The universality of equivariant complex bordism

We show that if A is an abelian compact Lie group, all A-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians. Received: 14 February 2000; in final form: 4 August 2000 / Published online: 19 October 2001     

Esmodil: an acetylcholine mimetic resurfaces in a Southern Australian marine sponge Raspailia (Raspailia) sp

Bioassay directed fractionation of a Raspailia (Raspailia) sp. (Order Poecilosclerida; Family Raspailiidae) collected during scientific trawling operations off the Northern Rottnest Shelf yielded as nematocidal agents the known metabolites, phorboxazoles A (1) and B (2). Further examination revealed the new natural product but known synthetic compound, esmodil (3). The structure for 3 was confirmed by spectroscopic analysis and total synthesis.     

Platinum(II) 1,10-phenanthroline complexes of acetylides containing redox-active groups

The new diimine ligand 3,8-di-n-pentyl-4,7-di(phenylethynyl)-1,10-phenanthroline (1) was used for the synthesis of a range of Pt(II) complexes, viz.[Pt(1)Cl2], [Pt(1)(C triple bond C-Ph)2], [Pt(1)(C triple bond C-Fc)2] and [Pt(1)(C triple bond C-p-C6H4-C triple bond C-Fc)2](Fc = ferrocenyl). Crystal structure analyses were performed for [Pt(1)Cl2] and [Pt(1)(C triple bond C-Ph)2] and revealed that the di(acetylide)pi-tweezer of the latter binds a molecule of chloroform through C-H...pi hydrogen bonds. The redox and optical properties of 1 and its complexes were investigated by (spectro-)electrochemistry, UV-Vis and luminescence spectroscopy, and an energy level diagram was derived for [Pt(1)(C triple bond C-Fc)2] and related compounds on the basis of the data collected. The ferrocenyl-substituted Pt(II) complexes are donor-sensitiser assemblies. Intramolecular quenching of the photoexcited Pt(II) diimine unit leads to very short luminescence lifetimes for [Pt(1)(C triple bond C-p-C(6)H(4)-C triple bond C-Fc)2](2 ns) and [Pt(1)(C triple bond C-Fc)2](0.3 ns), as opposed to [Pt(1)(C triple bond C-Ph)2](0.7 micros). Excimer formation has been observed for [Pt(1)(C triple bond C-Ph)(2)] at room temperature in dichloromethane and at low temperatures in frozen glassy dichloromethane and 2-methyltetrahydrofuran solution, but not in the solid state.     

Aqueous synthesis of derivatized cyclopentadienyl complexes of technetium and rhenium directed toward radiopharmaceutical application

Half-sandwich complexes of the type [(RCOCp)M(CO)(3)] with M = Re and (99(m))Tc were synthesized from [M(OH(2))(3)(CO)(3)](+) in water. The R group can be an organic residue or a receptor binding biomolecule with a spacer to cyclopentadienyl (Cp). This provides a general route to Cp complexes of technetium without the need for starting from [TcBr(CO)(5)]. The X-ray structure of [(C(6)H(5)CH(2)COC(5)H(4))Tc(CO)(3)] has been elucidated. The compound crystallizes in the monoclinic space group P2(1)/c with a = 16.1454(9), b = 7.6300(6), and c = 12.3922(7) A and beta = 107.792(6) degrees. We have chosen a serotonergic receptor ligand (WAY) as an example for the derivatization of Cp with a bioactive molecule. WAY is linked to Cp by an aliphatic chain of variable length. The half-sandwich complexes were prepared from water and organic solvents. The structure of [(WAY4-Cp)Re(CO)(3)] could be elucidated. The compound crystallizes in the monoclinic space group P2(1)/c with a = 15.7112(6), b = 6.8775(3), and c = 25.5217(12) A and beta = 103.778(5) degrees. Quantification of inhibition constants gave a clear structure-activity relationship. A single methylene group between the receptor binding site and the half-sandwich complex gave an IC(50) of 217 nM for HT(1A), whereas a butylene linker resulted in retention of the inhibition constant with an IC(50) of 6 nM with respect to underivatized WAY. For use as radiopharmaceuticals, the compounds have also been prepared with (99m)Tc in quantitative yield.     

