Related papers: Uniform stationary phase estimate with limited smo…
Phasor measurement units (PMUs) are widely used for sub-synchronous oscillation monitoring, yet the effect of windowed discrete Fourier transform (DFT)-based phasor estimation on oscillation observability is not fully characterized. This…
In this paper, we consider the $(2+1)-$dimensional oscillatory integral operators with cubic homogeneous polynomial phases, which are degenerate in the sense of \cite{Tan06}. We improve the previously known $L^2\to L^2$ decay rate to $3/8$…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to…
We determine the quantum Cram\'er-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard…
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the…
It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…
Let T be an oscillatory integral operator on L^2(R) with a smooth real phase function S(x,y). We prove that, in all cases but the one described below, after localization to a small neighborhood of the origin the norm of T decays like…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
A theorem of Varchenko gives the order of decay of the leading term of the asymptotic expansion of a degenerate oscillatory integral with real-analytic phase in two dimensions. His theorem expresses this order of decay in a simple geometric…
We develop a theory of oscillatory integrals whose phase is given by the trace of a polynomial over an algebraic number field. We present an application to the singular integral for a version of Tarry's problem for algebraic integers.
The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori…