0. Introduction The Genocchi numbers appear in many different contexts (see e.g. [1,4,5,7,6,14,20]). Probably the most well-known definition uses the Seidel triangle 155 155 17 17 155 310 3 3 17 34 138 448 1 1 3 6 14 48 104 552 1 1 1 2 2 8 8 56 56 608 By definition, the triangle is formedby the numbers gk,n (k is the number of a row counted frombottom to top and n is the number of a column from...

A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | x = y = z = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l,m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized tri...

In this paper we present an efficient face-based connectivity coding technique for the special class of quadrilateral and the hybrid triangular-quadrilateral meshes. This work extends the main ideas of non-split encoding presented by the first contribution of the authors (Khattab, Abd El-Latif, Abdel Wahab and Tolba, 2007) for triangle meshes and improves over the compression results provided s...

Realism of rendered human skin can be strongly enhanced by taking into account skin wrinkles. However, modeling wrinkles is a difficult task, and considerable time and effort are necessary to achieve satisfactory results. This paper presents a simple method to easily model wrinkles on human skin, nevertheless taking into account the properties of real wrinkles. Wrinkles are specified using intu...

An N-tiling of triangle ABC by triangle T (the “tile”) is a way of writing ABC as a union of N copies of T overlapping only at their boundaries. We continue the work of [1, 2] on classifying the possible triangle tilings. The results of all three papers together enable us to make some progress on two problems of Erdős about triangle tilings, one of which asks, “for which N is there an N-tiling ...

The variability in the arrangement of the superficial atrial muscle fibers in the areas of the triangle of Koch may be one of the factors influencing the route for impulses entering the AV node. The purpose of this study was to present the dimensions of the triangle of Koch and to describe the arrangement of the subendocardial atrial muscle fibers that form the approaches to the AV node, in and...

The complexity of the real world makes a perfect characterization impossible. Purely deliberative approaches such as classical planning are thus susceptible to unexpected failures. Preventive learning approaches address the imperfect theory problem through the diagnosis of such failures and the determination of fixes to avoid similar failures in the future. Curative learning approaches such as ...

Most research in learning for planning has concentrated on eeciency gains. Another important goal is improving the quality of nal plans. Learning to improve plan quality has been examined by a few researchers, however, little research has been done learning to improve both eeciency and quality. This paper explores this problem by using the Scope learning system to acquire control knowledge that...