In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act with the group on that diagram. Once it is possible to understand what the action of the group on every space in the diagram is, and what it does to the morphis...

The phase diagram of the two-dimensional extended q−states Potts model is investigated in the q → 1 limit. This is equivalent to studying the phase diagram of a two-dimensional infinite interacting lattice animal. An exact solution on the Bethe lattice and a Migdal-Kadanoff renormalization group calculation predict a line of θ transitions from an extended to a compact phase in the lattice anima...

The paper theoretically investigates the peculiarities of energy diagram of asymmetric graded-band-gap superlattices with linear coordinate dependences of band gap and electron affinity. For calculating the energy diagram of asymmetric graded-band-gap superlattices, linearized Poisson's equation has been solved for the two layers forming a period of the superlattice. The obtained coordinate dep...

Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a characterization of Seifert graphs in terms of Eulerian subgraphs. This charact...

Sheet metal forming boundaries are established using the limit diagram (FLD). The Nakajima and Marciniak tests, which based on stretching a material punch, most commonly used methods for determining FLD or fracture (FFLD). results usually evaluated by calculating local strain, strain rates, specimen thickness reduction strain. When amount of experimental is insufficient, miniaturization testing...