Related papers: Relationship between H\"{o}lder Divergence and Fun…
Recently (Science, 355, 6320, 2017, 49-52) it was argued that density functionals stray from the path towards exactness due to errors in densities (\rho) of 14 atoms and ions computed with several recent functionals. However, this…
Robust tests of general composite hypothesis under non-identically distributed observations is always a challenge. Ghosh and Basu (2018, Statistica Sinica, 28, 1133--1155) have proposed a new class of test statistics for such problems based…
A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
It is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of these divergences hints at a…
The universal density functional $F$ of density-functional theory is a complicated and ill-behaved function of the density-in particular, $F$ is not differentiable, making many formal manipulations more complicated. Whilst $F$ has been well…
Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations (DFAs) are published every year. To become available in program packages, the novel DFAs need to be (re)implemented.…
We study the interactions between two negatively charged macroscopic surfaces confining positive counterions. A density-functional approach is introduced which, besides the usual mean-field interactions, takes into account the correlations…
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference…
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review…
Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons…
To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a…
For a family $\mathcal{F}$ of subsets of a finite set, define $\mathcal{D}(\mathcal{F})=\{F\setminus F': F, F'\in\mathcal{F}\}$. A family $\mathcal{F}$ is called intersecting if $F\cap F'\not=\emptyset$ for all $F, F'\in\mathcal{F}$. Frankl…
In this work, we define a family of probability densities involving the generalized trigonometric functions defined by Dr\'abek and Man\'asevich [1], which we name Generalized Trigonometric Densities. We show their relationship with the…
Introduced by M\"uller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed…
The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and hence should be replaced by, in this…
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and…
(Abridged) We investigate the power of void statistics to constrain galaxy bias and the amplitude of dark matter fluctuations. We use the halo occupation distribution (HOD) framework to describe the relation between galaxies and dark…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes…