Related papers: Fundamentals of Molecular Integrals Evaluation
This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
This review article is devoted to application of precision molecular spectroscopy to studies of the possible spatial and temporal variations of the fundamental constants. Both astrophysical observations and laboratory experiments are…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
Fundamentals of energy density functional in nuclear physics are presented. Much attention is paid to a mathematically rigorous treatment of deriving the energy density functional. The specific features of the density functional used in…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation…
This document attempts to clarify potential confusion regarding electrostatics calculations, specifically in the context of biomolecular structure and specifically as regards the units typically used to contour/visualize isopotential…
In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach…
Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.
In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These…
Second quantization has been widely used in quantum mechanics and quantum chemistry, which is trivial and error-prone for researchers. Fortunately it is a good candidate for automatic evaluation with its simple, trivial and intrinsic…
We study an extension of modal $\mu$-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability…
A introduction into density-functional theory and electronic structure methods is given, that aims at providing an intuitive understanding of the underlying concepts for the novice as well as an entry point towards the more advanced…
Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…