Compact causal data interpolation

Consider a Hilbert space equipped with a time-structure, i.e., a resolution E of the identity on defined on subsets of some linearly ordered set Λ. For which x and y in is it possible to find a causal (time respecting) compact operator T, so that Tx = y? When T is required to be a Hilbert-Schmidt operator and (Λ, E) is sufficiently regular, this question is answered in terms of the “time-densities” of x and y. The condition is that the integral ∝_gLμ_x({s t})⁻¹ dμ_y(t) should be finite, where μ_x and μ_y are the measures on Λ given by μ_x(Ω) = ¦|E(Ω)x¦|² and μ_y(Ω) = ¦|E(Ω)y¦|². Further a solution is given for the related problem of minimizing the sum of ¦|Tx − y¦|² and the squared Hilbert-Schmidt norm ¦|R¦|₂² of T.     

Phenolic compounds,essential oil composition,and antioxidant activity of Angelica purpurascens (Avé-Lall.) Gill

In this study, methanol extracts (MEs) and essential oil (EO) of Angelica purpurascens (Avé-Lall.) Gill obtained from different parts (root, stem, leaf, and seed) were evaluated in terms of antioxidant activity, total phenolics, compositions of phenolic compound, and essential oil with the methods of 2,2-azino-bis(3ethylbenzo-thiazoline-6-sulfonic acid (ABTS•⁺), 2,2-diphenyl-1-picrylhydrazil (DPPH•) radical scavenging activities, and ferric reducing/antioxidant power (FRAP), the Folin–Ciocalteu, liquid chromatography−tandem mass spectrometry (LC−MS/MS), and gas chromatography-mass spectrometry (GC−MS), respectively. The root extract of A. purpurascens exhibited the highest ABTS•⁺, DPPH•, and FRAP activities (IC₅₀: 0.05 ± 0.0001 mg/mL, IC₅₀: 0.06 ± 0.002 mg/mL, 821.04 ± 15.96 µM TEAC (Trolox equivalent antioxidant capacity), respectively). Moreover, EO of A. purpurascens root displayed DPPH• scavenging activity (IC₅₀: 2.95 ± 0.084 mg/mL). The root extract had the highest total phenolic content (438.75 ± 16.39 GAE (gallic acid equivalent), µg/mL)). Twenty compounds were identified by LC−MS/MS. The most abundant phenolics were ferulic acid (244.39 ± 15.64 μg/g extract), benzoic acid (138.18 ± 8.84 μg/g extract), oleuropein (78.04 ± 4.99 μg/g extract), and rutin (31.21 ± 2.00 μg/g extract) in seed, stem, root, and leaf extracts, respectively. According to the GC−MS analysis, the major components were determined as α-bisabolol (22.93%), cubebol (14.39%), α-pinene (11.63%), and α-limonene (9.41%) among 29 compounds. Consequently, the MEs and EO of A. purpurascens can be used as a natural antioxidant source.     

Enhanced ethanol sensing properties of WO3 modified TiO2 nanorods

Pristine and WO₃ decorated TiO₂ nanorods (NRs) were synthesised to investigate n-n-type heterojunction gas sensing properties. TiO₂ NRs were fabricated via hydrothermal method on fluorine-doped tin oxide coated glass (FTO) substrates. Then, tungsten was sputtered on the TiO₂ NRs and thermally oxidised to obtain WO₃ nanoparticles. The heterostructure was characterised by X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDX) spectroscopy. Fabricated sensor devices were exposed to VOCs such as toluene, xylene, acetone and ethanol, and humidity at different operation temperatures. Experimental results demonstrated that the heterostructure has better sensor response toward ethanol at 200 °C. Enhanced sensing properties are attributed to the heterojunction formation by decorating TiO₂ NRs with WO₃.     

Investigation of Relationships between Grain Structure and Inhomogeneous Deformation by Means of Laboratory-Based Multimodal X-Ray Tomography: Strain Accuracy Analysis

Experimental Mechanics - The internal strain distribution developing during plastic deformation is important for understanding the mechanical properties of polycrystalline materials. Such...     

Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source

A coherent anti-Stokes Raman scattering microscope based on a Ti:sapphire femtosecond oscillator and a photonic crystal fiber is demonstrated. The nonlinear response of the fiber is used to generate the additional wavelength needed in the Raman process. The applicability of the setup is demonstrated by imaging of micrometer-sized polystyrene beads.     

