Finite dimensional semisimple Q-algebras

A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

Magnetotransport and magnetic properties of InAs/Mn digital alloys

We have investigated the magnetic and magneto-transport properties of a systematic sequence of five InAs/Mn digital alloys grown by a combination of molecular beam epitaxy and atomic layer epitaxy. The samples consist of 30 periods of Mn fractional monolayers (ML) (0.17–0.5 ML) separated by 14 ML thick InAs spacer layers in a superlattice configuration. Four samples show n-type electrical conduction while the fifth (0.25 ML Mn) is p-type. Squid magnetization measurements performed on these samples show remnant magnetization above room temperature, which is apparently related to a second phase.     

P-Chirogenic phosphonium salts: preparation and use in Rh-catalyzed asymmetric hydrogenation of enamides

P-Chirogenic trialkylphosphonium salts were prepared from the corresponding free phosphines by treatment with a strong acid (HBF₄ or HOTf). No racemization of the phosphonium salts occurred in methanol or water even at considerably high temperature. The salts were conveniently used in rhodium-catalyzed asymmetric hydrogenation of enamides.     

Spectrophotometric determination of copper(II) with carbon disulfide,a secondary amine and triton X-100

Copper(II) is determined by non-extractive spectrophotometry as a complex of butylene dithiocarbamate formed in situ by reaction between carbon disulfide and pyrrolidine in aqueous Triton X-100 medium. This method is similar to that with butylene dithiocarbamate as starting material in the sense of simplicity, sensitivity, precision and accuracy. Pyrrolidine is the best of seven secondary amines tested in this way for copper determinations.     

A new on-line sample preparation system for the liquid chromatography/time-of-flight mass spectrometry simultaneous analysis of pesticides in river water.

Current on-line solid-phase extraction methods combined with HPLC for shortening the clean-up operation are not suitable for simultaneously detecting compounds that have a wide variety of hydrophobicities. To solve these problems, we designed a new on-line sample preparation system. The system consists of an eluting pump, a mixing TEE connector, a 10-port 2-position valve and a solid-phase extraction precolumn. The eluate from the precolumn is diluted with a weak solvent from the HPLC at the TEE connection to load low hydrophobic compounds onto the analytical column. The proposed on-line sample preparation system was successfully applied to the simultaneous analysis of 21 pesticides in river water using LC/TOF-MS. In this method, the recoveries from river water samples were 67 to 126% (mean 83%), the reproducibility (CV%) was in the range from 1.1 to 11% (mean 5.6%), the calibration curve was linear in the range from 1 ppb to 500 ppb (r > 0.999) and the detection limits (S/N = 3) were in the range from 0.0034 ppb (daimuron) to 3.3 ppb (oxine-copper).     

Control of the bioluminescence starting time by inoculated cell density.

In this study, we attempted to control the timing of light-emission from bioluminescent bacteria, by changed cell numbers inoculated into medium. Luminous bacteria express bioluminescence when the number of cells reached a threshold. Inoculated cell density had an effect on the time of bioluminescence starting. Samples were prepared by varying cell density of inoculation. In the results, all the vials showed different luminescence profiles in the order of inoculated cell population.