Vacuum Einstein metrics with bidimensional Killing leaves. I-Local aspects

The solutions of vacuum Einstein's field equations, for the class of Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing fields, are explicitly described. They are parametrized either by solutions of a transcendental equation (the tortoise equation), or by solutions of a linear second order differential equation in two independent variables. Metrics, corresponding to solutions of the tortoise equation, are characterized as those that admit a 3-dimensional Lie algebra of Killing fields with bidimensional leaves.Comment: LateX file, 33 pages, 2 figure

Superintegrability in the Manev Problem and its Real Form Dynamics

We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation is characteristic of the Kepler model. If the orbits are bounded these invariants exist only when a certain rationality condition is met and thus we have superintegrability only on a subset of initial values. We analyze real form dynamics of the Manev model and derive that it is always superintegrable. We also discuss the symmetry algebras of the Manev model and its real Hamiltonian form.Comment: 12 pages, LaTeX, In: Prof. G. Manev's Legacy in Contemporary Astronomy, Theoretical and Gravitational Physics, V. Gerdjikov, M. Tsvetkov (Eds), Heron Press, Sofia 2005, pp. 155-16

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero--Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.Comment: 15 pages, No figures, EPJ-style (svjour.cls

Recursion Operators for CBC system with reductions. Geometric theory

We discuss some recent developments of the geometric theory of the Recursion Operators (Generating Operators) for Caudrey-Beals-Coifman systems(CBC systems) on semisimple Lie algebras. As is well known the essence of this interpretation is that the Recursion Operators could be considered as adjoint to Nijenhuis tensors on certain infinite-dimensional manifolds. In particular, we discuss the case when there are Zp reductions of Mikhailov type

Spin-1 gravitational waves

Gravitational fields invariant for a 2-dimensional Lie algebra of Killing fields [ X,Y] =Y, with Y of light type, are analyzed. The conditions for them to represent gravitational waves are verified and the definition of energy and polarization is addressed; realistic generating sources are described.Comment: 18 pages, no figures. A section on possible sources has been added. Version accepted for publication in Int. J. Mod. Phys.

Noncommutative Schwarzschild geometry and generalized uncertainty principle

We discuss a possible link between the deformation parameter $$\Theta ^{\mu \nu }$$ Θμν arising in the framework of noncommutative geometry and the parameter $$\beta$$ β of the generalized uncertainty principle (GUP). We compute the shift of the Hawking temperature induced by the $$\Theta ^{\mu \nu }$$ Θμν -deformed Schwarzschild geometry, and then we relate it to one obtained by GUP. Results suggest a granular structure of specetime at the Planck scales. The current bounds on $$\beta$$ β allow to constraint the noncommutative parameter $$\Theta ^{\mu \nu }$$ Θμν

Gateway Discovery and Selection in Mobile Hotspots

Gaining IP connectivity in mobile hotspots (e.g. public transport vehicles) through on-board local area networks and mobile gateways has recently attracted strong commercial and research interests. In this paper we propose a multi-dimensional protocol to support the process of gatewaydiscovery in mobile hotspots, and to help in selecting the best path able to satisfy the user's requirements and to guarantee a target end-to-end service quality. Our proposal is based on highly popular and almost standard protocols, such as SDPng for session description and AODV for route discovery

Sensors for the monitoring of analytes in the sweat

In the last decade, can be found an exceptional growth in research activity relating to the development of wearable devices, capable of continuously monitoring the health conditions of the wearer by analyzing body fluids such as blood, urine, saliva, tears and sweat. Among the body fluids available, sweat is a biofluid of particular interest, as it allows a non-invasive, continuous and comfortable collection. Human sweat contains useful information on the health of an individual and therefore is an excellent biofluid for the detection of specific analytes. The most abundant ions in the sweat are Na+ and Cl- (10 - 100 mM), and their monitoring is useful in patients with cystic fibrosis. Other constituents are Ca2+, K+, ascorbic acid, glucose (0.1-10 µM) related to osteoporosis, hypoaldosteronism, scurvy and diabetes disease. The sweat pH is in the range 3 to 8 [1] [2] and indicates the level of metabolism and homeostasis of the body. Wearable sensor needs to be flexible, compact and easily applicable. It must also offer a stable response, with high sensitivity and selectivity towards specific analytes [3]. Over the years, many wearable sensors for sweat monitoring have been developed, combining different form factors, substrates and sensing mechanism. In this work, electrochemical sensors based on polyaniline (PANi), which is pH sensitive, were studied. First, the best conditions of electrochemical deposition of PANi were studied [4], using as flexible substrate polyethylene terephthalate coated with indium-tin oxide (ITO-PET). In order to improve the sensor performance electrodes were also modified by electrochemical deposition of reduced graphene oxide (rGO). All samples were characterized by XRD, SEM and EDS analysis in order to study morphology and evaluate the crystalline phases of the deposited PANi. The electrodes were tested as pH sensors using different buffer solutions, from 2 to 8, by Open Circuit Potential (OCP) technique. The ITO-PET/rGO/PANi electrodes show good behavior in terms of sensitivity (62.3 mV/pH), very close to Nernstian response of 59 mV/pH and reproducibility of 3.8%. Flexibility and mechanical stability tests were carried out on the sensor to evaluate both the wearability and mechanical resistance. In addition, interference tests, in the presence of competing ions such as Na+, Cl-, K+, NH4+, aimed to verify the selectivity were also performed

Quantum Mechanics on SO(3) via Non-commutative Dual Variables

We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.Comment: 29 pages; matches the published version plus footnote 7, a journal reference include

On the SO(2,1) symmetry in General Relativity

The role of the SO(2,1) symmetry in General Relativity is analyzed. Cosmological solutions of Einstein field equations invariant with respect to a space-like Lie algebra G_r, with r between 3 and 6 and containing so(2,1) as a subalgebra, are also classified.Comment: 10 pages, latex, no figure