Model-theoretic aspects of the Gurarij operator system

We establish some of the basic model theoretic facts about the Gurarij operator system GS recently constructed by the second-named author. In particular, we show: (1) GS is the unique separable 1-exact existentially closed operator system; (2) GS is the unique separable nuclear model of its theory; (3) every embedding of GS into its ultrapower is elementary; (4) GS is the prime model of its theory; and (5) GS does not have quantifier-elimination, whence the theory of operator systems does not have a model companion. We also show that, for any q ∈ ?, the theories of M_q-spaces and M_q-systems do have a model companion, namely the Fra¨?ssé limit of the class of finite-dimensional M_q-spaces and M_q-systems respectively; moreover, we show that the model companion is separably categorical. We conclude the paper by showing that no C* algebra can be existentially closed as an operator system.     

Sampling of Paley-Wiener functions on stratified groups

We consider a generalization of entire functions of spherical exponential type on stratified groups. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a stratified group is uniquely determined by its values on some discrete subgroups. The main result of the article is reconstruction formula of spectral entire functions from their values on discrete subgroups using Lagrangian splines.     

Chaotic states in a random world: Relationship between the nonlinear differential equations of excitability and the stochastic properties of ion channels

Excitable membranes allow cells to generate and propagate electrical signals. In the nervous system these signals transmit information, in muscle they trigger contraction, and in heart they regulate spontaneous beating. A central question in excitability theory concerns the relationship between the aggregate properties of membranes (marcoscopic) and the properties of channels in the membranes (mircoscopic). Hodgkin and Huxley (1952) laid the foundations of membrane excitability, and Neher and Sakmann (1976) developed techniques to study individual channels. This article focuses on the relationship between the macroscopic domain, in which non-linear differential equations determine the electrical properties of cells, and the microscopic domain, in which the probabilistic nature of channels establishes the pattern of activity. Using nerve cell membranes as an example, we examine how information in one domain predicts behavior in the other. We conclude that the probabilistic nature of channels generates virtually all macroscopic electrical properties, including resting potentials, action potentials, spontaneous firing, and chaos.     

Spectral deformations of automorphic functions over graphs of groups

Supported by the Alfred P. Sloan and the National Science Foundations     

Spherical functions and integral geometry

The paper presents two proofs of an integral geometric formula concerningn-dimensional ellipsoids. One of the proofs is based on a representation theorem for spherical functions due to Harish-Chandra.     

Synthesis of substituted tetrahydropyrimido-[4, 5-b][1, 7]naphthyridines as potential antitumor agents

The synthesis of two linear trisubstituted 6, 7, 8, 9-tetrahydropyrimido[4, 5-b][1, 7]naphthyridines 1 and 3 were accomplished by the regiospecific cyclocondensation of two disubstituted 6-aminopyrimidines 10 and 11 with the ketoaldehyde 1-benzyl-4-hydroxymethylene-3-piperidone. Catalytic debenzylation of 1 afforded the disubstituted compound 2 . The linear structures of 1–3 were established by ¹H nmr and 13C nmr.     

Mechanism of visible light phototoxicity on Porphyromonas gingivalis and Fusobacterium nucleatum

Phototoxicity of visible light laser on the porphyrin-producing bacteria, Porphyromonas gingivalis, in the absence of photosensitizers and under aerobic conditions was shown in previous studies. Recently, we found that the noncoherent visible light sources at wavelengths of 400-500 nm, commonly used in restorative dentistry, induced a phototoxic effect on P. gingivalis, as well as on Fusobacterium nucleatum, and to a lesser extent on the Streptococci sp. To elucidate the mechanism of this phototoxic effect, P. gingivalis and F. nucleatum were exposed to light (1) under aerobic and anaerobic environments and (2) in the presence of scavengers of reactive oxygen species (ROS). Phototoxic effect was not observed when the bacteria were exposed to light under anaerobic conditions. Dimethyl thiourea, a hydroxyl radical scavenger, was effective in reducing phototoxicity (P 相似文献   

Measuring molecular weight by atomic force microscopy

Absolute-molecular-weight distribution of cylindrical brush molecules were determined using a combination of the Langmuir Blodget (LB) technique and Atomic Force Microscopy (AFM). The LB technique gives mass density of a monolayer, i.e., mass per unit area, whereas visualization of individual molecules by AFM enables accurate measurements of the molecular density, i.e., number of molecules per unit area. From the ratio of the mass density to the molecular density, one can determine the absolute value for the number average molecular weight. Assuming that the structure of brush molecules is uniform along the backbone, the length distribution should be virtually identical to the molecular weight distribution. Although we used only brush molecules for demonstration purpose, this approach can be applied for a large variety of molecular and colloidal species that can be visualized by a microscopic technique.     

The chemistry of 5-hydroxy-6-(hydroxyalkyl)uracils. Synthesis of spiro[pyrimidine-4,2′-pyrano[3,2-d]pyrimidines]

Both 5-acetoxy-6-(acetoxymethyl)-1-methyluracil 1 and its parent diol 11 are converted into the spiro[pyrimidine-4,2′-pyrano[3,2-d]pyrimidine] 6 when treated, respectively, with hot methanolic pyridine and with one equivalent of acetic anhydride. The formation of 6 can be explained in terms of the generation and dimerization of the reactive 5-oxo-6-methylene pyrimidine 2 . The structure of 6 was determined by ¹³C nmr spectroscopy and by chemical transformations that lead to the pyrimidinylethylhydantoin 9 and the 6,6′-[1,2-ethanediyl]bispyrimidine 10 . The more complex 5-hydroxy-6-(hydroxyalkyl)uracils represented by the 6,5′-cyclourid-ines 17 undergo an analogous dimerization when treated with acetic anhydride to give structures 22a and 22b . Dimer 22a was also prepared via the 5-phosphate ester 18 . The stereochemistry of dimers 22a and 22b , which is apparent from their ¹H nmr spectra, indicates that two molecules of the enones 21a or 21b dimerize in a highly stereoselective manner.