Re-exports: international comparison and implications for performance indicators

Since the mid eighties, re-exports in the Netherlands has been booming, with the exception of a short interruption in 2001 and 2002. This research shows that a relatively strong growth of re-exports is not just a Dutch phenomenon, but that there is an international trend going on. Re-exported products are at least doubly counted in world trade figures. This international re-exports trend contributes to the fact that world trade volume is growing faster than the volume of world export production. Besides, there are some serious implications for the indicators of countries' exports performances. If one doesn't take account of the implications of the international re-exports trend, the relevant export market growth for Dutch manufactures as well as the loss of market share of Dutch industrialists are overestimated.

The level of pairs of polynomials

Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this differential operator and the notion of `stratification' in the case of hyperelliptic curves. Next we extend the notion of level to that of a pair of polynomials. We prove some basic properties and we compute this level in certain special cases. In particular we present examples of polynomials $g$ and $f$ such that there is no differential operator raising $g/f$ to its $p$th power.Comment: 14 pages, comments are welcom

Topics in algebra, geometry and differential equations

The study of differential equations and the study of algebraic geometry are two disciplines within mathematics that seem to be mostly disjoint from each other. Looking deeper, however, one finds that connections do exist. This thesis gives in four chapters four examples of interesting mathematical insights that can be gained from combining the concepts and techniques from both of these fields. The first project shows how the behaviour of solutions of certain differential equations can be better understood by considering algebraic curves with a differential form. The second project proves the existence of certain higher differential operators in algebraic settings where these were not known to occur before. The third project shows that the existence or non-existence of power series solutions of partial differential equations can be interpreted from the perspective of tropical geometry. And the last project relates the old theorem of Siegel about integral points on elliptic curves to the monodromy of linear differential equations on this elliptic curve

Electromagnetic and mechanical AC loss of an ITER TF model coil conductor (DP4) under transverse cyclic loading

Energising a coil results in a transverse force on the strands pushing the cable towards one side of the jacket. This load causes a transverse compressive strain in strands and in particular in strand crossover points. Besides this, contact surfaces interfere by micro-sliding resulting in friction and anomalous contact resistance behaviour versus force. Two Central Solenoid Model Coil conductors have been tested previously in a cryogenic press and now the experimental results are presented for the Toroidal Field Model Coil (TFMC) conductor (DP4). The press can transmit a variable (cyclic) force of at least 650 kN/m directly to a cable section of 400 mm at 4.2 K. The magnetisation of the conductor and the interstrand resistance (Rc) between various strands inside the cable can be measured by varying pressure. The force on the cable and the displacement are monitored simultaneously in order to determine the effective cable Young's modulus and the mechanical heat generation due to friction and deformation. The mechanical heat generation, the coupling loss time constant n¿ and the Rc of the full-size ITER TFMC conductor have been studied under load up to 40 full loading cycles. The evolution of Rc is comparable to the behaviour found for the CS Model Coil type of conductors. A significant decrease of the cable coupling current time constant, n¿ and mechanical heat generation after cyclic loading is foun