On linear transformations preserving rank one matrices over commutative rings

We show that over any cummutative ring R,the combinations, of 2 × 2 minors are the only quadratic forms vanishing on the matrices of rank 1. Hence any invertible linear transformation on matrices that preserves the rank-1 set over R will automatically do the same over all extensions of R. Similarly, the linear combinations of 4 × 4 Paffians are the only quadratic forms vanishing on the alternating matrices of rank 2. Hence again any invertible transformation preserving that set over R will do so formally. This fact allows us to determine the collection of such transformations     

Real classification of complex quadrics

Canonical forms are given for complex quadric surfaces (and conics) under real changes of variable. The basic idea is to use known results on pairs of real quadratic forms.     

Notes toward higher differential algebra

This paper is a self-contained introduction to a theory of higher differential algebra. The results were originally accumulated in sporadic attempts to forge a link between differential algebra and the study of formal groups, and one trace of that goal is included here as motivation. Primarily, however, the theory is of interest because it preserves for arbitrary rings much of the formal structure of ordinary differential algebra for Ritt algebras. Some of the results have appeared in weaker form in the literature, so it seems worthwhile to put the theory on record.     

Continuous oxygen monitoring of mammalian cell growth on space shuttle mission STS-93 with a novel radioluminescent oxygen sensor

A compact, flow-through oxygen sensor device based on luminescence quenching was used to monitor dissolved oxygen levels during mammalian cell growth on the STS-93 mission of the Columbia space shuttle. Excitation of an oxygen-sensitive ruthenium complex was provided by a radiolumin escent light source (0.9 mm in diameter, 2.5 mm long), and the intensity of the resulting luminescence was measured by a simple photodiode detector. The use of radiolum inescence for the excitation light source is a unique approach that provides many features important for long-term and remote monitoring applications. For the spaceflight experiment, human lung fibroblast cells (WI-38) were grown in hollow-fiber bioreactors. Oxygen concentration was measured in the flow path both before and after the bioreactor cartridge in order to gain information about the metabolism of the cells. The sensor was found to be nonperturbing to cell growth and withstood the challenging physical conditions of shuttle launch and landing while maintaining a stable calibration function. In addition, the sensor provided physically meaningful oxygen predictions.     

Adhesion of amphipathic molecules to solid surfaces

Summary Oil/water contact angles, coefficient of friction and electron diffraction have been used to study the adsorption of three long chain surface-active substances (a fatty acid, a sulphate and a substituted amine, from aqueous solution on to electropolished copper, aluminium and iron. According to the p_H of the solution, the adsorption occurs by one of the following processes (a) physical adsorption, (b) chemisorption, (c) adherence of a precipitate, (d) sensitised adsorption to form a mixed film. Certain applications e.g. lubrication and the prevention of fretting corrosion, are discussed in relation to the structure and rate of adsorption of the four types of film. The first requirement for an efficient lubricant film is the chemisorption of the long chain compound as a basic metal soap. The film is considerably strengthened by subsequent adsorption of a less polar compound, such as cholesterol, by process (d). A suitable vehicle for the two compounds is an oil/water emulsion.Electron diffraction has been used to determine the physical and chemical nature of the electropolished metal surfaces. Adsorbed monolayers can only be detected on extremely smooth surfaces. A new technique is described for depositing insoluble monolayers on reactive metals, which avoids the roughening of the metal surface experienced in the normal Langmuir-Blodgett method.

