Über die Reaktion von W3O mit lod. Darstellung,Kristallstruktur und Eigenschaften von WOI3

On the Reaction of W₃O with Iodine: Preparation, Crystal Structure, and Properties of WOI₃ The novel tungsten oxide iodide WOI₃ is obtained from the reaction of the metalrich tungsten oxide W₃O (also known as ‘β-tungsten’) with iodine in a sealed glass tube placed in a temperature gradient (440–400°C). In the low-temperature region WOI₃ is formed as mouse-grey intergrown needle-like crystals. WOI₃ crystallizes in the tetragonal NbOCl₃ structure type, space group P4₂/mnm, with a = 12.346(2), c = 3.765(1) Å (20°C). The crystal structure at – 130°C was determined from single-crystal diffractometer data (R = 0.023). Results of magnetic susceptibility and vibrational spectroscopic measurements are given together with the mass spectrum of WOI₃ obtained on heating.     

Odd-even effects in the alignment of ferroelectric liquid crystals

Nine different poly-n-alkylterphthalamides have been synthesized, and their properties as alignment layers for chiral smectic C liquid crystals have been determined. Poly-n-hexylterphthalamide is found to be particularly well suited for one of the room temperature mixtures used in this study. The contrast between relaxed states shows an odd-even effect that can probably be explained by the crystal form of the different polymers. The tilt angle found between the relaxed states depends only on the polymer used, not on the inherent tilt of the chiral smectic C phases.     

Using the Donsker Delta Function to Compute Hedging Strategies

We use white noise calculus and the Donsker Delta Function to find explicit formulas for the replicating portfolios in a Black–Scholes market for a class of contingent T-claims.     

A stochastic maximum principle for processes driven by fractional Brownian motion

We prove a stochastic maximum principle for controlled processes X(t)=X^(u)(t) of the form

dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB^(H)(t),

where B^(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion.     

Transition-Metal Thiolates: From Molecular Fragments of Sulfidic Solids to Models for Active Centers in Biomolecules

Thiolates are presently a subject of great interest in the chemistry of complexes involving transition-metal elements and soft ligands. The manifold electronic and steric capabilities offered by the monodentate ligands RS^? and the bidentate chelate ligands ^?SRS^? have been used to stabilize a broad spectrum of mononuclear, oligomeric, and polymeric complexes with new and remarkable structures and properties. Impetus has especially been provided by the synthesis of polynuclear cagelike homo- and heteroleptic metal–sulfur frameworks, which can often be regarded as “molecular fragments” of the structures of inorganic sulfides. Thiolates and mixed sulfide-thiolates of the late open- and closed-shell 3d metals (Fe, Co, Ni, Cu, Zn) and some of their homologues (Au, Cd, Hg), as well as of Mo, are of particular importance as model complexes for biologically important metal centers coordinated by sulfur. They have played an important role in increasing our understanding of the structure, bonding, and function of the reactive centers in ferredoxins, rubredoxins, nitrogenases, blue copper proteins, metallothioneins, and antiarthritic drugs.     

Stability and exponential convergence for the Boltzmann equation

We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L ¹, and extend previous results in L for the non-homogeneous equation, as well as the more developed L ^p -theory for the spatially homogeneous Boltzmann equation.We also give new L -estimates for the spatially homogeneous equation in the case of Maxwellian interactions.     

On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

 The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L ¹ topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L ¹ to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term. (Accepted 25, October 2002) Published online March 14, 2003 Communicated by P.-L. Lions