Fundamental solutions of homogeneous fully nonlinear elliptic equations

We prove the existence of two fundamental solutions Φ and of the PDE \input amssym $F(D^2\Phi) = 0 \quad {\rm in} \ {\Bbb{R}}^n \setminus \{ 0 \}$ for any positively homogeneous, uniformly elliptic operator F. Corresponding to F are two unique scaling exponents α*, > −1 that describe the homogeneity of Φ and . We give a sharp characterization of the isolated singularities and the behavior at infinity of a solution of the equation F(D²u) = 0, which is bounded on one side. A Liouville‐type result demonstrates that the two fundamental solutions are the unique nontrivial solutions of F(D²u) = 0 in \input amssym ${\Bbb{R}}^n \setminus \{ 0 \}$ that are bounded on one side in both a neighborhood of the origin as well as at infinity. Finally, we show that the sign of each scaling exponent is related to the recurrence or transience of a stochastic process for a two‐player differential game. © 2010 Wiley Periodicals, Inc.     

Initial complex associated to a jet scheme of a determinantal variety

We show in this paper that the principal component of the first-order jet scheme over the classical determinantal variety of m×n matrices of rank at most 1 is arithmetically Cohen-Macaulay, by showing that an associated Stanley-Reisner simplicial complex is shellable.     

Insight into on-wafer crystallization of pure-silica-zeolite films through nutrient replenishment

Tetraethylorthosilicate (TEOS) is added to a pure-silica-zeolite MEL nanoparticle suspension and the mixture is subsequently used for preparing spin-on low-dielectric constant (low-k) films. The films are then characterized by ellipsometric porosimetry, transmission electron microscopy (TEM), and nanoindentation. Investigation into the film microstructure indicates that the addition of TEOS significantly increases the fraction of the crystalline domains, decreases the inter-crystal mesopore size, and narrows the pore size distribution. Films with 12% TEOS loading have a mean pore size distribution centered at 3.5 nm (diameter) with a full width at half maximum (fwhm) of 0.8 nm, while those with no TEOS have a distribution at 11.1 nm and fwhm of 7.9 nm. At 12% TEOS loading, the reduced modulus and hardness are 11.0 and 1.12 GPa, respectively; without TEOS, the values are 6.4 and 0.57 GPa.     

Subcycle dynamics of electron–hole pairs and high-harmonic generation in bulk diamond subjected to intense femtosecond laser pulse

We present calculation of photoexcitation and high-harmonic generation in bulk diamond induced by intense near-infrared laser pulse of photon energy 1.55 eV, time duration of 15 fs and peak field strength \(F= 0.4\) V/Å. Depending on the laser polarization direction, the pulsed irradiation creates electron–hole pairs and transient density fluctuations in a localized region of the crystal momentum space. As a consequence energetic inter- and intra-band harmonics are generated with alternating phase during each half-cycle of the driving pulse. The corresponding inter- and intra-band currents are in definite phase relation with the laser pulse, reflecting the build-up of coherent superposition of population between valence and conduction bands, and the accelerated motion of charge carriers in their respective bands.     

Identification of structures of nitrogen-containing compounds in crude oils in conjunction with chemometric resolution

A universal method was established for the systematically structural identification of nitrogen-containing compounds in crude oils. Pre-fractionation of the non-hydrocarbons in a crude oil sample into 7 fractions was performed by di-adsorption column chromatography using neutral aluminum oxide and silica gel; subsequent high-resolution separation of individual components was achieved by using capillary column gas chromatography, and compound types were detected by mass spectrometer. The two-dimensional data from the compounds in the fractions were further resolved by a chemometric method to obtained the deconvoluted chromatogram and mass spectrum of every compound, and then, the nitrogen-containing compounds were identified in combination with the retention indices. This method could relieve the difficulty of classical analysis in identifying those species with very low contents or incompletely separation, particularly in the cases where the authentic standards were not available for addition into the unknown samples in order to reveal what indeed existed in them. The structures of 168 nitrogen-containing compounds in a crude oil sample were determined by this method with satisfactory results.     

A BiVO4 Photoanode with a VOx Layer Bearing Oxygen Vacancies Offers Improved Charge Transfer and Oxygen Evolution Kinetics in Photoelectrochemical Water Splitting

Sluggish oxygen evolution kinetics are one of the key limitations of bismuth vanadate (BiVO₄) photoanodes for efficient photoelectrochemical (PEC) water splitting. To address this issue, we report a vanadium oxide (VO_x) with enriched oxygen vacancies conformally grown on BiVO₄ photoanodes by a simple photo-assisted electrodeposition process. The optimized BiVO₄/VO_x photoanode exhibits a photocurrent density of 6.29 mA cm⁻² at 1.23 V versus the reversible hydrogen electrode under AM 1.5 G illumination, which is ca. 385 % as high as that of its pristine counterpart. A high charge-transfer efficiency of 96 % is achieved and stable PEC water splitting is realized, with a photocurrent retention rate of 88.3 % upon 40 h of testing. The excellent PEC performance is attributed to the presence of oxygen vacancies in VO_x that forms undercoordinated sites, which strengthen the adsorption of water molecules onto the active sites and promote charge transfer during the oxygen evolution reaction. This work demonstrates the potential of vanadium-based catalysts for PEC water oxidation.     

Estimation of quartz concentration in the tropospheric mineral aerosols using combined Raman and high-spectral-resolution lidars

A remote sensing method is presented that enables the determination of quartz concentration in mineral aerosols from simultaneously measured, high-spectral-resolution lidar and quartz Raman lidar signals.     

Kernel principal component analysis residual diagnosis (KPCARD): An automated method for cosmic ray artifact removal in Raman spectra

A new, fully automated, rapid method, referred to as kernel principal component analysis residual diagnosis (KPCARD), is proposed for removing cosmic ray artifacts (CRAs) in Raman spectra, and in particular for large Raman imaging datasets. KPCARD identifies CRAs via a statistical analysis of the residuals obtained at each wavenumber in the spectra. The method utilizes the stochastic nature of CRAs; therefore, the most significant components in principal component analysis (PCA) of large numbers of Raman spectra should not contain any CRAs. The process worked by first implementing kernel PCA (kPCA) on all the Raman mapping data and second accurately estimating the inter- and intra-spectrum noise to generate two threshold values. CRA identification was then achieved by using the threshold values to evaluate the residuals for each spectrum and assess if a CRA was present.     

A variational principle and best proximity points

We generalize Ekeland's Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.     

On‐Wafer Crystallization of Ultralow‐κ Pure Silica Zeolite Films

A higher goal : An on‐wafer crystallization process to prepare pure silica zeolite (PSZ) MEL‐type films that is superior to the previously used hydrothermal process is reported. These striation‐free MEL‐type films (right, see picture) outperform the traditional spin‐on films (left) in terms of the κ value, mechanical properties, surface roughness, mesopore size, and size distribution.