Given a tangent vector
field X, JX is also tangent to S.
For a unit tangent vector
v [member of] UM, we denote by [[gamma].
With an atlas defined on M, given a point P in M and a coordinate chart about P, a tangent vector
to M at P can be defined as generalization of the usual notion of tangent vector
in Euclidean space using the directional derivative of a function or curve along the direction of tangent vector
6 depicts the tangent vector
at the event point earth.
Let us denote t([sigma]) = [alpha]' ([sigma]), and we call 1([sigma]) a unit tangent vector
1/2) Side of a square [A=area] [integral] (a,b)(((x'(t)) Arc length from time "a" to time ^2+(y'(t))^2)^(1/2))dt "b" of a parametric curve in vector format: x=x(t),y=y(t) [integral] (a,b)((1+ Arc length from point (a,f(a)) to (f'(x))^2)^(1/2))dx point (b,f(b)) of a function in the format: y=f(x) [integral] vdt Position [v=velocity] k*ln(W) Entropy [k=Boltzmann constant; W=number of microstates] T (PV)/(nR) Temperature (in Kelvins) [P=pressure; V=volume; n=amount; R=ideal gas constant] [PI]/(MR)=(dgh)/(MR) Temperature (in Kelvins) [j=osmotic pressure; M=concentration (molarity) of solution; R=ideal gas constant; d=density; g=gravitational constant; h=height] d/r Time [d=distance; r=rate] (r'(t))/[parallel] Unit tangent vector
[r(t)=position r'(t)[parallel] vector in terms of time] U 238.
p]M denotes the tangent vector
space of M at p and R is the real number space which satisfies
The tangent vector
field of [alpha] is denoted by [V.
where t(x) and t'(x) are the original tangent vector
and the smoothed tangent vector
at pixel x, respectively.
perpendicular to]], which represents the orthogonal complement of the tangent vector
field of the curve.
We denote t(v) = f'(v)and we call t(v) a unit tangent vector
of f at v.
A vector field is a construction that associates with each point on the manifold a tangent vector
in its tangent space.