Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

Hepatic effects of Cimicifuga racemosa extract in vivo and in vitro

Abstract.: Extracts of Cimicifuga racemosa are used frequently for menopausal complaints. Cimicifuga is well tolerated but can occasionally cause liver injury. To assess hepatotoxicity of cimicifuga in more detail, ethanolic C. racemosa extract was administered orally to rats, and liver sections were analyzed by electron microscopy. Tests for cytotoxicity, mitochondrial toxicity and apoptosis/necrosis were performed using HepG2 cells. Mitochondrial toxicity was studied using isolated rat liver mitochondria. Microvesicular steatosis was found in rats treated with > 500 μg/kg body weight cimicifuga extract. In vitro, cytotoxicity was apparent at concentrations ≥ 75 μg/mL, and mitochondrial β-oxidation was impaired at concentrations ≥ 10 μg/mL. The mitochondrial membrane potential was decreased at concentrations ≥ 100 μg/mL, and oxidative phosphorylation was impaired at concentrations ≥ 300 μg/mL. The mechanism of cell death was predominantly apoptosis. C. racemosa exerts toxicity in vivo and in vitro, eventually resulting in apoptotic cell death. The results are compatible with idiosyncratic hepatotoxicity as observed in patients treated with cimicifuga extract

Additional Ultracool White Dwarfs Found in the Sloan Digital Sky Survey

We identify seven new ultracool white dwarfs discovered in the Sloan Digital Sky Survey (SDSS). The SDSS photometry, spectra, and proper motions are presented, and additional BVRI data are given for these and other previously discovered ultracool white dwarfs. The observed colors span a remarkably wide range, qualitatively similar to colors predicted by models for very cool white dwarfs. One of the new stars (SDSS J1251+44) exhibits strong collision-induced absorption (CIA) in its spectra, while the spectra and colors of the other six are consistent with mild CIA. Another of the new discoveries (SDSS J2239+00A) is part of a binary system -- its companion is also a cool white dwarf, and other data indicate that the companion exhibits an infrared flux deficiency, making this the first binary system composed of two CIA white dwarfs. A third discovery (SDSS J0310-00) has weak Balmer emission lines. The proper motions of all seven stars are consistent with membership in the disk or thick disk.Comment: Accepted for Astrophysical Journal. 16 pages (includes 3 figures

The new carbon symbiotic star IPHAS J205836.43+503307.2

We are performing a search for symbiotic stars using IPHAS, the INT Halpha survey of the northern Galactic plane, and follow-up observations. Candidate symbiotic stars are selected on the basis of their IPHAS and near-IR colours, and spectroscopy and photometry are obtained to determine their nature. We present here observations of the symbiotic star candidate IPHAS J205836.43+503307.2. The optical spectrum shows the combination of a number of emission lines, among which are the high-excitation species of [OIII], HeII, [Ca V], and [Fe VII], and a red continuum with the features of a star at the cool end of the carbon star sequence. The nebular component is spatially resolved: the analysis of the spatial profile of the [NII]6583 line in the spectrum indicates a linear size of ~2.5 arcsec along the east-west direction. Its velocity structure suggests an aspherical morphology. The near-infrared excess of the source, which was especially strong in 1999, indicated that a thick circumstellar dust shell was also present in the system. The carbon star has brightened in the last decade by two to four magnitudes at red and near-infrared wavelengths. Photometric monitoring during a period of 60 days from November 2010 to January 2011 reveals a slow luminosity decrease of 0.2 magnitudes. From the observed spectrophotometric properties and variability, we conclude that the source is a new Galactic symbiotic star of the D-type, of the rare kind that contains a carbon star, likely a carbon Mira. Only two other systems of this type are known in the Galaxy.Comment: 6 pages, 4 figure