Orthogonal polynomials for exponential weights on

Let I=[0,d), where d is finite or infinite. Let , where and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight , obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.     

Influence of Solution Volume on the Dissolution Rate of Silicon Dioxide in Hydrofluoric Acid

Experimental data and modeling of the dissolution of various Si/SiO₂ thermal coatings in different volumes of hydrofluoric acid (HF) are reported. The rates of SiO₂‐film dissolution, measured by means of various electrochemical techniques, and alteration in HF activity depend on the thickness of the film coating. Despite the small volumes (0.6–1.2 mL) of the HF solution, an effect of SiO₂‐coating thickness on the dissolution rate was detected. To explain alterations detected in HF activity after SiO₂ dissolution, spectroscopic analyses (NMR and FTIR) of the chemical composition of the solutions were conducted. This is associated with a modification in the chemical composition of the HF solution, which results in either the formation of an oxidized species in solution or the precipitation of dissolution products. HF₂^? accumulation in the HF solution, owing to SiO₂ dissolution was identified as the source of the chemical alteration.     

Non‐centrosymmetric plasmonic crystals for second‐harmonic generation with controlled anisotropy and enhancement

Rectangular arrays of pyramidal recesses coated by silver film are investigated by means of polarization‐resolved nonlinear microscopy at 900 nm fundamental wavelength, demonstrating strong dependence of the dipole‐allowed SHG upon the lattice parameters. The plasmonic band gap causes nearly complete SHG suppression in arrays of 650 nm periodicity, whereas a sharp resonance at 550 nm periodicity is observed due to excitation of band edge Bloch states at fundamental frequency, accompanied by symmetry‐constrained interactions with similar modes at the second‐harmonic frequency. Additionally, coupling with modes at the bottom side of the silver film may lead to extraordinary optical transmission, opening a channel for SHG from the highly nonlinear GaAs substrate. Changing the lattice geometry enables SHG intensity modulation over three orders of magnitude, while the effective nonlinear anisotropy can be continuously switched between the two lattice directions, reaching values as high as ±0.96.

     

Modern approaches to chemical toxicity screening

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Determination of phytic acid and inositolphosphates in barley

Phytic acid (PA) and lower inositolphosphates (InsP(n) ) is the main storage form of phosphorus in grains or seeds. The content of PA and InsP(n) in different varieties of barley was analyzed by capillary isotachophoresis and online-coupled capillary isotachophoresis with CZE. The electrolytes (in demineralized water) for the isotachophoretic analysis consisted of 10?mM HCl, 14?mM glycylglycine, and 0.1% 2-hydroxyethylcellulose (leading) and 10?mM citric acid (terminating). The optimized electrolytes for the online coupling isotachophoresis with zone electrophoresis analysis were mixtures of 5?mM HCl, 7?mM glycylglycine, and 0.1% 2-hydroxyethylcellulose (leading), 20?mM citric acid, 10?mM glycylglycine, and 0.1% 2-hydroxyethylcellulose (background) and 10?mM citric acid (terminating). PA and all studied InsP(n) were separated within 25?min and detected by a conductivity detector. Simple sample preparation (acidic extraction), sufficient sensitivity, speed of analysis, and low running cost are important attributes of the electrophoretic methods. The method was used for the determination of PA and InsP(n) in barley varieties within an ongoing research project.     

The porosity, acidity, and reactivity of dealuminated zeolite ZSM-5 at the single particle level: the influence of the zeolite architecture

A combination of atomic force microscopy (AFM), high‐resolution scanning electron microscopy (HR‐SEM), focused‐ion‐beam scanning electron microscopy (FIB‐SEM), X‐ray photoelectron spectroscopy (XPS), confocal fluorescence microscopy (CFM), and UV/Vis and synchrotron‐based IR microspectroscopy was used to investigate the dealumination processes of zeolite ZSM‐5 at the individual crystal level. It was shown that steaming has a significant impact on the porosity, acidity, and reactivity of the zeolite materials. The catalytic performance, tested by the styrene oligomerization and methanol‐to‐olefin reactions, led to the conclusion that mild steaming conditions resulted in greatly enhanced acidity and reactivity of dealuminated zeolite ZSM‐5. Interestingly, only residual surface mesoporosity was generated in the mildly steamed ZSM‐5 zeolite, leading to rapid crystal coloration and coking upon catalytic testing and indicating an enhanced deactivation of the zeolites. In contrast, harsh steaming conditions generated 5–50 nm mesopores, extensively improving the accessibility of the zeolites. However, severe dealumination decreased the strength of the Brønsted acid sites, causing a depletion of the overall acidity, which resulted in a major drop in catalytic activity.     

The Max-Flow Min-Cut theorem for countable networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.     

Nanodrop on a nanorough hydrophilic solid surface: contact angle dependence on the size, arrangement, and composition of the pillars

A two-dimensional nanodrop on a hydrophilic solid surface decorated with nanopillars is examined using a nonlocal density functional theory. It is shown that, in contrast to the commonly used Wenzel formula, even an extremely small roughness can considerably increase the contact angle. The contact angle depends on the distance between pillars, their height and width, as well as their composition. It was found that for all selected pillar heights and compositions, the largest contact angle is obtained when the distance between pillars acquires a size at which the liquid molecules can no longer penetrate between them. The further decrease in the interpillar distance decreases the contact angle, in qualitative agreement with the Cassie-Baxter formula. Considering pillars of various compositions, the role of the gradient of the fluid-solid interaction potential is examined. The presence of such a gradient does not allow the formation of a stable nanodrop on the surface. However, asymmetrical metastable nanodrops can be formed.