Counterexamples in calculus of variations in L∞ through the vectorial Eikonal equation

We show that, for any regular bounded domain $\mathrm{\Omega }?{\mathbb{R}}^n$, $n=2,3$, there exist infinitely many global diffeomorphisms equal to the identity on ?Ω that solve the Eikonal equation. We also provide explicit examples of such maps on annular domains. This implies that the ∞-Laplace system arising in vectorial calculus of variations in $L^{\infty }$ does not suffice to characterise either limits of p-Harmonic maps as $p\to \infty$ or absolute minimisers in the sense of Aronsson.     

Preparation and Characterization of Substituted 3‐Benzothiazol‐2‐Ylcoumarins

A series of substituted 3‐benzothiazolylcoumarins was prepared from condensation of 2‐hydroxy‐benzaldehyde and 2‐cyanomethylbenzothiazole to investigate the effect of the nature and position of substituents on their absorption and fluorescent behavior. Compounds with a substituent containing a heteroatom which attached at the C6 position showed a split broad absorption band. Solutions of these compounds in various solvents exhibited brilliant blue fluorescence. The emission intensity for compounds with an alkoxy group at the C6 or C7 position in DMF was approximately 7‐ and 15‐fold higher than for the corresponding precursor and quinine sulfate solution, respectively. These compounds also exhibit high thermal stability in solid state.     

A study of a liquid-filled lens module with a flexible sensor for aberration correction

This study introduces the concept of a liquid-filled lens module; the module is composed of a flexible lens membrane, a flexible sensor membrane that is constructed by attaching sensor chips onto a flexible substrate and transparent liquid that fills the space between the flexible lens membrane and the sensor membrane. The image quality of the liquid-filled lens module is comparable to that of a solid lens module with a flat-type image sensor. However, the liquid-filled lens module has the advantages of requiring fewer parts, having better optical aberration compensation, a wider image range. This study identifies the optimized conditions for the sensor membrane to fulfill the Petzval surface of the optical module and the compensation mechanism of the flexible lens and the sensor membranes. The simulation results show that the distortion aberration, the field of curvature and the Modulation Transfer Function are good.     

Porous gadolinia-doped ceria with adjustable pore sizes using PI-b-PEO copolymer as the structure-directing agent

In this study, we report that by coupling the kinetics of both hydrolysis and condensation of the oxide precursors and the kinetics of self-assembly process of the block copolymer, we can synthesize both mesoporous and macroporous gadolinia-doped ceria (GDC) with one chemical composition but different processing conditions. Our process uses poly(isoprene-b-ethylene oxide) as the structure-directing agent and cerium and gadolinium acetylacetonates as the precursors for the sol?Cgel synthesis of GDC. By controlling the extent of the hydrolysis and condensation of the oxide precursor before mixing with the copolymer, we can adjust the hydrophilic domain size from nanometers to micrometers. As a result, highly crystalline porous GDC with dominant mesopores (15?nm?<?d?<?50?nm) or macropores (50?nm?<?d?<?5???m) are produced after removal of the copolymer via a two-step calcination treatment. The discovery of this study offers a facile and viable approach to produce meso- and macro-porous materials, in a ??one-pot?? synthesis with one chemical composition but different processing conditions to control pore sizes.     

Phase signature for particle detection with digital in-line holography

The spatial phase resulting from the digital reconstruction of an in-line hologram of a particle field is shown to yield a unique pattern that can be used for particle detection. This phase signature is present only when viewed along with the reference light. The existence of the phase pattern is verified computationally and confirmed in laboratory experiments with holograms of calibrated glass spheres. The phase signature provides an alternative to the widely used intensity method for particle detection.     

The potential of CO2 laser photoacoustic spectrometry for?detection of methanol in alcoholic beverage

The first use of CO₂ laser photoacoustic measurements for detecting the methanol contents in alcohol-like solutions is presented. With an intracavity cell configuration, the minimum detectable concentration was ∼200 ppm for methanol and the linear range of the calibration curve for methanol was from 200 to 70000 ppm. For demonstrating the reliability of analysis in alcoholic beverages, a series of different concentrations of two-component samples was prepared and measured by the same procedures. The results showed the feasibility on determining methanol and ethanol contents accurately within a specific tolerance, limited mainly by background signal and laser stability. This potential method with no pre-treatment of samples takes only ∼10 min to finish one single measurement. It suggests that the PA detection is suitable for routine diagnosis of adulterated wines in commercial products.     

Flexible statistical modelling detects clinical functional magnetic resonance imaging activation in partially compliant subjects

Clinical functional magnetic resonance imaging (fMRI) occasionally fails to detect significant activation, often due to variability in task performance. The present study seeks to test whether a more flexible statistical analysis can better detect activation, by accounting for variance associated with variable compliance to the task over time. Experimental results and simulated data both confirm that even at 80% compliance to the task, such a flexible model outperforms standard statistical analysis when assessed using the extent of activation (experimental data), goodness of fit (experimental data), and area under the operator characteristic curve (simulated data). Furthermore, retrospective examination of 14 clinical fMRI examinations reveals that in patients where the standard statistical approach yields activation, there is a measurable gain in model performance in adopting the flexible statistical model, with little or no penalty in lost sensitivity. This indicates that a flexible model should be considered, particularly for clinical patients who may have difficulty complying fully with the study task.     

Direct laser interference patterning of poly(3,4-ethylene dioxythiophene)-poly(styrene sulfonate) (PEDOT-PSS) thin films

We have developed a patterning procedure based on selective ablation using interference patterns with ns-laser pulses to fabricate periodic arrays on large areas of poly(3,4-ethylene dioxythiophene)-poly(4-styrene sulfonic acid) (PEDOT-PSS) thin films over a metallic gold–palladium layer. Single pulse laser-ablation experiments were performed to study the ablation characteristics of the thin films as a function of the film thickness. The ablation threshold fluence of the PEDOT-PSS films was found to be dependent on thickness with values ranging from 43 mJ/cm² to 252 mJ/cm². Additionally, fluences at which the PEDOT-PSS films could be ablated without inducing damage in the underlying metallic films were observed (128 mJ/cm² and 402 mJ/cm² for film thicknesses of 70 nm and 825 nm, respectively). Linear periodic arrays with line spacings of 7.82 μm and 13.50 μm were also fabricated. The surface topography of these arrays was analyzed using scanning electron and atomic force microscopy. For thicker polymeric layers, several peeled sub-layers of the conjugated polymer with average thicknesses of about 165–185 nm were observed in the ablation experiments. The size and scale of structures produced by this technique could be suitable for several biomedical applications and devices in which controlling cell adhesion, promoting cell alignment, or improving biocompatibility are important.     

The effect of word learning on the perception of non-native consonant sequences

Previous research in cross-language perception has shown that non-native listeners often assimilate both single phonemes and phonotactic sequences to native language categories. This study examined whether associating meaning with words containing non-native phonotactics assists listeners in distinguishing the non-native sequences from native ones. In the first experiment, American English listeners learned word-picture pairings including words that contained a phonological contrast between CC and CVC sequences, but which were not minimal pairs (e.g., [ftake], [ftalu]). In the second experiment, the word-picture pairings specifically consisted of minimal pairs (e.g., [ftake], [ftake]). Results showed that the ability to learn non-native CC was significantly improved when listeners learned minimal pairs as opposed to phonological contrast alone. Subsequent investigation of individual listeners revealed that there are both high and low performing participants, where the high performers were much more capable of learning the contrast between native and non-native words. Implications of these findings for second language lexical representations and loanword adaptation are discussed.