Proximal-isometric (P J) flows

We develop some new tools for the study of minimal transformation groups (flows) and apply these tools to extend the classification theory of minimal flows to a larger class than has previously been classified. The tools we develop arise from a simplification and unification of the techniques used by Furstenberg, Ellis, and Veech in their proofs of structure theorems about distal and point distal flows. This simplification is made possible largely through the use of recent results of Glasner on the structure of 2^X (whose points consist of closed subsets of the phase space X of a given flow).     

X-RAY INDUCED VISIBLE LUMINESCENCE OF PORPHYRINS

A concept has been presented whereby X-ray irradiation can be used to induce visible luminescence of chromophores such as porphyrins. The essential aspects of the idea have been demonstrated in a supramolecular assembly consisting of a water-dispersed polystyrene latex with an embedded scintillating compound, 2,5-diphenyloxa-zole, and an externally attached hematoporphyrin. X-ray excitation of the assembly yields an emission spectra typical for hematoporphyrin with fluorescent yields. of up to 3% with respect to 2,5-diphenyloxazole emission. Significant quenching in the presence of dioxygen indicates that singlet oxygen is formed at atmospheric conditions.     

The signature operator at 2

It is well known that the signature operator on a manifold defines a K-homology class which is an orientation after inverting 2. Here we address the following puzzle: What is this class localized at 2, and what special properties does it have? Our answers include the following:

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the K-homology class Δ_M of the signature operator is a bordism invariant;

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the reduction mod 8 of the K-homology class of the signature operator is an oriented homotopy invariant;

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the reduction mod 16 of the K-homology class of the signature operator is not an oriented homotopy invariant.

     

Optimization over Young diagrams

Journal of Algebraic Combinatorics - We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of...     

High-resolution separation of peptides by sodium dodecyl sulfate-polyacrylamide gel "focusing"

As a follow-up of our previous report (Anal. Chem. 2007, 79, 821-827) on analytical SDS-PAGE focusing, a refinement of the method for separation of peptides in the small to medium M(r) range (0.5-10 kDa) is here reported, based on a shallow gradient of immobilized positive charges (0-10 mM) onto a minimally sieving polyacrylamide gel matrix (4%T, 2.5%C). Unlike conventional SDS-PAGE, which rarely can achieve the separations of polypeptide chains below a critical value of 10 kDa, the present method can be fine-tuned to perform such separations even down to a size of only 500 Da. In the case of larger fragments, the major peptide zones are shown, under microscope observation, to be composed by envelopes of bands as narrow as 20-100 microm, spaced at regular intervals of 100-150 microm. It is hypothesized that such larger peptides could form complexes with rather small SDS micelles and that such peptide-SDS complexes could differ in charge by just a single negative charge.     

Photophysics of (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP): an experimental test for conical intersections

Fluorescence experiments on (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP) are reported in liquid and glassy solutions. The data indicate a fast decay in the fluid nonpolar, nonprotic solutions (decay times approximately 10(-12) s) and rapid but considerably slower decay in polar ones. In frozen solutions (polar and nonpolar), the fluorescence quantum yield is much higher (near 0.5 and around 0.1 in polar and nonpolar glasses, respectively). The rapid nonradiative transitions in fluid solutions are assigned to internal conversion in both solvent classes, as intersystem crossing is much slower and no net reaction is observed. These results are in agreement with predictions made for the closely related (in terms of electronic structure) but simpler molecule cyclopentadienyl-1,4-dihydropyridine (CPDHP) for which an S1/S0 conical intersection was recently proposed [Int. J. Quant. Chem. 2005, 102, 961]. The crossing of the two lowest singlet states is calculated to vanish in polar solvents such as methyl cyanide, leading to longer lifetime of S1 of CPDHP. As BIDP has a very similar electronic structure, the model predicts a corresponding change in this larger molecule. The strong fluorescence observed in the glassy environments is rationalized by the hindering of the internal torsion required to reach the geometry of the conical intersection.     

Crystallization of carbamazepine pseudopolymorphs from nonionic microemulsions

Crystallization of carbamazepine (CBZ), an antiepileptic drug, precipitated from confined spaces of nonionic microemulsions was investigated. The study was aimed to correlate the structure of the microemulsion [water-in-oil (W/O), bicontinuous, and oil-in-water (O/W)] with the crystalline structure and morphology of solid CBZ. The precipitated CBZ was studied by DSC, TGA, powder XRD, single-crystal XRD, SEM, and optical microscopy. The results suggest that the microstructure of the microemulsions influences the crystallization process and allows crystallizing polymorphs that exhibit different crystal structure and habits. W/O nanodroplets orient the crystallizing CBZ molecules to form a prismlike anhydrous polymorphic form with monoclinic unit cell and P21/n space group. Bicontinuous structures lead to platelike dihydrate crystals with orthorhombic unit cell and Cmca space group. The O/W nanodroplets cause the formation of needlelike dihydrate crystals with monoclinic unit cell and P21/c space group. The morphological features of solid CBZ remain predetermined by the basic symmetry and parameters of its unit cell. Precipitation of CBZ pseudopolymorphs from supersaturated microemulsion is discussed in terms of oriented attachment that provides perfect packing of numerous separately nucleated ordered nuclei of CBZ into microscale platelets and then into macroscopic crystals. Crystallization from microemulsion media enabling one to obtain the drug (CBZ) with predicted structure and morphology should be of great significance for pharmaceutical applications.     

Random graphs in the monadic theory of order

We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line). Received: 18 July 1996