Rigid chains admitting many embeddings

Rigid Chains Admitting Many Embeddings

1. Abstract A chain (linearly ordered set) is rigid if it has no non-trivial automor-phisms. The construction of dense rigid chains was carried out by Dushnik and Miller for subsets of R, and there is a rather diierent construction of dense rigid chains of cardinality , an uncountable regular cardinal, using stationary sets as`codes', which was adapted by Droste in 1] to show the existence of r...

Embeddings of Chains into Chains

Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.

Permanently Linked Rigid Superparamagnetic Chains

Rigid DNA chains near nanoparticles

Two-photon excitation time-resolved fluorescence anisotropy and lifetime measurements were used to study the conformation of DNA near oppositely charged nanoparticles. Negatively-charged rhodamine-labeled DNA was allowed to adsorb onto positively-charged nanoparticles in deionized water and surface-induced fluorescence quenching was observed by measuring the fluorescence lifetime. Fluorescence ...

Counting Euclidean embeddings of rigid graphs

A graph is called (generically) rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here we deal with the problem of determining the maximum number of planar Euclidean embeddings as a function of the number of the vertices. We obtain polynomial systems which totally capture the structure...