First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

Transcendental number theory, by Alan Baker. Pp. x, 147. £4·90. 1975. SBN 0 521 20461 5 (Cambridge University Press)

Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review

Theory of Equations. By J. V. Uspensky. Pp. vii, 353. 27s. 1948. (McGraw-Hill)

Numerical methods for Engineers and Scientists

Development of a suitable model for characterizing photovoltaic arrays with shaded solar cells

Theory of exponential splines

Lame's formulas for the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary conditions on an equilateral triangle are derived using direct elementary mathematical techniques. They are shown to form a complete orthonormal system. Various properties of the spectrum and nodal lines are explored. Implications for related geometries are considered.

https://www.jstor.org/stable/pdfplus/25054404.pdf

Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem

Lame's formulas for the eigenvalues and eigenfunctions of the Laplacian with Neumann boundary conditions on an equilateral triangle are derived using direct elementary mathematical techniques. They are shown to form a complete orthonormal system. Various properties of the spectrum and nodal lines are explored. Implications for related geometries are considered.

/pdf/eigenstructure-of-the-equilateral-triangle-part-ii-the-2be2qvo7cz.pdf

Eigenstructure of the equilateral triangle, Part II: The Neumann problem

Exponential fitting of the delayed recruitment/renewal equation

Pruess's investigations [J. Approx. Theory, 17 (1976), pp. 86–96], [Math. Comp., 33 (1979), pp. 1273–128 1] revealed the shape preservation properties of exponential splines and provided the impetus for further theoretical study of exponential splines [J. Approx. Theory, to appear]. Together, these theoretical results form the backdrop for the detailed analysis of issues in the computation of exponential splines contained herewith. Specifically, first and foremost the construction of tension parameter selection algorithms is considered. The conditioning and iterative solution of the spline equations, as well as the derivation and accuracy of end conditions, are discussed. This inquiry concludes with a potpourri of numerical considerations and the presentation of a variety of numerical examples.

Brian J. McCartin

Papers

Theory of exponential splines

Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem

Eigenstructure of the equilateral triangle, Part II: The Neumann problem

Exponential fitting of the delayed recruitment/renewal equation

Computation of exponential splines