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The Glasgow Mathematical Journal publishes high quality original research papers in pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included noncommutative algebra and representation theory, geometric group theory, functional analysis, operator algebras, differential equations, algebraic geometry, differential geometry, mathematical physics, number theory, algebraic and geometric topology, and the application of such methods in applied mathematics. The journal is owned by the Glasgow Mathematical Journal Trust, which is a registered charity; all surplus income is used to support mathematics and the mathematical community.
In this paper, we shall be concerned with an investigation of the solution of triple integral equations involving sine and cosine kernels. These type of equations arise in the study of certain two-dimensional mixed boundary value problems in infinite planes and infinitely long strips.
EJAM is a journal for original work in areas of mathematics in which an understanding of the application requires the use of new and interesting mathematical ideas. EJAM focuses on the high level of mathematics inspired by real world applications, and at the same time fostering the development of theoretical methods with broad areas of applicability.
Humbert's 5-nodal plane sextic first appeared in his 1894 paper. Its canonical curve C was identified in 1951, when it was shown that the sextic is the outcome of projecting C from one of its own chords on to a plane.
In this present paper it is remarked that there are 60 chords of C such that the projection has two tacnodes, each a confluence of two of Humbert's 5 nodes, and an equation is found for this tacnodal curve.
A certain specialization permits C to be invariant for a group of 32, not merely 16, projectivities. Further specializations, described in the proper place, permit groups of orders 64, 96, 160. The resulting tacnodal sextics have groups of birational self-transformations isomorphic to these.
Hadamard elementary solutions are found for the tri-axially symmetric potential equation in space of three dimensions and for the bi-axially symmetric potential equation in space of two dimensions. The elementary solutions involve hypergeometric functions of several variables.
This paper considers the properties of the spectrum of a differential operator derived from differential expressions of the fourth order. With certain conditions on the coefficients of the differential expression the spectrum of the operator is discrete and an estimate is obtained of the number of eigenvalues lying in a given bounded interval of the real line. The results are compared with those obtained by alternative methods. Additional restrictions on the coefficients give special cases previously considered by other authors.