Introduction In working out the basic logic of choice in his Principles of Economics, Carl Menger uses carefully described examples of the situations his agents face. Whether it is Robinson Crusoe, a small mountain community, or a ship lost at sea, the context in which decisions take place is always precisely circumscribed. The reason for this exactitude is simple: to choose is to elect over a ...

where H1 is the 1-dimensional Hausdorff measure in Rn, c(x, y, z) is the inverse of the radius of the circumcircle of the triangle (x, y, z), that is, following the terminology of [6], the Menger curvature of the triple (x, y, z). A Borel set E ⊂ Rn is said to be “purely unrectifiable” if for any Lipschitz function γ : R → Rn, H1(E ∩ γ(R)) = 0 whereas it is said to be rectifiable if there exist...

Given a set of affine varieties in <3, i.e. planes, lines, and points, the problem tackled in this paper is that of finding all possible configurations for these varieties that satisfy a set of pairwise euclidean distances between them. Many problems in Robotics –such as the forward kinematics of parallel manipulators or the contact formation problem between polyhedral models– can be formulated...

Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid. As our main tool, we prove for any infinite graph G with vertex sets A and B that if every finite subset of A is linked to B by disjoint paths, then the whole of A can be linked to the closure of B by disjoint paths or rays in a na...

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration ord...

Faudree, R.J., R.J. Gould and L.M. Lesniak, Generalized degrees and Menger path systems, Discrete Applied Mathematics 37/38 (1992) 179-191. For positive integers d and W, let P&,,(G) denote the property that between each pair of vertices of the graph G, there are m internally disjoint paths of length at most d. For a positive integer t, a graph G satisfies the minimum generalized degree conditi...