Therefore, the velocity field of the continuum is given by

Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source.

Therefore, negative values of the group velocity will occur in these areas.

Therefore, the spin angular velocity vector () about the spin axis will have to evolve in time so that the matrix product remains constant.

Therefore, the rotation is completely produced by the perpendicular motion around the origin, and the angular velocity is completely determined by this component.

Therefore, the most important fluid velocities are those inside this very thin region in which the change in velocity can be considered linear with normal distance from the surface.

Therefore the larger downward velocity produces a larger aft-leaning component and this leads to larger induced drag on the aircraft with the smaller wingspan and lower aspect ratio.

Therefore, the displacement vector r and its velocity v are always in the plane perpendicular to the constant vector L.

* That resistance of the flux is proportional to uv ( where v is the velocity of the particles and u that of gross matter ) and gravity is proportional to v < sup > 2 </ sup >, so the ratio resistance / gravity can be made arbitrarily small by increasing v. Therefore he suggested that the ultramundane corpuscles might move at the speed of light, but after further consideration he adjusted this to 10 < sup > 5 </ sup > times the speed of light.

Therefore, facial processing has been studied using measurements of mean cerebral blood flow velocity in the middle cerebral arteries bilaterally.

Therefore, based on the principles of fluid dynamics, in a tube of cross sectional area, A, and an average fluid velocity, u, the volume flow rate is given by the equation:

Therefore injecting a high velocity air mass into the air stream essentially tangent to the wall surface of the airfoil reverses the boundary layer friction deceleration thus the boundary layer separation is delayed.

Therefore, it does not accelerate faster and faster ; instead it moves with a finite average velocity, called the drift velocity.

Therefore the multistatic ambiguity function is mostly usefully defined as a function of two-or three-dimensional position and velocity vectors for a given multistatic geometry and transmitted waveform.

Therefore a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity.

Therefore, the higher the load applied to the muscle, the lower the contraction velocity.

Therefore another trick to achieve lower stresses is that rather than picking up a cargo from the ground at zero velocity, a rotovator could pick up a moving vehicle and sling it into orbit.

Therefore, the interference pattern obtained at each angular velocity of the platform features a different phase-shift particular to that angular velocity.

Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

Therefore, one method of searching for extraterrestrial civilizations would be to look for large objects radiating in the infrared range of the electromagnetic spectrum.

Therefore, these equations allow self-sustaining " electromagnetic waves " to travel through empty space ( see electromagnetic wave equation ).

Therefore, these particle-like properties of X-rays, such as their ionization of gases, caused William Henry Bragg to argue in 1907 that X-rays were not electromagnetic radiation.

Therefore, X-rays are the " sweetspot " for wavelength when determining atomic-resolution structures from the scattering of electromagnetic radiation.

Therefore an electromagnetic wave consists of two transverse waves, visible light being an example of an electromagnetic wave.

Therefore we can either abandon the principle of locality ( which most physicists are reluctant to do ) or we are forced to accept that the electromagnetic 4-potential-composed of Φ and A-offers a more complete description of electromagnetism than the electric and magnetic fields can.

Therefore, while the quantized electromagnetic field without charged particles is scale-invariant, QED is not scale-invariant.

Therefore each wave takes slightly less time to reach the observer than the previous wave.

Therefore the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency.

Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over space as a wave function.

Therefore, for the first part of its history, the torpedo was guided only in the sense that its course could be regulated so as to achieve an intended impact depth ( because of the sine wave running path of the Whitehead, this was a hit or miss proposition, even when everything worked correctly ) and, through gyroscopes, a straight course.

Therefore, a strong shock wave forms ahead of the ejecta, that heats the upstream plasma up to temperatures well above millions of K. The shock continuously slows down over time as it sweeps up the ambient medium, but it can expand over hundreds of thousands of years and over tens of parsecs before its speed falls below the local sound speed.

Therefore, the pressure wave produced by a high explosive is not significantly increased by confinement as detonation occurs so quickly that the resulting plasma does not expand much before all the explosive material has reacted.

Therefore, s-waves attenuate completely in the outer core, and the only s-waves that appear after a wave exits the outer core do so due to splitting of p-waves into an s-wave component.

Therefore, many of the standard measurements of coherence are indirect measurements, even in fields where the wave can be measured directly.

Therefore the Hartree product does not satisfy the Pauli principle ; that is to say: on the one hand, the interchange of fermions must give rise to negation of the wave function because fermions must have antisymmetric wavefunctions, yet on the other hand, they should still be indistinguishable, meaning the exchange of particles does not change the results of measurements performed on the system.

Therefore, problems in quantum mechanics center around the analysis of the wave function for a system.

Therefore, the wave energy between rays is concentrated as they converge, with a resulting increase in wave height.

Therefore, a " P " wave must be present for every " QRS " complex in a ratio of 1: 1.

Therefore, the converging ( partial ) spherical wave shown in the figure above produces an Airy disc in the image plane.

In both cases a 4-spinor is obtained and for both linearizations the g-factor is found to be equal to 2 ; Therefore, the factor 2 is a consequence of the wave equation dependency on the first ( and not the second ) derivatives with respect to space and time.

Therefore, ship hulls are generally designed to produce as small a bow wave as possible.

In fact the shape resonance occurs where the integral number of wave lengths of the particle sit within the potential of the nucleus of radius R. Therefore the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ± 1 x10-13 cm as it can be seen in the chapter " Elastic Cross Sections " of a textbook in Nuclear Physics by R. D.

Therefore reentry heating is largely convective heat transfer between the shock wave and the orbiter's skin through superheated plasma.

Therefore giving the surfer the speed needed to catch the wave successfully.