Tangent vector

To specify the directions of two different vectors at nearby points it is necessary to define tangent vectors (tangent space) at these points. Important... 

This derivative is the unit vector tangent to the curve defined by a succession of points r at the point r, and hence it must give the direction of the vector Vp(r) at this point. Thus... 

Figure 1 The Gauss map g between a surface E around a point P of position vector r and the unit sphere Si. Q ow Si corresponds to P on Z. The vector tangent plane n is the same. dQ transforms dL into dS = dG dT), changing its shape and area.

PFR. The reaction rate at constant density is a vector tangent to the trajectory of component concentration, because the length variation can be translated in time. 

Here, t is the vector tangent to the CSTR locus, as defined in Chapter 6. 

Rate vectors tangent to H(n, b), satisfying the condition n r(C) = 0. Points that satisfy this condition may or may not be achievable. 

Substituting - fii Vx, for qu where /t, is a 4D vector tangent to the surface of the 4D hypersphere at X having a modulus equal to the dipole moment fii of particle i, the dipole-dipole potential gives [20-22]... 

By varying e, we obtain a set of planes, each tangent to a two-dimensional sphere of one and the same radius. Therefore, the two vectors K, e, which satisfy the above equations, define uniquely a certain vector tangent to a two- dimensional sphere. This precisely proves the lemma since the bundle tangent to a sphere is defined as a four-dimensional manifold whose points are pairs of the form (e, ), where e is a point on the sphere, and ( is an arbitrary vector tangent to the sphere at the point e. 

Here t is any vector tangent to the interface and it follows that the potentials on either side of the interface differ by at most a constant. If no work is done in transferring charge across the interface, the constant is zero. 

Unit tangent vector Tangent surface vector... 

For the continuous curve the angular correlation is related to the relative orientation between the unit vector tangent tt> die curve... 

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