相关论文: The cohomological equation for Roth type interval …

We study the dynamics of holomorphic correspondences $f$ on a compact Riemann surface $X$ in the case, so far not well understood, where $f$ and $f^{-1}$ have the same topological degree. Under a mild and necessary condition that we call…

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…

This paper is concerned with networks of identical linear quantum stochastic systems which interact with each other and external bosonic fields in a translation invariant fashion. The systems are associated with sites of a multidimensional…

For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of…

We prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schr\"odinger operators. Let $\Lambda_L = (-L/2,L/2)^d$ and $H_L = -\Delta_L + V_L$ be a Schr\"odinger operator on $L^2 (\Lambda_L)$ with a…

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…

The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional,…

The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…

We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…

"Toeplitzification" or "redundancy (spatial) averaging", the well-known routine for deriving the Toeplitz covariance matrix estimate from the standard sample covariance matrix, recently regained new attention due to the important Random…

We build a bridge between geometric group theory and topological dynamical systems by establishing a dictionary between coarse equivalence and continuous orbit equivalence. As an application, we give conceptual explanations for previous…

Let the map $f:[-1,1]\to[-1,1]$ have a.c.i.m. $\rho$ (absolutely continuous $f$-invariant measure with respect to Lebesgue). Let $\delta\rho$ be the change of $\rho$ corresponding to a perturbation $X=\delta f\circ f^{-1}$ of $f$. Formally…

We prove the Riemann-Roch theorem for homotopy invariant $K$-theory and projective local complete intersection morphisms between finite dimensional noetherian schemes, without smoothness assumptions. We also prove a new Riemann-Roch theorem…

For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…

The Darboux transformation applied recurrently on a Schroedinger operator generates what is called a {\em dressing chain}, or from a different point of view, a set of supersymmetric shape invariant potentials. The finite-gap potential…

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state hybrid DFT (ngH-DFT) to calculate absorption spectra within linear-response time-dependent Generalized Kohn-Sham DFT (LR-GKS-TDDFT), for…

The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this…

We study geometric and statistical properties of complex rational maps satisfying the Topological Collet-Eckmann Condition. We show that every such a rational map possesses a unique conformal probability measure of minimal exponent, and…