Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space

The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even infinite-dimensional algebras or superalgebras. One presents here the infinite-dimensional superalgebra specific to the Dirac theory in manifolds carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an infinite-dimensional superalgebra that can be seen as a twisted loop superalgebra.Comment: 16 pages, LaTeX, references adde

Special solutions for Ricci flow equation in 2D using the linearization approach

The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving arbitrary functions are presented. Some special reductions are also discussed.Comment: 8 pages, latex, no figure

A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds. In this note we proved that there exists no proper doubly warped product contact CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page

Dynamical algebra and Dirac quantum modes in Taub-NUT background

The SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the discrete quantum modes are governed by reducible representations of the o(4) dynamical algebra generated by the components of the angular momentum operator and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT background. The consequence is that there exist central and axial discrete modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra

CONSIDERATIONS CONCERNING THE AUTOMATION OF PROTECTED SPACES

In the last period there is an intensification of the researches oriented towards the automation of the specific activities of the horticultural production in protected spaces. The greenhouses offer a shelter in which a microclimate suitable for plants is maintained, which is obtained by regulating / adjusting the heat and the amount of light coming from the sun, by means of actuation systems (actuators-technical devices that generate an action to reach a specific objective). The paper presents a brief communication on the main drive systems used in greenhouses: ventilation and cooling systems; heating systems; irrigation systems, whose drive systems are mainly composed of electrical devices, especially electric motors or pump

Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background

The algebra of conserved observables of the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the Dirac conserved operators have physical parts associated with Pauli operators that are also conserved in the sense of the Klein-Gordon theory. In this way one gets simpler methods of analyzing the properties of the conserved Dirac operators and their main algebraic structures including the representations of dynamical algebras governing the Dirac quantum modes.Comment: 16 pages, latex, no figure

Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics

The gravitational anomalies are investigated for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condition is computed. The role of the Killing-Yano tensors is discussed for these two types of quantum anomalies.Comment: 23 page