a tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. in this paper some special polygonal tiling of sphere, ellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.

The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material.  The freque...

We present results connecting the shape of the numerical range to intrinsic properties of a matrix A. When A is a nonnegative matrix, these results are to a large extent analogous to the Perron-Frobenius theory, especially as it pertains to irreducibility and cyclicity in the combinatorial sense. Special attention is given to polygonal, circular and elliptic numerical ranges. The main vehicles ...

We introduce a set of techniques that are used together to produce realistic-looking animations of burning objects. These include a new method for simulating spreading on polygonal meshes. A key component of our approach consists in using individual flames as primitives to animate and render the fire. This simplification enables rapid computation and gives more intuitive control over the simula...

In this paper, we introduce a practical modeling approach to improve the quality of polygonal mesh structures. Our approach is based on a discrete version of Gaussian-Bonnet theorem on piecewise planar manifold meshes and vertex angle deflections that determines local geometric behavior. Based on discrete GaussianBonnet theorem, summation of angle deflections of all vertices is independent of m...

In this paper we consider higher order infinitesimal bending of a surface in E3. Sufficient condition for a toroid generated by polygonal meridian to be non-rigid of higher order is given. This work is an extension of the results [1]-[7]. Examples of non-rigid surfaces, with visual presentation of infinitesimal bending are given. AMS Subj. Class.: 53A05, 53C45, 68U05

This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show tha...