Related papers: Fundamentals of Molecular Integrals Evaluation
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
The use of validated conceptual assessments alongside more standard course exams has become standard practice for the introductory courses in many physics departments. These assessments provide a more standard measure of certain learning…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
The Gaussian integral, denoted as \( \int_{-\infty}^{\infty} e^{-x^2} dx \), plays a significant role in mathematical literature. In this paper, we explore a family of integrals related to Gaussian functions. Specifically, we introduce…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
In this article we consider new generalized functions for evaluating integrals and roots of functions. The construction of these generalized functions is based on Rogers-Ramanujan continued fraction, the Ramanujan-Dedekind eta, the elliptic…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory, PBE, and a recently proposed modification designed specifically for solids, PBEsol, are identified as particular members of a…
We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…
For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
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…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace and (iii)…
In some other papers, the Lagrangians in the causal sets included coefficients that were to be computed by integrating over Alexandrov set. In those other papers, this integral was explicitly evaluated, which resulted in rather…