Beyond Biological Chelation: Coordination of f-Block Elements by Polyhydroxamate Ligands

The promise of polyhydroxamic acid ligands for the selective chelation of the f-block elements is becoming increasingly more apparent. The initial studies of polyhydroxamic acid siderophores showed the formation of highly stable complexes with Pu^IV, but a higher preference for Fe^III hindered effective applications. The development of synthetic routes toward highly pure and customizable ligands containing multiple hydroxamic acids allowed for the growth of new classes of compounds. Although the first round of these ligands focused on the incorporation of siderophore-like frameworks, the new synthetic strategies led to small molecules of various frameworks and even resins for applications in the field of f-block element separations and biological desorption. Unfortunately, a lack of consistent stability-constant data makes direct comparisons across this body of work difficult. More studies into the stability constants and separations of the f-block elements in a variety of pH ranges is necessary to truly realize the potential for polyhydroxamic acid ligands.     

Structural polymorphism of the actin-espin system: a prototypical system of filaments and linkers in stereocilia

We examine the interaction between cytoskeletal F-actin and espin 3A, a prototypical actin bundling protein found in sensory cell microvilli, including ear cell stereocilia. Espin induces twist distortions in F-actin as well as facilitates bundle formation. Mutations in one of the two F-actin binding sites of espin, which have been implicated in deafness, can tune espin-actin interactions and radically transform the system's phase behavior. These results are compared to recent theoretical work on the general phase behavior linker-rod systems.     

Nematic phase transitions in mixtures of thin and thick colloidal rods

We report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible fd virus) and thick (fd-PEG, fd virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, we observe a nematic-nematic coexistence region bound by a lower critical point. Moreover, we show that a rescaled Onsager-type theory for binary hard-rod mixtures qualitatively describes the observed phase behavior.     

Categorical Geometry and Integration Without Points

The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article (Segal, Bull Am Math Soc 71:419–489, 1965). In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology. First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical σ-algebra). Second (and here we have a major difference from the classical theory), we prove that every finite-additive function μ with values in [0,1] can be extended to a measure on an abstract σ-algebra; this correspondence is functorial and yields uniqueness. As an example we show that the Segal space can be characterized by completely canonical data. Furthermore, from our results it follows that a satisfactory point-free integration arises everywhere where we have a finite-additive probability function on a Boolean algebra.     

The homotopy limit problem for Hermitian K-theory, equivariant motivic homotopy theory and motivic Real cobordism

The homotopy limit problem for Karoubi?s Hermitian K-theory (Karoubi, 1980) [26] was posed by Thomason (1983) [44]. There is a canonical map from algebraic Hermitian K-theory to the Z/2-homotopy fixed points of algebraic K-theory. The problem asks, roughly, how close this map is to being an isomorphism, specifically after completion at 2. In this paper, we solve this problem completely for fields of characteristic 0 (Theorems 16, 20). We show that the 2-completed map is an isomorphism for fields F of characteristic 0 which satisfy cd₂(F[i])<∞, but not in general.     

Model filled polymers. IX. Synthesis of uniformly crosslinked polystyrene microbeads

Monodisperse sized crosslinked polystyrene (PS) beads prepared by reaction of styrene (S) and divinylbenzene (DVB), in batch emulsion copolymerization in the absence of emulsifiers, are not uniformly crosslinked, because DVB is more reactive than S. For copolymerization of 1 to 10 mol % DVB and S, within each crosslinked PS microbead, the crosslink density varies by a factor exceeding two and decreases with increased conversion. A semicontinuous copolymerization, involving incremental additions of DVB, produces uniformly crosslinked PS beads. For both copolymerization techniques, T_g correlates well with crosslink density and PS beads are spherical and monodisperse in size. © 1992 John Wiley & Sons, Inc.