The topological structure of the unitary and automorphism groups of a factor

It is proved that a large class ofII ₁ factors have unitary group which is contractible in the strong operator topology, but whose fundamental group in the norm topology is isomorphic to the additive real numbers as proven by Araki-Smith-Smith [1]. The class includes the approximately finite dimensional factor of typeII ₁ and the group factor associated with the free group on infinitely many generators. This contractibility is used to prove the contractibility of the automorphism group of the approximately finite dimensional factor of typeII ₁ and typeII . It is further shown that the fundamental group of the automorphism group of the approximately finite dimensional factor of typeIII , 0<<1, is isomorphic to the integer group .Dedicated to Huzihiro ArakiThis research is supported in part by NSF Grant DMS-9206984     

The axiom of spheres in quaternionic geometry

Summary We show that a quaternion manifold satisfying the axiom of quaternionic spheres is a quaternion space-form.

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Riassunto Si mostra che una varietà quaternionica che verifica l'assioma delle sfere quaternioniche è una forma spaziale quaternionica.

     

Some results on the existence of Nash equilibria for non-zero sum games with incomplete information

We prove the existence of Nash equilibria for two person non-zero sum repeated games with lack of information on one side and two states of nature.     

Optical manipulation of complex molecular systems by high density green photons: experimental and theoretical evidence

The recent revolution in modern optical techniques revealed that light interaction with matter generates a force, known as optical force, which produces material properties known in physics as optical matter. The basic technique of the domain uses forces exerted by a strongly focused beam of light to trap small objects and subsequently to manipulate their local structures. The purpose of this paper is to develop an alternative approach, using irradiations with high-density-green-photons, which induce electric dipoles by polarization effects. The materials used for the experiments were long carbon chains which represent the framework of biological macromolecules. The physical techniques used to reveal the locally induced molecular arrangements were: dynamic viscosity, zeta potential, chemiluminescence, liquid chromatography; mass spectrometry, and Raman and infrared spectroscopy. The principal result of our experiments was the detection of different molecular arrangements within the mixture of alkane chains, generated by our optical manipulations. This induced “optical matter” displayed two material properties: antioxidant effects and large molecular aggregation effects. In order to bring the experimental results in relation with theory, we developed a physical model and the interacting force between polarizable bodies was computed. By numerical calculations stable structures for N = 6 and N = 8 particles were obtained.     

Ion transport across a bilayer lipid membrane facilitated by valinomycin

The facilitated ion transport from one aqueous phase, W1, to another, W2, across a bilayer lipid membrane, BLM, containing valinomycin, Val, as an ionophore was investigated by voltammetry. Cyclic voltammograms for the ion transfer were symmetrical about the origin (0 V, 0 A) and the magnitude of the ion transfer current increased with an increase in the absolute value of the applied potential. The magnitude of the ion transfer current at a definite potential in the voltammograms depended on the cation species added to W1 and W2 and was proportional to the concentration of Val in the BLM. The magnitude of the ion transfer current at a definite potential also varied in proportion to the hydrophobicity of the counter anion in W1 and W2. Taking into account the conjugated ion transfers at the W1|BLM and BLM|W2 interfaces, the positive current that flowed from W1 to W2 across the BLM was attributable to both the transfer of the complex-forming cation from W1 to the BLM and the transfer of the anion, which was distributed in the BLM as the counter ion from W2 to W1. The transfer from the BLM to W1 occurred at the W1|BLM interface and both the transfer of the cation from the BLM to W2 and the transfer of the anion from W2 to the BLM at the BLM|W2 interface. The negative current was then attributed to the opposite reaction. The voltammograms were asymmetrical with the origin when the ion components in W1 and W2 were different.     

Synthesis and Stereochemistry of Some New Spiro-1,3-perhydrooxazines

Summary.  The synthesis and the stereochemistry of new spiro-1,3-perhydrooxazines are reported. The stereoisomerism of these compounds is discussed considering the data of conformational analysis, the helical chirality of the spiro[5.5]undecane skeleton, and the triligand virtual chiral center belonging to the 1,3-perhydrooxazine ring. Received February 21, 2000. Accepted (revised) April 18, 2000     

On Pointed Hopf Algebras of Dimension 2n

We give a structure theorem for pointed Hopf algebras of dimension2ⁿ, having coradical kC₂, where k is an algebraically closedfield of characteristic zero. 1991 Mathematics Subject Classification16W30.