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This paper investigates whether it is reasonable to bestow credit to one person or group for the famed theorem that relates to the side lengths of any right-angled triangle, a theorem routinely referred to as the “Pythagorean Theorem”. The author investigates the first-documented occurrences of the theorem, along with its first proofs. In addition, proofs that stem from different branches of mathematics and science are analyzed in an effort to display that credit for the development of the theorem should be shared amongst its many contributors rather than crediting the whole of the theorem to one man and his supporters.

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The usual virial theorem, relating kinetic and potential energy, is extended to a molecule by the use of the true wave function. The virial theorem is also obtained for a molecule from a trial wave function which is scaled separately for electronic and nuclear coordinates.

The motion of an incompressible fluid caused by the oscillation of a plane at plate of in nite length is termed Stokes' second problem. We assume zero velocity normal to the plate and thus simpli ed Navier-Stokes equations. For the unsteady Stokes' second problem, solutions may be obtained by using Laplace transforms, perturbation techniques, homotopy, di erential transform method or Adomian decomposition method. Stokes' second problem is discussed for second-grade and Oldroyd-B non-Newtonian fluids. This dissertation summarizes previously published work.

Thesis (M.S.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Considerable study h8s been devoted to the multiplicity function of a real variable. For any real valued function of a real variable, f(x), define its multiplicity function, N(Y), as the cardinal number of roots, either finite or infinite of y = f(x), i.e., when the cardinal number of roots is transfinite, assign the value infinite where it is understood that the range of the multiplicity function is the extended real number system. Banach^1 was the first to relate this function to a continuous function of bounded variation. He realized that the integral of this function over the Entire real line was precisely the total variation. He demonstrated analogous theorems for curves and surfaces. His approach is to express the curve on the surface parametrically. In the case of a simple arc in the plane, the original theorem can be applied to the parametric equations. This results in an expression for rectifiable arcs. To determine a surface of finite area requires a more careful study. Here, too, the method of parametric equations simplifies the problem. The proof consists chiefly in defining and in organizing the expressions of the surface in a manner that will allow the multiplicity theorem to be applied [TRUNCATED]. / 2031-01-01