On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Another connection between orthogonal polynomials and L-orthogonal polynomials

We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Partial hyperbolicity for symplectic diffeomorphisms

We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic. (c) 2005 Elsevier SAS. All rights reserved.

Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Non-periodic bifurcations of one-dimensional maps

We prove that a 'positive probability' subset of the boundary of '{uniformly expanding circle transformations}' consists of Kupka-Smale maps. More precisely, we construct an open class of two-parameter families of circle maps (f(alpha,theta))(alpha,theta) such that, for a positive Lebesgue measure subset of values of alpha, the family (f(alpha,theta))(theta) crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.

Relationship Between Speed and Time in Running

The purpose of this study was to evaluate the effect of using different mathematical models to describe the relationship between treadmill running speed and time to exhaustion. All models generated a value for an aerobic parameter (critical speed; S(critical)). 35 university students performed 5-7 constant-speed 0%-slope treadmill tests at speeds that elicited exhaustion in similar to 3 min to similar to 10 min. Speed and time data were fitted using 3 models: (1) a 2-parameter hyperbolic model; (2) a 3-parameter hyperbolic model; and (3) a hybrid 3-parameter hyperbolic + exponential model. The 2-parameter model generated values for S(critical) (mean (+/- SD): 186 +/- 33 m.min(-1)) and anaerobic distance capacity (ADC; 251 +/- 122 m) with a high level of statistical certainty (i.e., with small SEEs). The 3-parameter models generated parameter estimates that were unrealistic in magnitude and/or associated with large SEEs and little statistical certainty. Therefore, it was concluded that, for the range of exercise durations used in the present study, the 2-parameter model is preferred because it provides a parsimonious description of the relationship between velocity and time to fatigue, and it produces parameters of known physiological significance, with excellent confidence.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Kinetic properties of de-repressible alkaline phosphatase (EC 3.1.3.1) from Neurospora crassa

De-repressible alkaline phosphatase from N. crassa shows inhibition by PNP-P and a hyperbolic mixed-type inhibition by Pi. Both increasing concentrations of Pi and decreases in assay pH abolished inhibition by the substrate. Also, Pi promoted polymerization of the enzyme molecule, whose effect may account for the inhibitory behaviour shown by the enzyme in the presence of low Pi concentrations. © 1991 Rapid Communications of Oxford Ltd.

Some integrals occurring in a topology change problem

In a paper presented a few years ago, de Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes. The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space). ©2000 The American Physical Society.

Thermal Behavior and Spectroscopic Study of Neutral and Cationic Mononuclear Cyclopalladated Compounds

The reactions of the precursor [Pd(N,C-dmba)(MeCN)2](NO 3) (1) (dmba = N,N-dimethylbenzylamine), with the proligands 3,5-dimethylpyrazole (Hdmpz), 2-quinolinethiol (qnSH) and 1,1′- bis(diphenylphosphine)ferrocene (dppf) afforded the compounds [Pd(N,C-dmba)(Hdmpz)(ONO2)]0.5CH2Cl2 (2), [Pd(N,C-dmba)(qnSH)(ONO2)] 0.5CH2Cl2 (3) and [Pd(N,C-dmba)(dppf)](NO3) (4), respectively. The mononuclear species 2,3 and 4 were characterized by elemental analysis, infrared spectroscopy, NMR and thermogravimetric analysis. The IR spectra show bands which are consistent with terminal monodentate nitrate group for 2-3 and ionic nitrate for 4. The 1H and 13C NMR data confirm that coordination of the organic ligands has occurred and the 31P{1H} NMR data for 4 clearly evidences the occurrence in solution of three cyclopalladated species with the dppf acting as a bridging ligand in two cases and as a chelate in one. The thermal behavior of compounds 1-4 suggests that complex 2 is the most stable. The X-ray diffractometry results show the formation of PdO from 1 and 2, Pd2OSO4 from 3, and of a mixture of PdO and Fe 2(PO4)3 from 4, as final decomposition products.

Synthesis, characterization, and biological activity of a new palladium(II) complex with deoxyalliin

Synthesis, characterization, and biological activity of a new water-soluble Pd(II)-deoxyalliin (S-allyl-L-cysteine) complex are described in this article. Elemental and thermal analysis for the complex are consistent with the formula [Pd(C6H10NO2S)2]. 13C NMR, 1H NMR, and IR spectroscopy show coordination of the ligand to Pd(II) through S and N atoms in a square planar geometry. Final residue of the thermal treatment was identified as a mixture of PdO and metallic Pd. Antiproliferative assays using aqueous solutions of the complex against HeLa and TM5 tumor cells showed a pronounced activity of the complex even at low concentrations. After incubation for 24 h, the complex induced cytotoxic effect over HeLa cells when used at concentrations higher than 0.40 mmol/L. At lower concentrations, the complex was nontoxic, indicating its action is probably due to cell cycle arrest, rather than cell death. In agreement with these results, the flow cytometric analysis indicated that after incubation for 24 h at low concentrations of the complex cells are arrested in G0/G1. © 2005 NRC Canada.

O limiar de esforço percebido (LEP) corresponde à potência crítica e a um indicador de máximo estado estável de consumo de oxigěnio

The perceived exertion has been a target of several investigations, many times with association with objective physiological indicators in exercise. Recently, the identification of the perceived exertion threshold (PET) was proposed in the water running, which presented no difference in relation to the critical velocity. Theoretically, both parameters would be indicators of the maximum steady state of variables such as V̇O2 and blood lactate. The objective of this work was to verify the coincidence between PET, critical power (PCrit) and an indicator of maximum V̇O2 steady state (PCrit') in cycle ergometer. Eight male participants were submitted to progressive effort test in order to determine V̇O2peak (46.7 ± 8.5 ml/kg/min) and to four rectangular tests until exhaustion for the estimation of the critical power model parameters, PET and PCrit'. The hyperbolic relation between mechanical power and time spent for the V̇O2peak to be reached in each test was used for the PCrit' estimation, considered as the asymptote in the power axis, and the portion of the anaerobic work capacity (CTAnaer) depleted up to the establishment of the V̇O2peak (CTAnaer'). In order to identify PET, the straight lines angular coefficients of the perceived exertion in time (ordinate) and the powers used (abscissa) were adjusted to a linear function that provided a point in the power axis in which the perceived exertion would be kept indefinitely stable. The parameters PCrit and CTAnaer were estimated by means of the power-time non-linear equation. In order to compare the estimations of PET, PCrit and PCrit', the analysis of variance ANOVA for repeated measurements was employed, and the associations were established through the Pearson correlation. CTAnaer and CTAnaer' were compared through the t test. PET (180 W ± 61 W), PCrit (174 W ± 43 W) and PCrit' (176 W ± 48 W) were not significantly different and the correlations were of 0.92-0.98. CTAnaer' (14,080 ± 5,219 J) was lower than CTAnaer (22,093 ± 9,042 J). One concludes that the PET predicts the intensity of PCrit and PCrit' with accuracy.

Effects of the eccentricity on the primames in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Basin problem for Hénon-like attractors in arbitrary dimensions

We prove that Hénon-like strange attractors of diffeomorphisms in any dimensions, such as considered in [2],[7], and [9] support a unique Sinai-Ruelle-Bowen (SRB) measure and have the no-hole property: Lebesgue almost every point in the basin of attraction is generic for the SRB measure. This extends two-dimensional results of Benedicks-Young [4] and Benedicks-Viana [3], respectively.