Classical Lie symmetries and reductions of a nonisospectral Lax pair

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries provides a set of reductions that give rise to different nontrivial spectral problems in 1+1 dimensions. The form in which the spectral parameter of the 1+1 Lax pair is introduced is carefully described.Comment: 11 pages (v2: A typo corrected in the authors' names

About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane

The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in $JHEP {\bf 10} (2005) 071$, where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can be also constructed by means of the noncommutative extension of the uniton method proposed in $JHEP {\bf 0408} (2004) 054$ by Ki-Myeong Lee. Particularly some specific solutions of the nc Liouville model are explicit constructed.Comment: 24 page

Darboux Transformations for a Lax Integrable System in 2n2n-Dimensions

A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.Comment: Latex, 14 pages, to be published in Lett. Math. Phy

Patients' and Observers' Perceptions of Involvement Differ. Validation Study on Inter-Relating Measures for Shared Decision Making

OBJECTIVE: Patient involvement into medical decisions as conceived in the shared decision making method (SDM) is essential in evidence based medicine. However, it is not conclusively evident how best to define, realize and evaluate involvement to enable patients making informed choices. We aimed at investigating the ability of four measures to indicate patient involvement. While use and reporting of these instruments might imply wide overlap regarding the addressed constructs this assumption seems questionable with respect to the diversity of the perspectives from which the assessments are administered. METHODS: The study investigated a nested cohort (N = 79) of a randomized trial evaluating a patient decision aid on immunotherapy for multiple sclerosis. Convergent validities were calculated between observer ratings of videotaped physician-patient consultations (OPTION) and patients' perceptions of the communication (Shared Decision Making Questionnaire, Control Preference Scale & Decisional Conflict Scale). RESULTS: OPTION reliability was high to excellent. Communication performance was low according to OPTION and high according to the three patient administered measures. No correlations were found between observer and patient judges, neither for means nor for single items. Patient report measures showed some moderate correlations. CONCLUSION: Existing SDM measures do not refer to a single construct. A gold standard is missing to decide whether any of these measures has the potential to indicate patient involvement. PRACTICE IMPLICATIONS: Pronounced heterogeneity of the underpinning constructs implies difficulties regarding the interpretation of existing evidence on the efficacy of SDM. Consideration of communication theory and basic definitions of SDM would recommend an inter-subjective focus of measurement. TRIAL REGISTRATION: Controlled-Trials.com ISRCTN25267500

L’extrusion réactive, Une voie privilégiée pour la synthèse de nouveaux matériaux polymères et composites

International audienc

L’extrusion réactive, Une voie privilégiée pour la synthèse de nouveaux matériaux polymères et composites

International audienc