Optimal ellipsoids and decomposition of positive definite matrices

Given a positive definite matrix A, we characterize the unique diagonal matrix D, D?A, with the smallest determinant. Equivalently, given an ellipsoid A, we characterize the unique ellipsoid of the largest volume contained in A, with principal axes parallel to the coordinate axes.     

High-throughput determination of seven trace elements in food samples by inductively coupled plasma-mass spectrometry

A method was developed for high-throughput determinations of 7 elements in food samples, namely antimony (Sb), arsenic (As), cadmium (Cd), chromium (Cr), lead (Pb), mercury (Hg), and tin (Sn). The samples were digested by closed-vessel microwave-assisted digestion using concentrated nitric acid (HNO3) as the medium, followed by microwave- assisted evaporation to concentrate the sample solutions before dilution to the desired volume. The microwave-assisted evaporation procedure effectively reduced the final acid concentration to around 8% before analysis by inductively coupled plasma-mass spectrometry (ICP-MS). This reduction allows determination by ICP-MS to proceed without further sample dilution, which would affect the detection limit. The method was validated, and method recoveries for As, Cd, Cr, Pb, and Hg were within the certified ranges of the chosen certified reference materials. Recoveries of the 7 elements from spiked samples ranged from 93.1 to 103.6%. The standard uncertainties of precision for the 7 elements were between 3.1 and 4.3%. Interlaboratory comparison studies for As, Cd, and Pb gave z-scores ranging from -0.2 to 0.3.     

Magnetized hypermassive neutron-star collapse: a central engine for short gamma-ray bursts

A hypermassive neutron star (HMNS) is a possible transient formed after the merger of a neutron-star binary. In the latest axisymmetric magnetohydrodynamic simulations in full general relativity, we find that a magnetized HMNS undergoes "delayed" collapse to a rotating black hole (BH) as a result of angular momentum transport via magnetic braking and the magnetorotational instability. The outcome is a BH surrounded by a massive, hot torus with a collimated magnetic field. The torus accretes onto the BH at a quasisteady accretion rate [FORMULA: SEE TEXT]; the lifetime of the torus is approximately 10 ms. The torus has a temperature [FORMULA: SEE TEXT], leading to copious ([FORMULA: SEE TEXT]) thermal radiation that could trigger a fireball. Therefore, the collapse of a HMNS is a promising scenario for generating short-duration gamma-ray bursts and an accompanying burst of gravitational waves and neutrinos.     

Some compounds of iron(III) with tertiary and secondary nitrogen bases

Summary The iron(III) compound, FeCl(OH)(MeCO₂) · MeCO₂ H · 0.5 H₂O, combines with tertiary nitrogen bases, pyridine, quinoline and-picoline, to form FeCl(OH)(MeCO₂) · (Base) 0.5 H₂O and with-picoline to give FeCl(OH)(MeCO₂) (-picoline). The secondary nitrogen bases (BH), such as, piperidine, pyrrolidine and diethylamine, on the other hand, react with the elimination of base hydrochloride to form Fe(B)(OH)(MeCO₂) · 0.5 H₂O compounds, containing covalently bonded bases. Pyrrole and indole (BH) combine with the partial elimination of chlorine to give Fe₃Cl₂(B)(OH)₃(MeCO₂)₃ · 3(BH). Phthalimide (BH), however, forms a simple addition compound Fe₂Cl₂(OH)₂(MeCO₂)₂ · (BH). The i.r. spectra, room temperature magnetic susceptibilities, thermal decompositions wherever possible and molar conductance have been studied.     

Reductive deposition of Rh nanostructures on n-type porous silicon: X-ray absorption and X-ray excited optical luminescence studies

22Porous silicon (PS) prepared from an n-type Si(100) wafer was utilized as a reducing agent and a nanosubstrate for the reduction of rhodium complex ions [RhCl6]3- from aqueous solution to metallic Rh nanostructures on the surface of the n-type PS. The morphology and the electronic properties of the PS layers as well as the rhodium nanostructures were studied by field emission scanning electron microscopy, X-ray absorption fine structures spectroscopy, and X-ray excited optical luminescence (XEOL). The average particle size of Rh nanostructures on PS was estimated to be approximately 7 nm by the X-ray diffraction pattern. The specificity ofXEOL allowed for the investigation of the effect of Rh nanostructures on the optical properties of PS.     

Linewidths and line shapes in solid state ESCA studies: Electric field gradient broadening of Sn 3d lines

ESCA Sn 3d linewidths of nonconducting organometallic tin solids, prepared by in situ evaporation, are within about 10% of the values for analogous gas phase measurements. The similar line shapes (≈ 35% gaussian, 65% lorentzian) observed for solid state and gas phase spectra show that effects which give increasing gaussian components, such as charge broadening and phonon broadening, are very small in our solid state spectra. The general correlation between ESCA Sn 3d linewidths and Mössbauer quadrupole splittings indicates that electric field gradient splitting of the Sn 3d lines approaches ≈ 0.4 eV.