Thomas decompositions of parametric nonlinear control systems

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic behaviour of the system (in terms of observability, flatness, etc.). The constructive symbolic method is based on the differential Thomas decomposition into disjoint simple systems, in particular its elimination properties

Algorithmic Thomas Decomposition of Algebraic and Differential Systems

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The given paper is a revised version of a previous paper and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1008.376

Conley: Computing connection matrices in Maple

In this work we announce the Maple package conley to compute connection and C-connection matrices. conley is based on our abstract homological algebra package homalg. We emphasize that the notion of braids is irrelevant for the definition and for the computation of such matrices. We introduce the notion of triangles that suffices to state the definition of (C)-connection matrices. The notion of octahedra, which is equivalent to that of braids is also introduced.Comment: conley is based on the package homalg: math.AC/0701146, corrected the false "counter example

The Effect of Commitment, Communication and Participation on Resistance to Change: The Role of Change Readiness

There is growing concern surrounding the effect of resistance to change on organisational change success. The main purpose of the present research was to clarify the relationships between important contextual variables highlighted in the literature, and resistance to change and readiness for change. Participants completed an online survey while their organisation was about to or already going through a change. As predicted, the results show the importance that participant perception of the adequacy of communication had on resistance to change and that this relationship was mediated by the readiness dimension of viewing the change as appropriate. The relationship between other contextual variables of perceived opportunities for participation and affective organisational commitment, and resistance to change were not found to be mediated by readiness for change dimensions. Affective commitment however, showed a direct negative relationship with resistance to change. These findings highlight the importance of a planned approached to change-related communications, and its potential to reduce resistance to change by effectively creating readiness for change in an organisation. Implications of these results and suggestions for future research are discussed

Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables

In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential elimination and analyze the behavior of the dimension in the resulting Thomas decomposition. For such systems of algebraic dimension one, we show that all formal Puiseux series solutions can be approximated up to an arbitrary order by convergent solutions. We show that the existence of Puiseux series and algebraic solutions can be decided algorithmically. Moreover, we present a symbolic algorithm to compute all algebraic solutions. The output can either be represented by triangular systems or by their minimal polynomials.Agencia Estatal de InvestigaciónAustrian Science Fun