A Petrov-Galerkin method for solving the generalized equal width (GEW) equation

The generalized equal width (GEW) equation is solved numerically by the Petrov-Galerkin method using a linear hat function as the test function and a quadratic B-spline function as the trial function. Product approximation has been used in this method. A linear stability analysis of the scheme shows it to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. Finally, the Maxwellian initial condition pulse is studied.     

Back-propagating surface polaritons of a one-dimensional photonic crystal containing single negative metamaterials

The existence of the surface polaritons at the interface separating a semi-infinite uniform left-handed metamaterial and a one-dimensional photonic crystal composed of alternating layers of two kinds of single-negative materials is theoretically investigated. The dispersion characteristics of the surface polaritons are analyzed and demonstrated that in the presence of metamaterial, the surface polaritons are sensitive to light polarization, so that there exist only backward TM-polarized (or TE-polarized) kind of the surface polaritons depending on the ratio of the thicknesses of the two periodic stacking layers. The existence regions of the surface polariton modes are determined for both TM-polarized and TE-polarized surface polariton modes.     

Substructure and orientation of Pd-Cu solid solution thin films

The phase and elemental composition, substructure, orientation, and relief of Pd-Cu thin films produced by magnetron sputtering have been investigated using the techniques of TEM, HEED, and AFM. Three-orientation epitaxial β-phase structures (CsCl-type lattice) have been obtained by plasma-ion sputtering a Pd-Cu target on (001) fluorphlogopite (F) cleavages in the substrate temperature range of 550–800 K. The β-phase crystallites in the two-phase epitaxial solid solution films were oriented, with respect to the α-phase, according to Nishiyama—Wassermann and Kurdyumov—Sachs relations. Single-crystal films of α-and β-phase solid solutions have been grown on fluorphlogopite. The effect of the second component appeared as the formation of (001)[110] β_CuAu ∥ (001)[100]_F-type orientations.     

Phase behavior and microstructure of C12E5 nonionic microemulsions with chlorinated oils

New non-ionic microemulsions consisting of pentaethyleneglycol dodecyl ether, water, and 1-chloroalkanes were prepared, and their phase behavior was studied. A homologous series of five different 1-chloroalkanes from 1-chlorooctane to 1-chlorohexadecane was studied. The phase behavior of the microemulsions was determined by vertical sections through the Gibbs' phase prism ("fish" plots), from which valuable information such as the microemulsion balance temperature (T(0)), efficiency of the surfactant (phi*), temperature extension of the three-body phase (DeltaT), mean temperature (T(m)), and the monomeric solubility in oil (phi(mon,oil)) was obtained. The chlorinated alkanes in the microemulsions shift the balance temperature to about 14 degrees C lower compared with their n-alkane counterparts. This indicates the polar nature of the chlorinated oils and their ability to penetrate the surfactant film. The chlorinated alkanes thus behave as short n-alkane molecules and lower the spontaneous curvature of the microemulsion droplets. The efficiency of the surfactant and the monomeric solubility in oil systematically depend on the alkyl chain length of the oil, with the efficiency and solubility decreasing with increasing alkyl chain length of 1-chloroalkane. The size and shape of the microemulsion droplets in the microemulsion phase were studied by small-angle X-ray scattering (SAXS). For a surfactant-to-oil volume fraction ratio of 0.80, the droplets can be described by ellipsoidal shapes, and the size of the droplets increased with increasing alkyl chain length.     

Study of Forced Degradation Behaviour of Brinzolamide Using LC–ESI–Q-TOF and In Silico Toxicity Prediction

Brinzolamide (BZA) is a topical ophthalmic drug which is generally used to lower the intraocular pressure during glaucoma. It was subjected to forced degradation studies under hydrolytic (acidic, basic), oxidative, photolytic and thermal stress conditions; the drug degraded significantly in hydrolytic and oxidative conditions, leading to the formation of seven degradation products in total. It was stable on exposure to light and dry heat in the solid state. An ultra-performance liquid chromatography (UPLC) method was developed on a Waters CSH phenyl hexyl column (100 × 2.1 mm, 1.7 µm), using gradient elution of 0.1 % formic acid and methanol as mobile phase. The method was extended to quadrupole time-of-flight mass spectrometry (Q-TOF–MS) for the structural characterisation. All degradation products were comprehensively characterised by UHPLC–ESI/MS/MS experiments. The most probable mechanisms for the formation of degradation products were also proposed. In silico toxicity of the drug and its degradation products was determined using TOPKAT toxicity prediction software.

     

On the q-ampleness of the tensor product of two line bundles

Multiple zeta values (MZVs) are generalizations of Riemann zeta values at positive integers to multiple variable setting. These values can be further generalized to level N multiple polylog values by evaluating multiple polylogs at Nth roots of unity. In this paper, we consider another level N generalization by restricting the indices in the iterated sums defining MZVs to congruence classes modulo N, which we call the MZVs at level N. The goals of this paper are twofold. First, we shall lay down the theoretical foundations of these values such as their regularizations and double shuffle relations. Second, we will generalize the bracket functions related to multiple divisor sums defined by Bachmann and Kühn to arbitrary level N and study their relations to MZVs at level N. The brackets are all q-series and similar to MZVs, they have both weight and depth filtrations. But unlike that of MZVs, the product of brackets usually has mixed weights; however, after projecting to the highest weight we can obtain an algebra homomorphism from brackets to MZVs. Moreover, the image of the derivation \({\mathfrak{D}=q\frac{d}{dq}}\) on brackets vanishes on the MZV side, which gives rise to many nontrivial \({\mathbb{Q}}\)-linear relations.     

Chiral recognition of selenides and iodides by 1H NMR spectroscopy in the presence of a chiral dirhodium complex

Chiral recognition of aryl alkyl selenides and alkyl iodides can be achieved by ¹H NMR spectroscopy in the presence of dirhodium tetra-(R)-or tetra-(S)-α-methoxy-α-(trifluoromethyl)-phenylacetate [Rh₂(MTPA)₄, 1 ]. Generally, these classes of compounds are weak donors and fail when using the classical chiral lanthanoid shift reagent. Alkyl bromides do not show similar effects. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:471–474, 1998     

Intense deuteron beam investigation by activation yield-ratio technique

In this work, the intense deuteron beam from a plasma focus device is investigated by the activation yield-ratio technique. It is shown that boron-carbide (B₄C) and boron-nitride (BN) are complimentary targets for high energy deuteron beam studies. For deuteron spectra of the form dNd/dE∝E−n, when deuteron spectra decrease relatively gradually (n<6) BN is a better choice, while for the case of very rapidly decreasing deuteron spectra (n>6), B₄C is more suitable.