The specialization index of a variety over a discretely valued field

Let $X$ be a proper variety over a henselian discretely valued field. An important obstruction to the existence of a rational point on $X$ is the index, the minimal positive degree of a zero cycle on $X$. This paper introduces a new invariant, the specialization index, which is a closer approximation of the existence of a rational point. We provide an explicit formula for the specialization index in terms of an $snc$-model, and we give examples of curves where the index equals one but the specialization index is different from one, and thus explains the absence of a rational point. Our main result states that the specialization index of a smooth, proper, geometrically connected $\mathbb{C}((t))$-variety with trivial coherent cohomology is equal to one

Stable R&D cooperation between asymmetric partners.

The Impact of asymmetries between partners on the stability of R&D cooperation is assessed analytically in a supergame setting. Two asymmetric firms are repeatedly taking sequential R&D and production decisions, whereby they coordinate their R&D decisions, in order to maximise joint profits. The asymmetries are specified in terms of absorptive capacity (i.e. size of the spillovers), R&D efficiency (i.e. ability to implement know how) and productive efficiency or market size (i.e. net demand intercept).First of all, it is shown that these asymmetries may not be too large, in order to guarantee that the disadvantaged firm remains interested in joining an R&D cooperative agreement. Furthermore, each asymmetry is shown to make the advantaged firm more inclined to stick to the cooperative outcome (than in the symmetric case), while the reverse holds for the disadvantaged firm. Finally, these asymmetries, when occurring, simultaneously, mutually reinforce each other. All in all, R&D cooperation between asymmetric partners will typically be beneficial for the advantaged firm and will only be attractive for the disadvantaged firm if the asymmetries are not too large.Cooperation; R&D; R&D cooperation;

Social inequalities

Observations Economic and cultural globalisation The Brussels Capital Region has experienced a significant period of economic growth over the past few decades. The service sector has been particularly responsible for this economic performance, largely comprising the European, federal and regional administrations. However, overseas investments in the service sector have also been an important factor. In broad terms, Brussels has 2 000 foreign companies, which account for 234 000 jobs and 40% o..