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Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations
As the use of viscoelastic materials becomes increasingly popular, stability of viscoelastic structures under random loads becomes increasingly important. This paper aims at studying the asymptotic stability of viscoelastic systems under Gaussian and Poisson white noise excitations with Lyapunov functions. The viscoelastic force is approximated as equivalent stiffness and damping terms. A stochastic differential equation is set up to represent randomly excited viscoelastic systems, from which a Lyapunov function is determined by intuition. The time derivative of this Lyapunov function is then obtained by stochastic averaging. Approximate conditions are derived for asymptotic Lyapunov stability with probability one of the viscoelastic system. Validity and utility of this approach are illustrated by a Duffing-type oscillator possessing viscoelastic forces, and the influence of different parameters on the stability region is delineated
Tuning Optical Properties of Transparent Conducting Barium Stannate by Dimensional Reduction
We report calculations of the electronic structure and optical properties of
doped -type perovskite BaSnO3 and layered perovskites. While doped BaSnO
retains its transparency for energies below the valence to conduction band
onset, the doped layered compounds exhibit below band edge optical conductivity
due to transitions from the lowest conduction band. This gives absorption in
the visible for Ba2SnO4. Thus it is important to minimize this phase in
transparent conducting oxide (TCO) films. Ba3Sn2O7 and Ba4Sn3O10 have strong
transitions only in the red and infrared, respectively. Thus there may be
opportunities for using these as wavelength filtering TCO
Robust Principal Component Analysis?
This paper is about a curious phenomenon. Suppose we have a data matrix,
which is the superposition of a low-rank component and a sparse component. Can
we recover each component individually? We prove that under some suitable
assumptions, it is possible to recover both the low-rank and the sparse
components exactly by solving a very convenient convex program called Principal
Component Pursuit; among all feasible decompositions, simply minimize a
weighted combination of the nuclear norm and of the L1 norm. This suggests the
possibility of a principled approach to robust principal component analysis
since our methodology and results assert that one can recover the principal
components of a data matrix even though a positive fraction of its entries are
arbitrarily corrupted. This extends to the situation where a fraction of the
entries are missing as well. We discuss an algorithm for solving this
optimization problem, and present applications in the area of video
surveillance, where our methodology allows for the detection of objects in a
cluttered background, and in the area of face recognition, where it offers a
principled way of removing shadows and specularities in images of faces
Finite difference approximations for a size-structured population model with distributed states in the recruitment
In this paper we consider a size-structured population model where
individuals may be recruited into the population at different sizes. First and
second order finite difference schemes are developed to approximate the
solution of the mathematical model. The convergence of the approximations to a
unique weak solution with bounded total variation is proved. We then show that
as the distribution of the new recruits become concentrated at the smallest
size, the weak solution of the distributed states-at-birth model converges to
the weak solution of the classical Gurtin-McCamy-type size-structured model in
the weak topology. Numerical simulations are provided to demonstrate the
achievement of the desired accuracy of the two methods for smooth solutions as
well as the superior performance of the second-order method in resolving
solution-discontinuities. Finally we provide an example where supercritical
Hopf-bifurcation occurs in the limiting single state-at-birth model and we
apply the second-order numerical scheme to show that such bifurcation occurs in
the distributed model as well
The observed by the BES Collaboration
In the framework of the meson decay model, the strong decays of the
and states are investigated. It is found that in
the presence of the initial state mass being 2.24 GeV, the total widths of the
and states are about 438 MeV and 125 MeV,
respectively. Also, when the initial state mass varies from 2220 to 2400 MeV,
the total width of the state varies from about 100 to 132
MeV, while the total width of the state varies from about
400 to 594 MeV. A comparison of the predicted widths and the experimental
result of GeV, the width of the
with a mass of GeV recently observed by the
BES Collaboration in the radiative decay , suggests that it would be very difficult to identify the
as the state, and the seams a
good candidate for the state.Comment: 14 pages, 3 figures, typos corrected, Accepted by Physical Review
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
We consider the problem of recovering a low-rank matrix when some of its
entries, whose locations are not known a priori, are corrupted by errors of
arbitrarily large magnitude. It has recently been shown that this problem can
be solved efficiently and effectively by a convex program named Principal
Component Pursuit (PCP), provided that the fraction of corrupted entries and
the rank of the matrix are both sufficiently small. In this paper, we extend
that result to show that the same convex program, with a slightly improved
weighting parameter, exactly recovers the low-rank matrix even if "almost all"
of its entries are arbitrarily corrupted, provided the signs of the errors are
random. We corroborate our result with simulations on randomly generated
matrices and errors.Comment: Submitted to ISIT 201
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