Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.

Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of chlorhexidine and sodium hypochlorite on the microhardness of root canal dentin

Objective. The purpose of this study was to evaluate the effects of endodontic irrigants on the microhardness of root canal dentin.Study design. Thirty extracted single-rooted human teeth were used. The crowns were sectioned at the cementoenamel junction. Each root was transversely sectioned into cervical, middle, and apical segments, resulting in 90 specimens. The 3 sections of each root were separately mounted in an individual silicon device with acrylic resin. The specimens were randomly divided into the following 3 groups (n = 30), according to the irrigant solution used: (1) group 1, control (saline solution); (2) group 2, 2% chlorhexidine gluconate solution; and (3) group 3, 1% sodium hypochlorite (NaOCl). After 15 minutes of irrigation, dentin microhardness was measured on each section at 500 mu m and 1000 mu m from the pulp-dentin interface with a Vickers diamond microhardness tester in Vickers hardness number (VHN).Results. Data obtained were analyzed using analysis of variance and the Tukey test (5%). Specimens irrigated with 2% chlorhexidine (group 2) or 1% NaOCl (group 3) presented lower values of dentin microhardness, with significant difference in relation to the control group (P < .05).Conclusion. It could be concluded that chlorhexidine and NaOCl solutions significantly reduced the microhardness of root canal dentin at 500 mu m and 1000 mu m from the pulp-dentin interface.

Measurement of the nonlinear optical response of low-density lipoprotein solutions from patients with periodontitis before and after periodontal treatment: evaluation of cardiovascular risk markers

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

Avaliação qualitativa do efeito de agentes de limpeza na camada de lama dentinária: estudo ultra-estrutural em microscopia eletrônica de varredura

Quando qualquer instrumento abrasiona ou corta a dentina, produz na superfície uma camada de lama dentinária ou smear layer. Dependendo do agente de união indicado em Odontologia adesiva, há a necessidade ou não da remoção da camada de lama da superfície dentinária. Com a finalidade de verificar a ação de diferentes substâncias para a limpeza dentinária, utilizamos 20 dentes pré-molares superiores íntegros, mantidos em soro fisiológico, nos quais as coroas foram seccionadas ao meio no sentido mésio-distal. Com instrumento diamantado, removeu-se o esmalte da porção vestibular e da porção lingual da coroa e, com uma broca carbide cilíndrica lisa nº 56, cortou-se aproximadamente 1 mm de dentina com alta rotação sob abundante refrigeração ar/água, para produzir a camada de lama dentinária. em seguida, essa superfície foi tratada com diferentes substâncias e lavada por 30 segundos com spray ar/água. No controle, foi simplesmente utilizado o spray ar/água. Os espécimes foram montados em suportes metálicos, preparados e visualizados no MEV-DSM 950 da Zeiss, em aumentos que variaram de 100 a 5.000 vezes. Os materiais que mais removeram a camada de lama foram, em ordem crescente: 1. spray ar/água; 2. fluoreto de sódio 2%; 3. associação alternada de Dakin/Tergensol; 4. água oxigenada 3%; 5. jateamento com óxido de alumínio 50 mm; 6. flúor acidulado 1,27%; 7. ácido poliacrílico 25%; 8. ácido fosfórico 10%.

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Potential symmetries and new solutions of a simplified model for reacting mixtures

In this paper, we investigate potential symmetries of a simplified model for reacting mixtures. We find new similarity reductions and wider class of solutions through this approach. Further, we explore an invertible mapping which linearizes the reacting mixture model.

Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions

In this paper a relation between the Camassa-Holm equation and the non-local deformations of the sinh-Gordon equation is used to study some properties of the former equation. We will show that cuspon and soliton solutions can be obtained from soliton solutions of the deformed sinh-Gordon equation.

The structures underlying soliton solutions in integrable hierarchies

We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ''vacuum solutions'' such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those ''vacuum solitons'' by the dressing transformation procedure.

Renormalized new solutions for the massless Thirring model

We present a nonperturbative study of the (1 + 1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities - coming from the computation of the fermionic determinant - allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger-Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations

We compare phenomenological values of the frozen QCD running coupling constant (alpha(s)) with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on alpha(s)(0) and F (pi)(Q(2)) is found only for one of the Schwinger-Dyson equation solutions.

Asymptotic soliton train solutions of Kaup-Boussinesq equations

Asymptotic soliton trains arising from a 'large and smooth' enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup-Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr-Sommerfeld quantization rule which generalizes the usual rule to the case of 'two potentials' h(0)(x) and u(0)(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u(0)(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup-Boussinesq equations with predictions of the asymptotic theory is found. (C) 2003 Elsevier B.V. All rights reserved.

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.