Related papers: Cutoff estimates for the Becker-D\"oring equations
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…
We explore the norm attainment set and the minimum norm attainment set of a bounded linear operator between Hilbert spaces and Banach spaces. Indeed, we obtain a complete characterization of both the sets, separately for operators between…
In this paper we find out some new blow-up estimates for the positive explosive solutions of a paradigmatic class of elliptic boundary value problems of superlinear indefinite type. These estimates are obtained by combining the scaling…
We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper…
We address the problems of computing operator norms of matrices induced by given norms on the argument and the image space. It is known that aside of a fistful of "solvable cases," most notably, the case when both given norms are Euclidean,…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
We give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non cutoff. On one hand, the results disclose the link between the hyperbolic property…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad's angular cutoff assumption. This is done by an adaptation of the famous entropy method and…
We exhibit supercritical trade-off for monotone circuits, showing that there are functions computable by small circuits for which any circuit must have depth super-linear or even super-polynomial in the number of variables, far exceeding…
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor…
In this paper, we establish optimal hypoelliptic estimates for a class of kinetic equations, which are simplified linear models for the spatially inhomogeneous Boltzmann equation without angular cutoff.
A summary of the current understanding of methods of analytical higher order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is presented. As examples, the total cross section in electron…
We study higher-derivative gravity theories in arbitrary space-time dimension d with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to…
We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…
Regression discontinuity (RD) designs are a popular approach to estimating a treatment effect of cutoff-based interventions. Two current estimation approaches dominate the literature. One fits separate regressions on either side of the…
This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic…