Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Validation of the portuguese simple measure of impact of lupus erythematosus in youngsters (SMILEY) in Brazil

Background and Objective: Simple Measure of the Impact of Lupus Erythematosus in Youngsters (SMILEY) is a health-related quality of life (HRQOL) assessment tool for pediatric systemic lupus erythematosus (SLE), which has been translated into Portuguese for Brazil. We are reporting preliminary data on cross-cultural validation and reliability of SMILEY in Portuguese (Brazil). Methods: In this multi-center cross-sectional study, Brazilian children and adolescents 5-18 years of age with SLE and parents participated. Children and parents completed child and parent reports of Portuguese SMILEY and Portuguese Pediatric Quality of Life Inventory (PedsQLTM) Generic and Rheumatology modules. Parents also completed the Childhood Health Assessment Questionnaire (CHAQ). Physicians completed the SLE disease activity index (SLEDAI), Physician's Global Assessment of disease activity (PGA) and Systemic Lupus Erythematosus International Collaborating Clinics ACR Damage Index (SDI). Results: 99 subjects (84 girls) were enrolled; 93 children and 97 parents filled out the SMILEY scale. Subjects found SMILEY relevant and easy to understand and completed SMILEY in 5-15 minutes. Brazilian SMILEY was found to have good psychometric properties (validity and reliability), and the child-parent agreement was moderate. Conclusion: SMILEY may eventually be used routinely as a research/clinical tool in Brazil. It may be also adapted for other Portuguese-speaking nations offering critical information regarding the effect of SLE on HRQOL for children with SLE. © The Author(s), 2012.

Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.