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 throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.

Thus " pop music " may be used to describe a distinct genre, aimed at a youth market, often characterized as a softer alternative to rock and roll.

Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature.

Thus, assigning age significance to a result requires studying the metasomatic and thermal history of the rock, any metamorphic events, and any evidence of fluid movement.

Thus it is seen that a polyp is an animal of very simple structure, a living fossil that has not changed significantly for about half a billion years ( per generally accepted dating of Cambrian sedimentary rock ).

Thus when Apollo the infant was grown he pursued Python, making his way straight for Mount Parnassus where the serpent dwelled, and chased it to the oracle of Gaia at Delphi ; there he dared to penetrate the sacred precinct and kill it with his arrows beside the rock cleft where the priestess sat on her tripod.

Thus, a mountain route may be graded 5. 6 ( rock difficulty ), A2 ( aid difficulty ), WI3 ( ice climbing difficulty ), M5 * ( mixed climbing difficulty ), 70 degrees ( steepness ), 4000 ft ( length ), VI ( commitment level ), and many other factors.

Thus, it is impossible for the dissolution of carbonate rock to have formed the large vertical holes that swallowed up parts of Guatemala City in 2007 and 2010.

Thus mud opposite shale sections maintains its voltage difference with the surrounding rock.

Thus, the species can also be found in cities, where common prey such as rock pigeons and brown rats may support their populations.

Thus Steno's principle of original horizontality states that rock layers form in the horizontal position, and any deviations from this horizontal position are due to the rocks being disturbed later.

Thus, he refused to play any music for the villagers, instead hitting his lyre's strings with a rock over and over.

Thus, they were later embraced by the American indie rock scene.

Thus, according to them, any song in the rap, hip hop and rock genres is inherently evil because of the song's musical beat, regardless of the song's lyrics or message.

Thus, there are many underground rock, punk and metal bands such as All Else I Fail, Last Day of Beethoven, Yakkhadeva, Temper Level VIII, Tha Ta Lin Chate, Idiots, Offkeys, etc.

Thus in order for blueschist facies assemblages to be seen at the Earth's surface, the rock must be exhumed swiftly enough to prevent total thermal equilibration of the rocks which are under blueschist facies conditions with the typical geothermal gradient.

Thus rock bands received little or no funding, were not given any exposure by the media.

Thus, although a crystallization age is not recorded, the information is still useful in constructing the thermal history of the rock.

Thus when a folk-oriented style of music developed in the 1960s, Frith terms it " folk rock ", and the pop-infused styles of the 1970s were called " pop rock ".

Thus Emma continued her vocal training in 2001 and 2002 by taking singing lessons from vocal coach Maguy Vilette, and took guitar courses again for two months, because the musical style of pop rock attracted her.

Thus at Leucas a criminal was annually thrown from a rock into the sea as a scapegoat: but his fall was checked by live birds and feathers attached to his person, and men watched below in small boats, who caught him and escorted him beyond the boundary of the city.