the water vapour does not condense sufficiently to precipitate.

Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.

Thus it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced ( cf.

Thus, argued: "... in sufficiently broad contexts such analytic descriptions cease to be adequate ... ' the law of the whole ' will generally include the possibility of describing the ' loosening ' of aspects from each other, so that they will be relatively autonomous in limited contexts ... however, any form of relative autonomy ( and heteronomy ) is ultimately limited by holonomy, so that in a broad enough context such forms are seen to be merely aspects, relevated in the holomovement, rather than disjoint and separately existent things in interaction ".

Thus, when Congress passed the Judiciary Act of 1869, creating a new seat on the U. S. Supreme Court, he was sufficiently well known by associates of President Grant to be recommended as a Supreme Court nominee.

Thus, John asked Mary to wash him obeys Condition B: John is the antecedent of him, and him is sufficiently far away ; on the other hand, * John washed him, where John is intended to be the antecedent of him, is unacceptable.

Thus, analysis of the 993-locus dataset corroborates our earlier results: if enough markers are used with a sufficiently large worldwide sample, individuals can be partitioned into genetic clusters that match major geographic subdivisions of the globe, with some individuals from intermediate geographic locations having mixed membership in the clusters that correspond to neighboring regions.

344c: (" Thus, Socrates, injustice on a sufficiently large scale is a stronger, freer, and a more masterful thing than justice, and, as I said in the beginning, it is the advantage of the stronger that is the just, while the unjust is what profits man's self and is for his advantage.

Thus, under the Univis test, the Intel products sufficiently embodied the method patents, making the exhaustion doctrine applicable.