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In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was r ...
The behavior of the discrete spectrum of the Schr"odinger operator −\D−V, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel P(t;x,y) as t→0 and t→∞. If this behavior is powe ...
We consider a class of nonlinear eigenvalue problems including equations such as −Δu(x) + q(x)u(x) + γ u(x)2 ξ(x)2 + u(x)2 u = λu(x) for x ∈ R , where γ > 0, q ∈ L∞(RN ) and ξ ∈ L2(RN ) are given and we are interested in eigenvalues λ ∈ R for which this eq ...
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We present a direct comparison of phase sensitive sum-frequency generation experiments with phase reconstruction obtained by the maximum entropy method. We show that both methods lead to the same complex spectrum. Furthermore, we discuss the strengths and ...
Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve ...
We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...
Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, ...
Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve ...
A procedure for time-frequency analysis of time series is described, which is mainly inspired by singular-spectrum analysis, but it presents some modifications that allow checking the convergence of the results and extracting the detected spectral componen ...
This study presents a new algorithm developed in order to remove instabilities observed in the simulation of unsteady viscoelastic fluid flows in the framework of the spectral element method. In this study, we consider a particular model of the finite exte ...
