Related papers: Weak error expansion of the implicit Euler scheme

In this paper, we prove the non-uniqueness of stationary solutions to steady incompressible Euler equations with source terms. Based on the convex integration scheme developed by De Lellis and Sz\'{e}kelyhidi, the Euler system is…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

Most theoretically motivated work in the offline reinforcement learning setting requires precise uncertainty estimates. This requirement restricts the algorithms derived in that work to the tabular and linear settings where such estimates…

Our main goal in this article is to prove a new extension theorem for sections of the canonical bundle of a weakly pseudoconvex K\"ahler manifold with values in a line bundle endowed with a possibly singular metric. We also give some…

We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the…

In this paper we extend the Balian--Low theorem, which is a version of the uncertainty principle for Gabor (Weyl--Heisenberg) systems, to functions of several variables. In particular, we first prove the Balian--Low theorem for arbitrary…

Weak measurement [1,19] combined with quantum delayed-choice experiment that use quantum beam splitter instead of the beam splitter give rise to a surprising amplification effect, i.e., counterintuitive negative amplification effect. We…

We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method…

We extend the planar Markus-Yamabe Jacobian Conjecture to differential systems having jacobian matrix with eigenvalues with negative or zero real parts.

An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…

We give combinatorial generalizations of the Cayley-Bacharach theorem and induced map.

For any abelian group $A$, we prove an asymptotic formula for the number of $A$-extensions $K/\mathbb{Q}$ of bounded discriminant such that the associated norm one torus $R_{K/\mathbb{Q}}^1 \mathbb{G}_m$ satisfies weak approximation. We are…

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This equation resembles a computation of such Euler characteristics via a combinatorial…

In this paper we point out that the proof of Kable's extension of the Wiener-Ikehara Tauberian theorem can be applied to the case where the Dirichlet series has a pole of order "$l / m$" without much modification (Kable proved the case $l =…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.

We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…