Question: If M1CRN is an dimensional manifold
If M1CRN is an -dimensional manifold-with-boundary and M 2 C M1 - ∂M1 is an -dimensional manifold with boundary, and M1, M2 are compact, prove that
Answer to relevant QuestionsIf M is an oriented one-dimensional manifold in RN and c: [0, 1] →M is orientation-preserving, show thata. If c: [0, 2π] x [-1, 1] → c: [0 , 2π] x [-1, 1] → R3 is defined by c (u,v) = (2 eos (u) + vsin (u/2) eos (u), 2sin (u) + vsin (u/2) sin (u), veos (u/2)).A gas at 20°C may be rarefied if it contains less than 1012 molecules per mm3. If Avogadro’s number is 6.023E23 molecules per mole, what air pressure does this represent?The dimensionless Galileo number, Ga, expresses the ratio of gravitational effect to viscous effects in a flow. It combines the quantities density ρ, acceleration of gravity g length scale L, and viscosity μ. ...(“*” means “difficult”—not just a plug-and-chug, that is) For small particles at low velocities, the first (linear) term in Stokes’ drag law, Prob. 1.10, is dominant, hence F = KV, where K is a constant. Suppose ...
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