Reply on “How should we use the Visual Analogue Scale (VAS ) in Rehabilitation Outcomes?”

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The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

Supersymmetric Musings on the Predictivity of Family Symmetries

We discuss the predictivity of family symmetries for the soft supersymmetry breaking parameters in the framework of supergravity. We show that unknown details of the messenger sector and the supersymmetry breaking hidden sector enter into the soft parameters, making it difficult to obtain robust predictions. We find that there are specific choices of messenger fields which can improve the predictivity for the soft parameters.Comment: 20 pages, 5 figure

The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators

Gardner's deformations of the N=2 supersymmetric a=4-KdV equation

We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whenever it is assumed that they retract to Gardner's deformation of the scalar KdV equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the super-hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable towards the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.Comment: Extended version of the talks given by A.V.K. at 8th International conference `Symmetry in Nonlinear Mathematical Physics' (June 20-27, 2009, Kiev, Ukraine) and 9th International workshop `Supersymmetry and Quantum Symmetries' (July 29 - August 3, 2009, JINR, Dubna, Russia); 22 page

The consultation and relational empathy measure: an investigation of its scaling structure.

Purpose: The Consultation and Relational Empathy (CARE) measure is recommended to evaluate the quality of care. However, there is no evidence that it is valid in rehabilitation. Aims were to examine the internal construct (factorial) validity of the CARE in the assessment of the patient-therapist relationship. Method: CARE data were part of an experimental study of acupuncture and different currently used acupuncture placebo controls, including 213 patients (age 66.8, SD 8.3, 58% female) with chronic stable hip or knee pain of mechanical origin, waiting for a joint replacement. CARE was completed two weeks into the study and on completion, two weeks later. Data analysis: Cronbach alpha, factor analysis and Rasch analysis. Results: Internal construct validity was supported (82% of variance explained by the first factor; fit to the Rasch model χ( 2 ) = 18.2, P = 0.57). CARE was unidimensional, had local independence of items, good item fit, absence of Differential Item Functioning and invariance over time. Three percent of people did not complete items 9 & 10. Conclusions: CARE satisfied strict criteria for internal construct validity. An interval scale transformation is available that can be used in clinical practice and research. Further work is required to investigate item non-response and how this may be dealt with in clinical settings. [Box: see text]