23,949 research outputs found
A parabolic free boundary problem with Bernoulli type condition on the free boundary
Consider the parabolic free boundary problem For a
realistic class of solutions, containing for example {\em all} limits of the
singular perturbation problem we prove that one-sided
flatness of the free boundary implies regularity.
In particular, we show that the topological free boundary
can be decomposed into an {\em open} regular set (relative to
) which is locally a surface with H\"older-continuous space
normal, and a closed singular set.
Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli
(1981) to more general solutions as well as the time-dependent case. Our proof
uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace
the core of that paper, which relies on non-positive mean curvature at singular
points, by an argument based on scaling discrepancies, which promises to be
applicable to more general free boundary or free discontinuity problems
Topological partition relations to the form omega^*-> (Y)^1_2
Theorem: The topological partition relation omega^{*}-> (Y)^{1}_{2}
(a) fails for every space Y with |Y| >= 2^c ;
(b) holds for Y discrete if and only if |Y| <= c;
(c) holds for certain non-discrete P-spaces Y ;
(d) fails for Y= omega cup {p} with p in omega^{*} ;
(e) fails for Y infinite and countably compact
Laser Interferometer Gravitational-Wave Observatory beam tube component and module leak testing
Laser Interferometer Gravitational-Wave Observatory (LIGO) is a joint project of the California Institute of Technology and the Massachusetts Institute of Technology funded by the National Science Foundation. The project is designed to detect gravitational waves from astrophysical sources such as supernova and black holes. The LIGO project constructed observatories at two sites in the U.S. Each site includes two beam tubes (each 4 km long) joined to form an "L" shape. The beam tube is a 1.25 m diam 304 L stainless steel, ultrahigh vacuum tube that will operate at 1×10^–9 Torr or better. The beam tube was manufactured using a custom spiral weld tube mill from material processed to reduce the outgassing rate in order to minimize pumping costs. The integrity of the beam tube was assured by helium mass spectrometer leak testing each component of the beam tube system prior to installation. Each 2 km long, isolatable beam tube module was then leak tested after completion
Scaling and data collapse for the mean exit time of asset prices
We study theoretical and empirical aspects of the mean exit time of financial
time series. The theoretical modeling is done within the framework of
continuous time random walk. We empirically verify that the mean exit time
follows a quadratic scaling law and it has associated a pre-factor which is
specific to the analyzed stock. We perform a series of statistical tests to
determine which kind of correlation are responsible for this specificity. The
main contribution is associated with the autocorrelation property of stock
returns. We introduce and solve analytically both a two-state and a three-state
Markov chain models. The analytical results obtained with the two-state Markov
chain model allows us to obtain a data collapse of the 20 measured MET profiles
in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio
Subband Adaptive Generalized Sidelobe Canceller for Broadband Beamforming
In this paper, we propose a novel subband adaptive broadband beamforming architecture based on the generalised sidelobe canceller (GSC), in which we decompose each of the tapped delay-line signals feeding the adaptive part of GSC and the reference signal into subbands and perform adaptive minimisation of the mean squared error in each subband. Besides its lower computational complexity, this new subband adaptive GSC outperforms its fullband counterpart in terms of both convergence speed and steady-state error. Simulations based on different kinds of blocking matrices with different orders of derivative constraints are presented to support these findings
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
Can an electric current orient spins in quantum wells?
A longstanding theoretical prediction is the orientation of spins by an
electrical current flowing through low-dimensional carrier systems of
sufficiently low crystallographic symmetry. Here we show by means of terahertz
transmission experiments through two-dimensional hole systems a growing spin
orientation with an increasing current at room temperature.Comment: 5 pages, 2 figure
A Solid-State 11B NMR and Computational Study of Boron Electric Field Gradient and Chemical Shift Tensors in Boronic Acids and Boronic Esters
The results of a solid-state 11B NMR study of a series of 10 boronic acids and boronic esters with aromatic substituents are reported. Boron-11 electric field gradient (EFG) and chemical shift (CS) tensors obtained from analyses of spectra acquired in magnetic fields of 9.4 and 21.1 T are demonstrated to be useful for gaining insight into the molecular and electronic structure about the boron nucleus. Data collected at 21.1 T clearly show the effects of chemical shift anisotropy (CSA), with tensor spans (Ω) on the order of 10−40 ppm. Signal enhancements of up to 2.95 were achieved with a DFS-modified QCPMG pulse sequence. To understand the relationship between the measured tensors and the local structure better, calculations of the 11B EFG and magnetic shielding tensors for these compounds were conducted. The best agreement was found between experimental results and those obtained from GGA revPBE DFT calculations. A positive correlation was found between Ω and the dihedral angle (CCBO), which describes the orientation of the boronic acid/ester functional group relative to an aromatic system bound to boron. The small boron CSA is discussed in terms of paramagnetic shielding contributions as well as diamagnetic shielding contributions. Although there is a region of overlap, both Ω and the 11B quadrupolar coupling constants tend to be larger for boronic acids than for the esters. We conclude that the span is generally the most characteristic boron NMR parameter of the molecular and electronic environment for boronic acids and esters, and show that the values result from a delicate interplay of several competing factors, including hydrogen bonding, the value of CCBO, and the electron-donating or withdrawing substituents bound to the aromatic ring.Natural Sciences and
Engineering Research Council (NSERC) of Canada and the
Canada Foundation for Innovation
Cinderella - Comparison of INDEpendent RELative Least-squares Amplitudes
The identification of increasingly smaller signal from objects observed with
a non-perfect instrument in a noisy environment poses a challenge for a
statistically clean data analysis. We want to compute the probability of
frequencies determined in various data sets to be related or not, which cannot
be answered with a simple comparison of amplitudes. Our method provides a
statistical estimator for a given signal with different strengths in a set of
observations to be of instrumental origin or to be intrinsic. Based on the
spectral significance as an unbiased statistical quantity in frequency
analysis, Discrete Fourier Transforms (DFTs) of target and background light
curves are comparatively examined. The individual False-Alarm Probabilities are
used to deduce conditional probabilities for a peak in a target spectrum to be
real in spite of a corresponding peak in the spectrum of a background or of
comparison stars. Alternatively, we can compute joint probabilities of
frequencies to occur in the DFT spectra of several data sets simultaneously but
with different amplitude, which leads to composed spectral significances. These
are useful to investigate a star observed in different filters or during
several observing runs. The composed spectral significance is a measure for the
probability that none of coinciding peaks in the DFT spectra under
consideration are due to noise. Cinderella is a mathematical approach to a
general statistical problem. Its potential reaches beyond photometry from
ground or space: to all cases where a quantitative statistical comparison of
periodicities in different data sets is desired. Examples for the composed and
the conditional Cinderella mode for different observation setups are presented.Comment: 8 pages, 6 figures, A&A, in pres
- …