Caustics of plane curves, their birationality and matrix projections

After recalling the notion of caustics of plane curves and basic equations, we first show the birationality of the caustic map for a general source point S in the plane. Then we prove more generally a theorem for curves D in the projective space of 3x3 symmetric matrices B. For a general 3x1 vector S the projection to the plane given by B --- BS is birational on D, unless D is not a line and D is contained in a plane of the form Delta_v = {B | Bv = 0}.Comment: 10 pages, to appear in a Springer Verlag volume dedicated to Klaus Hulek on the occasion of his 60-th birthday. Final version, added some remarks by the refere

Research activities in the first two cycles of European Biosystems engineering university studies - Situation in the Netherlands

Wageningen University has implemented the bachelor – master model by 2003. The biosystems related programmes of Wageningen University are the BSc Agrotechnology and the MSc Agricultural and Bioresource Engineering. The bachelor programme has a size of 180 credits and the master programme a size of 120 credits. Both 1st and 2nd cycle programmes have a strong focus on research. A thesis is part of both programmes; the size is 12 credits for the bachelor thesis (to be increased to 24 by 2010) and 36 for the master thesis. An important difference between the bachelor and the master thesis is the level of independence. The bachelor thesis work is more structured than the master thesis work. Most of the thesis work is related to ongoing research projects. In the bachelor programme there are several courses that confront students with research and in which they learn research and academic skills. In this way the students gradually learn what research is and how to do it. In the master programme there are only a few courses related to the research skills; the students that start with the master are supposed to posses these skills. The BSc degree is not considered as an end point but is a pivot point for choosing a master. Therefore there are no research positions for persons having only BSc degree. Research positions in industry require at least a MSc degree but the trend is that more and more a PhD is required. Senior research positions within the research organizations require in most cased a PhD and within the university it is a basic requirement

Adaptive LQ control: Conflict between identification and control

We consider one of the fundamental limitations of indirect adaptive control based on the minimization of a quadratic cost criterion and the certainty equivalence principle. We show that the interaction between (closed-loop) identification and optimal control is conflictive in the sense that almost all possible limits of the sequence of parameter estimates induce suboptimal behavior of the adaptively controlled system

On the necessity of identifying the true parameter in adaptive LQ control

In adaptive control problems one may drop the requirement of identifying the true system in order to simplify the problem of control. It will be shown that in the adaptive LQ control problem this does not at all lead to an easier problem

A global-local optimization method for problems in structural dynamics

The optimization of complex structures involving many design variables and constraints can be performed using a multi-level approach: a structure consisting of several components is optimized as a whole (global) and on the component level (local). Earlier work [1], [2], [3], described a multilevel technique developed for the optimization the Airbus A380 vertical tail plane. In this application, a global model is used to calculate the loads on each of the components. These components are then optimized using the prescribed loads, followed by a new global calculation to update the loads. The component optimization strategy is based on Neural Networks (NN) and Genetic Algorithms (GA). This paper describes a strategy that makes this global-local optimization method possible for problems in structural dynamics. It is established that a parametrization of the component interactions (e.g. component loads) is problematic due to frequency dependence. Hence, a modified method is proposed in which the speed of Component Mode Synthesis (CMS) is used to avoid this parametrization. The effectiveness of this method is demonstrated in a test case concerning the placement of sensor and actuator locations in Active Structural Acoustic Control (ASAC). Special attention is paid to the behavior of the optimization strategy

Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence

The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction term. The characterization of tetrad fields as reference frames is addressed in the context of the Kerr space-time. It is also pointed out that Einstein's version of the principle of equivalence does not preclude the existence of a definition for the gravitational energy-momentum density.Comment: 17 pages, Latex file, no figure; minor correction in eq. (14), three references added, to appear in the GRG Journa

Geometry of isophote curves

In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface. Looking at those surface sections as isophote curves, of the pixel values of an image embedded in the real plane, this allows us to propose to combine object representation using a skeleton or symmetry set representation and the appearance modelling by representing image information as a collection of medial representations for the level-sets of an image.Comment: 15 pages, 7 figure

An analytic description of the vector constrained KP hierarchy

In this paper we give a geometric description in terms of the Grassmann manifold of Segal and Wilson, of the reduction of the KP hierarchy known as the vector $k$-constrained KP hierarchy. We also show in a geometric way that these hierarchies are equivalent to Krichever's general rational reductions of the KP hierarchy.Comment: 15 pages, Latex2