A study of the interaction between perylene and the TiO2(1 1 0)-(1 × 1) surface-based on XPS, UPS and NEXAFS measurements

The interaction between a semi-large aromatic hydrocarbon compound (perylene) and the TiO₂(1 1 0)-(1 × 1) surface under ultra high vacuum conditions has been probed by X-ray photoemission spectroscopy (XPS), ultraviolet photoemission spectroscopy (UPS) and near-edge X-ray absorption fine structure (NEXAFS) methods. UPS measurements of the adsorbate system have been compared with an experimental UPS spectrum of perylene in the gas phase and a calculated spectrum obtained by means of density functional theory (DFT) methods. NEXAFS results of perylene molecules adsorbed on TiO₂(1 1 0)-(1 × 1) were compared with data from an α-phase perylene single crystal. A novel analysis of the valence data has been employed to show that no strong chemical interaction takes place between perylene and the TiO₂(1 1 0)-(1 × 1) surface. Furthermore, angle-dependent NEXAFS measurements and the growth curve results suggest that the perylene molecules are oriented flat down onto the TiO₂ substrate due to weak van der Waals interactions.     

Similarity structure of wave-collapse

Similarity transformations of the cubic Schrödinger equation (CSE) are investigated. The transformations are used to remove the explicit time variation in the CSE and reduce it to differential equations in the spatial variables only. Two different methods for similarity reduction are employed and the significance of similarity in the evolution of a collapsing wave packet is investigated. Numerical solutions in radial symmetry demonstrate that the similarity behaviour is local in space and time, and that some similarity solutions must be classified as improper solutions. The nature of the collapsing singularity is reexamined.     

A nitrate-selective microelectrode based on a lipophilic derivative of iodocobalt(III)salen

The synthesis of iodo{2,2′-[1,2-octadecanediylbis(nitrilomethylidyne)]diphenolato}cobalt is described. Liquid membrane microelectrodes based on this carrier exhibit Nernstian behaviour with a selectivity sequence according to the Hofmeister series: I^– > NO₃ ^– > NO₂ ^– > Cl^– > HCO₃ ^– > AcO^–. The selectivity coefficient of nitrate over nitrite and chloride amounts to –1.6 and –2.7, respectively. The detection limit for nitrate in water amounts to 10^–5.2 mol/L. A nitrate profile measured in a nitrifying biofilm is presented as a practical application. Received: 11 November 1998 / Revised: 22 January 1999 / Accepted: 27 January 1999     

Iron oxide thin film growth on Al2O3/NiAl(1 1 0)

The electronic structure and the growth morphology of iron oxide thin films were studied by means of Synchrotron Radiation Photoelectron Spectroscopy (SRPES) and Low Energy Electron Diffraction (LEED). A thin well-ordered alumina film on a NiAl(1 1 0) single crystal surface as a template for iron oxide growth was employed. Two different methods of iron oxide film preparation were applied. In the first attempt, iron deposited at room temperature was subsequently annealed in oxygen. Even though a whole layer of iron was oxidized, an expected long-range order was not achieved. The second attempt was to perform reactive deposition. For this reason iron was evaporated in oxygen ambient at elevated substrate temperature. This method turned out to be more efficient. Diffused but clear LEED patterns of six-fold symmetry indicating hexagonal surface atoms arrangement were observed. From the PES measurements, binding energies for Fe2p for grown iron oxide film were established as well as energy distribution curves for the valence band. Growth curves based on Fe3p core-level peak intensities for iron and iron oxide were plotted identifying type of film growth for both deposition methods. Based upon these results we have found evidence for interdiffusion in the interface between alumina and iron oxide at the early stages of growth. Further deposition led to formation of Fe₃O₄(1 1 1) (magnetite) overlayer. Moreover, the quality of the film could also be improved by long-time annealing at temperatures not exceeding 575 K. Higher annealing temperature caused disappearance of LEED pattern indicating loss of long-range ordering.     

Computations of intermittent transport in scrape-off layer plasmas

Two-dimensional fluid simulations of interchange turbulence for geometry and parameters relevant for the scrape-off layer of magnetized plasmas are presented. The computations, which have distinct plasma production and loss regions, reveal bursty ejection of particles and heat from the bulk plasma in the form of blobs. These structures propagate far into the scrape-off layer where they are dissipated due to transport along open magnetic field lines. From single-point recordings it is shown that the blobs have asymmetric conditional wave forms and lead to positively skewed and flattened probability distribution functions. The radial propagation velocity may reach one-tenth of the sound speed. These results are in excellent agreement with recent experimental measurements.