Geodesics on the regular tetrahedron and the cube

Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern–Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics between certain pairs of vertices than other pairs. We also obtain the fact that there are no geodesics that start and end at the same vertex on the regular tetrahedron or the cube.     

Characterization of superabsorbing polymers by NMR imaging

 The use of NMR imaging techniques for the characterization of superabsorbing polymers is explored. Spatial differences in the cross-link densities of polyacrylate-based superabsorbing particles are investigated by parameter-selective ¹H NMR imaging of samples swollen with water. Images of the transverse relaxation time and of the self-diffusion coefficient of the absorbed water provide valuable information on the local water mobility and, thus, indirectly also on the polymer. The time evolution of the swelling process was also studied by NMR images acquired after different swelling times. Moreover, using magic-angle-spinning imaging, the influence of mechanical load on the swollen particle was investigated by taking advantage of the centrifugal forces on the spinning sample. These experiments indicate the presence of two water components, one strongly adsorbed, while the other is relatively mobile. Received: 2 November 1999 Accepted: 17 December 1999     

An analysis of the shiftedLR algorithm

Summary We introduce and analyze generalized shift strategies for theLR algorithm and prove that these strategies are generalizations of classical iterations for non-linear equations. We also study how certain matrix functions transform under theLR algorithm.This paper is based on work done while T. J. Dekker was visiting Bell Telephone Laboratories, Incorporated.Some of the material in this paper was presented by J. F. Traub in an invited talk at the Gatlinburg Symposium on Numerical Algebra, April 1969.     

High-resolution X-ray photoelectron spectroscopic studies of alkylated silicon(111) surfaces

Hydrogen-terminated, chlorine-terminated, and alkyl-terminated crystalline Si(111) surfaces have been characterized using high-resolution, soft X-ray photoelectron spectroscopy from a synchrotron radiation source. The H-terminated Si(111) surface displayed a Si 2p(3/2) peak at a binding energy 0.15 eV higher than the bulk Si 2p(3/2) peak. The integrated area of this shifted peak corresponded to one equivalent monolayer, consistent with the assignment of this peak to surficial Si-H moieties. Chlorinated Si surfaces prepared by exposure of H-terminated Si to PCl5 in chlorobenzene exhibited a Si 2p(3/2) peak at a binding energy of 0.83 eV above the bulk Si peak. This higher-binding-energy peak was assigned to Si-Cl species and had an integrated area corresponding to 0.99 of an equivalent monolayer on the Si(111) surface. Little dichloride and no trichloride Si 2p signals were detected on these surfaces. Silicon(111) surfaces alkylated with CnH(2n+1)- (n = 1 or 2) or C6H5CH2- groups were prepared by exposing the Cl-terminated Si surface to an alkylmagnesium halide reagent. Methyl-terminated Si(111) surfaces prepared in this fashion exhibited a Si 2p(3/2) signal at a binding energy of 0.34 eV above the bulk Si 2p(3/2) peak, with an area corresponding to 0.85 of a Si(111) monolayer. Ethyl- and C6H5CH2-terminated Si(111) surfaces showed no evidence of either residual Cl or oxidized Si and exhibited a Si 2p(3/2) peak approximately 0.20 eV higher in energy than the bulk Si 2p(3/2) peak. This feature had an integrated area of approximately 1 monolayer. This positively shifted Si 2p(3/2) peak is consistent with the presence of Si-C and Si-H surface functionalities on such surfaces. The SXPS data indicate that functionalization by the two-step chlorination/alkylation process proceeds cleanly to produce oxide-free Si surfaces terminated with the chosen alkyl group.     

Q branches in the rotational spectrum of HOC1

We have obtained the far-i.r. rotational spectrm of HOCI from 70–263 cm^?1. The most prominent features of the rotational spectrum are the Q branches, for which we have measured positions. Statistical strengths for the Q branches ave been calculated and μβ, the component of the dipole moment that allows Q branch transitions has been determined from P and R branch line intensities. We find μβ = 1.4 ± 0.2 D. We also calculate Q branch strengths and shifts at stratospheric temperature.     

Relating surface-enhanced Raman scattering signals of cells to gold nanoparticle aggregation as determined by LA-ICP-MS micromapping

The cellular response to nanoparticle exposure is essential in various contexts, especially in nanotoxicity and nanomedicine. Here, 14-nm gold nanoparticles in 3T3 fibroblast cells are investigated in a series of pulse-chase experiments with a 30-min incubation pulse and chase times ranging from 15 min to 48 h. The gold nanoparticles and their aggregates are quantified inside the cellular ultrastructure by laser ablation inductively coupled plasma mass spectrometry micromapping and evaluated regarding the surface-enhanced Raman scattering (SERS) signals. In this way, both information about their localization at the micrometre scale and their molecular nanoenvironment, respectively, is obtained and can be related. Thus, the nanoparticle pathway from endocytotic uptake, intracellular processing, to cell division can be followed. It is shown that the ability of the intracellular nanoparticles and their accumulations and aggregates to support high SERS signals is neither directly related to nanoparticle amount nor to high local nanoparticle densities. The SERS data indicate that aggregate geometry and interparticle distances in the cell must change in the course of endosomal maturation and play a critical role for a specific gold nanoparticle type in order to act as efficient SERS nanoprobe. This finding is supported by TEM images, showing only a minor portion of aggregates that present small interparticle spacing. The SERS spectra obtained after different chase times show a changing composition and/or structure of the biomolecule corona of the gold nanoparticles as a consequence of endosomal processing.     

Evaluation of different calibration strategies for the analysis of pure copper and zinc samples using femtosecond laser ablation ICP-MS

Solution-doped metal powder pellets as well as aspirated liquids were used as calibration samples to analyze pure copper and zinc certified reference materials (CRMs) by femtosecond laser ablation ICP-MS. It was demonstrated that calibration by copper pellets resulted in relative deviations up to 20%, whereas fs-LA-ICP-MS among copper-based CRMs led to inaccuracies in the same range unless nominal mass fractions were chosen to be <3 mg/kg. Calibration by zinc pellets generally provided better accuracy. Depending on the analyte considered, deviations below 10% were obtained even for mass fractions close to the limit of quantification. Our data, therefore, indicate solution-doped metal powder pellets to be suitable as calibration samples for fs-LA-ICP-MS of metals. Furthermore, the utilization of liquid standards for calibration was found to result in stronger deviations of up to 50% for both copper and zinc samples which, in addition, turned out to be dependent on the plasma conditions.