We give an algorithm of decomposition for a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem of Lie algebras.

We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles. This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of such particles. We tested this concept for spheroidal particles and obtained a bound on the minor-to-major axis ratio for the valid application of this technique. We show th...

In this paper we present the quasi-Gaussian entropy theory in a comprehensive and consistent way, introducing a new derivation of the theory very suited for applications to molecular systems, and addressing its use in the case of multi-phase systems. A general derivation of the possible connnement of the system within a part of phase space is given, and for water it is shown that for this a har...

Acousticians generally assess the acoustic qualities of a concert hall or any other room using impulse response-based measures such as the reverberation time, clarity index, and others. These parameters are used to predict perceptual attributes related to the acoustic qualities of the room. Various studies show that these physical measures are not able to predict the related perceptual attribut...

Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalised to find the general form of the potential in which an exact third integral exists.

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

Joint probability distributions are derived that are expressed in terms of the determinants that form the determinantal inequalities associated with the non-negative Fourier series that represent crystal structures. The derivation involves heuristic considerations. It is therefore appropriate to test the distributions extensively by making comparisons with results obtained by other theoretical ...

We consider the valued field K := R((Γ)) of generalized series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

An optical flow processor architecture is proposed. It offers accuracy and image-size scalability for video segmentation extraction. The Hierarchical Optical flow Estimation (HOE) algorithm [1] is optimized to provide an appropriate bit-length and iteration number to realize VLSI. The proposed processor architecture provides the following features. First, an algorithm-oriented data-path is intr...