Clones from Creatures

A clone on a set X is a set of finitary operations on X which contains all the projections and is closed under composition. The set of all clones forms a complete lattice Cl(X) with greatest element O, the set of all finitary operations. For finite sets X the lattice is "dually atomic": every clone other than O is below a coatom of Cl(X). It was open whether Cl(X) is also dually atomic for infinite X. Assuming the continuum hypothesis, we show that there is a clone C on a countable set such that the interval of clones above C is linearly ordered, uncountable, and has no coatoms.Comment: LaTeX2e, 20 pages. Revised version: some concepts simplified, proof details adde

A survey of clones on infinite sets

A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the clone lattice. We summarize what we know about the clone lattice on an infinite base set X and formulate what we consider the most important open problems.Comment: 37 page

Clones on infinite sets

A clone on a set X is a set of finitary functions on X which contains the projections and which is closed under composition. The set of all clones on X forms a complete algebraic lattice Cl(X). We obtain several results on the structure of Cl(X) for infinite X. In the first chapter we prove the combinatorial result that if X is linearly ordered, then the median functions of different arity defined by that order all generate the same clone. The second chapter deals with clones containing the almost unary functions, that is, all functions whose value is determined by one of its variables up to a small set. We show that on X of regular cardinality, the set of such clones is always a countably infinite descending chain. The third chapter generalizes a result due to L. Heindorf from the countable to all uncountable X of regular cardinality, resulting in an explicit list of all clones containing the permutations but not all unary functions of X. Moreover, all maximal submonoids of the full transformation monoid which contain the permutations of X are determined, on all infinite X; this is an extension of a theorem by G. Gavrilov for countable base sets.Comment: 70 pages; Dissertation written at the Vienna University of Technology under the supervision of Martin Goldstern; essentially consists of the author's papers "The clone generated by the median functions", "Clones containing all almost unary functions, "Maximal clones on uncountable sets that include all permutations" which are all available from arXi

Effects of Laser UV-Microirradiation (λ = 2573 A) on Proliferation of Chinese Hamster Cells

A laser uv-microbeam with a wavelength of 2573 Å having a minimum spot diameter of approx 0.5 μm was used to microirradiate interphase cells of a V-79 subline of Chinese hamster cells. The incident energy necessary to induce a significant decrease of proliferation was 30 to 60 times larger after microirradiation of cytoplasm as compared with microirradiation of nucleoplasm. The mean value of relative cell numbers 40 hr after irradiation as a function of incident energy did not differ whether the cells were microirradiated lying singly or together in small groups. Analysis of individual growth curves of singly lying cells microirradiated in the nucleoplasm with the same energy showed heterogeneous reactions. The incident energy per cell compatible with proliferation of about 50% of the cells after microirradiation of nucleoplasm was approx. 2× 10sup-3/sup ergs. From this value it is suggested that the energy density within the focus was in the region of several thousand ergs per square millimeter. Photochemical effects are thought to be the cause of growth disturbance, while thermal effects are excluded