Sigma Models and Minimal Surfaces

Correspondence is established between sigma models, minimal surfaces and the Monge–Ampére equation. The Lax pairs of the minimality condition of the minimal surfaces and the Monge–Ampére equations are given. Existence of infinitely many nonlocal conservation laws is shown and some Bäcklund transformations are also given.     

A Study of Protein and Glycoprotein Syntheses in Pre-implantation Mouse Embryos Using Mini-2D-Electrophoresis, Video Densitometer Scanning and Computer-Image Analysis

In the present study, proteins and glycoproteins of mouse embryos at 2-cell,morula and blastocyst stages were analyzed.The techniques of ~(35)S-Met incorporation,ConA antiserum-precipitating ConA-binding proteins, mini-2D-electrophoresis, fluorography,video densitometer scanning and the computer-lmage system were used for analyses.Results of the investigations indicated that proteins and glycoproteins were synthesized by the embryos in a gradual increase manner from 2-cell to blastocyst. A relatively large amount of glycoproteins was synthesized during the morula and blastocyst stages.Two specific small glycoproteins respectively with molecular weights about 6500 and 9000 and PIs at 5.0 and 6.5 were apparently synthesized in the blastocyst but not in the 2-cell or the morula.     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Optimal convex hull algorithms on enhanced meshes

In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.This work was supported by NASA under grant NCCI-99.Additional support by the National Science Foundation under grant CCR-8909996 is gratefully acknowledged.     

Spectropolarised ray-tracing simulations in densely packed particulate medium

Light scattering from particulate medium is simulated using the Monte Carlo ray-tracing technique. The medium is modelled as a randomly packed medium of ellipsoidal grains with stochastically rough surfaces, with an optional thin coating. Optical properties are modelled using a wavelength-dependent complex refractive index and taking Fresnelian reflections and refractions from the interfaces. The size and shape of the grains are assumed to be large and smooth enough for geometric optics to apply reasonably well.The ray-tracing technique uses parallel, weighted rays for computing simultaneously over a wide wavelength spectrum and a small roughness range, and scaling to obtain a large range of sizes and absorbities simultaneously. Polarisation is fully accounted for. The multiobservation technique is effectively used at each scattering point. The scattering from thinner sample layers is also received as a subresult.Simulations are run for a set of model samples to study the effects and sensitivities regarding the values of certain parameters. It has been found that the size and composition of the grains affect the scattering in a unique and invertible way. The shape of the grain causes similar significant effects that must certainly be taken into account if any accuracy is required, although inverting for the shape is difficult without further constraints. The packing density has a small but observable effect. Polarisation can be used to study the composition of low-albedo objects.     

Exact boundary observability for 1‐D quasilinear wave equations

By means of a direct and constructive method based on the theory of semi‐global C² solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

Optical properties of Fe-doped silica films on Si

Optical properties of Fe-doped silica films on Si were investigated by ellipsometric technique in the region 1-5 eV. Samples were produced by sol-gel method. Precursors were prepared by mixing tetraethoxysilane (TEOS) solution in ethanol and water with aqueous solution of Fe-chloride or Fe-acetate. The coating solution was deposited on Si substrates by spin on technique. The size of Fe-containing nanometric-sized particles depended on technology and varied from 20 to 100 nm. Optical response of complex hybrid samples SiO₂:Fe/Si was interpreted in a multi-layer model. In the inverse problem, the Maxwell equations were solved by transfer matrix technique. Dielectric function of Fe-doped silica layers was calculated in the model of effective media. Analysis of optical data has shown that various Fe-oxides formed. Experimental data for films obtained from precursors with Fe-acetate and annealed in hydrogen were well described by the model calculations taking into account a small contribution 1-5% of metal Fe imbedded in silica. The Fe/Fe-O contribution to optical response increased for samples grown from FeCl₃-precursor. Ellipsometric data for Fe-doped silica films on Si were interpreted taking into account the structural AFM studies as well as the results of magnetic measurements.     

Validation of fuzzy logic method for automated mass spectral classification for mineral imaging

Imaging mass spectrometry requires the acquisition and interpretation of hundreds to thousands of individual spectra in order to map the mineral phases within heterogeneous geomatrices. A fuzzy logic inference engine (FLIE) was developed to automate data interpretation. To evaluate the strengths and limitations of FLIE, the chemical images obtained using FLIE were compared with those developed using two chemometric methods: principle component analysis (PCA) and cluster analysis (K-Means). Two heterogeneous geomatrices, a low-grade chalcopyrite ore and basalt, were imaged using a laser-desorption Fourier transform mass spectrometer. Similar mineral distribution patterns in the chalcopyrite ore sample were obtained by the three data analysis methods with most of the differences occurring at the interfaces between mineral phases. PCA missed one minor mineral phase in the chalcopyrite ore sample and did not clearly differentiate among the mineral classes of the basalt. K-Means cluster analysis differentiated among the various mineral phases in both samples, but improperly grouped some spectra in the chalcopyrite sample that only contained unanticipated high mass peaks. Unlike the chemometric methods, FLIE was able to classify spectra as unknowns for those spectra that fell below the confidence level threshold. A nearest neighbor approach, included in FLIE, was used to classify the unknowns to form a visually complete image; however, the unknowns identified by FLIE can be informative because they highlight potential problems or overlooked results. In conclusion, this study validated the fuzzy logic-based approach used in our laboratory and reveald some limitations in the three techniques that were evaluated.     

Electron attenuation lengths in fullerene and fullerides

Using X-ray photoemission measurements, we have determined the attenuation length of C 1s photoelectrons in C₆₀ film to be 21.5 Å with the incident photon energy of Mg Kα radiation. The inelastic mean free path calculated with the TPP-2M algorithm coincides fairly well with the experimentally determined attenuation length, indicating the validity of the algorithm to fullerene and fullerides. The inelastic mean free paths for some fullerides, i.e. K₃C₆₀, K₆C₆₀, Ba₄C₆₀, Sm_2.75C₆₀ and Sm₆C₆₀ are calculated to help the quantitative analyses of the photoemission spectra for these compounds.