Abstract. The holomorph of a discrete group G is the universal semi-direct product of G. We construct a resolution for Hol(Zpr ) for every prime p, where Zm denotes a cyclic group of order m, and use it to compute the integer homology and mod p cohomology of Hol(Zpr ) (this computation is long and is omitted here, but will appear in [V]). Also, we study maps of holomorphs of groups and maps of ...

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

For certain classes of holomorphic correspondences which are matings between Kleinian groups and polynomials, we prove the existence of pinching deformations, analogous to Maskit’s deformations of Kleinian groups which pinch loxodromic elements to parabolic elements. We apply our results to establish the existence of matings between quadratic maps and the modular group, for a large class of qua...

A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve.

This paper addresses the problem of building large-scale maps of indoor environments with mobile robots. It proposes a statistical approach that phrases the map building problem as a constrained maximum-likelihood estimation problem, for which it devises a practical algorithm. Experimental results in large, cyclic environments illustrate the appropriateness of the approach.

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy.

The same holds for continuous maps of the real line into itself, except that we may have P (f) = ∅. All proofs of Sharkovsky’s Theorem inevitably lead to an idea of a “type” of a cycle. For instance, when ordering the points of a cycle p1 < p2 < · · · < pn, one gets a cyclic permutation σ corresponding to it, such that pi is mapped to pσ(i). Combinatorial Dynamics deals with types of cycles (de...

In this paper we study n ∏ i=1 Z2i -Additive Cyclic Codes. These codes are identified as Z2n [x]submodules of n ∏ i=1 Z2i [x]/〈x αi − 1〉; αi and i being relatively prime for each i = 1, 2, . . . , n. We first define a n ∏ i=1 Z2i -additive cyclic code of a certain length. We then define the distance between two codewords and the minimum distance of such a code. Moreover we relate these to binar...

A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3...

A subgroup G of automorphisms of a graph X is said to be 2 -arc-transitive if it is vertexand edgebut not arc-transitive. The graph X is said to be 2 -arc-transitive if Aut X is 1 2 -arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 2 -arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 2 -ar...