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Excerpt from An Application of Sturm-Liouville Theory to a Class of Two-Part Boundary-Value Problems The mathematical aspects of the theory of wave propagation in longitudinally uniform waveguides are discussed in sturm-liouville theory, which deals with the existence of a set of experimentally determinable normal modes or eigenfunctions and corresponding eigenvalues. Regardless of the transverse variation of the electrical properties of the guide in particular cases, the theory furnishes a list of qualitative properties which the eigenfunctions and eigenvalues share with all other eigenfunctions and eigenvalues corresponding to the same boundary conditions. When a semi-infinite bifurcation is introduced into the guide, two or more semi-infinite waveguides result; the difference between the electrical properties of these waveguides is mathematically exhibited in a change of boundary condition or interval of definition of the modes and also in the new eigenfunctions and eigenvalues that arise. These form a complete set of functions in the narrower waveguide created by the bifurcation. The qualitative properties of this new set of functions are not the same as those possessed by the functions relating to the undisturbed part of the waveguide. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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