Alternating sign matrices and descending plane partitions

An alternating sign matrix is a square matrix such that (i) all entries are 1, ?1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math.53 (1979), 193–225) have been discovered, but attempts to prove the existence of such a connection have been unsuccessful. This evidence, however, did suggest a method of proving the Andrews conjecture on descending plane partitions, which in turn suggested a method of proving the Macdonald conjecture on cyclically symmetric plane partitions (Invent. Math.66 (1982), 73–87). In this paper is a discussion of alternating sign matrices and descending plane partitions, and several conjectures and theorems about them are presented.     

Formation of a pyrazopyrazolone by the pyrolysis of antipyrine diazonium fluoroborate

The pyrolysis of antipyrine 4-dizaonium fluoroborate gave an antipyrylazopyrazopyrazolone instead of the desired 4-fluoroantipyrine. This compound was formed by intermolecular and intramolecular coupling of the diazo compound at elevated temperatures. J. Heterocyclic Chem., 14, 1107 (1977)     

EuFCl—A new mixed-halide rare-earth compound

This paper reports the synthesis and bulk magnetic properties of a new rare-earth compound, EuFCl, isostructural with tetragonal PbFCl, and solid solutions of it with several LnOCl compounds, where Ln = Eu, Sm, Nd, Gd.     

General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations

Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated.     

Planar nitric oxide (NO)-selective ultramicroelectrode sensor for measuring localized NO surface concentrations at xerogel microarrays

A planar ultramicroelectrode nitric oxide (NO) sensor was fabricated to measure the local NO surface concentrations from NO-releasing microarrays of varying geometries. The sensor consisted of platinized Pt (25 microm) working electrode and a silver paint reference electrode coated with a thin silicone rubber gas permeable membrane. An internal hydrogel layer separated the Pt working electrode and gas permeable membrane. The total diameter of the sensor was 相似文献   

n-Particle Quantum Statistics on Graphs

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.