A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

Large Scale Structure Formation with Global Topological Defects. A new Formalism and its implementation by numerical simulations

We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects or any other type of seeds. We then show that this system is well suited for numerical analysis of structure formation by applying it to seeds induced by fluctuations of a global scalar field. Our numerical results are complementary to previous investigations since we use substantially different methods. The resulting microwave background fluctuations are compatible with older simulations. We also obtain a scale invariant spectrum of fluctuations with about the same amplitude. However, our dark matter results yield a smaller bias parameter compatible with $b\sim 2$ on a scale of $20 Mpc$ in contrast to previous work which yielded to large bias factors. Our conclusions are thus more positive. According to the aspects analyzed in this work, global topological defect induced fluctuations yield viable scenarios of structure formation and do better than standard CDM on large scales.Comment: uuencoded, compressed tar-file containing the text in LaTeX and 12 Postscript Figures, 41 page

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation spectra which lead to anisotropy in the cosmic microwave background (CMB). The amplitudes and shapes of these spectra can be parametrized by $Q_S^2$, $r\equiv Q_T^2/Q_S^2$, $n_S$ and $n_T$ where $Q_S^2$ and $Q_T^2$ are the scalar and tensor contributions to the square of the CMB quadrupole and $n_S$ and $n_T$ are the power-lawspectral indices. Even if we restrict ourselves to information from angles greater than one third of a degree, three of these observables can be measured with some precision. The combination $130^{1-n_S}Q_S^2$ can be known to better than $\pm 0.3\%$. The scalar index $n_S$ can be determined to better than $\pm 0.02$. The ratio $r$ can be known to about $\pm 0.1$ for $n_S \simeq 1$ and slightly better for smaller $n_S$. The precision with which $n_T$ can be measured depends weakly on $n_S$ and strongly on $r$. For $n_S \simeq 1$ $n_T$ can be determined with a precision of about $\pm 0.056(1.5+r)/r$. A full-sky experiment with a $20'$beam using technology available today, similar to those being planned by several groups, can achieve the above precision. Good angular resolution is more important than high signal-to-noise ratio; for a given detector sensitivity and observing time a smaller beam provides significantly more information than a larger beam. The uncertainties in $n_S$ and $r$ are roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.Comment: 28 pages of uuencoded postscript with 8 included figures. A postscript version is also available by anonymous ftp at ftp://astro.uchicago.edu/pub/astro/knox/fullsim.p

Water abundances in high-mass protostellar envelopes: Herschel observations with HIFI

We derive the dense core structure and the water abundance in four massive star-forming regions which may help understand the earliest stages of massive star formation. We present Herschel-HIFI observations of the para-H2O 1_11-0_00 and 2_02-1_11 and the para-H2-18O 1_11-0_00 transitions. The envelope contribution to the line profiles is separated from contributions by outflows and foreground clouds. The envelope contribution is modelled using Monte-Carlo radiative transfer codes for dust and molecular lines (MC3D and RATRAN), with the water abundance and the turbulent velocity width as free parameters. While the outflows are mostly seen in emission in high-J lines, envelopes are seen in absorption in ground-state lines, which are almost saturated. The derived water abundances range from 5E-10 to 4E-8 in the outer envelopes. We detect cold clouds surrounding the protostar envelope, thanks to the very high quality of the Herschel-HIFI data and the unique ability of water to probe them. Several foreground clouds are also detected along the line of sight. The low H2O abundances in massive dense cores are in accordance with the expectation that high densities and low temperatures lead to freeze-out of water on dust grains. The spread in abundance values is not clearly linked to physical properties of the sources.Comment: 8 pages, 5 figures, accepted for publication the 15/07/2010 by Astronomy&Astrophysics as a letter in the Herschel-HIFI special issu

High-Throughput NMR Assessment of the Tertiary Structure of Food Allergens

In vitro component-resolved diagnosis of food allergy requires purified allergens that have to meet high standards of quality. These include the authentication of their conformation, which is relevant for the recognition by specific IgE antibodies from allergic patients. Therefore, highly sensitive and reliable screening methods for the analysis of proteins/allergens are required to assess their structural integrity. In the present study one-dimensional 1H Nuclear Magnetic Resonance (1D 1H-NMR) analysis was adopted for the assessment of overall structural and dynamic properties and authentication of a set of relevant food allergens, including non-specific lipid transfer proteins from apple, peach and hazelnut, 7/8S seed storage globulins from hazelnut and peanut, 11S seed storage globulins from hazelnut and peanut, caseins from cows' and goats' milk and tropomyosin from shrimp.Two sets of 1D 1H-NMR experiments, using 700 MHz and 600 MHz instruments at 298 K were carried out to determine the presence and the extent of tertiary structure. Structural similarity among members of the individual allergen families was also assessed and changes under thermal stress investigated. The nuclear magnetic resonance (NMR) results were compared with structural information available either from the literature, Protein Data Bank entries, or derived from molecular models.1D (1)H-NMR analysis of food allergens allowed their classification into molecules with rigid, extended and ordered tertiary structures, molecules without a rigid tertiary structure and molecules which displayed both features. Differences in thermal stability were also detected. In summary, 1D (1)H-NMR gives insights into molecular fold of proteins and offers an independent method for assessing structural properties of proteins

Water vapor toward starless cores: the Herschel view

SWAS and Odin provided stringent upper limits on the gas phase water abundance of dark clouds (x(H2O) < 7x10^-9). We investigate the chemistry of water vapor in starless cores beyond the previous upper limits using the highly improved angular resolution and sensitivity of Herschel and measure the abundance of water vapor during evolutionary stages just preceding star formation. High spectral resolution observations of the fundamental ortho water (o-H2O) transition (557 GHz) were carried out with Herschel HIFI toward two starless cores: B68, a Bok globule, and L1544, a prestellar core embedded in the Taurus molecular cloud complex. The rms in the brightness temperature measured for the B68 and L1544 spectra is 2.0 and 2.2 mK, respectively, in a velocity bin of 0.59 km s^-1. The continuum level is 3.5+/-0.2 mK in B68 and 11.4+/-0.4 mK in L1544. No significant feature is detected in B68 and the 3 sigma upper limit is consistent with a column density of o-H2O N(o-H2O) < 2.5x10^13 cm^-2, or a fractional abundance x(o-H2O) < 1.3x10^-9, more than an order of magnitude lower than the SWAS upper limit on this source. The L1544 spectrum shows an absorption feature at a 5 sigma level from which we obtain the first value of the o-H2O column density ever measured in dark clouds: N(o-H2O) = (8+/-4)x10^12 cm^-2. The corresponding fractional abundance is x(o-H2O) ~ 5x10^-9 at radii > 7000 AU and ~2x10^-10 toward the center. The radiative transfer analysis shows that this is consistent with a x(o-H2O) profile peaking at ~10^-8, 0.1 pc away from the core center, where both freeze-out and photodissociation are negligible. Herschel has provided the first measurement of water vapor in dark regions. Prestellar cores such as L1544 (with their high central densities, strong continuum, and large envelopes) are very promising tools to finally shed light on the solid/vapor balance of water in molecular clouds.Comment: Accepted for publication in Astronomy and Astrophysics (HIFI first results issue

Planck pre-launch status : The Planck-LFI programme

Peer reviewe

Planck early results V : The Low Frequency Instrument data processing

Peer reviewe

Planck early results I : The Planck mission

Peer reviewe

Planck 2013 results. V. LFI calibration

Peer reviewe