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Therefore, the displacement vector r and its velocity v are always in the plane perpendicular to the constant vector L.
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Therefore and displacement
Therefore, almost all radial engines use a two valve pushrod-type valvetrain and as a result produce less power for a given displacement than multi-valve inline or vee engines.
Therefore, the material displacement gradient components and the spatial displacement gradient components are approximately equal.
Therefore the sound waves at the throat are of high pressure and low displacement.
Therefore the original issue that turned the Young Lords street gang in Chicago into a bonafide human rights movement was the complete displacement of the Puerto Rican community in Lincoln Park, Chicago.
Therefore a preoccupation with musculature could be treated as an individual's unconscious displacement of sexual or emotional conflict ( or feelings of guilt, or even poor self-image ).
Therefore and vector
Therefore, the spin angular velocity vector () about the spin axis will have to evolve in time so that the matrix product remains constant.
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.
Therefore and r
Therefore, c divides the initial remainder r < sub > 0 </ sub >, since r < sub > 0 </ sub > = a − q < sub > 0 </ sub > b = mc − q < sub > 0 </ sub > nc = ( m − q < sub > 0 </ sub > n ) c. An analogous argument shows that c also divides the subsequent remainders r < sub > 1 </ sub >, r < sub > 2 </ sub >, etc.
Therefore, the greatest common divisor g must divide r < sub > N − 1 </ sub >, which implies that g ≤ r < sub > N − 1 </ sub >.
Therefore, the autocorrelation function c ( r ) of the electron density ( also known as the Patterson function ) can be computed directly from the reflection intensities, without computing the phases.
Therefore, when λ is very small, the solution approaches that of the unscreened Poisson equation, which, in dimension, is a superposition of 1 / r functions weighted by the source function f:
Therefore r ( x ) has n + 1 roots.
For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observed changes by a factor of r. Therefore we must take this into account.
Furthermore, replacing the unit circle by the unit square, the error term for the general problem can be as large as a linear function of r. Therefore getting an error bound of the form
Therefore, letting r tend to infinity ( we let r tend to infinity since f is analytic on the entire plane ) gives a < sub > k </ sub >
Therefore d and r are the sides of a right angled triangle with hypotenuse R and the area is given by:
Therefore, if the sections never simultaneously vanish, they determine a form: ...: s < sub > r </ sub > which gives a map from X to P < sup > r </ sup >, and the pullback of the dual of the tautological bundle under this map is L. In this way, projective space acquires a universal property.
omits text Εἰπέ οὖν ἡμῖν ( Therefore, tell us ) with it < sup > a, b, d, e, ff < sup > 1 </ sup >, ff < sup > 2 </ sup >, q, r < sup > 1 </ sup ></ sup > syr < sup > s </ sup > co < sup > bo < sup > ms </ sup ></ sup > Codex Schøyen
Therefore, increases in r must decrease the duration ( or, in the case of zero-coupon bonds, leave the unmodified duration constant ).
Therefore the coefficients of all the terms except r < sup > p </ sup > and s < sup > p </ sup > are divisible by p, the characteristic, and hence they vanish.
Therefore, the change in φ over one oscillation of u ( or, equivalently, one oscillation of r ) equals
Therefore if then there is no lifting of r to a root of f ( x ) mod p < sup > k + 1 </ sup >, while if then every lifting of r to modulus p < sup > k + 1 </ sup > is a root of f ( x ) mod p < sup > k + 1 </ sup >.
Therefore, s ≤ r and if equality holds then s
Therefore and its
Therefore, if the target can significantly change its location in something less than 30 minutes, the probability of having destroyed it is drastically lowered.
Therefore, the congruence of its secants, that is the image of a general plane field of lines, is of order Af and class Af.
Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.
Therefore, all primordial americium ( americium that was present on Earth during its formation ) should have decayed by now.
Therefore each pearl, natural or cultured, will have its own unique collage of colours.
Therefore, this group is generally now either included in the Brassicaceae or as its own family, Cleomaceae.
Therefore its status as a species is still questionable.
Therefore, a liquid will normally catch fire only above a certain temperature: its flash point.
Therefore, a company must analyze its business workflows and processes before choosing a technology platform ; some will likely need re-engineering to better serve the overall goal of winning and satisfying clients.
Therefore the quiet Sun always coincides with the equatorial zone and its surface is lower during the maximum of the solar cycle.
Therefore, the distillate will not be pure – its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law.
Therefore, each image engenders its opposite.
Therefore, a country's ability to learn from the leader is a function of its stock of " human capital ".
Therefore, the idea was born that only the elite should know the truth in its complete form and the rulers, Plato said, must tell the people of the city " The Noble Lie " to keep them passive and content, without the risk of upheaval and unrest.
Therefore, the most probable date for its composition is the second half of the year 63 or the beginning of 64, according to the Catholic Encyclopedia.
Therefore, earthquakes lower the Earth's available elastic potential energy and raise its temperature, though these changes are negligible compared to the conductive and convective flow of heat out from the Earth's deep interior.
Therefore, General Niazi and Air Marshal Enamul Haque, Commander of Eastern Air Force Command ( EAFC ), were failed to launch any operation in East Pakistan against Indian or its allies.
Therefore, it seems important to make the rules and focus of a discussion forum public to avoid misconceptions about its accepted use.
Therefore, the FDP wasn't able to form a coalition with its preferred partners, the CDU / CSU parties.
Therefore landing on a gas giant may or may not be possible, depending on the size and composition of its core.
Therefore, Hong Kong continues to play an active role in the international arena and maintains close contact with its international partners. Furthermore, Hong Kong continues to be an active, independent member of the World Trade Organization ( WTO ) and the Asia-Pacific Economic Cooperation ( APEC ) forum in the name of Hong Kong, China.
Therefore, with British permission, the Va ' ad raised its own taxes and ran independent services for the Jewish population.
Therefore, in spite of its condemnation by religious authorities, homosexuality persisted in a subterranean manner.
Therefore, to keep its economy afloat, Japan ran massive budget deficits ( added trillions in Yen to Japanese financial system ) to finance large public works programs.
Therefore, the underlying reason for gay behavior, he argues, must be to rebel against God, to wish to do something forbidden ( perhaps, implying some innate knowledge of its forbidden nature ).
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