Some important trends in geometric modeling are the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models, by using free-form objects in addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper we integrate all of these requirements ...

In this paper we examine the Laplacian on the product of two asymptotically hyperbolic spaces from the point of view of geometric scattering theory. In particular, we describe the asymptotic behavior of the resolvent applied to Schwartz functions and that of the resolvent kernel itself. We use these results to find the Martin boundary of the product space. This behaves (nearly) as expected when...

The present study aims at study of structure and properties of raw and thermal treated titanium-based powder material used to produce the thin-walled components by electron beam melting technology. Producing the end product means also studying the finishing cutting process. Examining the quality of end product in terms of geometric tolerance and thin walls thickness stability consists of contro...

We study the automorphisms of a graph product of finitely-generated abelian groups W . More precisely, we study a natural subgroup Aut W of AutW , with Aut W = AutW whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition Aut W = (InnW ⋊Out W )⋊Aut W . We also give a number of applications, some of wh...

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized projective geometries, where the former correspond to the Lie product of an associative algebra and the latter to its Jordan product. A further development of t...

The fuzzy supersphere S (2,2) F is a finite-dimensional matrix approximation to the supersphere S incorporating supersymmetry exactly. Here the ⋆-product of functions on S (2,2) F is obtained by utilizing the OSp(2, 1) coherent states. We check its graded commutative limit to S and extend it to fuzzy versions of sections of bundles using the methods of [1]. A brief discussion of the geometric s...

A. two-step sub-optimal algorithm for decoding binary product codes is discussed. This algorithm realizes at least half the minimum Euclidean distance of the code. The fundamental geometric properties associated with the algorithm are investigated, and bounds on the number of nearest neighbors are derived. This investigation also results with an improved algorithm which achieves the minimum eff...

We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in PU(2, 1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of this paper is that it uses a rigorous computer assisted proof to deal with di...

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden’s identity, the expression fo...