Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin-polarization operators and spin-polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2 + 1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.

Quantitative estimates of time-averaging in terebratulid brachiopod shell accumulations from a modern tropical shelf

Quantitative estimates of time-averaging in marine shell accumulations available to date are limited primarily to aragonitic mollusk shells. We assessed time-averaging in Holocene assemblages of calcitic brachiopod shells by direct dating of individual specimens of the terebratulid brachiopod Bouchardia rosea. The data were collected from exceptional (brachiopod-rich) shell assemblages, occurring surficially on a tropical mixed carbonate-siliciclastic shelf (the Southeast Brazilian Bight, SW Atlantic), a setting that provides a good climatic and environmental analog for many Paleozoic brachiopod shell beds of North America and Europe. A total of 82 individual brachiopod shells, collected from four shallow (5-25 m) nearshore (<2.5 km from the shore) localities, were dated by using amino acid racemization (D-alloisoleucine/L-isoleucine value) calibrated with five AMS-radiocarbon dates (r(2) = 0.933). This is the first study to demonstrate that amino acid racemization methods can provide accurate and precise ages for individual shells of calcitic brachiopods.The dated shells vary in age from modern to 3000 years, with a standard deviation of 690 years. The age distribution is strongly right-skewed: the young shells dominate the dated specimens and older shells are increasingly less common. However, the four localities display significant differences in the range of time-averaging and the form of the age distribution. The dated shells vary notably in the quality of preservation, but there is no significant correlation between taphonomic condition and age, either for individual shells or at assemblage level.These results demonstrate that fossil brachiopods may show considerable time-averaging, but the scale and nature of that mixing may vary greatly among sites. Moreover, taphonomic condition is not a reliable indicator of pre-burial history of individual brachiopod shells or the scale of temporal mixing within the entire assemblage. The results obtained for brachiopods are strikingly similar to results previously documented for mollusks and suggest that differences in mineralogy and shell microstructure are unlikely to be the primary factors controlling the nature and scale of time-averaging. Environmental factors and local fluctuations in populations of shell-producing organisms are more likely to be the principal determinants of time-averaging in marine benthic shelly assemblages. The long-term survival of brachiopod shells is incongruent with the rapid shell destruction observed in taphonomic experiments. The results support the taphonomic model that shells remain protected below (but perhaps near) the surface through their early taphonomic history. They may be brought back up to the surface intermittently by bioturbation and physical reworking, but only for short periods of time. This model explains the striking similarities in time-averaging among different types of organisms and the lack of correlation between time-since-death and shell taphonomy.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

Upregulation of gp91(phox) Subunit of NAD(P)H Oxidase Contributes to Erectile Dysfunction Caused by Long-term Nitric Oxide Inhibition in Rats: Reversion by Regular Physical Training

OBJECTIVES To test the hypothesis that glyco protein 91phox (gp91(phox)) subunit of nicotinamide adenine dinucleotide phosphate [NAD(P) H] oxidase is a fundamental target for physical activity to ameliorate erectile dysfunction (ED). Vascular risk factors are reported to contribute to ED. Regular physical exercise prevents cardiovascular diseases by increasing nitric oxide (NO) production and/or decreasing NO inactivation.METHODS Male Wistar rats received the NO synthesis inhibitor N(omega)-nitro-L-arginine methyl ester (L-NAME) for 4 weeks, after which animals were submitted to a run training program for another 4 weeks. Erectile functions were evaluated by in vitro cavernosal relaxations and intracavernous pressure measurements. Expressions of gp91(phox) subunit and neuronal nitric oxidase synthase in erectile tissue, as well as superoxide dismutase activity and nitrite/nitrate (NO(x)) levels were determined.RESULTS The in vitro acetylcholine-and electrical field stimulation-induced cavernosal relaxations, as well as the increases in intracavernous pressure were markedly reduced in sedentary rats treated with L-NAME. Run training significantly restored the impaired cavernosal relaxations. No alterations in the neuronal nitric oxidase synthase protein expression (and its variant penile neuronal nitric oxidase synthase) were detected. A reduction of NO(x) levels and superoxide dismutase activity was observed in L-NAME-treated animals, which was significantly reversed by physical training. Gene expression of subunit gp91(phox) was enhanced by approximately 2-fold in erectile tissue of L-NAME-treated rats, and that was restored to basal levels by run training.CONCLUSIONS Our study shows that ED seen after long-term L-NAME treatment is associated with gp91(phox) subunit upregulation and decreased NO bioavailability. Exercise training reverses the increased oxidative stress in NO-deficient rats, ameliorating the ED. UROLOGY 75: 961-967, 2010. (C) 2009 Elsevier B.V.

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the N-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the N-body problem is reduced to N one-body problems.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Ex vivo biocompatibility tests of regular and white forms of mineral trioxide aggregate

Aim: To examine the genotoxicity and cytotoxicity of regular and white mineral trioxide aggregate (MTA) ex vivo by the single-cell gel (comet) assay and trypan blue exclusion test, respectively. Methodology: Aliquots of 1 × 10 4 Chinese hamster ovary cells were incubated at 37°C for 3 h with grey and white forms of MTA at final concentrations ranging from 1 to 1000 μg mL -1. The negative control group was treated with vehicle control phosphate buffer solution for 3 h at 37°C and the positive control group was treated with methyl metasulfonate (at 1 μg mL -1) for 1 h at 37°C. After incubation, the cells were centrifuged at 180 g for 5 min and washed twice with fresh medium and resuspended with fresh medium. Each individual treatment was repeated three times consecutively to ensure reproducibility. Parameters from single-cell gel (comet) and cytotoxicity assays were assessed by the Kruskal-Wallis nonparametric test. Results: Neither compounds produced genotoxic effects with respect to the single-cell gel (comet) assay in all concentrations evaluated. In the same way, the dose-response relationships of all compounds tested at concentrations ranging from 1 to 1000 μg mL -1 on cell viability assessed by the trypan blue assay displayed no statistically significant differences (P > 0.05) for either endodontic material. Conclusions: Regular (grey) and white MTA are not genotoxins and do not induce cellular death. © 2006 International Endodontic Journal.

Genotoxicity in primary human peripheral lymphocytes after exposure to regular and white mineral trioxide aggregate

Objective: Taking into consideration that DNA damage plays an important role in carcinogenesis, the purpose of this study was to evaluate whether regular and white mineral trioxide aggregate (MTA) are able to induce genetic damage in primary human cells. Study design: Human peripheral lymphocytes obtained from 10 healthy volunteers were exposed to 2 presentation forms of MTA at final concentrations ranging from 1 to 1000 μg/mL for 1 hour at 37°C. The negative control group was treated with vehicle control (phosphate buffer solution, PBS) for 1 hour at 37°C and the positive control group was treated with hydrogen peroxide (at 100 μM) for 5 minutes on ice. Results were analyzed by the Friedman nonparametric test. Results: The results pointed out that either regular or white MTA in all concentrations tested did not induce DNA breakage in human peripheral lymphocytes as depicted by the mean tail moment. Conclusion: In summary, our results indicate that exposure to MTA may not be a factor that increases the level of DNA lesions in human peripheral lymphocytes as detected by single cell gel (comet) assay. © 2006 Mosby, Inc. All rights reserved.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.