Free subgroups of one-relator relative presentations

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1. 4 page

The Kervaire-Laudenbach conjecture and presentations of simple groups

The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free. Key words: Kervaire--Laudenbach conjecture, relative presentations, simple groups, car motion, cocar comotion. AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure

Shape computations without compositions

Parametric CAD supports design explorations through generative methods which compose and transform geometric elements. This paper argues that elementary shape computations do not always correspond to valid compositional shape structures. In many design cases generative rules correspond to compositional structures, but for relatively simple shapes and rules it is not always possible to assign a corresponding compositional structure of parts which account for all operations of the computation. This problem is brought into strong relief when design processes generate multiple compositions according to purpose, such as product structure, assembly, manufacture, etc. Is it possible to specify shape computations which generate just these compositions of parts or are there additional emergent shapes and features? In parallel, combining two compositions would require the associated combined computations to yield a valid composition. Simple examples are presented which throw light on the issues in integrating different product descriptions (i.e. compositions) within parametric CAD

On Quasiperiodic Morphisms

Weakly and strongly quasiperiodic morphisms are tools introduced to study quasiperiodic words. Formally they map respectively at least one or any non-quasiperiodic word to a quasiperiodic word. Considering them both on finite and infinite words, we get four families of morphisms between which we study relations. We provide algorithms to decide whether a morphism is strongly quasiperiodic on finite words or on infinite words.Comment: 12 page

Connections between Relation Algebras and Cylindric Algebras

Abstract. We give an informal description of a recursive representability-preserving reduction of relation algebras to cylindric algebras.

On residualizing homomorphisms preserving quasiconvexity

H is called a G-subgroup of a hyperbolic group G if for any finite subset M G there exists a homomorphism from G onto a non-elementary hyperbolic group G_1 that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. Here we show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity

Actuator and electronics packaging for extrinsic humanoid hand

The lower arm assembly for a humanoid robot includes an arm support having a first side and a second side, a plurality of wrist actuators mounted to the first side of the arm support, a plurality of finger actuators mounted to the second side of the arm support and a plurality of electronics also located on the first side of the arm support