If M is an oriented one-dimensional manifold in RN and c: [0, 1] →M is orientation-preserving, show that
Answer to relevant QuestionsIf M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^ . . . ^ dxn, so that the volume of M, as defined in this section, is the volume as defined in Chapter 3. (Note that this depends on the ...If there is a nowhere-zero k-form on a k -dimensional manifold M, show that M is orientableThe earth’s atmosphere can be modeled as a uniform layer of air of thickness 20 km and average density 0.6 kg/m3 (see Table A-6). Use these values to estimate the total mass and total number of molecules of air in the ...The Stokes-Oseen formula  for drag on a sphere at low velocity V is: F = 3πμ DV + 9π/16pV2D2 Where D = sphere diameter, μ = viscosity, and ρ = density. Is the formula homogeneous?Marangoni convection arises when a surface has a difference in surface tension along its length. The dimensionless Marangoni number M is a combination of thermal diffusivity α = k/ (ρcp) (where k is the thermal ...
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