LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

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

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

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

Using the current Brazilian value for the biological exposure limit applied to blood lead level as a lead poisoning diagnostic criterion

Tradicionalmente, os limites de tolerância biológica são utilizados exclusivamente para a promoção e a preservação da saúde dos trabalhadores, não sendo aplicados com fins diagnósticos. Entretanto, com relação a algumas intoxicações profissionais, o assunto é polêmico. Neste artigo, defende-se a utilização do limite de tolerância aplicado atualmente no Brasil à plumbemia como um critério importante para a realização do diagnóstico da intoxicação profissional pelo chumbo. Argumenta-se que, em oposição ao tradicional critério clínico, deve-se abordar o problema do diagnóstico da intoxicação pelo chumbo sob um ponto de vista epidemiológico, utilizando-se o atual valor do limite de tolerância para a plumbemia como um marcador de risco relativo significativamente aumentado.

Influence of the type of vehicle and limit of obturation on apical and periapical tissue response in dogs' teeth after root canal filling with mineral trioxide aggregate

The purpose of this study was to investigate the influence of the type of vehicle (distilled water or propyleneglycol) on the response of apical tissues of dogs' teeth after root canal filling with mineral trioxide aggregate (MTA) at two different limits. Forty roots of incisors and premolars of two adult dogs were used. After pulpectomy, the root canals were prepared biomechanically, and the roots had the apical cemental barrier penetrated with a #15 K-file and widened to a #25 K-file. The root canals were assigned to four groups according to the vehicle used for MTA (ProRoot-MTA; Tulsa Dental, Tulsa, OK) preparation and the limit of root canal filling: group 1, filling with MTA/distilled water to the limit of the cemental canal; group 2, overfilling with MTA/distilled water, group 3, filling with MTA/propyleneglycol to the limit of the cemental canal; and group 4, overfilling with MTAlpropyleneglycol. The animals were killed by anesthetic overdose 90 days after endodontic treatment and the anatomic pieces were prepared for histomorphological analysis. The sections were stained with hematoxylin and eosin and Brown and Brenn techniques. The results showed that MTA pastes prepared with either distilled water or propyleneglycol as vehicles had similar biological behavior (p > 0.05); root fillings placed at the cemental canal limit showed better results than the overfillings (p = 0.01), and MTA/propyleneglycol paste was more easily placed into the root canals than MTA/distilled water paste.

Effect of water storage on the shear strength and fatigue limit of the reline resin bond to denture base resins

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

Discussion on the limit cycles of the Lev Ginzburg equation by M. Bellamy and R.E. Mickens, Journal of Sound and Vibration 308 (2007) 337-342

The authors M. Bellamy and R.E. Mickens in the article "Hopf bifurcation analysis of the Lev Ginzburg equation" published in Journal of Sound and Vibration 308 (2007) 337-342, claimed that this differential equation in the plane can exhibit a limit cycle. Here we prove that the Lev Ginzburg differential equation has no limit cycles. (C) 2012 Elsevier Ltd. All rights reserved.

Scaling limit of weakly bound triatomic states

The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of the Rb-87 dimer to estimate the critical value of the ground-state energy of the corresponding trimer (greater than or equal to 1.5 mK), in order to allow for one Efimov state above the ground state.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Limit on the fermion masses in technicolor models

Recently it has been pointed out that no limits can be put on the scale of fermion mass generation (M) in technicolor models, because the relation between the fermion masses (m(f)) and M depends on the dimensionality of the interaction responsible for generating the fermion mass. Depending on this dimensionality it may happen that m(f) does not depend on M at all. We show that exactly in this case m(f) may reach its largest value, which is almost saturated by the top quark mass. We make a few comments on the question of how large a dynamically generated fermion mass can be.

Three helium atoms and the scaling limit

We show that a scaling limit approach, previously applied in three-body low-energy nuclear physics, is realized for the first excited state of He-4 trimer. The present result suggests that such approach has a wider application.

Confusing the extragalactic neutrino flux limit with a neutrino propagation limit

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cold-atom systems and the scaling limit

With perspective to applications of cold-atom systems, some aspects of few-body physics at very low energies will be reviewed. By exploring the possibilities of varying the two-body interaction via the Feshbach resonance mechanism, some recent results are reported for condensed systems in optical lattices.

Universality and Scaling Limit of Weakly-Bound Tetramers

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B-3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited N-th tetramer energy B-4((N)) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B-4((N))/B-3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

Combined Tevatron upper limit on gg -> H -> W+W- and constraints on the Higgs boson mass in fourth-generation fermion models

We combine results from searches by the CDF and D0 collaborations for a standard model Higgs boson (H) in the process gg -> H -> W+W- in p (p) over bar collisions at the Fermilab Tevatron Collider at root s = 1.96 TeV. With 4.8 fb(-1) of integrated luminosity analyzed at CDF and 5.4 fb(-1) at D0, the 95% confidence level upper limit on sigma(gg -> H) x B(H -> W+W-) is 1.75 pb at m(H) = 120 GeV, 0.38 pb at m(H) = 165 GeV, and 0.83 pb at m(H) = 200 GeV. Assuming the presence of a fourth sequential generation of fermions with large masses, we exclude at the 95% confidence level a standard-model-like Higgs boson with a mass between 131 and 204 GeV.