A palladium-oxo complex. Stabilization of this proposed catalytic intermediate by an encapsulating polytungstate ligand

A terminal Pd-oxo unit is reported. The unit is encapsulated in a cavity defined by two [A-alpha-PW9O34]9- units fused together by one [WO(OH2)]4+ center and forms from Pd(II) in buffered media in the presence of O2. Both X-ray diffraction and EXAFS data are consistent with a Pd-oxo bond distance of ca. 1.65 A. 17O NMR studies confirm that the solid-state structure is maintained in solution.     

The power of 2 dividing the class-number of a binary quadratic discriminant

In this paper we study congruence conditions on class numbers of binary quadratic discriminants d, modulo powers of 2, where d has two or three distinct prime divisors.     

Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem

Fermionic quantization, or Clifford algebra, is combined with pseudodifferential operators to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold.     

Affine stratifications from finite misère quotients

Given a morphism from an affine semigroup to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof rests on mesoprimary decomposition of monoid congruences and a novel list of equivalent conditions characterizing the existence of an affine stratification. The motivating consequence of the main result is a special case of a conjecture due to Guo and the author on the existence of affine stratifications for (the set of winning positions of) any lattice game. The special case proved here assumes that the lattice game has finite misère quotient, in the sense of Plambeck and Siegel.     

Stanley's Simplicial Poset Conjecture,After M. Masuda

ABSTRACT

M. Masuda recently provided the missing piece proving a conjecture of R.P. Stanley on the characterization of f-vectors for Gorenstein? simplicial posets. We propose a slight simplification of Masuda's proof.     

A flexible microfluidic processor for molecular biology: application to microarray sample preparation

We describe a programmable microfluidic system with onboard pumps and valves that has the ability to process reaction volumes in the sub-microlitre to hundred microlitre range. The flexibility of the architecture is demonstrated with a commercial molecular biology protocol for mRNA amplification, implemented without significant modification. The performance of the microchip system is compared to conventional bench processing at each stage of the multistep protocol, and DNA microarrays are used to assess the quality and performance of bench- and microchip-amplified RNA. The results show that the microchip system reactions are similar to bench control reactions at each step, and that the microchip- and bench-derived amplified RNAs are virtually indistinguishable in differential microarray analyses.     

Employment of [Amim] Cl in the effort to upgrade the properties of cellulose acetate based polymer electrolytes

Transparent thin film polymer electrolytes were prepared by solvent casting technique with the doping of environmental-friendly ionic liquid, 1-allyl-3-methylimidazolium chloride ([Amim] Cl) into the matrix formed by cellulose acetate (CA) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). The ionic conducting nature of this system improves significantly from the order of 10^?7–10^?2 S cm^?1 upon increasing doping of [Amim] Cl content till a maximum of 4.68 × 10^?2 S cm^?1 is attained for the composition CA:LiTFSI:[Amim] Cl (14:6:80 wt%). The improving trend in ionic conductivity results from the bond weakening between the connecting atoms in the crystalline region that induces to the increase in amorphous counterpart fractions in the CA matrix. This observation was proved via the accountancies in the reduction of relative viscosity, root mean square value and increase in void as increase in [Amim] Cl doping. The resultant phase conversion hence permits immense lithium ion (Li⁺) fluidity along the polymer backbone and assisting the improvement in ionic conductivity. The thin film polymer electrolyte is found to be elastic in the presence of crystalline fraction and radically deforms upon the chains diffusion into the amorphous fraction. The linear curvatures of the Arrhenius plot justify the conductivity improvement as via the increasing frequency of Li⁺ ions hopping as the temperature increases. The increasing addition of [Amim] Cl diminishes both the heat-resistivity and thermal stability of CA:LiTFSI:[Amim] Cl matrix.     

Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings

Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a convex polyhedral pseudomanifold. We prove that S has a polyhedral nonoverlapping unfolding into , so the metric space S is obtained from a closed (usually nonconvex) polyhedral ball in by identifying pairs of boundary faces isometrically. Our existence proof exploits geodesic flow away from a source point v∈S, which is the exponential map to S from the tangent space at v. We characterize the cut locus (the closure of the set of points in S with more than one shortest path to v) as a polyhedral complex in terms of Voronoi diagrams on facets. Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v on S produces an algorithmic method for constructing Voronoi diagrams in each facet, and hence the unfolding of S. The algorithm, for which we provide pseudocode, solves the discrete geodesic problem. Its main construction generalizes the source unfolding for boundaries of three-polytopes into . We present conjectures concerning the number of shortest paths on the boundaries of convex polyhedra, and concerning continuous unfolding of convex polyhedra. We also comment on the intrinsic nonpolynomial complexity of nonconvex manifolds. The first author was partially supported by the National Science Foundation, and he acknowledges the Mathematisches Forschungsinstitut Oberwolfach for a stimulating research environment during the week-long program on Topological and Geometric Combinatorics (April, 2003). Most of this work was completed while the first author was at the Massachusetts Institute of Technology (Cambridge, MA) and the Mathematical Sciences Research Institute (Berkeley, CA). The second author was partially supported by the National Security Agency and the National Science Foundation. He thanks the organizers of the “Second Geometry Meeting dedicated to A.D. Aleksandrov” held at the Euler International Mathematical Institute in St. Petersburg (June, 2002), where these results were originally presented.