Completeness of the Grid Translates of Functions

If $f\in L^{p}(\mathbb{R}^{d})$ is a bounded real valued continuous function which has a unique maximum or a unique minimum at a point $x_{0}\in \mathbb{R}^{d}$ and if the inverse image of the neighborhoods of f(x ₀) shrinks regularly to x ₀, then $\mathrm{ span }\{f^{m}(x-2^{-m}\varSigma_{i=1}^{d} j_{i} e_{i})\mid m\in\mathbb{N}, j_{i}\in\mathbb{Z}\}$ is a dense subset of $L^{p}(\mathbb{R}^{d}), 1\le p<\infty$ where f ^m (x)=f(x) ^m and {e _i } is the natural basis of $\mathbb{R}^{d}$ . The result extends to all homogeneous groups, Riemannian symmetric spaces of noncompact type, Damek-Ricci spaces etc.     

Highly Converged Valence Bands and Ultralow Lattice Thermal Conductivity for High‐Performance SnTe Thermoelectrics

A two‐step optimization strategy is used to improve the thermoelectric performance of SnTe via modulating the electronic structure and phonon transport. The electrical transport of self‐compensated SnTe (that is, Sn_1.03Te) was first optimized by Ag doping, which resulted in an optimized carrier concentration. Subsequently, Mn doping in Sn_1.03?xAg_xTe resulted in highly converged valence bands, which improved the Seebeck coefficient. The energy gap between the light and heavy hole bands, i.e. ΔE_v decreases to 0.10 eV in Sn_0.83Ag_0.03Mn_0.17Te compared to the value of 0.35 eV in pristine SnTe. As a result, a high power factor of ca. 24.8 μW cm^?1 K^?2 at 816 K in Sn_0.83Ag_0.03Mn_0.17Te was attained. The lattice thermal conductivity of Sn_0.83Ag_0.03Mn_0.17Te reached to an ultralow value (ca. 0.3 W m^?1 K^?1) at 865 K, owing to the formation of Ag₇Te₄ nanoprecipitates in SnTe matrix. A high thermoelectric figure of merit (z T≈1.45 at 865 K) was obtained in Sn_0.83Ag_0.03Mn_0.17Te.     

Electrochemically Tunable Proton-Coupled Electron Transfer in Pd-Catalyzed Benzaldehyde Hydrogenation

Acid functionalization of a carbon support allows to enhance the electrocatalytic activity of Pd to hydrogenate benzaldehyde to benzyl alcohol proportional to the concentration of Brønsted-acid sites. In contrast, the hydrogenation rate is not affected when H₂ is used as a reduction equivalent. The different responses to the catalyst properties are shown to be caused by differences in the hydrogenation mechanism between the electrochemical and the H₂-induced hydrogenation pathways. The enhancement of electrocatalytic reduction is realized by the participation of support-generated hydronium ions in the proximity of the metal particles.     

Application of TXRF for burn leach test of TRISO coated UO2 particles

A Total Reflection X-Ray Fluorescence (TXRF) methodology, employing burn-leach test, was developed to assess the quality of SiC layer in tristructural isotropic (TRISO) coated UO₂ particles prepared in BARC. The coated particles were heated at 1,123 K for about 96 h to constant weight. The calcined particles, thus obtained, were then heated in suprapure concentrated nitric acid. The supernatant was analysed for trace elements by TXRF. No uranium was detected in this supernatant solution. The study demonstrates the good quality of SiC layer and applicability of TXRF for burn leach test of TRISO coated UO₂ particles prepared.     

A Self-Consistent Model for Sorption and Transport in Polyimide-Derived Carbon Molecular Sieve Gas Separation Membranes

Demand for energy-efficient gas separations exists across many industrial processes, and membranes can aid in meeting this demand. Carbon molecular sieve (CMS) membranes show exceptional separation performance and scalable processing attributes attractive for important, similar-sized gas pairs. Herein, we outline a mathematical and physical framework to understand these attributes. This framework shares features with dual-mode transport theory for glassy polymers; however, physical connections to CMS model parameters differ from glassy polymer cases. We present evidence in CMS membranes for a large volume fraction of microporous domains characterized by Langmuir sorption in local equilibrium with a minority continuous phase described by Henry's law sorption. Using this framework, expressions are provided to relate measurable parameters for sorption and transport in CMS materials. We also outline a mechanism for formation of these environments and suggest future model refinements.     

Influence of pH and organic modifiers on the dissociation constants of selected drugs using reversed‐phase thin‐layer chromatography: Comparison with other techniques and computational tools

Knowledge of the acid–base dissociation constants of drugs is the key to understanding their biopharmaceutical characteristics. In the present work, the effect of pH and organic modifiers (acetonitrile and methanol) was investigated in the determination of dissociation constants (pK_a) of nine representative drugs (atenolol, betahistine, clarithromycin, deferiprone, diclofenac, ibuprofen, metoprolol, naproxen and propranolol) using reversed‐phase thin‐layer chromatography. Mobile phase consisting of various buffers and methanol–acetonitrile (10, 20, 30, 40, 50 and 60%, v/v) was used to evaluate the retention pattern on reversed‐phase plates. Compared with methanol, acetonitrile gave better results for the experimentally determined pK_a values by extrapolation to zero organic modifier volume fractions. To assess the effectiveness of the developed method the results were correlated using principal component analysis and hierarchical cluster analysis. The calculated values of the aqueous dissociation constant were compared with those reported previously using potentiometry and capillary electrophoresis and also with different computational platforms like ACD/Lab, ChemAxon and Jchem calculator. The results obtained by the RPTLC method were in good agreement with potentiometric methods for pK_a determination.     

High-pressure behaviour and elastic properties of heavy rare-earth Gd monopnictides

Pressure-induced structural phase transition of gadolinium monopnictides GdX (X=As and Sb) has been studied theoretically using an inter-ionic potential theory. This method has been found quite satisfactory in case of the pnictides of rare-earth and describes the crystal properties in the framework of rigid-ion model. We have modified the ionic charge so that it may include the Coulomb-screening effect by the delocalization of f electron of the rare-earth ion. The anomalous structural properties of these compounds with many f electrons have been interpreted in terms of the hybridization of f electrons with the conduction band and strong mixing of f states of Gd ion with the p orbital of neighbouring pnictogen ion. Both the compounds are found to undergo from their initial NaCl (B₁) structure to body centered tetragonal (BCT) structure at high pressure and agree well with the experimental results. The BCT structure is viewed as distorted CsCl structure and is highly anisotropic with c/a=0.82–0.85. The nature of bonds between the ions is predicted by simulating the ion–ion (Gd–Gd and Gd–X) distance at high pressure. Elastic properties of these compounds have also been studied with their second-order elastic constants.     

Analysis of wavy flow and blood oxygenation in two-dimensional channels with constriction

A steady wavy incompressible Newtonian fluid flow in a channel with irregular surfaces is studied to understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels. Analytical solutions are obtained under the assumption that the spread of the surface roughness to be large compared to the mean width of the channel. Expressions for the stream function, vorticity, the wall shear stress distribution and viscous energy loss per unit cycle are derived and the effects of various pertinent parameters upon them have been investigated for symmetric and non-symmetric channels with graphical representations. In order to determine the effects of the wall roughness upon the blood oxygenation in a membrane oxygenator, the haemodynamical solution is used. It is found that oxygen concentration increases with increase of channel constriction due to increase of cell-plasma and cell-cell interaction as well as waviness of flow field and this is predicted graphically.