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In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…
Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for…
Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…
Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss…
Real-Time Time-Dependent Density Functional Theory (TDDFT) has become an attractive tool to model quantum dynamics on a first-principles Density Functional Theory level. In recent years, several developments and applications in this field…
The onset of condensation of hard spheres in a gravitational field is studied using density functional theory. In particular, we find that the local density approximation yields results identical to those obtained previously using the…
We analyze the structure of the Fundamental Measure Theory for the free energy density functional of hard sphere mixtures. A comparative study of the different versions of the theory, and other density functional approaches, is done in…
The journey of theoretical study on semiconductors is reviewed in a non-conventional way. We have started with the basic introduction of Hartree-Fock method and introduce the fundamentals of Density Functional Theory (DFT). From the oldest…
There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent…
We propose a new approach to quantum phase transitions in terms of the density-functional fidelity, which measures the similarity between density distributions of two ground states in parameter space. The key feature of the approach, as we…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Time-dependent density-functional theory (TDDFT) is a formally exact approach to the time-dependent electronic many-body problem which is widely used for calculating excitation energies. We present a survey of the fundamental framework,…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
Dependability is an umbrella concept that subsumes many key properties about a system, including reliability, maintainability, safety, availability, confidentiality, and integrity. Various dependability modeling techniques have been…
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…
Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…