Examples 1. A K3 surface of degree two is a double cover of P, ramified in a smooth sextic. K3 surfaces of degree four are smooth quartics in P. A K3 surface of degree six is a smooth complete intersection of a quadric and a cubic in P. And, finally, K3 surfaces of degree eight are smooth complete intersections of three quadrics in P. The Picard group of a K3 surface is isomorphic to Zn where n...

We show that the Chow group Ch of a non-singular projective quadric has no torsion if dimension of the quadric is greater than 10 (while a non-trivial torsion appears for a certain 10-dimensional quadric over a suitable field). We apply the same method (based on an index reduction formula) to Ch too and show that it is torsionfree if dimension of the quadric is greater than 22. Let F be a field...

We describe a method for constructing rational quadratic patch boundary curves for scattered data in B3. The method has quadric boundary precision; if the given point and normal data are extracted from a quadric, then the boundary curves will lie on this quad&. Each boundary curve is a conic section represented in the rational BCzier representation.

Tohoku University, Japan is developing a new hand-held land mine detection dual-sensor (ALIS) which is equipped with a metal detector and a GPR. ALIS is equipped with a sensor tracking system, which can record the GPR and Metal detector signal with its location. The Migration processing drastically increases the quality of the imaging of the buried objects.Evaluation test of ALIS has been condu...

In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, biand three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite sta...

We continue the classiication, begun in 11], 14] and 12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurface in P 3. In this paper, we consider those cases where the quadric has rank 3. We also give suucient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be t...