Related papers: Weak error expansion of the implicit Euler scheme
In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the…
Instrumental variables estimation has gained considerable traction in recent decades as a tool for causal inference, particularly amongst empirical researchers. This paper makes three contributions. First, we provide a detailed theoretical…
We review Fujiwara's scheme, a sixth order weak approximation scheme for the numerical approximation of SDEs, and embed it into a general method to construct weak approximation schemes of order $ 2m $ for $ m \in \mathbf{N} $. Those schemes…
In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk-Meyer and is closely related to coarse expanding…
The aim of this work is to prove a Tauberian theorem for the Ingham summability method. The Tauberian theorem we prove is then applied to analyze asymptotics of mean values of multiplicative functions on natural numbers.
We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some…
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…
We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
Let $\mathcal{S} = \{ \tau_n \}_{n=1}^\infty \subset (0,T)$ be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions…
Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the…
In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…
In this paper, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler--Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error…
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.
We generalize Rado's extension theorem to complex spaces.
Small errors are corrected