On the orthogonality of the phase velocity and its feasibility for plane waves

Phase and group velocities of plane waves may have different directions in a linear and homogeneous medium. This difference may lead to interesting situations such as the phase reversal propagation and the orthogonal phase velocity. Although the former has been analyzed in depth and it has found many applications, the latter has been left as a hypothesis. Actually, due to our best knowledge there is no evidence of such media where the phase velocity is orthogonal to the group velocity. In this paper we discuss this situation thoroughly. We show that a plane wave with orthogonal phase velocity cannot possess linear momentum. Moreover, we show that a plane wave without the linear momentum cannot propagate at all, so the orthogonality of the phase velocity does not take place in reality for electromagnetic plane waves.     

On the encapsulation of azafullerenes inside the single-walled carbon nanotubes: Density-functional theory based treatments

We theoretically studied the encapsulation of azafullerene (C₅₉N) inside the single-walled carbon nanotubes (SWCNTs) from the first-principles. Adsorption energy is calculated, and the azafullerene affinities for the typical semiconducting and metallic nanotubes are investigated and compared with those of pure C₆₀ fullerene. It has been found that the azafullerene as well as the fullerene affinity for the semiconducting nanotubes is stronger than that for the metallic ones, and the energy values and binding distances are typical for the physisorption. Our first-principles results indicate that the interaction between SWCNTs and azafullerenes is comparable with the nanotubes-C₆₀ system. The charge analysis shows, however, that the charges have been transferred from the cage to the tube in the azafullerene peapods, while in the fullerene peapods the charges were found to be transferred from the tube to the fullerene nanocage. Furthermore, it was found that the interaction between the considered fullerenes and host nanotubes strongly depends on the tube diameters.     

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption linings are modeled as a bulk media with a complex speed of sound and mean density. Domain decomposition and parallel processing techniques are applied to address the high computational and memory requirements. The comparison of the computationally predicted and the experimentally measured transmission loss shows a good agreement.     

Preparation,characterization and application of 1,4-disulfopiperazine-1,4-diium chloride ([Piper-(SO<Subscript>3</Subscript>H)<Subscript>2</Subscript>]·2Cl) as an efficient dicationic ionic catalyst for the <Emphasis Type="Italic">N</Emphasis>-Boc protection of amines

In this work, 1,4-disulfopiperazine-1,4-diium chloride ([Piper-(SO₃H)₂]·2Cl), as a novel Brönsted acidic ionic catalyst is synthesized and characterized using a series of techniques including FT-IR, TGA, DTA, SEM, pH analysis and Hammett acidity function. This substance can significantly catalyze the N-Boc protection of amines without solvent interference at room temperature. The advantages of this manner are chemoselectivity, short reaction times, suitable yields, excellent yields of the products, without solvent interference and ease of preparation as well as reusability of the catalyst.     

A polyaniline-magnetite nanocomposite as an anion exchange sorbent for solid-phase extraction of chromium(VI) ions

This work describes a novel polyaniline-magnetite nanocomposite and its application to the preconcentration of Cr(VI) anions. The material was obtained by oxidative polymerization of aniline in the presence of magnetite nanoparticles. The parameters affecting preconcentration were optimized by a Box-Behnken design through response surface methodology. Extraction time, amount of magnetic sorbent and pH value were selected as the main factors affecting sorption. The sorption capacity of the sorbent for Cr(VI) is 54 mg g⁻¹. The type, volume and concentration of the eluents, and the elution time were selected as main factors in the optimization study of the elution step. Following sorption and elution, the Cr(VI) ions were reacted with diphenylcarbazide, and the resulting dye was quantified by HPLC with optical detection at 546 nm. The limit of detection is 0.1 μg L⁻¹, and all the relative standard deviations are <6.3 %. The nanocomposite was successfully applied to the rapid extraction and determination of trace quantities of Cr(VI) ions in spiked water samples.

A schematic procedure of magnetic solid phase extraction

     

A polyaniline-magnetite nanocomposite as an anion exchange sorbent for solid-phase extraction of chromium(VI) ions

This work describes a novel polyaniline-magnetite nanocomposite and its application to the preconcentration of Cr(VI) anions. The material was obtained by oxidative polymerization of aniline in the presence of magnetite nanoparticles. The parameters affecting preconcentration were optimized by a Box-Behnken design through response surface methodology. Extraction time, amount of magnetic sorbent and pH value were selected as the main factors affecting sorption. The sorption capacity of the sorbent for Cr(VI) is 54 mg g^?1. The type, volume and concentration of the eluents, and the elution time were selected as main factors in the optimization study of the elution step. Following sorption and elution, the Cr(VI) ions were reacted with diphenylcarbazide, and the resulting dye was quantified by HPLC with optical detection at 546 nm. The limit of detection is 0.1 μg L^?1, and all the relative standard deviations are <6.3 %. The nanocomposite was successfully applied to the rapid extraction and determination of trace quantities of Cr(VI) ions in spiked water samples. Figure

A schematic procedure of magnetic solid phase extraction     

Adsorption of Metanil Yellow Azoic Dye from Aqueous Solution onto Mg‐Fe‐NO3 Layered Double Hydroxide

We report the preparation and characterization of a layered double hydroxide (LDH) adsorbent for azoic dye, metanil yellow (yellow GX; YGX) removal. The nanoparticles of Mg‐Fe‐LDH‐NO₃ adsorbent were prepared with Mg/Fe molar ratio of 3:1 by a hydrothermal process and coprecipitation method at pH 9.5 and were characterized by X‐ray powder diffraction (XRPD), thermal gravimetric analysis (TGA), elemental analysis, and Fourier transform infrared spectroscopy (FT‐IR). The size and morphology of nanoparticles were examined by scanning electron microscopy (SEM). The XRD patterns indicate that the intercalation of YGX between the LDH layers has not occurred and surface adsorption has happened. In the adsorption experiments, the Gibbs free energy ΔG⁰ values, the enthalpy ΔH⁰, and entropy ΔS⁰ was determined. The isotherms showed that the adsorption of YGX by Mg‐Fe‐LDH‐NO₃ was both consistent with Langmuir and Freundlich equations.     

Riemann–Roch theory for weighted graphs and tropical curves

We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann–Roch theorem holds in both cases. We extend Baker’s Specialization Lemma to weighted graphs.