Related papers: On nodal lines of Neumann eigenfunctions

In this article we determine bounds on the maximal order of vanishing for eigenfunctions of a generalized Dirichlet-to-Neumann map (which is associated with fractional Schr\"odinger equations) on a compact, smooth Riemannian manifold,…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

We present examples of bounded planar domains with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This shows that Payne's nodal line conjecture can at most hold for…

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…

We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…

We construct a Riemannian metric on the $ 2 $-dimensional torus, such that for infinitely many eigenvalues of the Laplace-Beltrami operator, a corresponding eigenfunction has infinitely many isolated critical points. A minor modification of…

We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been shown that MMBM may be expressed as the limit of a…

We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…

We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of the Helmholtz equation. Using the exterior conformal mapping…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

This paper is devoted to the Neumann-Kirchhoff Laplacian on a finite metric graph. We prove an index theorem relating the nodal deficiency of an eigenfunction with (1) the Morse index of the Dirichlet-to-Neumann map, (2) its positive index…

In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…

We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…

We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1)…

We use reflecting Brownian motion (RBM) to prove the well known Gauss-Bonnet-Chern theorem for a compact Riemannian manifold with boundary. The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary…

We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dimensions. An expansion in curvilinear coordinates leads us to…

We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems…

We present a novel data-driven approach for learning linear representations of a class of stable nonlinear systems using Koopman eigenfunctions. By learning the conjugacy map between a nonlinear system and its Jacobian linearization through…

The aim of this paper is to derive Fokker - Planck equation in curvilinear coordinates using physical argumentation. We get the same result, as in our previous article [1], but for broader class of arbitrary holonomic mechanical systems.

The geometric linearization of nonlinear differential equation is a robust method for the construction of analytic solutions. The method is related to the existence of Lie symmetries which can be used to determine point transformations such…