In the study of approximation order, particularly in a multivariable setting, quasi-interpolants have played a major role. This report points out some limitations of quasi-interpolants and describes some recent results on approximation order obtained without the benefit of the quasi-interpolant idea. §1. Approximation Order In most general terms, “approximation order” is defined as follows. Def...

and Applied Analysis 3 It is well known that, in an infinite dimensional Hilbert space, the normal Mann iterative algorithm has only weak convergence, in general, even for nonexpansive mappings. Hybrid projection algorithms are popular tool to prove strong convergence of iterative sequences without compactness assumptions. Recently, hybrid projection algorithms have received rapid developments;...

In my research I apply tools from model theory, a branch of mathematical logic, to study sets obtained from certain integral manifolds. (A good reference for Model Theory is [8].) This program has two central aspects: (1) I extend results that are known to be true on the ordered field of real numbers R := 〈R,+,×, <, 0, 1〉 to larger classes of real closed fields, and (2) I then use model theoret...

Type, Neurology and Neurobiology (Hutton, J . -1. & Kenny, A. D., eds.), vol. 18, pp. 337-35 I . Alan R. Liss, New York 10. Ruyan, J. ( 1987) Drugs Future 12. 53 1-532 I I . Newhouse, P. A,, Sunderland, T., Tariot, P. N., Blumhardt, C. L.. Weingartner. H., Mellow, A. & Murphy. D. L. (1987) Psychophnrmacology 95, 171 175 12. Caine. E. D. (1980) N . Engl. J. Med. 303,585-586 13. Wettstein, A. ( 1...

We consider birth-death processes on the nonnegative integers, where {1, 2, . . . } is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional conditions on the transition rates for the existence of a quasi-stationary distribution. Inspired...

We show that if X is a quasi-Banach space with trivial dual then every continuous function f : [0, 1] → X has a primitive, answering a question of M.M. Popov. Let X be a quasi-Banach space and let f : [0, 1] → X be a continuous function. We say that f has a primitive if there is a differentiable function F : [0, 1] → X so that F (t) = f(t) for 0 ≤ t ≤ 1. M.M. Popov has asked where every continu...