Abstract We consider the blowup X ( a , b c ) of weighted projective space $${\mathbb {P}}(a,b,c)$$ P ( a , b c ) at general nonsingular point. give sufficient condition for curve to be...

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line” and “off-line” methods for solving the one-dimensional viscous Bergers’ equation. For the on-line method, we have computed the slow manifold by extracti...

We give a new simple on-line incremental algorithm for the additively weighted Voronoi diagram, whose primitive operations are completely based on orientation tests. It is known that the closest site diagram can be disconnected, and that the furthest site diagram can have disconnected faces. The algorithm avoids such nuisances by using the oriented projective plane as an underlying geometry. In...

We show that each Jordan homomorphism R→ R′ of rings gives rise to a harmonic mapping of one connected component of the projective line over R into the projective line over R′. If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over R. Mathematics Subject Classification (2000): 51C0...

Abstract We introduce the notion of a simple fibration in $(1,2)$ -surfaces – that is, hypersurface inside certain weighted projective space bundle over curve such general fibre is minimal surface type with $p_g=2$ and $K^2=1$ . prove almost all Gorenstein fibrations line at worst canonical singularities are threefolds ‘on Noether line’ $K^3=\frac 43 p_g-\frac {10}3$ , we classify them. Among t...