Supersymmetric and shape-invariant generalization for nonresonant and intensity-dependent Jaynes-Cummings systems

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the coupled-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent Jaynes-Cummings Hamiltonians, widely used in quantized theories of lasers. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The use of the challenge test to analyse preservative efficiency in non-sterile cosmetic and health products: applications and critical points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Critical exponents for a transition from integrability to non-integrability via localization of invariant tori in the Hamiltonian system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has nontrivial fixed points, they will correspond to extrema of the vacuum energy. This relationship provides a different method to determine fixed points.

Multiplicity of Boardman strata and deformations of map germs

We define algebraically for each map germ f: Kn, 0→ Kp, 0 and for each Boardman symbol i = (il, . . ., ik) a number ci(f) which is script A sign-invariant. If f is finitely determined, this number is the generalization of the Milnor number of f when p = 1, the number of cusps of f when n = p = 2, or the number of cross caps when n = 2, p = 3. We study some properties of this number and prove that, in some particular cases, this number can be interpreted geometrically as the number of Σi points that appear in a generic deformation of f. In the last part, we compute this number in the case that the map germ is a projection and give some applications to catastrophe map germs.

Uses of QCD sumrules (QCDSR) from different points of view

We support the idea that the baryon, B with mass MB, couples to its current with a coupling λ2 B ∼ 0.71 M6 B from an analysis of magnetic moment sum rules. And we find a sum rule among the experimental magnetic moments which is independent of the parameters of QCDSR. © 1998 Elsevier Science B.V. All rights reserved.

Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

Comment on 'Relativistic extension of shape-invariant potentials'

This comment criticizes the recently published approach of Alhaidari for solving relativistic problems. It is shown that his gauge considerations are inaccurate and that the class of exactly solvable relativistic problems is not as large as the author claims.

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the regularization via relocalization scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples. © 2006 The American Physical Society.

In vitro antimicrobial activity of different gutta-percha points and calcium hydroxide pastes

The aim of this study was to evaluate the antimicrobial activity of different trademarks and compositions of gutta-percha points and calcium hydroxide pastes used in endodontic therapy. The evaluated material consisted of gutta-percha points containing calcium hydroxide (Roeko™), gutta-percha points containing chlorhexidine (Roeko™), two convencional gutta-percha points (Endo Points™ and Roeko™) and two calcium hydroxide pastes (Calen™ and Calen/PMCC™). Antimicrobial tests included five species of microorganisms: Escherichia coli (ATCC10538), Staphylococcus epidermidis (ATCC12228), Staphylococcus aureus (ATCC6538), Pseudomonas aeruginosa (ATCC27853), and Micrococcus luteus (ATCC9341). The Agar difusion method was employed. The plates were kept at room temperature for 2 h for prediffusion and then incubated at 37°C for 24 h. The triphenyltetrazolium chloride gel was added for optimization and the zones of inhibition were measured. Statistical evaluation was carried out using analysis of variance and Tukey Test. The obtained results showed that all microbial species used in the study were inhibited by the gutta-percha points containing chlorhexidine and by the calcium hydroxide pastes (Calen™ and Calen/ PMCC™), with similar results (p > 0.05). No antimicrobial activity was observed for the other groups. It was concluded that the gutta-percha points containing chlorhexidine presented antimicrobial activity, whereas the gutta-percha points containing calcium hydroxide did not.

Influence of brush type as a carrier of adhesive solutions and paper points as an adhesive-excess remover on the resin bond to root dentin

Purpose: To evaluate the influence of the brush type as a earner of priming adhesive solutions and the use of paper points as a remover of the excess of these solutions on the push-out bond strength of resin cement to bovine root dentin. The null hypotheses were that brush type and the use of paper points do not affect the bond strength. Materials and Methods: The canals of 80 single-root bovine roots (16 mm in length) were prepared at 12 mm using the preparation drill (FRC Postec Plus, Ivoclar). Half of each root was embedded in acrylic resin and the specimens were divided into 8 groups, considering the factors brush type (4 levels) and paper point (2 levels) (n = 10): Gr 1: small microbrush (Cavi-Tip, SDI); Gr 2: Microbrush (Dentsply); Gr 3: Endobrush (Bisco); Gr 4: conventional brush (Bisco); Gr 5: Cavi-Tip (SDI) + paper points; Gr 6: Microbrush (Dentsply) + paper points; Gr 7: Endobrush (Bisco) + paper points; Gr 8: conventional brush (Bisco) + paper points. The root dentin was treated with a multistep total-etch adhesive system (All Bond 2). The adhesive system was applied using each microbrush, with and without using paper points. One fiber post was molded with addition silicon and 80 posts were made of resin cement (Duolink), The resin posts were luted (Duolink resin cement), and the specimens were stored for 24 h in water at 37°C. Each specimen was cut into 4 disk-shaped samples (1.8 mm in thickness), which were submitted to the push-out test. Results: The brush type (p < 0.0001) (small microbrush > microbrush = endobrush = conventional brush) and the use of paper points (p = 0.0001) (with > without) influenced the bond strength significantly (two-way ANOVA). The null hypotheses were rejected. Conclusion: The smallest brush (Cavi-Tip) and the use of paper points significantly improved the resin bond to bovine root dentin.

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.