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Zusammenfassung Randwinkel öl-Wasser, Reibungskoeffizient und Elektronenstrahlbeugung wurden benutzt zum Studium der Adsorption dreier langkettiger Substanzen (eine Fettsäure, ein Sulfat und ein substituiertes Amin) aus wäßriger Lösung heraus auf elektropoliertes Kupfer, Aluminium und Eisen. Entsprechend dem p_H-Wert der Lösung geschieht die Adsorption durch einen der folgenden Prozesse:a) Physikalische Adsorption, b) Chemisorption, c) Haftung eines Niederschlags und d) sensibilisierte Adsorption unter Bildung eines Mischfilms.Einige Anwendungen, z. B. Schmierung und die Verhinderung von Reibungskorrosion, wurden unter BerÜcksichtigung der Struktur und der Adsorptionsgeschwindigkeit der vier genannten Typen von Adsorptionsschichten diskutiert. Die erste Bedingung fÜr wirksame Schmierung ist die Chemisorption der langkettigen Substanz als basische, metallorganische VerdÜnnung (Seife). Der erhaltene Adsorptionsfilm erfährt eine beachtliche Verfestigung durch nachfolgende Adsorption (nach dem Prozeß d) einer schwächer polaren Substanz, wie des Cholesterols. Ein brauchbarer Träger fÜr beide Komponenten ist eine öl-Wasser-Emulsion.Zur Aufklärung der chemischen und physikalischen Eigenschaften der elektropolierten Metalloberflächen wurde die Elektronenstrahlbeugung eingesetzt. Adsorbierte Monoschichten können nur auf extrem ebenen Oberflächen beobachtet werden. Zur Verhinderung der Aufrauhung von Metalloberflächen, wie sie von der Langmuir-Blodgett-Methode her bekannt ist, wurde eine neue Auftragungstechnik fÜr unlösliche Monoschichten auf reaktionsfähige Metalloberflächen entwickelt.

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This work was carried out during the tenure of Consolidated Zinc Studentships at Trinity Hall, Cambridge, on the part of two of the authors (R. B. W. & J. A. S.). Further financial support was provided by Almin Limited and C. S. I. R. O. (Australia).     

Hollow PtFe Alloy Nanoparticles Derived from Pt-Fe3O4 Dimers through a Silica-Protection Reduction Strategy as Efficient Oxygen Reduction Electrocatalysts

The development of efficient and stable electrocatalysts for the oxygen reduction reaction (ORR) is critical for the large-scale production of fuel cells. Platinum (Pt) nanoparticle catalysts show excellent performance for ORR, though the high cost of Pt is a limiting factor that directly impacts fuel cell production costs. Alloying Pt with other transition metals is an effective strategy to reduce Pt utilization whilst maintaining good ORR performance. In this work, novel hollow PtFe alloy catalysts were successfully synthesized by high-temperature pyrolysis of SiO₂-coated Pt-Fe₃O₄ nanoparticle dimers supported on carbon at 900 °C, followed by SiO₂ shell removal and partial dealloying of the PtFe nanoparticles formed using HF. The obtained hollow PtFe nanoparticle catalysts (denoted herein as PtFe-900) showed a 2.3-fold enhancement in ORR mass activity compared to PtFe nanoparticles synthesized without SiO₂ protection, and a remarkable 7.8-fold enhancement relative to a commercial Pt/C catalyst. Further, after 10 000 potential cycles, the ORR mass activity of PtFe-900 remained very high (90.9 % of the initial mass activity). The outstanding ORR performance of PtFe-900 can be attributed to the modification of Pt lattice and electronic structure by alloying with Fe at high temperature under the protection of the SiO₂ coating. This work guides the development of improved, highly dispersed Pt-based alloy nanoparticle catalysts for ORR and fuel cell applications.     

Book review

Skew Fields, by P. K. Draxl. London Mathematical Society Lecture Notes No. 18, Cambridge University Press, 1983, ix + 182 pp.     

Defining Sets of Full Designs with Block Size Three II

A defining set of a t?(v, k, ??) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. The unique simple design with parameters ${{t-\left(v, k, \begin{array}{ll}\left(\begin{array}{ll}v-t\\ k-t\end{array}\right)\end{array}\right)}}$ is said to be the full design on v elements. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. The largest known minimal defining set is given. The existence of a continuous section of the spectrum comprising asymptotically 9v ²/50 values is shown. This gives a quadratic length section of continuous spectrum where only a linear section with respect to v was known before.     

A general thermolabile protecting group strategy for organocatalytic metal-organic frameworks

We present a general strategy for incorporating organocatalytic moieties into metal-organic frameworks (MOFs). The organocatalytic units are protected by a thermolabile protecting group during MOF synthesis and then unveiled by a simple postsynthetic heating step. The strategy is exemplified using a thermolabile tert-butoxycarbonyl (Boc) protecting group for a proline moiety, the removal of which endows the resulting cubic zinc(II) IRMOF with catalytic activity for asymmetric aldol reactions. The bulky Boc groups also prevent framework interpenetration, producing open MOFs that can admit relatively large substrates.