78 research outputs found
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 on a scale of 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 , , and where and are the scalar and
tensor contributions to the square of the CMB quadrupole and and
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 can be
known to better than . The scalar index can be determined to
better than . The ratio can be known to about for and slightly better for smaller . The precision with which
can be measured depends weakly on and strongly on . For
can be determined with a precision of about . A
full-sky experiment with a 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
and 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
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