Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Residual plastids of bleached mutants of Euglena gracilis and their effects on the expression of nucleus-encoded genes

Bleached mutants of Euglena gracilis were obtained by treatment with ofloxacin (Ofl) and streptomycin (Sm) respectively. As shown by electron microscopy, the residual plastids contain prothylakoids in an Ofl mutant, and the highly developed and tightly stacked membranous structure found in cells of two Sm, mutants. Nine genes of the plastid genome were examined with PCR, showing that ribosomal protein genes and most other plastid genes were lost in all but one Sm mutant. Using differential display and RT-PCR, it was shown that chloroplast degeneration could cause changes in transcription of certain nucleus-encoded genes during heterotrophic growth in darkness.

MOBILITY AND TRANSFER OF RESIDUAL HEXACHLOROCYCLOHEXANE (HCH) IN AQUATIC ENVIRONMENT

An investigation was carried out to study the mobility and transfer of HCH-residues in Yanjia lake, Hubei, China, from 1990-1993. By sampling at different locations, the horizontal distribution of HCH-residues was determined; by sampling at different depths in the same location, the vertical mobility of HCH-residues and its penetration were measured. The vertical profiles of HCH-residues in sediment showed a gradient distribution, which was reduced with the increase in depth. This was very similar in shape to the organic carbon and nitrogen content profiles. The penetration of HCH-residues was measured as 60cm approximately. Meanwhile, water, sediment (0-12cm), benthos and benthic fish collected from the lake were analyzed to determine the transfer of HCH-residues along aquatic food chain. The BCF values of HCH-residues indicated that the bioaccumulation of HCH-residues in freshwater food chain still exsisted in spite of the banning of HCH since 1983. The maxium BCF value of HCH-residues in the liver samples of 5-year-old common carp was up to 61966 (calculated by beta-HCH).

A comparison of silicon oxide and nitride as host matrices on the photoluminescence from Er3+ ions

This paper compares the properties of silicon oxide and nitride as host matrices for Er ions. Erbium-doped silicon nitride films were deposited by a plasma-enhanced chemical-vapour deposition system. After deposition, the films were implanted with Er3+ at different doses. Er-doped thermal grown silicon oxide films were prepared at the same time as references. Photoluminescence features of Er3+ were inspected systematically. It is found that silicon nitride films are suitable for high concentration doping and the thermal quenching effect is not severe. However, a very high annealing temperature up to 1200 degrees C is needed to optically activate Er3+ which may be the main obstacle to impede the application of Er-doped silicon nitride.

Gallium antisite defect and residual acceptors in undoped GaSb

Undoped Ga-Sb samples were investigated by positron lifetime spectroscopy (PAS) and the coincident Doppler broadening (CDB) technique. PAS measurement indicated that there were monovacancy-type defects in undoped Ga-Sb samples, which were identified to be predominantly Ca vacancy (V-Ga) related defects by combining the CDB measurements. After annealing of these samples at 520 C, positron shallow trapping have been observed and should be due to Ga-Sb defects. Undoped Ga-Sb is intrinsically p-type having a residual carrier density of 10(16)-10(17) cm(-3). And the Ga-Sb antisite defects are stable in the (0), (1-) and (2-) charge states and act as a double acceptor. Thus, we infer that Ga-Sb antisite defects are the acceptor contributing to the p-type conduction for undoped samples. (C) 2004 Elsevier B.V All rights reserved.

Gallium vacancy and the residual acceptor in undoped GaSb studied by positron lifetime spectroscopy and photoluminescence

Positron lifetime, photoluminescence (PL), and Hall measurements were performed to study undoped p-type gallium antimonide materials. A 314 ps positron lifetime component was attributed to Ga vacancy (V-Ga) related defect. Isochronal annealing studies showed at 300 degreesC annealing, the 314 ps positron lifetime component and the two observed PL signals (777 and 797 meV) disappeared, which gave clear and strong evidence for their correlation. However, the hole concentration (similar to2x10(17) cm(-3)) was observed to be independent of the annealing temperature. Although the residual acceptor is generally related to the V-Ga defect, at least for cases with annealing temperatures above 300 degreesC, V-Ga is not the acceptor responsible for the p-type conduction. (C) 2002 American Institute of Physics.

