On the potential in a strip with a pair of U notches
1. Synopsis and introduction. The potential in a strip with a pair of V or U notches was solved by the author in a recent paper [1], The solution is expressed as a linear combination of a set of harmonic functions in addition to some linear terms. Each harmonic function satisfies the requirements of the problem, except the boundary conditions on the curves of notch. Subsequently, one curve of notch is transformed conformally into a portion of the circumference of a unit circle, on which the boundary condition is adjusted. The corresponding condition on the curve of the other notch is automatically satisfied by antisymmetry. The present paper is endeavored to give an alternate solution of the problem. Since the strip with V notches is perhaps the less crucial case, the solution is formulated with reference to the U notches only. The present solution differs from the previous one essentially in the following two aspects: (i) The set of harmonic functions is a subset of the harmonic functions derived systematically from a single function. (ii) The boundary conditions on the curves of notch are adjusted without the use of conformal transformation. Each curve is merely regarded as a piecewise continuous curve. Finally, several numerical examples are given for illustration.