INTRODUCTION JOHN AuBREY described Sir William Paddy, M.D. as 'an incomparable person', and 'one of the first learned men who made a physician's practice his study'.' Paddy's medical leadership influenced the professional development and legal responsibilities of contemporary English physicians, and his literary interests exemplified the qualities and difficulties around him during the Elizabet...

A generalized ( G′ G ) -expansion method is devised to construct the exact traveling wave solutions of mKdV equation. With the aid of symbolic computation, many hyperbolic function solutions, trigonometric function solutions and rational function solutions are obtained. It is shown that the proposed method is more effective and powerful than the ( G′ G ) -expansion method in constructing the tr...

We demonstrate that the generalized Gell-Mann–Low theorem permits for a systematic expansion around the nonrelativistic limit when applied to bound states in the Wick-Cutkosky model, Yukawa theory, and QED (in Coulomb gauge). We apply this expansion to obtain new results for the fine and hyperfine structure of bound states in the cases of the Wick-Cutkosky model and Yukawa theory, and reproduce...

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) Hq relevant to the fluctuation spectrum and poles of the order-q power spectrum is proposed. The “partition function” is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A so...

We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

In this paper we investigate generalized binomial expansions that arise from two-dimensional sequences satisfying a broad generalization of the triangular recurrence for binomial coefficients. In particular, we present a new combinatorial formula for such sequences in terms of a ’shift by rank’ quasi-expansion based on ordered set partitions. As an application, we give a new proof of Dilcher’s ...