Now showing items 1-10 of 53
Shocks and Business Cycles
A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique equilibrium if there are payoff shocks of any size. This equilibrium still has the desirable property that ...
Can Every Face of a Polyhedron Have Many Sides?
The simple question of the title has many different answers, depending on the kinds of faces we are willing to consider, on the types of polyhedra we admit, and on the symmetries we require. Known results and open problems about this topic are presented.
Graphs of polyhedra; polyhedra as graphs
Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and ...
An enduring error
No abstract or description.
A catalogue of simplicial arrangements in the real projective plane
An arrangement is the complex generated in the real projective plane by a family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the set of lines generating the arrangement. An arrangement is simplicial if all faces are triangles. Simplicial ...
Euler's ratio-sum theorem and generalizations
A theorem of Euler concerns sums of ratios in which Cevians of a triangle are divided by a common point. Generalizations of this result in three directions are presented: polygons instead of triangles, higher-dimensional polytopes, and several kinds of ratios.
Every finite family of (straight) lines in the projective plane, not forming a pencil, is well know to have at least one "ordinary point" –– that is, a point common to precisely two of the lines. A line of a family is said to be "omittable" if it contains no ordinary point of the family. Despite the large extent of work on ...
What symmetry groups are present in the Alhambra?
(American Mathematical Society, 2006)
The question which of the seventeen wallpaper groups are represented in the fabled ornamentation of the Alhambra has been raised and discussed quite often, with widely diverging answers. Some of the arguments from these discussions will be presented in detail. This leads to the more general problem about the validity and ...
Bosonic Quantum Field Theory
The purpose of these notes is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role.
Topics in Topology and Homotopy Theory
(Hopf Topology Archive, 2005-01)
This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology. Granted these prerequisites, my intention is to provide at the core a state of the art treatment of the homotopical foundations of ...