Therefore, it is impossible ( without measuring ) to know the definite state of spin of either particle in the spin singlet.

Therefore, the space Δ is also a Lie algebra representation of called a spin representation.

Therefore BB's lack the spin stabilization required for long-range accuracy, and usage in any but the cheapest rifled guns is discouraged.

" Therefore, according to Fredkin, at the Planck scale, ordinary matter could have spin angular momentum that violates the equivalence principle. There might be weird Fredkin forces that cause a torsion in spacetime.

Therefore it would most often see the spin as a counter-clockwise rotation while flying away from the decay point.

Therefore, spin casting with metal requires not only a furnace with fine temperature control, but knowledge of at what range to cast.

Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, ℓ and m ( both are integers ).

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 smallest angular separation two objects can have before they significantly blur together is given as stated above by

Therefore if the system is initialized in one of these levels, time evolution will make the population of each of the levels oscillate with some characteristic frequency, whose angular frequency is also known as the Rabi frequency.

Therefore, the angular diameter of an object with visual diameter d at a distance D, expressed in arcseconds, is given by:

Therefore any angular bandwidth contained in the source, which extends past the edge angle of the lens ( i. e., lies outside the bandwidth of the system ), is essentially wasted source bandwidth because the lens can't intercept it in order to process it.

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

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 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 velocity of an electromagnetic wave in such a medium is

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, each column vector of is a linear combination of the columns of.

Therefore any directional derivative can be identified with a corresponding vector, and any vector can be identified with a corresponding directional derivative.

Therefore, the state vector remains in the plane spanned by and after each application of the operators and, and it is straightforward to check that the operator of each Grover iteration step rotates the state vector by an angle of.

Therefore, v < sub > 3 </ sub > is neither a polar vector nor a pseudovector.

Therefore the baroclinic vector is nonzero, and the sense of the baroclinic vector is to create vorticity to make the interface level out.

Therefore, the relative position vector remains bounded, having its smallest magnitude at periapsis r < sub > p </ sub > which is given by:

Therefore the components of a tangent vector transform via

Therefore, X is reflexive as topological vector space if and only if it is reflexive as normed space, namely, when the injection J is bijective.

Therefore the bracket on A is just the Lie bracket of tangent vector fields and the anchor map is just the identity.

Therefore, the magnitude of a vector from the origin of the Ewald's sphere to the intersection of any reciprocal lattice rods is equal in magnitude to that of the incident beam.

Therefore every conservative vector field is also an irrotational vector field.

Therefore, the RHS can be written in vector form as

Therefore, an-graded vector space, as defined above, is just an I-graded vector space where the set I is ( the set of natural numbers ).

Therefore, many equations of electromagnetism can be written either in terms of the E and B, or in terms of the magnetic vector potential and electric potential.

where is a unit vector lying along the line joining M and m and pointing from m to M. Therefore, the gravitational field of M is

Therefore, by ( 3 ), such a representation of G will have a nonzero invariant vector, establishing ( 4 ).

Therefore, the rules and define a functor from the category of complex vector spaces to itself.