Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

The Teleparallel Lagrangian and Hamilton-Jacobi Formalism

We analyze the Teleparallel Equivalent of General Relativity (TEGR) from the point of view of Hamilton-Jacobi approach for singular systemsComment: 11 pages, no figures, to appear in GR

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

f-symbols, Killing tensors and conserved Bel-type currents

In the framework of the General Relativity we show that from three generalizations of Killing vector fields, namely f-symbols, symmetric St\"{a}ckel-Killing and antisymmetric Killing-Yano tensors, some conserved currents can be obtained through adequate contractions of the above mentioned objects with rank four tensors having the properties of Bel or Bel-Robinson tensors in Einstein spaces.Comment: 13 pages, accepted for publication in Mod. Phys. Lett.

NIMRAD: novel technique for respiratory data treatment

© 2012, Springer-Verlag London. This paper illustrates the efficiency and simplicity of a new technique which is determined in this paper as NIMRAD (the non-invasive methods of the reduced analysis of data) for describing information extracted from biological signals. As a specific example, we consider the respiratory data. The NIMRAD can be applied for quantitative description of data recorded for complex systems in cases where the adequate model is absent and the treatment procedure should not contain any uncontrollable error. The theoretical developments are applied to signals measured from the respiratory system by means of the forced oscillation technique based on non-invasive lung function test. In order to verify the feasibility of the proposed algorithm for developing new diagnosis tools, we apply NIMRAD on two different respiratory data sets, namely from a healthy subject and from a patient diagnosed with asthma. The results are promising and suggest that NIMRAD could be further tailored and used for specific clinical applications

Cosmological Models with Fractional Derivatives and Fractional Action Functional

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.Comment: 14 page

Hamilton-Jacobi treatment of a non-relativistic particle on a curved space

In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.Comment: 10 pages, LaTe

Extraction of reliable information from hme-domain pressure and flow signals measured by means of forced oscillation techniques

This paper aims to give a proof-of-concept for the possible application of the forced oscillation lung function test to assess the viscoelastic properties of the airways and tissue. In particular, a novel signal processing algorithm is employed on non-stationary, noisy, (relatively) short time series of respiratory pressure and flow signals. This novel technique is employed to filter the useful information from the signals acquired under two measurement conditions: pseudo-functional residual capacity (PFRC) and pseudo-total lung capacity (PTLC). The PFRC is the measurement performed at lowest lung volume with maximum deflation, and the PTLC is measurement performed at the maximum lung volume under maximum inflation. The results suggest that the proposed technique is able to extract information on the viscoelastic properties of the lung tissue at a macroscopic level. The conclusion of this preliminary study is that the proposed combination of signal processing method and lung function test is suited to be employed on a large database in order to deliver reference values and perform further statistical analysis

Fractional Dirac Bracket and Quantization for Constrained Systems

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical Review