Heat content and horizontal mean curvature on the Heisenberg group

We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van den Berg–Le Gall and van den Berg–Gilkey to the sub-Riemannian context, and identifies the first few coe?cients in the sub-Riemannian heat content in terms of the horizontal perimeter and the total horizontal mean curvature of the boundary. The proof is probabilistic, and relies on a characterization of the heat content in terms of Brownian motion.     

Determination of trace elements in marine plankton by inductively coupled plasma mass spectrometry (ICP-MS)

A method has been developed for the determination of 23 elements in marine plankton in which inductively coupled plasma (ICP) source mass spectrometry (MS) was used to quantify the elements in the solution after digestion in a mixture of hydrofluoric and nitric acids in sealed PTFE vessels in a microwave field. The procedure was validated by the analysis of a standard reference soil (SRM 2709 San Joaquin Soil) and a standard reference fresh water plankton (CRM 414). The method was applied to the analysis of several marine plankton samples grown under controlled conditions including several whose growth media had been enriched with selenium. Matrix induced signal suppressions and instrumental drift were corrected by internal standardization. The suitabilities of germanium, indium, rhodium, scandium and yttrium as internal standard elements were evaluated. Neither scandium nor yttrium could be used due to the presence of these elements in the samples, germanium was used for the determination of As, Co, Cu, Fe, Ni, Se, Si and Zn, indium was used for Al, Ba, Ca, Eu, Sr, and Tl, and rhodium was used for Cd, Cr, Hg, Mg, Pb, Sb, Sn, and V. For Al, Ca, Cr, Cu, Fe, Mg, Mn, Ni, Si, Sr, V, and Zn internal standardization did not completely compensate for the suppressive effect of the heavier elements and the solutions were diluted. However, for As, Ba, Cd, Co, Eu, Hg, Pb, Sb, Se, Sn and Tl, it was possible to obtain accurate results despite the 35–¶40% suppression in the signals. Isobaric overlap was only a problem in the cases of ⁴²Ca and ⁷⁸Se; ⁴⁴Ca and ⁷⁷Se, respectively, were used. Memory effects were only observed with Hg for which a nitric acid-sodium chloride solution was the most effective wash-out solution. The marine plankton samples were able to tolerate a higher concentration of Hg as the selenium concentration increased.     

Flow injection calibration techniques

Summary The role of calibration in the overall analytical procedure is discussed and the potential role of flow injection techniques are assessed. The factors affecting the dispersion obtained in a flow injection system are described and examples given of how control of the various factors can be exploited to produce manifolds for calibration purposes. Most of these examples concern atomic spectrometry methods for which there is considerable interest at present in developing extended range calibrations and flow injection versions of the standard additions method. Several examples of the latter are given.

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Anwendung der Fließinjektions-Technik für Eichmethoden

     

Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups

In any Carnot (nilpotent stratified Lie) group G of homogeneous dimension Q, Green's function u for the Q-Laplace equation exists and is unique. We prove that there exists a constant so that is a homogeneous norm in G. Then the extremal lengths of spherical ring domains (measured with respect to N) can be computed and used to give estimates for the extremal lengths of ring domains measured with respect to the Carnot-Carathéodory metric. Applications include regularity properties of quasiconformal mappings and a geometric characterization of bi-Lipschitz mappings. Received: 18 September 2000/ revised version: 19 November 2001 / Published online: 17 June 2002     

Structural effects on encapsulation as probed in redox-active core dendrimer isomers

Three pairs of isomeric, iron-sulfur core dendrimers were prepared. Each isomer pair was distinguished by a 3,5-aromatic substitution pattern (extended) versus 2,6-aromatic substitution pattern (backfolded). Several observations were made that supported the hypothesis that the iron-sulfur cluster cores were encapsulated more effectively in the backfolded isomers as compared to their extended isomeric counterparts. The backfolded isomers were more difficult to reduce electrochemically, consistent with encapsulation in a more hydrophobic microenvironment. Furthermore, heterogeneous electron-transfer rates for the backfolded molecules were attenuated compared to the extended molecules. From diffusion measurements obtained by pulsed field gradient spin-echo NMR and chronoamperometry, the backfolded dendrimers were found to be smaller than the extended dendrimers. Comparison of longitudinal proton relaxation (T(1)) values also indicated a smaller, more compact dendrimer conformation for the backfolded architectures. These findings indicated that the dendrimer size was not the major factor in determining electron-transfer rate attenuation. Instead, the effective electron-transfer distance, as determined by the relative core position and mobility in a dendrimer, is most relevant for encapsulation.     

Analytical selenoamino acid studies by chromatography with interfaced atomic mass spectrometry and atomic emission spectral detection

Consumption of selenium enriched plants or yeast-based nutritional supplements has been reported to provide anticarcinogenic benefits which are selenium compound dependent. Separation and identification of these selenium compounds is critical to understand the activity. Plants and yeast convert inorganic selenium in the soil or growth media into organoselenium compounds, probably following a route similar to the sulfur assimilatory pathway. Non-volatile selenium compounds produced include selenoamino acids, some of which have shown anticarcinogenic activity. Volatile compounds produced by chemical reaction of involatile precursors have also been found. An ion pair chromatographic method with ICP-MS detection for the separation of selenoamino acid standards potentially present in real samples is given. The method allows separation of selenoamino acids including such analytes as the cis-trans isomers of Se-1-propenyl-dl-selenocysteine. The method also provides the capability of determining the presence of selenoxides and possibly selenones, and tracking of other functionalities and reactions by selective derivatization. Alternatively, selenoamino acids are treated with ethylchloroformate to produce stable volatile derivatives which are amenable to GC separation with element specific atomic emission detection (GC-AED). Results of total selenium determination and speciation of selenium enriched yeast-based nutritional supplements, selenium enriched allium vegetables and bioremediation samples are presented. Received: 16 February 1998 / Revised: 4 June 1998 / Accepted: 9 June 1998     

Flow injection calibration methods for atomic absorption spectrometry

The use of an atomic absorption spectrometer as a detector in flow injection analysis is briefly reviewed. A new simplified model is described for the dispersion effects observed with such systems; the model is based on considering the dispersion to be due to a single hypothetical mixing chamber located immediately prior to the measurement stage. The utility of this approach is demonstrated for two methods of calibration commonly used in atomic absorption spectrometry, and it is shown that flow injection sample and standard handling techniques are comparable to manipulation with volumetric apparatus. The flow injection method has a number of advantages for the analogue of the standard addition method. The use of an exponential concentration gradient is proposed as a novel method of calibration using a single concentrated standard. Results are presented for the determination of chromium in standard steels.     

Putting the chemistry back into analytical chemistry

Aspects of the current status of and research in analytical chemistry are briefly discussed and the need for cost effective analytical procedures is emphasized. The present and future of a number of aspects of flow-injection analysis are considered. These include the basic theory, the kinetic features, the control features, time-based methodology, and the coupling of sample pretreatment with instrumentation. Several aspects of this latter topic are considered with particular reference to the flow-injection atomic spectrometry combination. Problems of kinetic mismatch between chemistry, manifold residence, and instrument operation are discussed and some possible solutions proposed including the use of closed loop manifolds.