Asymptotic behavior of semigroups of ρ-non-expansive and holomorphic mappings on the Hilbert Ball

We study generated semigroups of those self-mappings of the Hilbert ball which are non-expansive with respect to the hyperbolic metric. We find optimal convergence rates for such semigroups to interior stationary and boundary sink points. Since the hyperbolic metric is not defined on the boundary, the usual approach treats these two cases separately. In contrast with this practice, we use a special non-Euclidean “distance” (which induces the original topology) to present a unified theory. Our approach leads to new results even in the one-dimensional case. When the semigroups consist of holomorphic self-mappings, we obtain the rather unexpected phenomenon of universal rates of convergence of an exponential type. In particular, in the case of a boundary sink point we establish a continuous analog of the celebrated Julia–Wolff–Carathéodory theorem. Received: January 3, 2001; in final form: November 28, 2001?Published online: October 30, 2002     

Hydrogen Bonding and Solvent Effects on Complexation of Alkali Metal Cations by Lower Rim Calix[4]arene Tetra(O-[N -acetyl-D -phenylglycine methyl ester]) Derivative

Complexation of alkali metal cations with 5,11,17,23-tetra-tert-butyl-26,28,25,27-tetrakis(O-methyl-D-α-phenylglycylcarbonylmethoxy)calix[4]arene (L) was studied by means of spectrophotometric, conductometric and potentiometric titrations at 25 °C. The solvent effect on the binding ability of L was examined by using two solvents with different affinities for hydrogen bonding, viz. methanol and acetonitrile. Despite the presence of intramolecular NH···O=C hydrogen bonds in L, which need to be disrupted to allow metal ion binding, this calix[4]arene amino acid derivative was shown to be an efficient binder for smaller Li⁺ and Na⁺ cations in acetonitrile (lg K_LiL > 5, lg K_NaL = 7.66), moderately efficient for K⁺ (lg K_KL = 4.62), whereas larger Rb⁺ and Cs⁺ did not fit in its hydrophilic cavity. The complex stabilities in methanol were significantly lower (lg K_NaL = 4.45, lg K_KL = 2.48). That could be explained by different solvation of the cations and by competition between the cations and methanol molecules (via hydrogen bonds) for amide carbonyl oxygens. The influence of cation solvation on complex stability was most pronounced in the case of Li⁺ for which, contrary to the quite stable LiL⁺ complex in acetonitrile, no complexation was observed in methanol under the conditions used.     

GC-MS studies of the chemical composition of two inedible mushrooms of the genus Agaricus

Background  

Mushrooms in the genus Agaricus have worldwide distribution and include the economically important species A. bisporus. Some Agaricus species are inedible, including A. placomyces and A. pseudopratensis, which are similar in appearance to certain edible species, yet are known to possess unpleasant odours and induce gastrointestinal problems if consumed. We have studied the chemical composition of these mushrooms using GC-MS.     

A characterization of nonlinear φ-accretive operators

Let E be a Banach space and E(–,] a proper lower semi-continuous convex function. The main purpose of this paper is to characterize those m-accretive operators AE x E that are also -accretive. This is done by using the semigroup S generated by -A, and by first establishing a necessary and sufficient condition for to be a Lyapunov function for S. We also obtain similar results for accretive operators that are not necessarily m-accretive, and deduce invariance and order-preserving criteria for nonlinear semigroups.This research was partially supported by the National Science Foundation under Grant MCS-8102086.     

A convergence theorem for asymptotic contractions

We show that to each asymptotic contraction T with a bounded orbit in a complete metric space X, there corresponds a unique point x _* such that all the iterates of T converge to x _*, uniformly on any bounded subset of X. If, in addition, some power of T is continuous at x _*, then x _* is a fixed point of T. Dedicated to Professor Felix E. Browder with admiration and respect     

Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

The problem considered in this paper is that of finding a point which iscommon to almost all the members of a measurable family of closed convexsubsets of R₊₊ ⁿ , provided that such a point exists.The main results show that this problem can be solved by an iterative methodessentially based on averaging at each step the Bregman projections withrespect to f(x)=_i=1 ⁿx_i· ln x_i ofthe current iterate onto the given sets.