An Explicit Solution with Correctors for the Green–Naghdi Equations

In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green–Naghdi equations can be derived and justified when the bottom is variable (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dispersive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.     

Chelates and corrosion inhibition of newly synthesized Schiff bases derived from <Emphasis Type="Italic">o</Emphasis>-tolidine

New copper(II), nickel(II), iron(III) and palladium(II) Schiff base complexes derived from o-tolidine and selected aldehydes, namely salicyaldehyde and 2-hydroxynaphthaldehyde have been synthesized and characterized by a combination of elemental analyses, magnetic moments, spectral (u.v.–vis., i.r.) and thermal (tg, dtg) mesurements. The corrosion inhibition of aluminium and copper in 1 M HCl and chromium–nickel steel in crude oil using N,N′bis(salicyledene)-o-tolidine have been studied by weight loss method.     

Analytical examples of diffusive waves generated by a traveling wave

We construct analytical solutions for a system composed of a reaction–diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction–diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher–KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails whose exponents are roots of second-, third-, or fourth-order polynomials. These raise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered.     

Determination of capsaicin and dihydrocapsaicin in Capsicum fruit samples using high performance liquid chromatography

The aim of the present study was to determine the content of capsaicin and dihydrocapsaicin in Capsicum samples collected from city markets in Riyadh (Saudi Arabia), calculate their pungency in Scoville heat units (SHU) and evaluate the average daily intake of capsaicin for the population of Riyadh. The investigated samples consisted of hot chillies, red chillies, green chillies, green peppers, red peppers and yellow peppers. Extraction of capsaicinoids was done using ethanol as solvent, while high performance liquid chromatography (HPLC) was used for separation, identification and quantitation of the components. The limit of detection (LOD) of the method was 0.09 and 0.10 μg/g for capsaicin and dihydrocapsaicin, respectively, while the limit of quantification (LOQ) was 0.30 and 0.36 μg/g for capsaicin and dihydrocapsaicin, respectively. Hot chillies showed the highest concentration of capsaicin (4249.0 ± 190.3 μg/g) and the highest pungency level (67984.60 SHU), whereas green peppers had the lowest detected concentration (1.0 ± 0.9 μg/g); green peppers, red peppers and yellow peppers were non pungent. The mean consumption of peppers for Riyadh city population was determined to be 15.5 g/person/day while the daily capsaicin intake was 7.584 mg/person/day.     

Anion dependent redox changes in iron bis-terdentate nitroxide {NNO} chelates

The reaction of [Fe(II)(BF(4))(2)]·6H(2)O with the nitroxide radical, 4,4-dimethyl-2,2-di(2-pyridyl) oxazolidine-N-oxide (L(?)), produces the mononuclear transition metal complex [Fe(II)(L(?))(2)](BF(4))(2) (1) which has been investigated using temperature dependent susceptibility, Mo?ssbauer spectroscopy, electrochemistry, density functional theory (DFT) calculations, and X-ray structure analysis. Single crystal X-ray diffraction analysis and Mo?ssbauer measurements reveal an octahedral low spin Fe(2+) environment where the pyridyl donors from L(?) coordinate equatorially while the oxygen containing the radical from L(?) coordinates axially forming a linear O(?)··Fe(II)··O(?) arrangement. Magnetic susceptibility measurements show a strong radical-radical intramolecular antiferromagnetic interaction mediated by the diamagnetic Fe(2+) center. This is supported by DFT calculations which show a mutual spatial overlap of 0.24 and a spin density population analysis which highlights the antiparallel spin alignment between the two ligands. Similarly the monocationic complex [Fe(III)(L(-))(2)](BPh(4))·0.5H(2)O (2) has been fully characterized with Fe-ligand and N-O bond length changes in the X-ray structure analysis, magnetic measurements revealing a Curie-like S = 1/2 ground state, electron paramagnetic resonance (EPR) spectra, DFT calculations, and electrochemistry measurements all consistent with assignment of Fe in the (III) state and both ligands in the L(-) form. 2 is formed by a rare, reductively induced oxidation of the Fe center, and all physical data are self-consistent. The electrochemical studies were undertaken for both 1 and 2, thus allowing common Fe-ligand redox intermediates to be identified and the results interpreted in terms of square reaction schemes.     

