In this paper, we consider the planar Sierpinski measures μM,D generated by an expanding integer matrix M ∈ M2(Z) and the digit set D = {( 0 0 )

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the prod...

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...

A neglected effect of monopoly is the distortion in the quantity of resources supplied. Monopoly not only affects the economy's output mix, it also results in factor prices that are below social marginal value products. This latter distortion is shown to be quantitatively important when other policies, such as taxes on labor earnings, also depress factor prices. Under plausible conditions, the ...