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...

A generalized triangle group is a group that can be presented in the form G = x, y | x p = y q = w(x, y) r = 1 where p, q, r ≥ 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Z p * Z q = x, y | x p = y q = 1. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibl...

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...

background and aims. resonance frequency analysis (rfa) offers a noninvasive clinical measurement of stability and osseointegration of implants; it is a useful tool to establish implant loading time. the rfa values are represented by a quantitative unit called the implant stability quotient (isq) on a scale from 1 to 100. the aim of the present study was to measure the stability of astra tech a...

A complex hyperbolic triangle group is a group generated by three complex reflections fixing complex slices (complex geodesics) in complex hyperbolic space. Our purpose in this paper is to improve the result in [3] and to discuss discreteness of complex hyperbolic triangle groups of type (n, n,∞; k).

Introduction: The survival of an implant system is affected by the choice of antirotational design, which can include an external or internal hex. Implant success also is affected by the maintenance of the crestal bone around implants. The aim of present study was to evaluate the crestal bone loss and clinical parameters related to bone loss in patients loaded with an external or internal hex 3...