Reaction of bis(phosphine)(hydrotris(3,5-dimethylpyrazolyl)borato)rhodium(I) with phenylacetylene,p-nitrobenzaldehyde,and triphenyltin hydride: structures of [Rh(Tp)(PPh(3))(2)], [Rh(Tp)(H)(C(2)Ph)(P(4-C(6)H(4)F)(3))], [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PPh(3))], and [Rh(Tp)(H)(SnPh(3))(PPh(3))

The complexes [Rh(Tp)(PPh(3))(2)] (1a) and [Rh(Tp)(P(4-C(6)H(4)F)(3))(2)] (1b) combine with PhC(2)H, 4-NO(2)-C(6)H(4)CHO and Ph(3)SnH to give [Rh(Tp)(H)(C(2)Ph)(PR(3))] (R = Ph, 2a; R = 4-C(6)H(4)F, 2b), [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PR(3))] (R = Ph, 3a), and [Rh(Tp)(H)(SnPh(3))(PR(3))] (R = Ph, 4a; R = 4-C(6)H(4)F, 4b) in moderate to good yield. Complexes 1a, 2b, 3a, and 4a have been structurally characterized. In 1a the Tp ligand is bidentate, in 2b, 3a, and 4a it is tridentate. Crystal data for 1a: space group P2(1)/c; a = 11.9664(19), b = 21.355(3), c = 20.685(3) A; beta = 112.576(7) degrees; V = 4880.8(12) A(3); Z = 4; R = 0.0441. Data for 2b: space group P(-)1; a = 10.130(3), b = 12.869(4), c = 17.038(5) A; alpha = 78.641(6), beta = 76.040(5), gamma = 81.210(6) degrees; V = 2100.3(11) A(3); Z = 2; R = 0.0493. Data for 3a: space group P(-)1; a = 10.0073(11), b = 10.5116(12), c = 19.874(2) A; alpha = 83.728(2), beta = 88.759(2), gamma = 65.756(2) degrees; V =1894.2(4) A(3); Z = 2; R = 0.0253. Data for 4a: space group P2(1)/c; a = 15.545(2), b = 18.110(2), c = 17.810(2) A; beta = 95.094(3) degrees; V = 4994.1(10) A(3); Z = 4; R = 0.0256. NMR data ((1)H, (31)P, (103)Rh, (119)Sn) are also reported.     

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

We study the existence theory for parabolic variational inequalities in weighted L ² spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L ² setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.     

New proof and some generalizations of the minimum principle in optimal control

An optimal control problem is reduced to the finite-dimensional problem of minimizing the terminal payoff over the intersection of the target set with the reachable set. The pointwise Pontryagin minimum principle is derived from two simple preliminary results: the first states that the intersection of two inseparable derived cones at a common point of two given sets is contained in the quasitangent cone (hence, in the contingent cone) to their intersection; the second identifies a derived cone to the reachable set. The standard variants of the minimum principle are easily generalized to problems defined by non-differentiable terminal payoffs on arbitrary target sets.     

Small-angle X-ray scattering and light scattering on lysozyme and sodium glycocholate micelles

Small-angle X-ray scattering (SAXS) together with static (SLS) and dynamic light scattering (DLS) measurements were carried out on aqueous solutions of lysozyme (LY) and of the ionic biological detergent sodium glycocholate (NaGC). Apparent diffusion coefficients (D app), excess Rayleigh ratio, and SAXS spectra were measured for 0.1 M NaGC solutions at different ionic strengths (0.05-0.30 M NaCl). The same data were collected for LY in sodium acetate buffer 50 mM without and with 92 mM NaCl as a function of protein concentration (10-80 g L(-1)). A correlated analysis of SLS data and SAXS spectra was first tested on the LY samples and then extended to the interpretation of the NaGC data to infer information on particle structure and interaction potential. A hard-core (HC) interaction shell of uniform thickness, a screened Coulomb potential of the electric double layer (EDL) or the complete DLVO potential were alternatively used to represent the long-range tail of the interaction potential. Whenever an essentially repulsive tail is expected, all the representations give reasonable results, but the data analysis does not allow the discrimination between the oblate and the prolate symmetries of the NaGC aggregates. The DLVO model allows the interpretation of the data even when the attractive component determines the tail character. With this model an overall fit of the micelle data at all the NaCl concentrations was successfully performed by assuming a simple spherical symmetry of the micelles and invariant values of their ionization degree and Hamaker constant, thus considering just the screening effect of the added electrolyte. Whatever model is used, the results point out that the aggregates are quite hydrated (26-38 water molecules per monomer) and very slightly grow by increasing the NaCl concentration. When spherical symmetry is assumed the aggregate radii for all the samples fall in the range 15-16 A. From the SAXS and SLS, best fitting geometrical parameters, and interparticle structure factor, a D app value was calculated for each sample. An excellent consistence is achieved for LY results. On the contrary, calculated D app values systematically lower than the experimental values are always obtained for the NaGC micelles. Micelle polydispersity and internal dynamics seem to be the most probable reasons of the bad agreement.     

