1-Meixner Random Vectors

Journal of Theoretical Probability - A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we...     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

Continuous-time Markov model for geriatric patients behavior. Optimization of the bed occupancy and computer simulation

Previous research has shown that the flow of patients around departments of geriatric medicine and ex-patients in the community may be modelled by the application of a mixed-exponential distribution. In this paper we considered a five-compartment model using a continuous-time Markov process to describe the flow of patients. Using a M/Ph/c queuing model, we present a way of optimizing the number of beds in order to maintain an acceptable delay probability at a sufficiently low level. Finally, we constructed a Java computer simulation, using data from St George’s Hospital, London.     

Mechanical properties of single motor molecules studied by three-dimensional thermal force probing in optical tweezers.

A new method combining three-dimensional (3D) force measurements in an optical trap with the analysis of thermally induced (Brownian) position fluctuations of a trapped probe was used to investigate the mechanical properties of a single molecule, the molecular motor kinesin. One kinesin molecule attached to the probe was bound in a rigorlike state to one microtubule. The optical trap was kept weak to measure the thermal forces acting on the probe, which were mainly counterbalanced by the kinesin tether. The stiffness of kinesin during stretching and compression with respect to its backbone axis were measured. Our results indicate that a section of kinesin close to the motor domain is the dominating element in the flexibility of the motor structure. The experiments demonstrate the power of 3D thermal fluctuation analysis to characterize mechanical properties of individual motor proteins and indicate its usefulness to study single molecule in general     

Pyrolysis of vinyl and vinylidene fluoride polymers: Influence of prior γ-irradiation

Quantitative comparisons were made between the rates of thermal volatilization of several fluoropolymers before and after exposure to γ-radiation. The effects of γ-irradiation on poly(vinyl fluoride) and poly(vinylidene fluoride) were also investigated by swelling and sol-gel ratios. With both polymers as well as with polytrifluoroethylene, crosslinks occur predominantly, though there is an appreciable number of scissions. The rates of volatilization and char formation were enhanced by γ-radiation, whereas the previously studied polytrifluoroethylene did not produce more char upon irradiation, although radiation did accelerate its volatilization. It is believed that in polytrifluoroethylene the enhanced rates of volatilization occur by a different mechanism than in the case of the vinyl and vinylidene fluoride polymers.     

Regioselectivity of Friedel-Crafts acylation of aromatic compounds with several cyclic anhydrides

The Friedel-Crafts acylations of various aromatic compounds with cyclic anhydrides such as 2-(p-substituted phenyl)butanedioic, 3-phenylpentanedioic and homophathlic anhydrides were carried out under various conditions in order to obtain informations about the regioselectivity of the ring opening of the cyclic anhydrides and about the possible reaction pathways in the acylations.     

High-resolution submicron patterning of self-assembled monolayers using a molecular fluorine laser at 157 nm

Using a molecular fluorine laser at 157 nm wavelength, submicron patterning of organosilane self-assembled monolayers (SAMs) is demonstrated utilizing mask-contact photolithography. An organosilane, namely, octadecyltrimethoxysilane [ODS, CH(3)(CH(2))(17)Si(OCH(3))(3)], SAM is chemisorbed onto Si substrates covered with a 2 nm thick oxide layer and subsequently patterned using the laser. The optical path of the laser beam and the photomask-sample space are evacuated and then backfilled and purged with nitrogen during laser firing. The resulting pattern is investigated using various measurement techniques. The scanning probe microscopy images show that patterns are transferred to the SAM-covered Si substrates and that 500 nm features are successfully photoprinted in this way.     

Chemoenzymatic synthesis of highly enantiomerically enriched secondary alcohols with a thiazolic core

Stereoselective preparative enzymatic acylation and hydrolysis/methanolysis of various C-substituted rac-thiazol-2-yl-methanols were achieved for the preparation of enantiopure or enantiomerically enriched, naturally occurring 2-hydroxymethylthiazoles. The absolute configurations of the resulting secondary alcohols were determined by a detailed ¹H NMR study of Mosher’s derivatives.