120,421 research outputs found
Sharp RIP Bound for Sparse Signal and Low-Rank Matrix Recovery
This paper establishes a sharp condition on the restricted isometry property
(RIP) for both the sparse signal recovery and low-rank matrix recovery. It is
shown that if the measurement matrix satisfies the RIP condition
, then all -sparse signals can be recovered exactly
via the constrained minimization based on . Similarly, if
the linear map satisfies the RIP condition ,
then all matrices of rank at most can be recovered exactly via the
constrained nuclear norm minimization based on . Furthermore, in
both cases it is not possible to do so in general when the condition does not
hold. In addition, noisy cases are considered and oracle inequalities are given
under the sharp RIP condition.Comment: to appear in Applied and Computational Harmonic Analysis (2012
Existence of Dyons in Minimally Gauged Skyrme Model via Constrained Minimization
We prove the existence of electrically and magnetically charged particlelike
static solutions, known as dyons, in the minimally gauged Skyrme model
developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically
symmetric, depend on two continuous parameters, and carry unit monopole and
magnetic charges but continuous Skyrme charge and non-quantized electric charge
induced from the 't Hooft electromagnetism. The problem amounts to obtaining a
finite-energy critical point of an indefinite action functional, arising from
the presence of electricity and the Minkowski spacetime signature. The
difficulty with the absence of the Higgs field is overcome by achieving
suitable strong convergence and obtaining uniform decay estimates at singular
boundary points so that the negative sector of the action functional becomes
tractable.Comment: 24 page
Optimal mistuning for enhanced aeroelastic stability of transonic fans
An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom
Constrained Quadratic Risk Minimization via Forward and Backward Stochastic Differential Equations
In this paper we study a continuous-time stochastic linear quadratic control
problem arising from mathematical finance. We model the asset dynamics with
random market coefficients and portfolio strategies with convex constraints.
Following the convex duality approach, we show that the necessary and
sufficient optimality conditions for both the primal and dual problems can be
written in terms of processes satisfying a system of FBSDEs together with other
conditions. We characterise explicitly the optimal wealth and portfolio
processes as functions of adjoint processes from the dual FBSDEs in a dynamic
fashion and vice versa. We apply the results to solve quadratic risk
minimization problems with cone-constraints and derive the explicit
representations of solutions to the extended stochastic Riccati equations for
such problems.Comment: 22 page
Kohn-Sham equations for nanowires with direct current
The paper describes the derivation of the Kohn-Sham equations for a nanowire
with direct current. A value of the electron current enters the problem as an
input via a subsidiary condition imposed by pointwise Lagrange multiplier.
Using the constrained minimization of the Hohenberg-Kohn energy functional, we
derive a set of self-consistent equations for current carrying orbitals of the
molecular wire
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