Two different constructions are given of a rank 8 arc-transitive graph with 165 vertices and valency 8, whose automorphism group is M11. One involves 3-subsets of an 11-set while the other involves 4-subsets of a 12-set, and the constructions are linked with the Witt designs on 11, 12 and 24 points. Four different constructions are given of a rank 9 arc-transitive graph with 55 vertices and val...

We show how to use the elements of a sharply k-transitive permutation group of degree n to form error-correcting codes, as suggested by Blake [1], presenting suitable decoding algorithms for these codes. In particular, we concentrate on using the Mathieu group M12 to form a (12,95040,8)-code to correct three errors. The algorithm we give for this code differs from that given by Cohen and Deza [2].

A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a mixed mock modular form in a more general sense than is typically used. We relate v(q) to generating functions studied in connection with “Moonshine of the Mathieu group” and the smallest parts of a p...

Among several optical devices in integrated optics, the fundamental characteristics of collinear optical switching devices have been studied about optical dielectric waveguides. Conventional waveguidetype acousto-optic (A-O) devices use collinear and longitudinal interactions with mode coupling based on the Bragg condition between optical waves and surface acoustic waves (SAW). Collinear A-O de...

For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related differential equations by means of standard methods for a direct solution and by means of integral equations. Our implementation is tested and exemplarily demon...

and in which a and 6 are constants, arises in applied mathematics in two main groups of problems. The first group, of which Mathieu's problem of the transverse vibrations of a taut elliptic membrane is typical, consists of boundary problems relative to some partial differential equation, such as the wave equation, where the boundary is an ellipse—or possibly a hyperbola. Here a fundamental requ...