An end point estimate for maximal commutators

In this paper we prove that the maximal commutator of singular integral operator [b, T]^* satisfies the inequality:

Ueber die Ozonometrie

Ohne Zusammenfassung     

Validated spectrophotometric methods for the simultaneous determination of ciprofloxacin hydrochloride and metronidazole in tablets

A binary mixture of ciprofloxacin hydrochloride (CIP) and metronidazole (MET) was determined by five simple and accurate methods, without prior separation. In the first method, CIP was determined by second derivative spectrophotometric method ((2)D) by measuring the amplitude at 282 nm (zero ordinate value of MET). On the other hand, the determination of MET was based on isosbestic point technique, where the total content of the mixture was determined at 294.5 nm (isosbestic point), then the content of MET could be calculated by subtraction. The second method was first derivative ratio spectrophotometric method ((1)DD) where the total amplitude at 261 and 285 nm and the amplitude at 295.5 nm were selected to simultaneously determine CIP and MET in binary mixture, respectively. The third method was based on dual wavelength analysis, in which two wavelengths were selected, at which the absorbances of the other component were the same. The fourth method depends on using Q-analysis method (absorbance ratio) which involves the formation of Q-absorbance equation using the respective absorptivity values at 294.5 nm (isosbestic point) and 281.5 nm (λ(max) of CIP). The fifth method is partial least-squares (PLS) chemometric technique for determination of CIP and MET. The developed methods were successfully applied to the analysis of CIP and MET in laboratory prepared mixtures and tablets with good recoveries and their validation was carried out following the International Conference on Harmonization (ICH) guidelines. The results obtained were statistically compared with each other showing no significant difference with respect to accuracy and precision.     

Calculation of the eigenvalues of Schrödinger equations by an extension of Hill's method

The eigenfunctions of the one dimensional Schrödinger equation Ψ″ + [E ? V(x)]Ψ=0, where V(x) is a polynomial, are represented by expansions of the form $\text{∑}\text{k}\text{=0}\text{∞}{}^{\mathrm{<mtext>c</mtext>}}\text{k}{}^{\mathrm{?}}\text{k}\text{(ω,}\text{x}\text{)}$. The functions ?_k (ω, x) are chosen in such a way that recurrence relations hold for the coefficients c_k: examples treated are D_k(ωx) (Weber-Hermite functions), exp (?ωx²)x^k, exp (?cx^q)D_k(ωx). From these recurrence relations, one considers an infinite bandmatrix whose finite square sections permit to solve approximately the original eigenproblem. It is then shown how a good choice of the parameter ω may reduce dramatically the complexity of the computations, by a theoretical study of the relation holding between the error on an eigenvalue, the order of the matrix, and the value of ω. The paper contains tables with 10 significant figures of the 30 first eigenvalues corresponding to V(x) = x^2m, m = 2(1)7, and the 6 first eigenvalues corresponding to V(x) = x² + λx¹⁰ and x² + λx¹², λ = .01(.01).1(.1)1(1)10(10)100.     

Synthesis process of nanowired Al/CuO thermite

Al/CuO nanothermites were fabricated by thermal oxidation of copper layer at 450 °C for 5 h and by aluminum thermal evaporation: thermal evaporation allows producing thin layer less than 2 μm in size. The copper has been deposited by electroplating or thermal evaporation depending on the required thickness. The obtained diameter of Al/CuO nanowires is 150-250 nm. Al/CuO nanowires composite were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry (DSC) and differential thermal analysis (DTA). Two distinct exothermic reactions occurred at 515 and 667 °C and total energy release of this thermite is 10 kJ/cm³.     

Stereoselective isomerisation of N-allyl aziridines into geometrically stable Z enamines by using rhodium hydride catalysis

In the presence of rhodium(I) hydride catalysts, tertiary N-allylamines are known to isomerise into E enamines. In contrast, we have recently found that N-allylaziridines isomerise to form Z enamines. On the basis of literature data, the most likely mechanism of isomerisation would involve a rhodium hydride addition/beta-hydride elimination sequence. We show that the observed selectivity cannot be adequately explained by this pathway and is more consistent with initial CH-activation followed by rearrangement to form a five-membered cyclometallated rhodium intermediate. This intermediate subsequently undergoes reductive elimination to form a C--H bond. The resulting geometrically stable Z enamines are useful building blocks for stereoselective synthesis.     

Usefulness of cyclodextrin media for the determination of α-cypermethrin by photochemically induced fluorescence: analytical applications to natural waters

The photochemically induced fluorescence (PIF) spectral properties of α-cypermethrin in organic solvents (hexane, dichloromethane, acetonitrile, ethanol) and in cyclodextrin aqueous solutions (β-CD and 2-hydroxypropyl-β-CD, 2-HP-β-CD) were investigated. The photolysis kinetics of α-cypermethrin were evaluated in the various media. The PIF signal was found to be significantly enhanced in the CD media relative to the organic solvents. The stoichiometry and the formation constants of the α-cypermethrin inclusion complexes formed with the CDs were determined. The analytical performances of the PIF method were improved in the presence of HP-β-CD relative to the other media, and a CD-enhanced PIF analytical method was developed. The limits of detection and limits of quantification ranged, respectively, between 6 and 98 ng/mL and between 24 and 343 ng/mL, depending on the medium. Application to the analysis of tap water and Senegal natural water samples collected close to agricultural areas and spiked with α-cypermethrin yielded satisfactory recoveries going from about 77% to 98%. An interference study of foreign species, including pesticides and inorganic ions likely to be present in natural waters, was also carried out. Figure Photolysis reaction of α-cypermethrin in presence of HP-β-CD     

A validated RP‐HPLC method for the evaluation of the influence of grapefruit juice on liver S9 activation of sacubitril

Grapefruit juice inhibits esterase enzyme. Therefore, a possible interaction with ester prodrugs should be taken into consideration. In this study, the influence of grapefruit juice on sacubitril (SAC) rat liver S9 activation by esterase enzyme was evaluated. An RP‐HPLC method was developed and validated for estimation of SAC in rat liver S9 fraction using a C₁₈ Cyano column as stationary phase and acetonitrile–sodium di‐hydrogen phosphate buffer (0.02 m , pH 4 adjusted by o‐phosphoric acid, 40:60, v/v), as mobile phase at a flow rate of 1 mL/min and UV detection at 254 nm. The method was successfully applied to an in vitro study in which SAC was incubated with rat liver S9 fraction prepared from rats that had previously ingested grapefruit juice for a week. The calculated SAC concentration after incubation was compared with that of SAC incubated with rat liver S9 fraction from the rat control group. The statistical significance between the results of test and control incubation sets was assessed. In conclusion, the current study demonstrated that grapefruit juice decreased SAC hydrolysis, hence delaying its activation to sacubitrilat (active form) in gut lumen. Based on this food–drug interaction, it may be required that grapefruit juice should be consumed with caution in patients receiving SAC.     

A characterization of projective subspaces of codimension two as quasi-symmetric designs with good blocks

Consider an incidence structure whose points are the points of a PG_n(n+2,q) and whose block are the subspaces of codimension two, where n?2. Since every two subspaces of codimension two intersect in a subspace of codimension three or codimension four, it is easily seen that this incidence structure is a quasi-symmetric design. The aim of this paper is to prove a characterization of such designs (that are constructed using projective geometries) among the class of all the quasi-symmetric designs with correct parameters and with every block a good block. The paper also improves an earlier result for the special case of n=2 and obtains a Dembowski-Wagner-type result for the class of all such quasi-symmetric designs.