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, 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, they appear as hexagonal net in transverse section.

Thus even transverse pairs of wheels in an independent suspension are usually called " an axle ".

Thus there is no transverse Doppler shift, and the lower frequency of the moving source can be attributed to the time dilation effect alone.

Thus, a simple liquid will not typically support a transverse acoustic phonon, or shear wave.

Thus switching from the Mini type in-sump gearbox arrangement used also in the 204 and 304 to the now-universal end-on gearbox configuration ( pioneered by the Autobianchi Primula ), of front-wheel drive with a transverse engine and a gearbox on the end of the engine and unequal-length drive shafts.

Thus its decay products tend to have higher transverse momentum ( momentum perpendicular to the original direction of the bottom quark, and therefore of the b-jet ).

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Thus, the monetary model predicts that the velocity of money will increase as a result of an excessive increase in the money supply.

Thus a ruler that is one meter long in one frame of reference will not be one meter long in a reference frame that is travelling at a velocity relative to the first frame.

Thus the velocity can be measured from the amount of redshift ( or blueshift ) of the star's spectrum.

Thus, an object starting from rest will attain a velocity of 9. 81 m / s ( 32. 2 ft / s ) after one second, 19. 62 m / s ( 64. 4 ft / s ) after two seconds, and so on, adding 9. 81 m / s ( 32. 2 ft / s ) to each resulting velocity.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

Thus, if V < sub > g </ sup > is the group velocity of a phonon wave packet, then the relaxation length is defined as:

Thus, velocity is the time rate of change of position, and the dot denotes the derivative with respect to time.

Thus, for bodies in pure translation the velocity and acceleration of every point P in the body are given by

Thus, the magnitude of the angular velocity vector at a given time t is consistent with the two dimensions case.

Thus, the relative difference in velocity between a source and an observer is what gives rise to the doppler effect.

Thus shot to shot consistency is maintained for longer than in an unregulated rifle, at the expense of efficiency, shots per fill and often at a lower velocity.

Thus, the perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude,.

Thus, in cases of very viscous flows ( e. g. Couette Flow ), the vorticity will be diffused throughout the flow field and it is probably simpler to look at the velocity field ( i. e. vectors of fluid motion ) rather than look at the vorticity field ( i. e. vectors of curl of fluid motion ) which is less intuitive.

Thus if a rocket burst is in the direction of the velocity, in the reversed case it is opposite to the velocity.

Thus, for a subsonic flow to be accelerated to supersonic velocities, the nozzle needs to have a converging section in which the flow is subsonic, a throat, at which the flow velocity is the local speed of sound, and a diverging section with supersonic flow.

Thus, since the velocity of sound is approximately 343 m / s at a normal room temperature of about 25 ° C, the reflecting object must be more than 11. 3 m from the sound source at this temperature for an echo to be heard by a person at the source.

Thus the time-of-flight is used to measure velocity, from which the mass-to-charge ratio can be determined.

Thus specific impulse is a velocity, as opposed to the common usage of the word as the ratio of momentum and weight ( weight would not make much sense in this context ).

Thus, it is the velocity of a reference point fixed to the body.

Thus, in animals with early signs of diabetes-induced neuropathy, C peptide treatment in replacement dosage results in improved peripheral nerve function, as evidenced by increased nerve conduction velocity, increased nerve Na +, K + ATPase activity, and significant amelioration of nerve structural changes.