In this note we construct a non-singular algebraic variety VG encoding the incidence information of a simple graph G, by a sequence of blow-ups of a projective space along suitable linear subspaces. The aim is to translate into the geometry of VG the combinatorial information about G; we nd that this can be done with surprising ease and e ciency. For example, we prove that the chromatic polynom...

The paper looks at some of the techniques (separation of variables, Fourier series, Carleman estimates) used to obtain observability and nullcontrollability results to determine qualitatively the asymptotic behavior of the estimates obtained with respect to relevant parameters. We are particularly concerned with blow-up as the control time becomes short (T → 0).

In the present work, we derive that electric fields blow up as a pair of spherical perfect conductors approach each other, and calculate the blow-up rate by a simple method. In the case of two dimensional space, referring to an anti-plane shear model, we can assume that the conductors and the electric fields represent the cross-sections of parallel stiff fibers and the stresses, respectively. H...

We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet condition. Our analysis is based on a blow-up procedure which involves Almgren type monotonicity formulae and provides classification all possible homogeneity degrees limiting entire profiles. As consequence, we establish strong unique continuation principle from p...

The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with equivariant blow-ups and blow-downs, and get an easy criterion to determine whether a given nonsingular toric variety is a Fano variety or not. As applications of...

We study the size-cost of boolean operations on constant height deterministic pushdown automata. We prove an asymptotically optimal exponential blow-up for union and intersection, as well as polynomial blow-up for complement.