Pentopyranosyl Oligonucleotide Systems. 9th Communication

Pyranosyl‐RNA (‘p‐RNA’ ) is an oligonucleotide system isomeric to natural RNA and composed of the very same building blocks as RNA. Its generational, chemical, and informational properties are deemed to be those of an alternative nucleic acid system that could have been a candidate in Nature's evolutionary choice of the molecular basis of genetic function. We consider the study of the chemistry of p‐RNA as etiologically relevant in the sense that knowledge of its structural, chemical, and informational properties on the chemical level offers both a perspective and reference points for the recognition of specific structural assets of the RNA structure that made it the (supposedly) superior system among possible alternatives and, therefore, the system that became part of biology as we know it today. The paper describes the chemical synthesis of β‐d‐ (and L )‐ribopyranosyl‐(4′→2′)‐oligonucleotide sequences, presents a resume of their structural and chemical properties, and cautiously discusses what we may and may not have learned from the pyranosyl isomer of RNA with respect to the conundrum of RNA's origin.     

The change of the superstructure of semicrystalline polymers during deformation: results from small-angle scattering with synchrotron radiation

The change of the superstructure of different polyethylenes during uniaxial deformation is investigated. The method used is small-angle scattering with synchrotron radiation. For branched polyethylene (Lupolen 1840D) the whole deformation range is analyzed. Beginning with superstructure of the lamellar cluster type, the superstructure partly disappears on a time scale of a few minutes and the fibrillar structure is built up. The degree of destruction and rebuilding depends on the drawing temperature. For very high molecular weight polyethylene (GUR) a reversible change of the superstructure at higher deformation ratios and at different temperatures is observed. The superstructure of (ethylene—hexene) copolymers (TIPELIN) at high draw ratios depends on the drawing temperature and is almost independent of the side group content. Interfibrillar microcracks parallel to the draw direction are produced in samples with a low side group content for draw ratios λ ≥ 1.5.     

The many facets of linear programming

We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interior-point, and other methods. Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001     

Cores and retracts

Theretracts (idempotent, isotone self-maps) of an ordered set are naturally ordered as functions. In this note we characterize the possible ways that one retract can cover another one. This gives some insight into the structure of the ordered set of retracts and leads to a natural generalization of the core of an ordered set.Supported by NSERC Operating Grant 41702.     

Coboundaries of irreducible markov operators onC(K)

LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup _N ‖Σ _j ^=0N T ^j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.