Microwave assisted synthesis and unusual coupling of some novel pyrido[3,2-f][1,4]thiazepines

3-Amino-3-thioxopropanamide (1) reacted with ethyl acetoacetate to form 6-hydroxy-4-methyl-2-thioxo-2,3-dihydropyridine-3-carboxamide (2), which reacted with α-haloketones 3 to produce 2,3-disubstituted-8-hydroxy-6-methyl-2H,5H-pyrido[3,2-f]-[1,4]thiazepin-5-ones 4a-c. Benzoylation of 4c led to the formation of the dibenzoate derivative 9. Compounds 4a-c could be prepared stepwise through the formation of S-alkylated derivatives 10a-c. Compounds 2, 4a-c, 9 and 10a-c were prepared using microwave as a source of heat, and gave better yields in shorter times than those achieved by traditional methods. Coupling of 4a-c with arenediazonium chlorides proceeded unusually to give the 6-hydroxy-4-methyl-2-(arylazo)thieno[2,3-b]pyridin-3(2H)-one ring contraction products 14. Structures of the newly synthesized compounds were proven by spectral and chemical methods.     

Simultaneous determination of rofecoxib and celecoxib in human plasma by high-performance liquid chromatography

An innovative reversed-phase high-performance liquid chromatographic method is validated for the simultaneous determination of rofecoxib and celecoxib in human plasma. The internal standard is 4-n-pentyl-phenyl-acetic acid. Good chromatographic separation is achieved using a Zorbax SB-CN (5 microm) analytical column operated at room temperature and mobile phase consisting of acetonitrile and water containing 0.1M potassium dihydrogen orthophosphate buffer adjusted to pH 2.4 with 85% orthophosphoric acid (42:58, v/v). UV detection is performed at 254 nm, and the flow rate is maintained at 1.0 mL/min. Plasma samples are extracted into an organic solvent (1-chlorobutane) and evaporated under an air flow. The calibration curve for rofecoxib is linear over the range of 10 to 500 microg/L, and the celecoxib calibration curve is linear over the range of 20 to 2000 microg/L. The lower limit of quantitation for rofecoxib and celecoxib is 10 and 20 microg/L, respectively, using 1.0 mL of human plasma. The validation data show that the assay is sensitive, accurate, specific, and reproducible for the determination of rofecoxib and celecoxib. This method is therefore appropriate for pharmacokinetic studies to quantitate these therapeutic agents in patients with arthritis conditions.     

Vortex-creep activation energy in YBa2Cu3O7/PrBa2Cu3O7 superlattices

YBa₂Cu₃O₇/PrBa₂Cu₃O₇ (YBCO/PBCO) superlattices with a different ratio of the superconducting and insulating layer thicknesses were prepared by high pressure dc sputtering. The vortex-creep activation energy U₀ was determined by analyzing the in-plane resistive transition of 200 μm wide bridges with the external magnetic field B oriented along the c axis. It was found that U₀ is proportional to the thickness of the YBCO layers, and does only weakly depend on the PBCO layer thickness, when the latter exceeds two unit cells. We observed a change in the variation of U₀ with the current I in the specimen: U₀ exhibits a plateau in the low-I region, then decreases significantly with increasing I. This behaviour is explained in terms of a crossover plastic vortex creep – elastic (collective) creep induced by the transport current.     

Three-dimensional polarization control in microscopy

We propose an approach to optical microscopy that enables full control over the three-dimensional polarization vector at the focal spot of a high-numerical-aperture lens. The input field to the lens is linearly polarized and no polarization optics are needed. This technique utilizes the azimuthal spatial degree of freedom of the input field. We find that only a small set of low-order azimuthal spatial harmonics contributes to the focused field on axis, and a simple transformation exists between the linear vector space of these harmonics and the three-dimensional polarization-vector space. Controlling the relative complex weights of these azimuthal harmonics produces any desired three-dimensional state of polarization.     

Remarks on pseudo-valuation rings

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ε A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.