Filling Length in Finitely Presentable Groups

We study the filling length function for a finite presentation of a group , and interpret this function as an optimal bound on the length of the boundary loop as a van Kampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of . We look at 'AD-pairs' (f,g) for a finite presentation : that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for . Further we show that (up to multiplicative constants) if is an isoperimetric function ( ) for a finite presentation then ( ) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.Partially supported by NSF grant DMS-9800158Supported by EPSRC Award No. 98001683 and Corpus Christi College, Oxford.     

Free convection from a horizontal line source of heat

Summary In this paper a study is made of finite Grashof number effects upon the flow, in an unbounded domain, in the buoyant plume which forms over a horizontal line source of heat. The consequences of introducing a plane boundary into the domain are also assessed for two particular configurations.

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Zusammenfassung In dieser Arbeit wird der Effekt der endlichen Grashof-Zahl auf die Strömung untersucht, in einem unbegrenzten Medium mit natürlicher Konvektion, die durch eine horizontale linienförmige Quelle erzeugt wird. Die Folgen einer ebenen Begrenzungsfläche werden für zwei besondere Konfigurationen untersucht.

     

A micro co-precipitation technique for use in X-ray fluorescence analysis

An apparatus and a procedure are described for the preconcentration of nanogram amounts of trace elements. Co-precipitation and pressure filtration confine the precipitate to a 1.27 mm diameter spot on a filter membrane. Trace elements in the 10-100 ng range are collected reproducibly and detected with high sensitivity by X-ray fluorescence, by use of a milliprobe instrument. Advantages of the technique for quantitative applications are discussed.     

A single extraction method for the analysis by liquid chromatography/tandem mass spectrometry of fumonisins and biomarkers of disrupted sphingolipid metabolism in tissues of maize seedlings

The fungus Fusarium verticillioides is a pathogen of many plants and produces fumonisins. In addition to their well-studied animal toxicoses, these toxins contribute to the development of maize seedling disease in susceptible maize varieties. Fumonisin disruption of sphingolipid biosynthesis occurs during pathogenesis. An extraction method was developed for the simultaneous analysis of fumonisins B₁ (FB₁), B₂ (FB₂) and B₃ (FB₃), free sphingoid bases and sphingoid base 1-phosphates in maize tissues by liquid chromatography/linear ion trap tandem mass spectrometry. The method involved a single extraction using 1:1 acetonitrile:water + 5% formic acid (1 ml per 10 mg tissue). Mean recoveries ranged from approximately 50 to 99 percent, and limits of detection ranged from 10 fg μl⁻¹ to 6900 fg μl⁻¹. To test the efficacy of the method, seeds of a susceptible maize line were inoculated with a pathogenic, fumonisin-producing strain of F. verticillioides. The seedlings were then harvested, and fumonisin content, as well as sphingoid bases and their 1-phosphates, were measured in the leaf and root tissues. Fumonisin accumulation was significantly greater in leaf one compared to leaves two and three. While FB₁, FB₂, and FB₃ were detected in root tissues, FB₁ was preferentially accumulated in leaf tissues. Accumulation of sphingoid bases and their 1-phosphates was evident in roots and leaves of seedlings grown from inoculated seed, with the level of accumulation being similar in leaves 1, 2 and 3. The method developed was effective, fast, and sensitive for use in simultaneously measuring fumonisin in tissues and their effects on sphingolipid metabolite biomarkers of disease. The method should be useful for screening maize cultivars for susceptibility to F. verticillioides-induced seedling diseases. Figure Lesion with chromatography     

Photosensitization of nanocrystalline TiO2 by self-assembled layers of CdS quantum dots

CdS quantum dots can be self-assembled on high surface area nanocrystalline TiO2 electrodes; spectroscopic and photoelectrochemical studies indicate that the size, and hence the absorption edge, of the CdS particles can be controlled; efficient photosensitization of the TiO2 electrode by the Q-particles has been achieved.