Related papers: Spectral Selection and Minimal Morse Structures on…
We study geometric characterizations of the Poincar\'{e} inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
By extending and generalising previous work by Ros and Savo, we describe a method to show that the Morse index of every closed minimal hypersurface on certain positively curved ambient manifolds is bounded from below by a linear function of…
We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
We use an inverse scattering approach to study multi-peakon solutions of the Degasperis-Procesi (DP) equation, an integrable PDE similar to the Camassa-Holm shallow water equation. The spectral problem associated to the DP equation is…
We develop a fully intrinsic Bayesian framework for nonparametric regression on the unit sphere based on isotropic Gaussian field priors and the harmonic structure induced by the Laplace-Beltrami operator. Under uniform random design, the…
We prove that projectivised finite-dimensional linear random dynamical systems possess a unique finest weak Morse decomposition. Based on this result, we define the Morse spectrum and investigate its basic properties. In particular, we show…
In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…
A self-dual harmonic 2-form on a 4-dimensional Riemannian manifold is symplectic where it does not vanish. Furthermore, away from the form's zero set, the metric with the 2-form give a compatible almost complex structure and thus…
In this contribution to the proceedings of the 11th Mathematical Society of Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent work on a mathematical model for small deformations of a spherical membrane. The idea…
The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2.…
Given a compact manifold with a non-empty boundary and equipped with a generic Morse function (that is, no critical point on the boundary and the restriction to the boundary is a Morse function), we already knew how to construct two Morse…
In this work, the phase function method (PFM) is employed for the first time to explicitly construct scattering wavefunctions for the $\alpha\alpha$ system using a single-term Morse potential. Unlike earlier PFM-based studies that primarily…
We consider space-cutoff $P(\varphi)_{2}$ models with a variable metric of the form \[ H= \d\G(\omega)+ \int_{\rr}g(x):P(x, \varphi(x)):\d x, \] on the bosonic Fock space $L^{2}(\rr)$, where the kinetic energy $\omega= h^{\12}$ is the…
We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dissimilarity. The resulting spectra encode how coherence…
In this article we analyze the spectral properties of the curl operator on closed Riemannian 3-manifolds. Specifically, we study metrics that are optimal in the sense that they minimize the first curl eigenvalue among any other metric of…
In this paper, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two and three dimensions. The analysis relies on an identity for the errors of…
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…