相关论文: Microlocal analysis of a spindle transform

This is the first of a series of papers devoted to the stabilization of the twisted trace formula. It is just an introduction. We present the local theory of twisted endoscopy, following the fundamental works of Kottwitz-Shelstad, Labesse…

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian…

Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…

In this paper spectral methods are applied to investigate the hydrodynamic instability of swirling flow with application to Francis hydraulic turbine. Spectral methods imply representing the problem solution as truncated series of smooth…

We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…

For a locally compact abelian group $\textbf{R}$ with a uniform lattice $\Lambda$ and a group $G$ that acts on $\textbf{R}$ by continuous automorphisms, we study operators commuting with the representation of $G \rtimes \Lambda$ on…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…

The invertibility of integral linear operators is a major problem of both theoretical and practical importance. In this paper we investigate the relation between an operator invertibility and the rank of its integral kernel to develop a…

We propose a quantum-Hamiltonian-learning-based sequential reconstruction framework for dynamic two-dimensional magnetic-field maps using a local likelihood model derived from a nitrogen-vacancy-center spin-1 Hamiltonian. Local measurements…

We present a novel microlocal analysis of a non-linear ray transform, $\mathcal{R}$, arising in Compton Scattering Tomography (CST). Due to attenuation effects in CST, the integral weights depend on the reconstruction target, $f$, which has…

We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation on the product…

Suppose $\alpha$ is an orientation-preserving diffeomorphism (shift) of $\mR_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$. In \cite{KKLsufficiency} we found sufficient conditions for the Fredholmness of the singular…

We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral…

In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that…

In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…

Let $B$, $I$ be the unweighted backward shift and the identity operator respectively on $l^{\infty}(\mathbb{N})$, the space of bounded sequences over the complex numbers endowed with the supremum norm. We prove that $I+\lambda B$ is locally…

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…

Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the…

In this paper, we first introduce the notion of the Laplace transform for an abstract-valued function from $[0, \infty)$ to a $\mathcal{T}_{\varepsilon, \lambda}$-complete random normed module $S$. Then, combining respective advantages of…