We consider the class of non-commutative ∗-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such ∗-algebras. An analog of the solution of the truncated Hamburger moment problem [Fia91] for path ∗-algebras is presented and non-commutative positivstellensatz is proved. We aslo present an analog...

Einthoven's equations for the heart vector are based on the assumption that voltages measured across the trunk horizontally (or vertically) are proportional to the horizontal (or vertical) component of the dipole moment of the heart's electromotive forces. One necessary consequence of this assumption is that all the horizontal (or vertical) voltages be similar, and that heart vectors calculated...

Over recent decades, atomic and molecular physics has blossomed, with much of the work springing from new techniques to translationally manipulate—especially to slow and trap—gaseous atoms and molecules. The ensuing study of slow (cold) atoms and molecules has led researchers into uncharted territories—not just of atomic and molecular physics, but of physics and even chemistry at large. Achievi...

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles ...

The Röntgen quantum phase shift is exhibited by the interference of point particles endowed with an electric dipole moment due to their motion relative to a source of the magnetic field. Here we show, using arguments involving the classical concepts of force and its impulse, that the Röntgen phase shift arises within a largely classical (semiclassical) theoretical framework. All the subtleties ...

A generalization from 2D to 3D of the tensor method for derivation of both affine invariants and rotation, translation and scaling (TRS) invariants is described. The method for generation of the 3D TRS invariants of higher orders is automated and experimentally tested.

Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers $vn%n50 ` to represent the ‘‘entropic moments’’ * [0,a]@r(x)# dx of an unknown non-negative, decreasing and differentiable ~a.e.! density function r(x) with a finite interval support. These moments are called entropic moments because they are closely conne...

We consider the class of non-commutative ∗-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such ∗-algebras. An analog of the solution of the truncated Hamburger moment problem [12] for path ∗-algebras is presented and non-commutative positivstellenzatz is proved. We aslo present an analog of...

This work concerns a comparison of experimental and theoretical results of the electron charge density distribution and the electrostatic potential around the m-nitrophenol molecule (m-NPH) known for its interesting physical characteristics. The molecular experimental results have been obtained from a high-resolution X-ray diffraction study. Theoretical investigations were performed using the D...