Related papers: Time Eigenvalues for the One-dimensional Infinite …
We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\] for general linear operators $R$ in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localized…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We introduce a general method for understanding the late time tail for solutions to wave equations on asymptotically flat spacetimes with odd space dimensions. In particular, for a large class of equations, we prove that the precise late…
The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron, which is in a 3-dimensional spherical space of constant curvature +1. One formula is given in terms of dihedral angles, and another one is…
In this paper, we address the space-time decay properties for strong solutions to the incompressible viscous resistive Hall-MHD equations. We obtained the same space-time decay rates as those of the heat equation. Based on the temporal…
The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. In this paper, the properties of this algebra are studied from the point of view of motivic periods.
We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner-Nordstrom families of black holes.…
We compute asymptotics of eigenvalues approaching the bottom of the continuous spectrum, and associated resonances, for Schr\"odinger operators in dimension two. We distinguish persistent eigenvalues, which have associated resonances, from…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been…
We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.
The adiabatic invariant nature of black hole horizon area in classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which…
We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
The influence of various damping on the performance of Schwarz methods for time-harmonic waves is visualized by Fourier analysis.
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the…
We prove a conjecture of Dekimpe, De Rock and Penninckx concerning the existence of eigenvalues one in certain elements of finite groups acting irreducibly on a real vector space of odd dimension. This yields a sufficient condition for a…
The convergence of the so-called quadratic method for computing eigenvalue enclosures of general self-adjoint operators is examined. Explicit asymptotic bounds for convergence to isolated eigenvalues are found. These bounds turn out to…
This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads…
A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with {\em any} finite dimensional unitary irrep for these…