Reducible expansions and related sharp crossovers in Feigenbaum's renormalization field

We discuss reducible aspects of Mao and Hu's multiple scaling expansion [J. Stat. Phys. 46, 111 (1987); Int. J. Mod. Phys. B 2, 65 (1988)] in the framework of renormalization theory. After establishing a suitable form of reduced expansion, we present numerical evidence showing sharp crossovers from Feigenbaum's constant (delta) to Mao and Hu's constant (delta (')) in the first-order reduced expansion. We find that the crossover is caused by the universal scaling relation existing in constant coefficients of Mao and Hu's expansion. Special attention is paid to constant coefficients corresponding to scaling terms including delta ('). We show numerically that they converge to zero in universal ways with convergence ratios larger than delta. Here, the convergence direction is transversal to the unstable eigendirection of the linearized renormalization operator. From this observation, we propose a concise form of expansion for Feigenbaum's universal function g(r)(x).     

Complex probabilities on R(N) as real probabilities on C(N) and an application to path integrals

We establish a necessary and sufficient condition for averages over complex-valued weight functions on R(N) to be represented as statistical averages over real, non-negative probability weights on C(N). Using this result, we show that many path integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics.     

Iridium-catalyzed H/D exchange into organic compounds in water

The air-stable complex Cp(PMe(3))IrCl(2) efficiently catalyzes the exchange of deuterium from D(2)O into both activated and unactivated C-H bonds of organic molecules without added acid or stabilizers. Selectivity is observed in many cases, with activation of primary C-H bonds occurring preferentially. A number of new stoichiometric transformations involving the iridiym catalyst precursor are also presented, including an oxidation-decarbonylation reaction with primary alcohols.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Mass spectrometric methods: an answer for macromolecule analysis in the 1990s

The field of mass spectrometry is now well developed for solving analytical and structural problems involving substances with molecular weights less than ca. 1000. The future challenge for mass spectrometry is in the area of macromolecule analysis and structural biology. This challenge will be met on two fronts. One is structural analysis of pieces of macromolecules, a task for tandem mass spectrometers. Tandem sector instruments offer sufficient control, reproducibility of results and ease of set-up that they will play a major role in structure studies. When designed to operate with extended array detectors, tandem sector instruments will also offer subpicomole detection limits. The second front is molecular weight measurements. Exciting advances include matrix-assisted laser desorption and electrospray ionization. The need for better means of mass analysis is forecast, and it is suggested that the Fourier transform mass spectrometer can meet the challenge. Success awaits a better understanding of the dynamics of high-mass ions. One route to improved understanding is outlined.     

Atomic level control over surface species via a molecular precursor approach: isolated Cu(I) sites and Cu nanoparticles supported on mesoporous silica

A nonaqueous molecular precursor grafting approach was employed for the generation of well-defined surface structures featuring Cu on a mesoporous silica support. X-ray absorption measurements (XANES and EXAFS) were used to determine that [CuOSi(OtBu)3]4 provided 100% isolated Cu(I) sites upon grafting (without thermal treatment), whereas [CuOtBu]4 gave isolated species with most of the original Cu-O-Cu linkages intact, but in a more relaxed straight chain form. Upon heating under inert conditions, the vast majority of Cu in the materials from [CuOSi(OtBu)3]4 remained as isolated Cu(I) sites (up to 88% isolation), with significant stabilization provided from the -OSi(OtBu)3 ligands. In stark contrast, approximately 100% of the Cu in the materials generated from [CuOtBu]4 was readily reduced upon heating, forming isolated Cu metal particles with an average diameter of 0.7 nm.     

Examples of rational homotopy types of blow-ups

We give an example of two homotopic embeddings of manifolds with isomorphic complex normal bundles but such that the blow-ups of along and along have different rational homotopy types.