Skip to main content
European Commission logo print header
Contenu archivé le 2022-12-23

Studies on the perception and transduction of cytokinins in higher plants

Objectif

Completion to involution is a fundamental technology for dealing with general systems of partial differential equations. This can already be seen from their close relationship to Gröbner bases for polynomial ideals. Completion alone does not directly answer many questions about a given system; but without a suitable basis many questions cannot be answered at all. It is not difficult to forecast that very soon involution will play in the theory of differential equations a similar role as Gröbner bases already do now in commutative algebra and algebraic geometry.
The project is divided into three equally important tasks: fundamental theory, completion algorithms, applications. The main objective of the first task is to obtain a deeper understanding of the meaning of involution. Involution will be compared to classical concepts in differential algebra like Gröbner bases or characteristic sets; in addition the Spencer cohomology will be studied in detail. As a result the foundation of involution will become much clearer which is not only of considerable scientific interest but also very important for the design of algorithms.
The objective of the second task is to provide efficient implementations of completion algorithms for linear and non-linear differential systems (algebraic equations are considered as a special case of linear differential systems) on several platforms. This includes a geometric version of the algorithms which allows for the computation of intrinsic results independent of the used co-ordinate system.
As in the purely algebraic case, the complexity of the completion represents a major obstacle. For this reason so much emphasis is put on algorithmic aspects. Without fast computer algebra programs no progress can be achieved in this field. Consequently, the teams deliberately did not choose to select just one specific computer algebra system for implementing the algorithms. Instead, efficient implementations for a number of systems will result from the project which is crucial for spreading the use of involutive techniques in applied mathematics.
The objective of the third task is to demonstrate the power of involution in applications. Both group analysis of differential equations (with special emphasis on viscous heat conducting gas dynamics) and the symbolic and numerical analysis of constrained mechanical systems will be studied. In the first case, the results will not only be new exact solutions of an important physical model but also new techniques to handle extremely large differential systems. In the latter case, the main theoretical result will be the unification of some physical and numerical theories in a single framework. In addition, the prototype of a combined symbolic-numerical environment for treating constrained systems will be developed.
The project unites some of the leading teams in the field of involution. All participating teams have already made important contributions in this field. Their collaboration within the project will lead to further significant progress.

Appel à propositions

Data not available

Régime de financement

Data not available

Coordinateur

University of Wales, Aberystwyth
Contribution de l’UE
Aucune donnée
Adresse
Edward Lloyd Building
SY23 3DA Aberystwyth
Royaume-Uni

Voir sur la carte

Coût total
Aucune donnée

Participants (5)