Obstruction theory in model categories

Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obstruction theory with respect to all fibrations. Up to weak equivalence, retract, and cobase change, they are the cofibrations with weakly contractible target. Equivalently, they are the retracts of principal cofibrations. Without properness, the same classification holds for cofibrations with cofibrant source. Our results dualize to give a classification of fibrations that have an obstruction theory.     

The Elementary Geometric Structure of Compact Lie Groups

We give geometric proofs of some of the basic structure theoremsfor compact Lie groups. The goal is to take a fresh look atthese theorems, prove some that are difficult to find in theliterature, and illustrate an approach to the theorems thatcan be imitated in the homotopy theoretic setting of p-compactgroups. 1991 Mathematics Subject Classification 22E15, 55P35.     

Kinetics and Mechanism of the Reduction of Sodium Chlorite by Sodium Hydrogen Ascorbate in Aqueous Solution at Near Neutral pH

The reduction of chlorite ion by the hydrogen ascorbate ion in a neutral solution safely produces chlorine dioxide. The decrease in absorbance at 268 nm with the presence of dimethyl sulfoxide (DMSO) allows measurement of the ascorbate disappearance in the reaction with excess chlorite. The measured rate constant at 25 ± 0.02°C, 3.67 × 10^?4 M DMSO, ionic strength 0.51 M (NaClO₄), and in the presence of 3.32 × 10^?9 M ethylenediaminetetraacetic acid is 13.81 ± 1.30 M^?1 s^?1. Rate constant measurements over the range 15–35°C gave an Arrhenius activation energy of 75.51 ± 4.53 kJ mol^?1. This result is the first reported determination of the kinetics of this reaction and is consistent with either electron‐ or oxygen‐transfer mechanisms. Anomalously, reduction of chlorite results in its oxidation, because intermediate hypochlorite oxidizes chlorite.     

The atom pencil: serial writing in the sub-micrometre domain

The atom pencil we describe here is a versatile tool that writes arbitrary structures by atomic deposition in a serial lithographic process. This device consists of a transversely laser-cooled and collimated cesium atomic beam that passes through a 4-pole atom-flux concentrator and impinges on to micron- and sub-micron-sized apertures. The aperture translates above a fixed substrate and enables the writing of sharp features with sizes down to 280 nm. We have investigated the writing and clogging properties of an atom pencil tip fabricated from silicon oxide pyramids perforated at the tip apex with a sub-micron aperture.     

Random convex hulls in a product of balls

Summary The convex hull of a set of points sampled independently and uniformly from the Cartesian product of balls of various dimensions is investigated. Bounds on the asymptotic behavior of the expected combinatorial complexity volume, and mean width are derived when the distribution is held fixed and the sample size approaches infinity. The expected combinational complexity and volume are found to depend (up to constant factors) only on the greatest dimension of any factor ball and the number of balls of that dimension. On the other hand, the expected mean width depends only on the number of balls and the dimensions of the product.Supported by the National Science Foundation under Grants CCR-8658139 and CCR-8908782     

Qualitative Analyse

Ohne Zusammenfassung     

A study of the initial reaction of water vapor with Fe(001) surface

LEED and AES have been used to study the structural changes and kinetics of the initial interaction between Fe(001) and water vapor at temperatures from 298 to 473 K. A disordered c(2 × 2) structure was formed at all temperatures, and only 80% of the total number of sites were filled at saturation. The initial sticking coefficient was 0.56 ± 0.03, and the reaction rate increased with increasing temperature. A model was proposed that successfully accounted for these experimental observations. Irreversible chemisorption of water is proposed to take place via a precursor of physically adsorbed water molecules. The precursor, which is adsorbed on both bare surface and surface covered by chemisorbed species, is mobile and retains most of its degrees of rotational freedom. Water molecules in the precursor state can either desorb or dissociate, and the difference in activation energies for these reactions was found to be 5.7 ± 0.5 $\text{kcal}\text{mol}$. Only 80% of the available c(2 × 2) sites are filled and the surface layer is disordered because the chemisorbed species are immobile, and because each one blocks four nearest neighbor sites for further adsorption. The chemisorbed species occupy the fourfold symmetric sites either above the iron atoms or above the interstitial “holes” betweeh iron atoms.     

Miniaturized RPLC for the rapid determination of total tryptophan in pediatric plasma samples

Summary A 8.3cm column packed with 3μm C₁₈ particles was used for the quantitative analysis of total tryptophan in plasma. The plasma samples were deproteinized with cold perchloric acid and 5–20μl of the plasma extract were injected into the RPLC column The tryptophan was readily separated from other plasma components in 5 minutes using isocratic elution. Thus the method can be readily automated. The minimum detection limit was 5pmoles using UV detection, and 1 pmole using fluorescence detection. Since low concentrations of total tryptophan in small volumes (⩽ 500μl) of plasma can be determined reproducibly and rapidly, this fast RPLC method can be used in pharmaceutical and clinical laboratories for newborn, and infant and pediatric samples.     

A whitehead theorem for long towers of spaces

We show that one can construct the universalR-homology isomorphismK →E _RX of Bousfield [1] by a transfinite iteration of an elementary homology correction map. This correction map is essentially the same as the one used classically to define Adams spectral sequence. This yields a topological characterization of the class of local spaces as the smallests containingK(A, n)’s and closed under homotopy inverse limit. This research was partially supported by the National Science Foundation, Grant # MCS76-08795, and by the U.S.-Israel Bi-National Science Foundation Grant # 680.