45,439 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
Stein factors for negative binomial approximation in Wasserstein distance
The paper gives the bounds on the solutions to a Stein equation for the
negative binomial distribution that are needed for approximation in terms of
the Wasserstein metric. The proofs are probabilistic, and follow the approach
introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are
used to quantify the accuracy of negative binomial approximation to parasite
counts in hosts. Since the infectivity of a population can be expected to be
proportional to its total parasite burden, the Wasserstein metric is the
appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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
Cavity-free nondestructive detection of a single optical photon
Detecting a single photon without absorbing it is a long standing challenge
in quantum optics. All experiments demonstrating the nondestructive detection
of a photon make use of a high quality cavity. We present a cavity free scheme
for nondestructive single-photon detection. By pumping a nonlinear medium we
implement an inter-field Rabi-oscillation which leads to a ?pi phase shift on
weak probe coherent laser field in the presence of a single signal photon
without destroying the signal photon. Our cavity-free scheme operates with a
fast intrinsic time scale in comparison with similar cavity-based schemes. We
implement a full real-space multimode numerical analysis of the interacting
photonic modes and confirm the validity of our nondestructive scheme in the
multimode case.Comment: 4 figures, 5 page
Development of a hybrid multi-scale simulation approach for spray processes
This paper presents a multi-scale approach coupling a Eulerian interface-tracking method and a Lagrangian particle-tracking method to simulate liquid atomisation processes. This method aims to represent the complete spray atomisation process including the primary break-up process and the secondary break-up process, paving the way for high-fidelity simulations of spray atomisation in the dense spray zone and spray combustion in the dilute spray zone. The Eulerian method is based on the coupled level-set and volume-of-fluid method for interface tracking, which can accurately simulate the primary break-up process. For the coupling approach, the Eulerian method describes only large droplet and ligament structures, while small-scale droplet structures are removed from the resolved Eulerian description and transformed into Lagrangian point-source spherical droplets. The Lagrangian method is thus used to track smaller droplets. In this study, two-dimensional simulations of liquid jet atomisation are performed. We analysed Lagrangian droplet formation and motion using the multi-scale approach. The results indicate that the coupling method successfully achieves multi-scale simulations and accurately models droplet motion after the Eulerian–Lagrangian transition. Finally, the reverse Lagrangian–Eulerian transition is also considered to cope with interactions between Eulerian droplets and Lagrangian droplets.This work was supported by the Engineering and Physical Sciences Research Council of the UK (grant number EP/L000199/1)
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