Corner view on the crown domain

In this paper we raise a question about the boundary of the crown domain of a Riemannian symmetric space X. In case X is of Hermitian type we give an affirmative answer.     

Radiation conditions and uniqueness for stationary oscillations in elastic plates

Sommerfeld-type radiation conditions are indicated for the solutions of the system governing the small stationary oscillations in plates with transverse shear deformation, and a uniqueness theorem is proved in the case of the corresponding exterior Dirichlet and Neumann problems.

     

Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.     

Decomposition of multiattribute expected-utility functions

This paper integrates and extends the theory of the decomposition of multiattribute expected-utility functions based on utility independence. In a preliminary section, the standard decision model of expected utility is briefly discussed, including the fact that the decision maker's preference forlotteries with two outcomes determines the utility function uniquely. The decomposition possibilities of a utility function are captured by the concept ofautonomous sets of attributes, an affine separability of some kind known as generalized utility independence.Overlapping autonomous sets lead to biaffine-associative, i.e.multiplicative oradditive decompositions. The multiplicative representation shows that autonomy has strongerclosure properties than utility independence, for instance with respect to set-theoretic difference. Autonomy is also a concept with a wider scope since it applies to the decomposition of Boolean functions, games and a number of other topics in combinatorial optimization. This relationship to the well-known theory ofsubstitution decomposition in discrete mathematics also reveals a kind of discrete core behind the decomposition of utility functions. The entirety of autonomous sets can be represented by a compact data structure, the so-calledcomposition tree, which frequently corresponds to a natural hierarchy of attributes. Multiplicative/additive ormulti-affine functions correspond to the hierarchy steps. The known representation of multi-affine functions is shown to be given by aMoebius inversion formula. The entire approach has the advantage that it allows the application of more sophisticated representation methods on a detailed level, whereas it employs onlyfinite set theory andarithmetic on the main levels in the hierarchy.     

Fe(CO)5 thin films adsorbed on Au(111) and on self-assembled organic monolayers: I. Structure

The adsorption of Fe(CO)(5) onto Au(111)/mica and C(4), C(8), C(12), and C(16) SAMs/Au(111)/mica surfaces has been studied using infrared spectroscopy to elucidate the coverage-dependent structures of these films and the intermolecular couplings that determine the form of the spectra. For all substrates, the first layer is composed of molecules physisorbed with one axial and two equatorial carbonyl groups directed toward the substrate; subsequent layers are preferentially oriented with the C(3) molecular axis aligned perpendicular to the substrate (i.e., one axial carbonyl group directed toward the substrate). The axial vibrational band systematically shifts to higher frequencies with increasing surface coverage because of the effects of intermolecular coupling of the quasiparallel transition dipole moments. The strong effects of dipolar coupling are also witnessed by the trends of the band positions when the distance to the image plane is systematically varied using highly organized self-assembled organic substrates; no band shifts are observed when dilute Fe(CO)(5) is embedded in Xe matrixes under identical experimental conditions. The as-deposited films are structurally stable below 125 K on Au(111)/mica surfaces and below 100 K on the organic self-assembled monolayers. The instability of the films above these temperatures demonstrates that the as-adsorbed films do not form thermodynamically well-defined phases but are structurally metastable. The results presented herein and in the companion paper provide a consistent framework to interpret the spectroscopy of these systems that resolves outstanding issues concerning these films and provides a structural model that explains the dynamic properties of these films during exposure to low-energy electron beams.     

Synthesis of some substituted 3-alkenyl-1-phenylpyrazoles

The regioselective synthesis of new 3-alkenyl-1-phenylpyrazoles 4 from the reaction of phenylhydrazine with 2,3-dihydro-4H-pyran-4-ones 1 is described.