This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium.
Fejer monotonicity and weak convergence of an accelerated method of projections by H. H. Bauschke, F. Deutsch, H. Hundal, and S.-H. Park General "squeeze theorems" in nonsmooth analysis by J. Benoist and J.-B. Hiriart-Urruty Ramanujan's short unpublished manuscript on integrals and series related to Euler's constant by B. C. Berndt and D. C. Bowman An efficient algorithm for the Riemann zeta function by P. Borwein On periods of elements from real quadratic number fields by E. B. Burger and A. J. van der Poorten Vector-valued perturbed minimization principles by R. Deville and C. Finet Continued fractions, comparison algorithms, and fine structure constants by P. Flajolet and B. Vallee A class of dynamical systems with a convex Lyapunov function by M. Gabour, S. Reich, and A. J. Zaslavski On a convergence of lower semicontinuous functions linked with the graph convergence of their subdifferentials by M. Geoffroy and M. Lassonde Rotundity related to Lipschitz separation by J. R. Giles and J. D. Vanderwerff Codirectional compactness, metric regularity and subdifferential calculus by A. Ioffe Complete dual characterizations of optimality for convex semidefinite programming by V. Jeyakumar and M. J. Nealon A second-welfare theorem in nonconvex economies by A. Jofre Auxiliary problem and the approximation of variational inequalities with non-symmetric multi-valued operators by A. Kaplan and R. Tichatschke Dynamic emission tomography-Regularization and inversion by J. Maeght, D. Noll, and S. Boyd Semi-spaces and bases on convexity systems in complete lattices by J. E. Martinez-Legaz and I. Singer On variational characterizations of Asplund spaces by B. S. Mordukhovich and B. Wang Transposition of relations by J.-P. Penot On a classical existence theorem for nonlinear elliptic equations by B. Ricceri Limiting convex subdifferential calculus with applications to integration and maximal monotonicity of subdifferential by L. Thibault.