Related papers: Algorithms for estimating spectral density functio…
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which…
We introduce a \emph{spectral Dehn function} \[ \Lambda_{\mathcal{P}}(n):=\inf \lambda_1(\Delta), \] where $\lambda_1(\Delta)$ is the first Dirichlet eigenvalue of the random-walk Laplacian on a van Kampen diagram $\Delta$, and the infimum…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
Among the variety of statistical intervals, highest-density regions (HDRs) stand out for their ability to effectively summarize a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
We study the approximation of the spectrum of a second-order elliptic differential operator by the Hybrid High-Order (HHO) method. The HHO method is formulated using cell and face unknowns which are polynomials of some degree $k\geq0$. The…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Fox's H-function provide a unified and elegant framework to tackle several physical phenomena. We solve the space fractional diffusion equation on the real line equipped with a delta distribution initial condition and identify the…
Phonon frequencies at Gamma-point in non-magnetic rhombohedral phase of LaCoO3 were calculated using density functional theory (DFT) with hybrid exchange correlation functional PBE0. The calculations involved a comparison of results for two…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…
A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. {\bf 136}, 224109 (2012)]. As illustrated, a convenient…
In this paper we develop the theory of Schauder estimates for the fractional harmonic oscillator $H^\sigma=(-\Delta+|x|^2)^\sigma$, $0<\sigma<1$. More precisely, a new class of smooth functions $C^{k,\alpha}_H$ is defined, in which we study…
We consider in this paper the Hahn polynomials and their application in numerical methods. The Hahn polynomials are classical discrete orthogonal polynomials. We analyse the behaviour of these polynomials in the context of spectral…
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the…
We describe a finite-field approach to compute density response functions, which allows for efficient $G_0W_0$ and $G_0W_0\Gamma_0$ calculations beyond the random phase approximation. The method is easily applicable to density functional…
We investigate the performance of the range-separated hybrid (RSH) scheme, which combines long-range Hartree-Fock (HF) and a short-range density-functional approximation (DFA), for calculating photoexcitation/photoionization spectra of the…
Density functional methods were developed, in which the Coulomb electron-electron interaction is split into a long- and a short-range part. In such methods, one term is calculated using traditional density functional approximations, like…
We calculate the spectral functions of model systems describing 5f-compounds adopting Cluster Perturbation Theory. The method allows for an accurate treatment of the short-range correlations. The calculated excitation spectra exhibit…
We present a method to numerically estimate the densities of a discretely sampled data based on binary space partitioning tree. We start with a root node containing all the particles and then recursively divide each node into two nodes each…