Stationary probability measures and topological realizations

We establish the generic inexistence of stationary Borel probability measures for aperiodic Borel actions of countable groups on Polish spaces. Using this, we show that every aperiodic continuous action of a countable group on a compact Polish space has an invariant Borel set on which it has no σ-compact realization.     

β-Mannosidase and β-hexosaminidase inhibitors: synthesis of 1,2-bis-epi-valienamine and 1-epi-2-acetamido-2-deoxy-valienamine from d-mannose

A partially protected C-5C-5a unsaturated carbasugar with α-lyxo configuration is synthesised in five steps and 26% overall yield from a known mannose-derived hemiacetal, using ring-closing metathesis as a key step. This carbasugar is converted into valienamine derivatives with β-lyxo (i.e., corresponding to β-manno at C-1–C-4), α-lyxo (i.e., corresponding to α-manno at C-1–C-4) and β-2-acetamido-2-deoxy-xylo (i.e., corresponding to β-GlcNAc at C-1–C-4) configurations. This is the first report of the synthesis of the β-lyxo compound, 1,2-bis-epi-valienamine, which was found to inhibit Cellulomonas fimi β-mannosidase (CfMan2A) with K_i 140 μM. We report the crystal structures of three protected C-5C-5a unsaturated carbasugars with lyxo configuration.     

Block liposomes from curvature-stabilizing lipids: connected nanotubes, -rods, or -spheres

We report on the discovery of block liposomes, a new class of chain-melted (liquid) vesicles, with membranes comprised of mixtures of the membrane-curvature-stabilizing multivalent lipid MVLBG2 of colossal charge +16 e and neutral 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC). In a narrow MVLBG2 composition range (8-10 mol%), cryo-TEM revealed block liposomes consisting of distinctly shaped, yet connected, nanoscale spheres, pears, tubes, or rods. Unlike typical liposome systems, where spherical vesicles, tubular vesicles, and cylindrical micelles are separated on the macroscopic scale, within a block liposome, shapes are separated on the nanometer scale. Diblock (pear-tube) and triblock (pear-tube-pear) liposomes contain nanotubes with inner lumen diameter of 10-50 nm. Diblock (sphere-rod) liposomes were found to contain micellar nanorods approximately 4 nm in diameter and several micrometers in length, analogous to cytoskeletal filaments of eukaryotic cells. Block liposomes may find a range of applications in chemical and nucleic acid delivery and as building blocks in the design of templates for hierarchical structures.     

Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement

The discrete ordinates method (DOM) and finite-volume method (FVM) are used extensively to solve the radiative transfer equation (RTE) in furnaces and combusting mixtures due to their balance between numerical efficiency and accuracy. These methods produce a system of coupled partial differential equations which are typically solved using space-marching techniques since they converge rapidly for constant coefficient spatial discretization schemes and non-scattering media. However, space-marching methods lose their effectiveness when applied to scattering media because the intensities in different directions become tightly coupled. When these methods are used in combination with high-resolution limited total-variation-diminishing (TVD) schemes, the additional non-linearities introduced by the flux limiting process can result in excessive iterations for most cases or even convergence failure for scattering media. Space-marching techniques may also not be quite as well-suited for the solution of problems involving complex three-dimensional geometries and/or for use in highly-scalable parallel algorithms. A novel pseudo-time marching algorithm is therefore proposed herein to solve the DOM or FVM equations on multi-block body-fitted meshes using a highly scalable parallel-implicit solution approach in conjunction with high-resolution TVD spatial discretization. Adaptive mesh refinement (AMR) is also employed to properly capture disparate solution scales with a reduced number of grid points. The scheme is assessed in terms of discontinuity-capturing capabilities, spatial and angular solution accuracy, scalability, and serial performance through comparisons to other commonly employed solution techniques. The proposed algorithm is shown to possess excellent parallel scaling characteristics and can be readily applied to problems involving complex geometries. In particular, greater than 85% parallel efficiency is demonstrated for a strong scaling problem on up to 256 processors. Furthermore, a speedup of a factor of at least two was observed over a standard space-marching algorithm using a limited scheme for optically thick scattering media. Although the time-marching approach is approximately four times slower for absorbing media, it vastly outperforms standard solvers when parallel speedup is taken into account. The latter is particularly true for geometrically complex computational domains.     

New emissive fac-tricarbonylchlorobis(ligand)rhenium(I) complexes prepared from pyridine/thiophene hybrid ligands

Stille coupling between tributyl-(2,3-dihydro-thieno[3,4-b][1,4]dioxin-5-yl)-stannane and 4-bromopyridine resulted in the preparation of the new pyridine/thiophene hybrid ligand 4-(2,3-dihydro-thieno[3,4-b][1,4]dioxin-5-yl)-pyridine [4-py-EDOT] (1). Reaction of 1, 4-thiophen-2-yl-pyridine (2), or 4-[2,2^′]bithiophenyl-5-yl-pyridine (3) with ClRe(CO)₅ resulted in the isolation of complexes 4-6, ClRe(L)₂(CO)₃, where L=1, 2, or 3 respectively. The solid-state structure of 4 was determined by X-ray crystallography, which clearly shows the fac arrangement of the three CO ligands and the two 4-py-EDOT ligands arranged cis to one another. The metal complexes 4-6 have been characterized by ¹H and ¹³C NMR, ESI or FAB MS, FTIR, UV-Vis, fluorescence, and elemental analysis.     

Interactive Optimization Aspects of Electronic Spreadsheet Models for Design and Planning

This paper extends the discussion of the relationship between optimization and electronic spreadsheet modelling. Previous authors have described two connections. These are, first, the use of spreadsheets to facilitate optimization projects and, second, the use of optimization within the spreadsheet model itself such as for cell value computation. In this paper we argue that use of the spreadsheet model for planning and design problems often may actually be viewed as interactive multi-criterion optimization per se. This provides a third connection between optimization and spreadsheet models. We base our arguments on a simplified example arising in insurance consulting work and note other examples as well. We also propose a method for incorporating this observation into existing spreadsheet models and indicate desirable innovations in spreadsheet software.     

A binuclear rhodium(I) complex with two tetraphosphine ligands at 100 K

Bis(μ‐3,11‐diethyl‐6,8‐di­phenyl‐3,6,8,11‐tetraphosphatri­dec­ane‐κ⁴P³,P⁶:P⁸,P¹¹)­dirhodium(I) bis­(tetra­fluoro­borate), [Rh₂(C₂₅H₄₀P₄)₂](BF₄)₂, is a bimetallic complex containing two binucleating tetra‐tertiary phosphine ligands. The distance between the metal centers is 5.4555 (11) Å, with no metal–metal bond. The Rh—P bond distances range from 2.2483 (14) to 2.3295 (14) Å. The geometry about the Rh^I atoms is tetrahedrally distorted square planar and the dihedral angle between the two coordination planes is 66.28 (5)°.