Related papers: The Evans function as a lower bound on the spectra…
We revisit the analysis by R.A. Gardner of convergence of spectra of periodic traveling waves in the homoclinic, or infinite-period limit, extending his results to the case of essential rather than point spectra of the limiting homoclinic…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
In the setting of real vector spaces, we establish a general set-valued Ekeland variational principle (briefly, denoted by EVP), where the objective function is a set-valued map taking values in a real vector space quasi-ordered by a convex…
To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…
The construction of Ekman boundary layer solutions near the non-flat boundaries presents a complex challenge, with limited research on this issue. In Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483], the Ekman…
This paper studies sensor calibration in spectral estimation where the true frequencies are located on a continuous domain. We consider a uniform array of sensors that collects measurements whose spectrum is composed of a finite number of…
The central objective function of a variational autoencoder (VAE) is its variational lower bound (the ELBO). Here we show that for standard (i.e., Gaussian) VAEs the ELBO converges to a value given by the sum of three entropies: the…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
If $u : \Omega\subset \mathbb{R}^d \to {\rm X}$ is a harmonic map valued in a metric space ${\rm X}$ and ${\sf E} : {\rm X} \to \mathbb{R}$ is a convex function, in the sense that it generates an ${\rm EVI}_0$-gradient flow, we prove that…
We make rigorous spectral stability analysis for non-resonant capillary-gravity waves as well as resonant Wilton ripples of sufficiently small amplitude. Our analysis is based on a periodic Evans function approach, developed recently by the…
A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$ f((x+y)/2) \le (f(x)+f(y))/2 + 1. $$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper…
We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in…
The paper is concerned with sharp estimates of constants in Poincare type inequalities for functions having zero mean value on the boundary of a Lipschitz domain or on a measurable part of it. These estimates are useful for various…
This paper analyzes a model in which an outcome equals a frontier function of inputs minus a nonnegative unobserved deviation. The inputs may be endogenous (statistically dependent on the deviation). If zero lies in the support of the…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
For smooth bounded domains in $\mathbb{R}$, we prove upper and lower $L^2$ bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary data in a spectral window. The bounds are tight in the sense…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…