Investigation of Residual Donor Defects in Undoped and Fe-Doped LEC InP

The free electron concentration of as-grown liquid encapsulated Czochralski (LEC) InP measured by Hall effect is much higher than the concentration of net donor impurity determined by glow discharge mass spectroscopy. Evidence of the existence of a native donor hydrogen-indium vacancy complex in LEC undoped and Fe-doped InP materials can be observed with infrared absorption spectra. The concentration increase of the donor complex correlates with the increase of ionized deep acceptor iron impurity Fe~(2+) concentration in Fe-doped semi-insulating (SI) InP. These results indicate that the hydrogen-indium vacancy complex is an important donor defect in as-grown LEC InP, and that it has significant influence on the compensation in Fe-doped SI InP.

Relationship between luminescence and matrices in the system Al2O3-B2O3-Ce2O3

The system Al2O3-B2O3-Ce2O3, with Al/B ratio varying from 4.5 to 2 and Ce/(Al + B) = 0.02, has been prepared at the temperature from 1 200 to 1 400 degrees C. Relationship between luminescence and matrices in the system Al2O3-B2O3-Ce2O3 was investigated. It was found that some changes of the matrices occurred with Al/B ratio varying from 4.5 to 2. These results lead to a great change in luminescence properties, indicating variation of Ce-surroundings of crystal field. With the decrease of the ratio from 3 to 2, the excitation and emission peaks shift to shorter wavelengths. it was also found that a new type of rare earth luminescent materials was obtained with appropriate Al/B ratio.

EFFECT OF ETHYLENE-PROPYLENE COPOLYMER WITH RESIDUAL PE CRYSTALLINITY ON MECHANICAL-PROPERTIES AND MORPHOLOGY OF PP/HDPE BLENDS

Morphology and mechanical properties of polypropylene (PP)/high density polyethylene (HDPE) blends modified by ethylene-propylene copolymers (EPC) with residual PE crystallinity were investigated. The EPC showed different interfacial behavior in PP/HDPE blends of different compositions. A 25/75 blend of PP/HDPE (weight ratio) showed improved tensile strength and elongation at break at low EPC content (5 wt %). For the PP/HDPE = 50/50 blend, the presence of the EPC component tended to make the PP dispersed phase structure transform into a cocontinuous one, probably caused by improved viscosity matching of the two components. Both tensile strength and elongation at break were improved at EPC content of 5 wt %. For PP/HDPE 75/25 blends, the much smaller dispersed HDPE phase and significantly improved elongation at break resulted from compatibilization by EPC copolymers. (C) 1995 John Wiley & Sons, Inc.

Pervasive autocorrelation of the chemical index of alteration in sedimentary profiles and its palaeoenvironmental implications

The chemical index of alteration has been used widely for reconstruction of the palaeoclimate. However, the mechanisms and environmental factors controlling the chemical index of alteration of sediments are not yet fully understood. In this study, autocorrelations of the chemical index of alteration in nine sedimentary profiles, from both the land and the sea, spanning different geological times, are discussed. The sediments of these profiles have different origins (dust, fluvial or ocean sediments) and are from various climate situations and sedimentary environments. Autocorrelations of chemical index of alteration series are ubiquitously evident in all profiles. It is suggested here that autocorrelations may be caused by post-depositional changes such as persistent weathering and diagenesis. As a result, the chemical index of alteration may not reflect climatic conditions during the time of sediment deposition. This study strongly recommends the confirmation of the reliability and veracity of the chemical index of alteration before it is adopted to evaluate the weathering degree of parent rocks and to reconstruct the past climate. Significant autocorrelations in loess profiles were specifically observed, suggesting that the existing understanding of loess deposition in terms of climate conditions requires re-examination, and that previous reconstructions of rapid climate changes (for example, in centennial-millennial scales) should be treated with caution.