Bulletin of the American Mathematical Society Volume 10

Bulletin of the American Mathematical Society Volume 10

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...transversal if 1 and n are perpendicular, that is if the discontinuity vector lies in the wave front. From this it follows that a longitudinal wave does not affect the curl; nor a transversal wave, the density (divergence). A short treatment of the effect produced by a discontinuity of order n upon the derivatives of order higher than?i closes this remarkable chapter. After this elaborate discussion of the kinematics of the problem, follows a short chapter of 14 pages containing the formulation of the dynamic problem in case of fluids whether liquids or gases. Passing over the establishing of the equations of motion and the discussion of the physical equation which connects the pressure, temperature, and density, we come to the essential idea underlying the whole work. The motion of a fluid is determined by three sets of data: first the equations of motion, second the initial conditions which state the positions and velocities of the particles at the initial instant t = C, third the boundary conditions which include the motion of the walls of the containing vessel and the pressure p at all points of the free surfaces. In the case of liquids these conditions allow us to calculate the value of dp/dn at every point of the containing vessel. If there are no free surfaces the problem of the solution becomes the problem of Neumann which was treated at length in the first chapter. If there are free surfaces we have the "mixed" problem concerning which little more is known than that it has a unique solution provided the solution exists. The results arising from discontinuities in the given conditions are taken up in the fifth chapter. In the case of gases matters are far different. The given conditions are redundant or contradictory....show more

Product details

  • Paperback | 218 pages
  • 189 x 246 x 12mm | 399g
  • Rarebooksclub.com
  • United States
  • English
  • Illustrations, black and white
  • 123675803X
  • 9781236758033