Category
Topics in analysis
Related publications (117)
Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing
Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
CAMBRIDGE UNIV PRESS2021Hyperbolic Fourier series
In this article we explain the essence of the interrelation described in [PNAS 118, 15 (2021)] on how to write explicit interpolation formula for solutions of the Klein-Gordon equation by using the recent Fourier pair interpolation formula of Viazovska and ...
arXiv2021Uniformly perfect finitely generated simple left orderable groups
We show that the finitely generated simple left orderable groups G(rho) constructed by the first two authors in Hyde and Lodha [Finitely generated infinite simple groups of homeomorphisms of the real line. Invent. Math. (2019), doi:10.1007/s00222-01900880- ...
CAMBRIDGE UNIV PRESS2021A p-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids
This paper presents an accuracy-preserving p-weighted limiter for discontinuous Galerkin methods on one-dimensional and two-dimensional triangular grids. The p-weighted limiter is the extension of the second-order WENO limiter by Li et al. [W. Li, J. Pan a ...
2020Two-dimensional nanochannel membranes for molecular and ionic separations
Shaoyu Wang, Guangwei He, Yifan Li, Zheyu Jiang
Two-dimensional (2D) nanosheets have emerged as promising functional materials owing to their atomic thickness and unique physical/chemical properties. By using 2D nanosheets as building blocks, diverse kinds of two-dimensional nanochannel membranes (2DNCM ...
ROYAL SOC CHEMISTRY2020Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)
Jan Sickmann Hesthaven, Lijing Zhao
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...
SCIENCE PRESS2020Inverse Modelling and Predictive Inference in Continuum Mechanics: a Data-Driven Approach
Claire Marianne Charlotte Capelo
The explosive growth of machine learning in the age of data has led to a new probabilistic and data-driven approach to solving very different types of problems. In this paper we study the feasibility of using such data-driven algorithms to solve classic ph ...
2020Normal approximation of the solution to the stochastic heat equation with Levy noise
Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...
SPRINGER2020Pulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds
Nicola Marzari, Iurii Timrov, Matteo Cococcioni, Francesco Aquilante, Luca Binci
We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The de ...
AMER PHYSICAL SOC2020The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise
We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...
INST MATHEMATICAL STATISTICS2020