On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Hybrid reflections in InGaP/GaAs(001) by synchrotron radiation multiple diffraction

Hybrid reflections (HRs) involving substrate and layer planes (SL type) [Morelhao et al., Appl. Phys. Len. 73 (15), 2194 (1998)] observed in Chemical Beam Epitaxy (CBE) grown InGaP/GaAs(001) structures were used as a three-dimensional probe to analyze structural properties of epitaxial layers. A set of (002) rocking curves (omega-scan) measured for each 15 degrees in the azimuthal plane was arranged in a pole diagram in phi for two samples with different layer thicknesses (#A -58 nm and #B - 370 nm) and this allowed us to infer the azimuthal epilayer homogeneity in both samples. Also, it was shown the occurrence of (1 (1) over bar3) HR detected even in the thinner layer sample. Mappings of the HR diffraction condition (omega:phi) allowed to observe the crystal truncation rod through the elongation of HR shape along the substrate secondary reflection streak which can indicate in-plane match of layer/substrate lattice parameters. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated. © 1995.

Activation function study for wavelet network

The main purpose of this paper is to investigate theoretically and experimentally the use of family of Polynomial Powers of the Sigmoid (PPS) Function Networks applied in speech signal representation and function approximation. This paper carries out practical investigations in terms of approximation fitness (LSE), time consuming (CPU Time), computational complexity (FLOP) and representation power (Number of Activation Function) for different PPS activation functions. We expected that different activation functions can provide performance variations and further investigations will guide us towards a class of mappings associating the best activation function to solve a class of problems under certain criteria.

Correcting coils in end magnets of accelerators

We present an empirical investigation of the correcting coils behavior used to homogenize the field distribution of the race-track microtron accelerator end magnets. These end magnets belong to the second stage of the 30.0 MeV cw electron accelerator under construction at IFUSP, the race-track microtron booster, in which the beam energy is raised from 1.97 to 5.1 MeV. The correcting coils are attached to the pole faces and are based on the inhomogeneities of the magnetic field measured. The performance of these coils, when operating the end magnets with currents that differ by ±10% from the one used in the mappings that originated the coils copper leads, is presented. For one of the magnets, adjusting conveniently the current of the correcting coils makes it possible to homogenize field distributions of different intensities, once their shapes are practically identical to those that originated the coils. For the other one, the shapes are changed and the coils are less efficient. This is related to intrinsic factors that determine the inhomogeneities. However, we obtained uniformity of 0.001% in both cases. © 1998 The American Physical Society.

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.

Studying the satisfaction of patients on the outcome of an aesthetic dermatological filler treatment

Background: Many factors contribute to extend productive life in the modern world. Competition makes people worry about physical appearance, mosftly in respect to facial and skin aging. This has motivated new developments in cosmetic dermatology and the need of evaluating patient satisfaction with the new proposed treatments. Poll questionnaire has been used for such evaluation, and the analysis of the electroencephalogram (EEG) mapping obtained while the patient answers the satisfaction questionnaire may render the results less subjective. Objectives: The purpose of this paper is to study the satisfaction of a group of 33 women (mean age, 44.years) treated with hyaluronic acid filling of nasolabial folding or lips, combining the EEG brain mapping and questionnaire techniques. Methods: At the third month of evaluation, two networked personal computers were used for the EEG recording and for presenting the patient with a questionnaire about her well-being feeling; self-evaluation of her face; her satisfaction with the results of the aesthetic treatment; how the family, friends, and people at work evaluated the result of the treatment; and her decision to repeat the treatment and to recommend it to friends and family. Results: Poll results showed that patients were feeling well and were satisfied with the results of the aesthetic treatment. Furthermore, the regression EEG mappings showed patients to be satisfied with their appearance and with the treatment involving similar brain areas. Conclusion: Patients decided to undergo the treatment because they were already considering it (54%) or because they were dissatisfied with their lips or nasolabial folding (52%). The fact that the treatment was free of charge solidified the decision. Patients consider themselves as good-looking and they wanted to preserve such a condition. © 2008 Wiley Periodicals, Inc.

Environment mapping for mobile robots navigation using hierarchical neural network and omnivision

Autonomous robots must be able to learn and maintain models of their environments. In this context, the present work considers techniques for the classification and extraction of features from images in joined with artificial neural networks in order to use them in the system of mapping and localization of the mobile robot of Laboratory of Automation and Evolutive Computer (LACE). To do this, the robot uses a sensorial system composed for ultrasound sensors and a catadioptric vision system formed by a camera and a conical mirror. The mapping system is composed by three modules. Two of them will be presented in this paper: the classifier and the characterizer module. The first module uses a hierarchical neural network to do the classification; the second uses techiniques of extraction of attributes of images and recognition of invariant patterns extracted from the places images set. The neural network of the classifier module is structured in two layers, reason and intuition, and is trained to classify each place explored for the robot amongst four predefine classes. The final result of the exploration is the construction of a topological map of the explored environment. Results gotten through the simulation of the both modules of the mapping system will be presented in this paper. © 2008 IEEE.

Profilometry of semiconductor components by two-colour holography with Bi12TiO20 crystals

We studied the shape measurement of semiconductor components by holography with photorefractive Bi12TiO20 crystal as holographic medium and two diode lasers emitting in the red region as light sources. By properly tuning and aligning the lasers a synthetic wavelength was generated and the resulting holographic image of the studied object appears modulated by cos2-contour fringes which correspond to the intersection of the object surface with planes of constant elevation. The position of such planes as a function of the illuminating beam angle and the tuning of the lasers was studied, as well as the fringe visibility. The fringe evaluation was performed by the four stepping technique for phase mapping and through the branch-cut method for phase unwrapping. A damage in an integrated circuit was analysed as well as the relief of a coin was measured, and a precision up to 10 μm was estimated. © 2009 SPIE.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. © 2010 Elsevier B.V. All rights reserved.

Zoneamento do parque ecológico de ourinhos SP

The aim of this study was to carry out a zoning in the municipal ecological park of Ourinhos, SP, located southwest of São Paulo State, aiming to subsidize the planning and management of this area. With this purpose it was made an inventory of the landscape resources of this park with hypsometry, declivity, use of soil and zoning mappings. From this zoning, we analyzed the possibilities of implementing purposes of use, with the objective of preserving this area, minimizing the negative environmental impacts. Thus, this research was of extreme importance, since it allowed to identify and rank, in the territory, areas or sectors that are priority to the development of activities, as well as contribute to the conservation of natural and socio-cultural heritage.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.