High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Hidden structure in the randomness of the prime number sequence?

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy–Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Continuous automatic determination of ammonia by using an integrated separation/detection unit

An automatic continuous-flow photometric method for the determination of ammonia is proposed. It is based on the Berthelot reaction, the product of which is temporarily immobilized on a suitable support (Sephadex QAE) located in the flow-cell. The retained product is eluted after measurement by a cationic surfactant contained in the carrier solution. The method allows the determination of the analyte between 0.4 and 20.0 gmg/ml, with an RSD of 0.8%, at a sampling frequency of 13/hr. The determination limit can be reduced by a factor of ten by using a flow-cell with a two-fold longer path length, but the sampling frequency is also reduced as a result. The method was applied to the determination of this analyte in agricultural samples (plants and soils) and compared with standard methods for these types of samples.     

Carbon deposition on a Ni/α-Al2O3 catalyst

The kinetics of carbon deposition over a Ni/α-Al₂O₃ commercial catalyst, has been studied using CH₄−H₂ gas mixtures in the range of 748–873 K. A Hougen-Watson type model gives good agreement with the experimental rates.     

Topological properties of the electronic density of CO-MgF2 and OC-MgF2 adducts

By means of Bader's approach on topological properties of the electronic density, the major stability of the O-bonded adduct over the C-bonded one between MgF₂ and CO is reinforced.     

Study of the feasibility of focused microwave-assisted soxhlet extraction of N-methylcarbamates from soil

A fast microwave-assisted dansylation procedure has been developed for the derivatization of N-nitrosamines prior to high-performance liquid chromatography determination. N-Nitrosomorpholine, N-nitrosodimethylamine, N-nitrosodiethylamine, N-nitrosopyrrolidine and N-nitrosopiperidine are first denitrosated by hydrobromic acid-acetic acid to produce secondary amines, which are then quantitatively dansylated in 5 min using radiation power of 378 W and a maximum pressure of 1.4 bar inside the reactor. The reaction mixture is separated on a C18 column with acetonitrile-water (55:45, v/v) as mobile phase with fluorimetric detection at 531 nm (excitation at 339 nm). The detection limits range from 8 to 75 pg for N-nitrosomorpholine and N-nitrosodiethylamine, respectively. The method was applied to study the recoveries of N-nitrosamines in beer and their determination in cigarette smoke.     

Cluster Build-up Reactions using Di-gold Cationic Fragments: Synthesis and Structural Characterization of [Os7(CO)19(Au2dppm)]

The reaction of the di-gold cation [Au₂(dppx)]²⁺ with the heptanuclear cluster dianion [Os₇(CO)₂₀]^2– affords the mixed metal cluster [Os₇(CO)₂₀{Au₂(dppx)}] (x=m (1), e (2), b (3)). On standing, in solution, this complex undergoes decarbonylation to give the cluster [Os₇(CO)₁₉{Au₂(dppx)}] (x=m (4), e (5), b (6)). The complexes have been characterised spectroscopically, and an X-ray structure determination of the dppm derivative shows that it contains a metal core based on an Os₇ edge-bridged bicapped tetrahedron with the two ₃-Au atoms capping adjacent triangular Os₃ faces of the central tetrahedron. In an analogous reaction, the carbido anion [Os₇(H)C(CO)₁₉]^– affords the neutral cluster [Os₇C(CO)₁₉{Au₂(dppm)}] (7) when treated with [Au₂(dppm)]²⁺ in the presence of base.     

Photolytic oxidation of As species for determination of total As (including the ‘hidden’ As fraction) in coastal seawater by hydride generation-atomic fluorescence spectrometry

Ultraviolet irradiation (photolysis) in alkaline medium was applied for pretreatment of seawater samples so as to accurately determine total As by continuous-flow hydride generation-atomic fluorescence spectrometry. This sample pretreatment is meant to convert non-reducible As forms into inorganic As, which easily forms arsine. The optimised parameters were the treatment time and the pH of the medium. The behaviour of four hydride-reactive As species [As(III), As(V), MMA, DMA], and AsB, i.e. a typical non-hydride-reactive As species, when subjected to UV irradiation was studied. UV irradiation at pH 1 lead to conversion of all species into As(V) with the exception of AsB and DMA. Conversions of DMA and AsB into As(V) at pH 11 in less than 30 min were observed under UV irradiation. The limit of detection of As (measured as As(V)) by hydride generation-atomic fluorescence spectrometry was 0.1 μg/L and the repeatability of the oxidation procedure was about 10%. The method was applied to determination of total and directly reducible As at 11 sampling points of the Galician Coast (Atlantic Ocean, Spain). Total As concentrations were in the range 1.4-4.8 μg/L. A significant As fraction, between 20 and 44%, depending on the sampling point, corresponded to non-reducible As which was converted by UV irradiation into hydride-reactive As. This fraction should represent the sum of DMA, which yields a low sensitivity in the continuous flow-AFS system, and the hidden As fraction.