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     

The physics of diamond

The accurate measurement of the thermal conductivity of metals still poses considerable experimental difficulty. The reasons for this, and the main ways in which the problem has been approached, are summarized. A detailed examination of the development in technique and methods of measurement shows that while most of the steady-state methods introduced over 50 years ago are still being improved, the emphasis in the last few years has been on the development of methods which give more rapid results, particularly at high temperatures.     

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.     

Compact operators in Banach lattices

Disjoint sequence methods from the theory of Riesz spaces are used to study compact operators on Banach lattices. A principal new result of the paper is that each positive map from a Banach latticeE to a Banach latticeF with compact majorant is itself compact provided the norms onE′ andF are order continuous.     

Partial coherence in multivariate random processes

The ideas of residual spectral density and partial coherence are developed in general terms by using the known spectral response relationships for multivariate random processes, and avoiding specific reference to least-squares prediction. An alternative approach is presented in which an analogous block diagram facilitates the analysis of higher-order partial coherence functions, and brings fresh insight to the problem.     

Use of the mixed basis method for ab initio SCF MO calculations

A previously described mixed basis method for performing SCF MO calculations has been applied to the benzene molecule and to the allyl cation. A basis set of Slater type orbitals is used to calculate the one-electron and one-centre two-electron integrals whilst the many-centre two-electron integrals are approximated by small gaussian type orbital expansions of the STO basis. Comparison of the results with all-gaussian basis sets and literature values indicates that the mixed basis 2-GTO approximation is inadequate for molecules of this size because of the consistent underestimation of the electron repulsion integrals. The use of gaussian exponents chosen by a least-squares procedure rather than variationally gives better mixed basis results, but the indications are that a 4-GTO expansion is necessary for reliable mixed basis calculations. A method for more accurate integral evaluation by gaussian expansions of orbital products is suggested.

---

Zusammenfassung Eine früher beschriebene Methode mit gemischter Basis zur Durchführung von SCF-MO-Berechnungen wurde auf das Benzolmolekül sowie das Allylkation angewendet. Ein Basissatz aus Slaterorbitalen wird verwendet, um die Einelektronen- und die Einzentrenzweielektronenintegrale zu berechnen, während die Mehrzentrenzweielektronenintegrale mit Hilfe von Entwicklungen der Slaterorbitale nach wenigen Gaußfunktionen angenähert werden. Ein Vergleich mit Ergebnissen von Rechnungen mit Gesamtbasissätzen von Gaußfunktionen und mit Literaturwerten zeigt, daß der gemischte Basissatz 2-GTO ungeeignet für Moleküle von dieser Größe ist, da die Elektronenabstoßungsintegrale durchgehend zu klein berechnet werden. Die Verwendung von Exponenten der Gauß-funktion, die mit Hilfe einer Methode der kleinsten Quadrate gewonnen wurde, ergibt bei der gemischten Basis bessere Ergebnisse als diejenigen, die nach der Variationsmethode gewonnen wurden; es zeigt sich jedoch, daß 4-GTO-Entwicklungen für angemessene Berechnungen mit gemischter Basis notwendig werden. Eine Methode für eine genauere Integralberechnung mit Hilfe der Entwicklung von Orbitalprodukten nach Gaußfunktionen wird vorgeschlagen.

---

Résumé Application à la molécule de benzène d'une méthode de base mixte précédemment décrite pour effectuer les calculs SCF MO. Une base d'orbitales de Slater est utilisée pour calculer les intégrales monoélectroniques et les intégrales biélectroniques monocentriques; les intégrales biélectroniques polycentriques sont approchées au moyen d'une expression des orbitales de Slater en orbitales gaussiennes. La comparaison des résultats avec ceux obtenus en bases gaussiennes et avec ceux donnés dans la littérature indique que l'approximation 2-GTO n'est pas adaptée aux molécules de cette taille car elle provoque une sous-estimation constante des intégrales de répulsion électronique. L'emploi d'exposants gaussiens choisis par un procédé de moindres carrés plutôt que par une méthode variationnelle donne de meilleurs résultats en bases mixtes mais il s'avère nécessaire d'utiliser un développement du type 4-GTO. On propose une méthode pour l'évaluation plus précise des intégrales par développement gaussien des produits d'orbitales.