Abstract The recently developed theory of partial actions discrete groups on C *-algebras is extended. A related concept inverse semigroups defined, including covariant representations and crossed products. main result that every product a by semigroup action.

A synchrony subspace of $\mathbb{R}^{n}$ is defined by setting certain components the vectors equal according to an equivalence relation. Synchrony subspaces invariant under a given set square matrices ordered inclusion form lattice. Applications these include equitable and almost partitions vertices graph used in many areas theory, balanced exo-balanced coupled cell networks, coset Cayley graphs. We study basic properties provide examples applications. also present what we call split cir...

Abstract Groupoid actions on C*-bundles and inverse semigroup C *-algebras are closely related when the groupoid is r -discrete.

Anderson and Harary introduced two impartial games on finite groups. Both are played by players who alternately select previouslyunselected elements of a group. The first player builds generating set from the jointly-selected wins game. cannot an element without building loses second We determine nim-numbers, therefore outcomes, these for symmetric alternating

The Bifurcation from a Simple Eigenvalue (BSE) Theorem is the foundation of steady-state bifurcation theory for one-parameter families functions.When eigenvalues multiplicity greater than one are caused by symmetry, Equivariant Branching Lemma (EBL) can often be applied to predict branching solutions.The EBL interpreted as application BSE fixed point subspace.There functions which have invariant linear subspaces that not symmetry.For example, networks identical coupled cells such...

A pebbling move on a weighted graph removes some pebbles at vertex and adds one pebble an adjacent vertex. The number of removed is the weight edge connecting vertices. reachable from distribution if it possible to that using moves. smallest m needed guarantee any pebbles. Regular problems unweighted graphs are special cases when every 2. regular problem often simplifies simpler graph. We present algorithm find graphs. use this together with simplifications all connected most nine

We seek discrete approximations to solutions $u:\Omega\to\mathbb{R}$ of semilinear elliptic PDE the form $\Delta u+f_s(u)=0$, where $f_s$ is a one-parameter family nonlinear functions and $\Omega$ domain in $\mathbb{R}^d$. The main achievement this paper approximation on cube $\Omega=(0,\pi)^3\subseteq\mathbb{R}^3$. There are 323 possible isotropy subgroups cube, which fall into 99 conjugacy classes. bifurcations with symmetry problem quite interesting, including many 3-dimensional critical...

We seek solutions u ∈ ℝ n to the semilinear elliptic partial difference equation -Lu + f s (u) = 0, where L is matrix corresponding Laplacian operator on a graph G and one-parameter family of nonlinear functions. This article combines ideas introduced by authors in two papers: (a) Nonlinear equations graphs (J. Experimental Mathematics, 2006), which introduces analytical numerical techniques for solving such equations, (b) Symmetry automated branch following PDE fractal region (SIAM J....

An animal is an edge connected set of finitely many cells a regular tiling the plane. The site-perimeter number empty to by edge. minimum with given cell size found for animals on triangular and hexagonal grid. formulas are used show effectiveness simple random strategy in full achievement games.

We apply the gradient Newton–Galerkin algorithm (GNGA) of Neuberger and Swift to find solutions a semilinear elliptic Dirichlet problem on region whose boundary is Koch snowflake. In recent paper, we described an accurate efficient method for generating basis eigenfunctions Laplacian this region. that work, used symmetry snowflake analyze postprocess basis, rendering it suitable input GNGA. The GNGA uses Newton’s eigenfunction expansion coefficients problem. This article introduces...

The notions of Busby-Smith and Green type twisted actions are extended to discrete unital inverse semigroups. connection between the two types, with partial actions, investigated. Decomposition theorems for crossed products given.

We define a graph network to be coupled cell where there are only one type of and symmetric coupling between the cells. For difference-coupled vector field on system, all cells have same internal dynamics, is identical, symmetric, depends difference states interacting four nested sets fields by adding further restrictions dynamics functions. These require that these functions preserve zero or odd linear. characterize synchrony antisynchrony subspaces with respect subsets admissible fields....

Abstract This article considers numerical semigroups S that have a nonprincipal relative ideal I such μ (I)μ (S − I) = (I + I)). We show the existence of an infinite family pairs (S, in which S\{0}. also examples are not members this family. discuss computational process used to find these and present some open questions pertaining them. Key Words: DualMinimal generating setNumerical semigroupRelative idealMathematics Subject Classification: 20M14 Notes Communicated by I. Swanson.