W. A. J. Luxemburg: a remarkable mathematician

This is an article describing some of the mathematical contributions of W. A. J. Luxemburg.     

Pushing the frontiers of hard and soft scorpionate chemistry

The preparation and structure of the first scorpionate complex of a group 16 element, [Te(kappa(2)-Tm(Me))(2)], is reported. It displays square planar geometry at the Te atom and two distinct ligand conformations. In addition, the first pyrazolylborate complex of a group 15 element, [Bi(Tp)(2)(pzH)Cl], has been synthesized and characterized.     

Magnetic field dependence of impurity-induced muon depolarization in noble metals

We have measured the magnetic field dependence of the muon depolarization rate up to 5 kOe in AuGd (350 ppm), AgGd (340 ppm) and AgEr (300 ppm). A simple model which includes both dipolar and nearest-neighbor contact interactions between the muon and the magnetic impurity does not fit the data. An axial crystal-field interaction, arising from the electric field gradient induced by the muon at the site of the impurity, is found to dominate the Hamiltonian, and may have a large effect on the field dependence.Supported in part by the U.S. Department of Energy and the National Science Foundation.Work performed at Sandia National Laboratories supported by the U.S. Department of Energy under contract DE-AC04-76DP000789.     

Universal behavior in a generalized model of contagion

Models of contagion arise broadly in both the biological and the social sciences, with applications ranging from the transmission of infectious diseases to the spread of cultural fads. In this Letter, we introduce a general model of contagion which, by explicitly incorporating memory of past exposures to, for example, an infectious agent, rumor, or new product, includes the main features of existing contagion models and interpolates between them. We obtain exact solutions for a simple version of the model, finding that under general conditions only three classes of collective dynamics exist. Furthermore, we find that, for a given length of memory, the class into which a particular system falls is determined by only two parameters. Our model suggests novel measures for assessing the susceptibility of a population to large contagion events, and also a possible strategy for inhibiting or facilitating them.     

Submajorisation inequalities for convex and concave functions of sums of measurable operators

It is shown that non-negative, increasing, convex (respectively, concave) functions are superadditive (respectively, subadditive) with respect to submajorisation on the positive cone of the space of all τ-measurable operators affiliated with a semifinite von Neumann algebra. This extends recent results for n × n-matrices by Ando-Zhan, Kosem and Bourin-Uchiyama. This work was partially supported by the Australian Research Council.     

Interaction of an Endosomolytic Polyamidoamine ISA23 with Vesicles Mimicking Intracellular Membranes: A SANS/EPR Study

The mechanism of ISA23 · HCl interaction with model membrane vesicles (80–100 nm in diameter) was investigated using EPR in conjunction with SANS. For EPR, 16‐DSE was dissolved in the vesicle membrane to measure its dynamics and polarity, whereas a spin‐labeled (Tempo)‐ISA 23 analogue was used to give a measure of the polymer flexibility. When ISA23 was added to the external vesicle surface, no interaction was found. This observation conflicts with the reported ability to lyse RBC, but is in agreement with recent studies that showed no effect on membrane permeability when a PAA was added to an incubation medium containing isolated lysosomal vesicles. The vesicle‐mimetic models used here provide a new and useful tool for studying endosomolytic polymer/membrane interactions.

     

Diverse Modes of Guest Inclusion in a Cyclodextrin: X-ray Structural and Thermal Characterization of a 4:3 β-cyclodextrin—Cyclizine Complex

Abstract

1-Diphenylmethyl-4-methylpiperazine (cyclizine) is an antiemetic drug which forms an inclusion complex with β-cyclodextrin of formula (β-cyclodextrin)₄ · (cyclizine)₃ · 50H₂O. This species crystallizes in the monoclinic space group P2₁ with a = 15.246(1), b = 65.075(5), c = 15.609(1) Å, β = 102.62(1)° and Z = 2 formula units. Complex water content and the host:drug stoichiometric ratio were determined by thermogravimetry and UV spectrophotometry respectively. Differential scanning calorimetry showed that the crystals dehydrate in at least two stages and begin to decompose from approximately 250°C. The crystal structure was solved by a combination of Patterson search and direct methods. Isotropic refinement converged at R = 0.094 for 8806 reflections with I > 2σ(I). The unusual stoichiometry is accounted for as follows: the four β-cyclodextrin molecules comprising the asymmetric unit occur as two independent head-to-head dimers, each formed by O—H…O hydrogen bonding across the macro-cyclic secondary surfaces. One dimer contains two cyclizine guest molecules in head-to-tail orientation, thus accounting for two distinct modes of drug inclusion. In the second dimer, only one β-cyclodextrin molecule is significantly occupied by a cyclizine molecule (in a mode analogous to one of those in the first dimer), the other half of the dimer being largely devoid of guest. A possible mechanism for the formation of this unusual structure is proposed and the crystal packing arrangement is shown to be based on a novel disrupted tetrameric channel motif.     

Rheological properties of HyperMacs—long‐chain branched analogues of hyperbranched polymers

HyperMacs are long chain branched analogues of hyperbranched polymers, differing only in the sense that they have polymer chains, rather than monomers between branch points. Although the building blocks for HyperMacs and AB₂ macromonomers can be well defined in terms of molecular weight and polydispersity, the nature of the coupling strategy adopted for the synthesis of the HyperMacs results in branched polymers with a distribution of molecular weights and architectures. Melt rheology showed polystyrene HyperMacs to be thermorheologically simple, obeying William–Landel–Ferry behavior. Zero shear viscosities of the polymers were shown to increase with average molecular weight and the melts display shear‐thinning behavior. HyperMacs showed little evidence for relaxation by reptation and the rheological behavior agreed well with the Cayley tree model for hierarchical relaxation in tube models of branched polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2762–2769, 2007     

Polymorphism and Cyclodextrin Inclusion of Salbutamol Laurate

Salbutamol laurate is a novel salt form of the well-known bronchodilator salbutamol (albuterol). Its polymorphism and inclusion in (2-hydroxypropyl)-β-cyclodextrinwere investigated by thermogravimetry, differential scanning calorimetry, infrared and powder X-ray diffraction techniques. Two polymorphic forms of the salt were identified. Conditions for inclusion complex formation between the salt and (2-hydroxypropyl)-β-cyclodextrin, namely prolonged co-grinding and kneading, were established by a combination of the above methods. This revised version was published online in August 2006 with corrections to the Cover Date.