Development and validation of an integrated computational approach for the study of ionic species in solution by means of effective two-body potentials. The case of Zn2+, Ni2+, and Co2+ in aqueous solutions

In this paper we have developed an effective computational procedure for the structural and dynamical investigation of ions in aqueous solutions. Quantum mechanical potential energy surfaces for the interaction of a transition metal ion with a water molecule have been calculated taking into account the effect of bulk solvent by the polarizable continuum model (PCM). The effective ion-water interactions have been fitted by suitable analytical potentials, and have been utilized in molecular dynamics (MD) simulations to obtain structural and dynamical properties of the ionic aqueous solutions. This procedure has been successfully applied to the Co2+-H2O open-shell system and, for the first time, Co-oxygen and Co-hydrogen pair potential functions have been determined and employed in MD simulations. The reliability of the whole procedure has been assessed by applying it also to the Zn2+ and Ni2+ aqueous solutions, and the structural and dynamical properties of the three systems have been calculated by means of MD simulations and have been found to be in very good agreement with experimental results. The structural parameters of the first solvation shells issuing from the MD simulations provide an effective complement to extended X-ray absorption fine structure (EXAFS) experiments.     

Crystal structure of the 2:1 inclusion compound between deoxycholic acid and quadricyclane

The 2:1 inclusion compound formed between deoxycholic acid (C₂₄H₄₀O₄,M _r=392.58) and quadricyclane (C₇H₈,M _r=92.14) crystallizes in space groupP2₁2₁2₁ witha=27.150(7),b=13.359(3),c=14.161(4) Å,Z=4. The structure was refined toR=0.08₆ andR _w=0.08₈ for 2079 observed reflections withI>2.5(I). The crystal packing is very similar to that found in the norbornadiene-deoxycholic acid inclusion compound and is characterized by an assembly of antiparallel pleated bilayers, formed by molecules of deoxycholic acid held together through hydrogen bonds. Quadricyclane occupies approximately the same position of norbornadiene and its atoms give rise to good van der Waals interactions with some methyl groups of deoxycholic acid. Supplementary Data relating to the article are deposited with the British Library as Supplementary Publication No. SUP 82006 (14) pages. To obtain copies, see page ii of this issue.     

Stable Transitivity of Certain Noncompact Extensions of Hyperbolic Systems

Let be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, we find transitive extensions for any finite-dimensional connected Lie group extension. If, in addition, the group is perfect and has an open set of elements that generate a compact subgroup, we find open sets of stably transitive extensions. In particular, we find stably transitive -extensions. More generally, we find stably transitive -extensions for all n ≥ 1. For the Euclidean groups SE(n) with n ≥ 4 even, we obtain a new proof of a result of Melbourne and Nicol stating that there is an open and dense set of extensions that are transitive.For groups of the form where K is compact, a separation condition is necessary for transitivity. Provided X is a hyperbolic attractor, we show that an open and dense set of extensions satisfying the separation condition are transitive. This generalizes a result of Niţică and Pollicott for -extensions.Communicated by Viviane Baladisubmitted 24/05/04, accepted 11/10/04     

Spectral analysis of an acoustic multistratified perturbed cylinder

We look into the operator of acoustic propagation H := -V . pV,with Dirichlet condition, in a domain R := 0' x IR, 0' being boundedin Rn-'(n > 2). The function p is assumed to be real, greater than astrictly positive constant and belongs to Lm(R). When (-1)3x, + oo itis obtained by short-range and long-range perturbations of the functionspi = p(j) @ l(j = 1,2), where E Lm(R') are real and bounded belowby a strictly positive constant. By using a variant of the conjugateoperator method of Mourre [15], and some ideas of the N-body problem in quantum mechanics, we develop the spectral analysis of operator H

and obtain a limiting absorption principle.     

Tables of Rosseland mean opacities for candidate atmospheres of life hosting free-floating planets

The existence of life on a free-floating planet is conditioned by the existence of an optically thick atmosphere. This may ensure the long-term thermal stability of a (liquid) solvent on the surface of that body. Requirements to be fulfilled by a hypothetic gas constituent of a free-floating planet atmosphere are studied. The four gases analyzed here (nitrogen, carbon dioxide, methane and ethane) are candidates. They may induce a higher opacity than molecular hydrogen, which has been considered in previous research. The paper deals with preparation of tables of Rosseland mean opacity values. Selection of the ranges of temperature and pressure is guided by life existence considerations. The range of temperatures involved (50 to 650 K) is lower than usually found in the literature. The tables may be useful for studies related to free-floating planets, where the usage of absorption opacity is a straightforward way to compute the energy flux in the atmosphere. Also, the results are useful in all cases where radiation is transferred through dense layers of the gases considered in this paper.