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.

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

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, 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.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus, when you have prepared your foundation and laid the floor, these can be trucked to the site and erected with a small crew of friends in a weekend.

Thus the film can be applied to back-lighted translucent plastics faces ; ;

Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus, for aqueous media, we can think of the idealized organic active as an oleophilic or hydrophobic surface-active agent, and of an idealized builder as a oleophobic or hydrophilic surface-active agent.

Thus, the larvae of the intruder can develop at the expense of the rightful inhabitants and the store of beebread.

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, one can think of a dictionary entry as a word rather than a form.

Thus the unstressed it of it rarely snows here gets its significance from its use with snows: nothing can snow snow but `` it ''.

Thus in it's incredible what that boy can eat dominant stress is likely to be on incredible, and eat will have strong stress also.

Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.

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 a man who is butting a stone wall at the office may become unusually aggressive in bed -- the one place he can still be champion.

Thus, man can readily deduce that the primary objective end of the conjugal act is procreation, the propagation of the race.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus an algorithm can be an algebraic equation such as y

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

Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus areas can be measured in square metres ( m < sup > 2 </ sup >), square centimetres ( cm < sup > 2 </ sup >), square millimetres ( mm < sup > 2 </ sup >), square kilometres ( km < sup > 2 </ sup >), square feet ( ft < sup > 2 </ sup >), square yards ( yd < sup > 2 </ sup >), square miles ( mi < sup > 2 </ sup >), and so forth.

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: