The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.

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)

Some Initial Conditions for Disposed Satellites of the Systems GPS and Galileo Constellations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the first nu(6) anti-aligned librating asteroid family of Tina

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

Fine structure of lamellated nerve endings in the gingiva of man and the Cebus apella monkey

Gingival mucosae of man and the adult Cebus apella monkey were fixed for 3 hr in modified Karnovsky fixative containing 2.5% glutaraldehyde, 2% formaldehyde in 0.1 M sodium phosphate buffer (pH=7.4). The specimens were postfixed in 1% osmium tetroxide in 0.1 M sodium phosphate buffer at 4°C for 2 hr, dehydrated in a graded alcohol series and embedded in Epon 812. Thick sections of 1-3 μm and ultrathin sections of 40-80 nm in thickness were cut with glass knives on an LKB ultramicrotome. The thick sections were stained with toluidine blue solution, and the grids were stained with uranyl acetate and lead citrate and examined under a Philips EM-301 electron microscope. Our observations permitted us to conclude that: both gingival mucosae, of man and the Cebus apella monkey, have lamellar nerve endings; these corpuscles are localized in the papillar space of the epithelium and do not contact closely with the basement membrane; the nerve endings are composed of an afferent fiber which subdivides several times and forms irregular flattened or discoidal expansions; the laminae of the lamellar cells are very thin near the terminal axon and are larger and irregular in shape at the peripheral portion of the corpuscle; the terminal axon shows abundant mitochondria, myelin figures, clear vesicles, and multivesicular bodies; between the axoplasm membrane and adjacent cytoplasmic lamina and between the lamellae, small desmosome type junctions are noted; and the cytoplasmic material of the lamellae cells is characterized by the presence of numerous microfilaments, microtubules, mitochondria, rough endoplasmic reticulum, and caveolae.

New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

On the picture dependence of Ramond-Ramond cohomology

Closed string physical states are BRST cohomology classes computed on the space of states annihilated by b- 0. Since b- 0 does not commute with the operations of picture changing, BRST cohomologies at different pictures need not agree. We show explicitly that Ramond-Ramond (RR) zero-momentum physical states are inequivalent at different pictures, and prove that non-zero-momentum physical states are equivalent in all pictures. We find that D-brane states represent BRST classes that are non-polynomial on the superghost zero-modes, while RR gauge fields appear as polynomial BRST classes. We also prove that in x-cohomology, the cohomology where the zero-mode of the spatial coordinates is included, there is a unique ghost-number one BRST class responsible for the Green-Schwarz anomaly, and a unique ghost number minus one BRST class associated with RR charge. © 1998 Elsevier Science B.V.

Time analysis for temporary gravitational capture: Satellites of Uranus

We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of different capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elements - inclination (i), longitude of the node (Ω), argument of pericenter (ω), and time of pericenter passage (τ) - are first taken to be zero. Then we investigate the cases with ω = 90°, 180°, and 270°. We also present a sample of results for Ω = 90°, considering the cases i = 60°, 120°, 150°, and 180°. Special attention is given to the influence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0° to 180° in steps of 10°. The success of the final stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60°-70° and 160°. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Identification of structural parameters for active vibration control

The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.

Effect of plastic film mulch on the production of butterhead lettuce cultivars under protected cultivation

The study was performed in a greenhouse with the aim of evaluating the production of butterhead lettuce cultivars with and without plastic film mulch in the summer. The cultivars studied were 'Elisa', 'Lídia', 'Herman' and 'Luísa'. The experimental design was a split plot, in which the main plot was plastic film mulch (with or without black polyethylene film) and the subplots were the cultivars, with three repetitions. The seedlings were grown in Styrofoam trays of 288 cells and transplanted 25 days after seeding in a space of 25 × 25 cm. Harvests were carried out 45 days after transplanting and the following variables were determined: fresh and dry weights of the aerial part, number of leaves per plant, plant height and the longitudinal and transverse diameters of the plant. Significant differences were found only among the cultivars for the characteristics studied, with no cover × cultivar interaction. Fresh weight of the aerial part of 'Lídia' (270.9 g) was greater than that of 'Herman' (142.5 g), but did not differ from those of 'Luísa' (229.8 g) or 'Elisa' (204.8). The dry weight of the aerial part of 'Lídia' (12.4 g) differed statistically only with respect to that of 'Herman' (7.9 g). The cultivars 'Luísa' and 'Elisa' had an aerial part dry weight of 11.4 and 11.2 g, respectively. The number of leaves per plant of the cultivars 'Luísa' (45.1) and 'Elisa' (43.0) was higher than for 'Herman' (24.05), but did not differ from that of the cultivar 'Lídia' (39.5). The mean transverse and longitudinal diameters, as well as the mean height of the plants, showed that 'Lídia', 'Elisa' and 'Luísa' had the greatest values. The cultivars 'Lídia', 'Elisa' and 'Luísa' were the most productive and plastic film mulch had no effect on lettuce production under protected cultivation.

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.

Visualizing the ac magnetic susceptibility of superconducting films via magneto-optical imaging

We have established a link between the global ac response and the local flux distribution of superconducting films by combining magnetic ac susceptibility, dc magnetization, and magneto-optical measurements. The investigated samples are three Nb films: a plain specimen, used as a reference sample, and other two films patterned with square arrays of antidots. At low temperatures and small ac amplitudes of the excitation field, the Meissner screening prevents penetration of flux into the sample. Above a certain ac drive threshold, flux avalanches are triggered during the first cycle of the ac excitation. The subsequent periodic removal, inversion, and rise of flux occurs essentially through the already-created dendrites, giving rise to an ac susceptibility signal weakly dependent on the applied field. The intradendrite flux oscillation is followed, at higher values of the excitation field, by a more drastic process consisting of creation of new dendrites and antidendrites. In this more invasive regime, the ac susceptibility shows a clear field dependence. At higher temperatures a smooth penetration occurs, and the flux profile is characteristic of a critical state. We have also shown that the regime dominated by vortex avalanches can be reliably identified by ac susceptibility measurements. © 2011 American Physical Society.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Dynamics of rotation of super-Earths

We numerically investigate the dynamics of rotation of several close-in terrestrial exoplanet candidates. In our model, the rotation of the planet is disturbed by the torque of the central star due to the asymmetric equilibrium figure of the planet. We model the shape of the planet by a Jeans spheroid. We use surfaces of section and spectral analysis to explore numerically the rotation phase space of the systems adopting different sets of parameters and initial conditions close to the main spin-orbit resonant states. One of the parameters, the orbital eccentricity, is critically discussed here within the domain of validity of orbital circularization timescales given by tidal models. We show that, depending on some parameters of the system like the radius and mass of the planet, eccentricity etc., the rotation can be strongly perturbed and a chaotic layer around the synchronous state may occupy a significant region of the phase space. 55 Cnc e is an example. © 2013 Springer Science+Business Media Dordrecht.