Abstract. Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in [4]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in [22, Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies and an explicit solution class are derived. 1991 Mathematics Subject Classification. 35Q53; 46L55; 37K35.

he recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here considered. Specifically, evolution equations wherein the unknown is an operator acting on a Banach space are investigated. Here, the mirror non-Abelian Burgers equation is considered: it can be written as rt=rxx+2rxr. The structural properties of the admitted recursion operator are studied; thus, it is proved to be a strong symmetry for the mirror non-Abelian Burgers equation as well as to be the hereditary. These results are proved via direct computations as well as via computer assisted manipulations; ad hoc routines are needed to treat non-Abelian quantities and relations among them. The obtained recursion operator generates the mirror non-Abelian Burgers hierarchy. The latter, when the unknown operator r is replaced by a real valued function reduces to the usual (commutative) Burgers hierarchy. Accordingly, also the recursion operator reduces to the usual Burgers one

A mathematical model, based on a statistical system approach, has been implemented and tested on the basis of a four-year-long experimental data set, with the aim of analyzing the performance and clinical outcome of an existing medical ward, and predicting the effects that possible readjustments and/or interventions on the structure may produce on it. The dynamics of the system is assumed to be connected to a variable called "atmosphere" that refers to the perceived social and organizational climate, as well as the comfort and ease realized in the ward. In this context, the atmosphere is intuitively related to the "quality" that is (or is perceived as being) offered by the service, as it affects the ability to satisfy the patients' needs, to provide a livable environment for patients and medical staff, and to guarantee more efficient performances and a more complete professional development. Identifying variables, parameters and events that control the atmosphere is therefore of the deepest importance from a social and health-care point of view. The proposed interdisciplinary approach, referring to paradigms of physical and mathematical models integrated with theories and methods typical of social sciences, has chances of gaining the attention of the scientific community in both fields, and higher possibilities of obtaining appreciation and generalization. © 2011 Elsevier Ltd

An TV-map Iterated Fuzzy Set System (IFZS), introduced in [4] and to be denoted as (w, ), is a system of N contraction maps w,; : X -*• X over a compact metric space (X, d), with associated "grey level" maps , :Associated with an IFZS (w, <1>) is a fixed point u e &*(X), the class of normalized fuzzy sets on X, u : X -> [0, 1]. We are concerned with the continuity properties of u with respect to changes in the ID, and the