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 IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In vitro evaluation of the action of irrigating solutions associated with intracanal medications on Escherichia coli and its endotoxin in root canals

Objective: The purpose of this study was to evaluate the efficacy of auxiliary chemical substances and intracanal medications on Escherichia coli and its endotoxin in root canals. Material and Methods: Teeth were contaminated with a suspension of E. coli for 14 days and divided into 3 groups according to the auxiliary chemical substance used: G1) 2.5% sodium hypochlorite (NaOCl); G2) 2% chlorhexidine gel (CLX); G3) pyrogen-free solution. After, these groups were subdivided according to the intracanal medication (ICM): A) Calcium hydroxide paste (Calen (R)), B) polymyxin B, and C) Calcium hydroxide paste+2% CLX gel. For the control group (G4), pyrogen-free saline solution was used without application of intracanal medication. Samples of the root canal content were collected immediately after biomechanical preparation (BMP), at 7 days after BMP, after 14 days of intracanal medication activity, and 7 days after removal of intracanal medication. The following aspects were evaluated for all collections: a) antimicrobial activity; b) quantification of endotoxin by the limulus Amebocyte lysate test (LAL). Results were analyzed by the kruskal-wallis and Dunn's tests at 5% significance level. Results: The 2.5% NaOCl and CLX were able to eliminate E. coli from root canal lumen and reduced the amount of endotoxin compared to saline. Conclusions: It was concluded that 2.5% NaOCl and CLX were effective in eliminating E. coli. Only the studied intracanal medications were to reduce the amount of endotoxin present in the root canals, regardless of the irrigant used.

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)

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.

Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

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.