Optical birefringence in cubic ZnSe crystals

Optical birefringence of the spatial dispersion type has been observed in cubic ZnSe crystals.     

Stable rank-2 vector bundles on ℙ3 withc 1=0 andc 2=3

Mathematische Annalen -     

Velocity distribution in horizontal slug flow

An experimental device for measurement of the velocity distribution in a two-phase slug is developed. Velocity profiles both in the film and the liquid slug besides velocity variation along the pipe bottom (at a distance of 1 mm) through the slug front are presented.     

An intersection number for the punctual Hilbert scheme of a surface

We compute the intersection number between two cycles and of complementary dimensions in the Hilbert scheme parameterizing subschemes of given finite length of a smooth projective surface . The -cycle corresponds to the set of finite closed subschemes the support of which has cardinality 1. The -cycle consists of the closed subschemes the support of which is one given point of the surface. Since is contained in , indirect methods are needed. The intersection number is , answering a question by H. Nakajima.

     

A new method for determining droplet size distribution of an unstable dispersion

The droplet size distribution (DSD) of unstable water/oil dispersions has been studied with a new technique. The technique is based on a fast dilution of the dispersion injected into an analysis vessel where the DSD is analyzed with a video camera and a image analyzing tool. Dispersions generated with no pressure drop in the flow rig were compared to those generated with a pressure drop over a needle valve. The latter dispersion showed a much narrower DSD and a lower average droplet diameter. The results are from preliminary experiments in order to evaluate the method.     

Bott's formula and enumerative geometry

We outline a strategy for computing intersection numbers on
smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed. The results are consistent with predictions made from mirror symmetry computations. We also compute degrees of some loci in the linear system of plane curves of degrees less than 10, like those corresponding to sums of powers of linear forms, and curves carrying inscribed polygons.

     

Creating lasso-solutions for the traveling salesman problem with pickup and delivery by Tabu search

We consider the Traveling Salesman Problem with Pickup and Delivery (TSPPD) where the same costumers might require both deloverie of goods and pickup of other goods. All the goods should be transported from/to the same depot. A vehicle on a TSPPD-tour could often get some practical problems when arranging the load. Even if the vehicle has enough space for all the pickups, one has to consider that they are stored in a way that doesn't block the delivery for the next customer. In real life problems this occurs for instance for breweries when they deliver bottles of beer or mineral water and collects empty bottles from the same customers on the same tour. In these situations we could relax the constraints of only checking Hamiltonian tours, and also try solutions that can visit customers in a way giving rise to a ‘alsso’ model. A solution which first only delivers bottles until the vehicle is partly unloaded, then do both delivery and pickup at the remaining customers and at last picks up the empty bottle from the first visited customers, could in these situations be better than a pure Hamiltonian tour, at least in a practical setting. To find such solutions, we will use the metaheuristic Tabu Search on some well known TSPPD-problems, and compare them to other kinds of solutions on the same problems.