35,602 research outputs found
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Searches for Gauge-Mediated SUSY Breaking Topologies with the L3 Detector at LEP
Searches for topologies predicted by gauge-mediated SUSY breaking models were
performed using data collected with the L3 detector at LEP. All possible
lifetimes of the next-to-lightest SUSY particle (NLSP), neutralino or scalar
tau, were considered. No evidence for these new phenomena was found and limits
on the production cross sections and sparticle masses were derived. A scan over
the parameters of the minimal GMSB model was performed, leading to lower limits
of 62.2 GeV, 11 TeV, and 0.07 eV on the NLSP mass, the mass scale parameter
Lambda, and the gravitino mass, respectively. The status of the LEP combined
searches is also discussed.Comment: 4 pages, 2 figures, 1 table; to appear in Proceedings of SUSY06, the
14th International Conference on Supersymmetry and the Unification of
Fundamental Interactions, UC Irvine, California, 12-17 June 200
NMR Investigation of the Low Temperature Dynamics of solid 4He doped with 3He impurities
The lattice dynamics of solid 4He has been explored using pulsed NMR methods
to study the motion of 3He impurities in the temperature range where
experiments have revealed anomalies attributed to superflow or unexpected
viscoelastic properties of the solid 4He lattice. We report the results of
measurements of the nuclear spin-lattice and spin-spin relaxation times that
measure the fluctuation spectrum at high and low frequencies, respectively, of
the 3He motion that results from quantum tunneling in the 4He matrix. The
measurements were made for 3He concentrations 16<x_3<2000 ppm. For 3He
concentrations x_3 = 16 ppm and 24 ppm, large changes are observed for both the
spin-lattice relaxation time T_1 and the spin-spin relaxation time T_2 at
temperatures close to those for which the anomalies are observed in
measurements of torsional oscillator responses and the shear modulus. These
changes in the NMR relaxation rates were not observed for higher 3He
concentrations.Comment: 23 pages, 10 figure
Radiance and Doppler shift distributions across the network of the quiet Sun
The radiance and Doppler-shift distributions across the solar network provide
observational constraints of two-dimensional modeling of transition-region
emission and flows in coronal funnels. Two different methods, dispersion plots
and average-profile studies, were applied to investigate these distributions.
In the dispersion plots, we divided the entire scanned region into a bright and
a dark part according to an image of Fe xii; we plotted intensities and Doppler
shifts in each bin as determined according to a filtered intensity of Si ii. We
also studied the difference in height variations of the magnetic field as
extrapolated from the MDI magnetogram, in and outside network. For the
average-profile study, we selected 74 individual cases and derived the average
profiles of intensities and Doppler shifts across the network. The dispersion
plots reveal that the intensities of Si ii and C iv increase from network
boundary to network center in both parts. However, the intensity of Ne viii
shows different trends, namely increasing in the bright part and decreasing in
the dark part. In both parts, the Doppler shift of C iv increases steadily from
internetwork to network center. The average-profile study reveals that the
intensities of the three lines all decline from the network center to
internetwork region. The binned intensities of Si ii and Ne viii have a good
correlation. We also find that the large blue shift of Ne viii does not
coincide with large red shift of C iv. Our results suggest that the network
structure is still prominent at the layer where Ne viii is formed in the quiet
Sun, and that the magnetic structures expand more strongly in the dark part
than in the bright part of this quiet Sun region.Comment: 10 pages,9 figure
A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements
A parallel fast direct solver for rank-compressible block tridiagonal linear
systems is presented. Algorithmic synergies between Cyclic Reduction and
Hierarchical matrix arithmetic operations result in a solver with arithmetic complexity and memory footprint. We provide a
baseline for performance and applicability by comparing with well known
implementations of the -LU factorization and algebraic multigrid
with a parallel implementation that leverages the concurrency features of the
method. Numerical experiments reveal that this method is comparable with other
fast direct solvers based on Hierarchical Matrices such as -LU and
that it can tackle problems where algebraic multigrid fails to converge
Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas
In complementary images of coordinate-space and momentum-space density in a
trapped 2D Bose gas, we observe the emergence of pre-superfluid behavior. As
phase-space density increases toward degenerate values, we observe a
gradual divergence of the compressibility from the value predicted by
a bare-atom model, . grows to 1.7 before
reaches the value for which we observe the sudden emergence of a spike
at in momentum space. Momentum-space images are acquired by means of a 2D
focusing technique. Our data represent the first observation of non-meanfield
physics in the pre-superfluid but degenerate 2D Bose gas.Comment: Replace with the version appeared in PR
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