On the syzygies and Hodge theory of nodal hypersurfaces

We give lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for the graded pieces with respect to the Hodge filtration of the top cohomology of the hypersurface complement in many new cases. A classical result by Severi on the position of the singularities of a nodal surface in \(\mathbb {P}^3\) is improved and applications to deformation theory of nodal surfaces are given.     

Design and fabrication of teflon-coated tungsten nanorods for tunable hydrophobicity

The nature of water interaction with tungsten nanorods (WNRs) fabricated by the glancing-angle deposition technique (GLAD)-using RF magnetron sputtering under various Ar pressures and substrate tilting angles and then subsequent coating with Teflon-has been studied and reported. Such nanostructured surfaces have shown strong water repellency properties with apparent water contact angles (AWCA) of as high as 160°, which were found to depend strongly upon the fabrication conditions. Variations in Ar pressure and the substrate tilting angle resulted in the generation of WNRs with different surface roughness and porosity properties. A theoretical model has been proposed to predict the observed high AWCAs measured at the nanostructure interfaces. The unique pyramidal tip geometry of WNRs generated at low Ar pressure with a high oblique angle reduced the solid fraction at the water interface, explaining the high AWCA measured on such surfaces. It was also found that the top geometrical morphologies controlling the total solid fraction of the WNRs are dependent upon and controlled by both the Ar pressure and substrate tilting angle. The water repellency of the tungsten nanorods with contact angles as high as 160° suggests that these coatings have enormous potential for robust superhydrophobic and anti-icing applications in harsh environments.     

Using Clar sextets for two- and three-dimensional aromatic systems

After a brief history of the aromaticity concept, the use of Clar sextet circles is reviewed for explaining various aspects of planar aromatic systems (benzenoids, heterocycles) and of tridimensional carbon aggregates. When folding a graphene sheet for obtaining nanotubes, nanotori, or nanocones, the congruence of Clar sextet circles allows the classification of all such aggregates into two classes (congruent or incongruent) with marked differences in properties; this is in agreement with the well-known condition h - k ≡ 0 (mod 3), equivalent to congruence, in terms of the chiral vectors h and k for graphene sheets.     

Asymptotic behaviour of families of real curves

We consider the family of fibres of a polynomial function f on a smooth noncompact algebraic real surface and we characterise the regular fibres of f which are atypical due to their asymptotic behaviour at infinity. We compare to the similar problem in the complex case. Received: 5 May 1998 / Revised version: 20 March 1999     

A geometric approach to the classification of pencils of quadrics

Geometriae Dedicata -     

A new algorithm that generates the image of the attractor of a generalized iterated function system

Numerical Algorithms - We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space...