Analyse de complexité pour un théorème de Hall sur les fractions continues

We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4. Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25.     

Composite mix design in the production of asbestos/cement pipes

A mathematical model is presented for the determination of optimal mix of asbestos fibres to satisfy a set of desired pipe properties which vary with pipe size, class, and material availability. The approach utilizes a linear/separable programming model which is aimed at minimizing the total cost of fibres used. The fibre properties, such as reinforcing strength, processability, and length as well as cost and stocks available are taken into account in the model. Also represented are the profile of the ideal mix relative to the required composite strength, processability, and ‘dust content’. Asbestos mixes designed using the model have been implemented in the production of asbestos/cement pipes in one of the asbestos/cement pipe manufacturing plants in the Gulf area. Optimum model mixes have demonstrated significant technical and economic merits over the conventionally designed mixes.     

Indirect spectrophotometric determination of perchlorate using nitron as reagent

An indirect method is outlined for the spectrophotometric determination of small amounts of perchlorate. Perchlorate is quantitatively precipitated as nitron perchlorate in the presence of excess nitron. After separating off the precipitate, the excess reagent is determined in the supernatant liquid as nitron cobaltothiocyanate. The latter compound is extracted in 30% cyclohexanone in carbon tetrachloride and the absorbance of the extract measured at 625 nm. The method is simple, reproducible, and accurate to ±1%. The interferences of other anions were also investigated.     

A versatile new synthesis of quinolines and related fused pyridines. Part III.

The action of dimethylformamide in phosphorus oxychloride on acylanilides gives 2-chloro-3-substituted quinolines, which may be dechlorinated to give 3-substituted quinolines in good yield. Similarly, N-nitrosodimethylamine in phosphorus oxychloride converts acylanilides into 2-chloro-3-substituted quinoxazolines.     

Crystal structure of monomethylammonium tribromocadmate(II)

CH₃NH₃CdBr₃ crystallizes in the space group Ccm2₁, a = 13.693(1) Å, b = 7.906(1) Å, c = 6.886(1) Å, V = 745.46(15) ų, Z = 4, D _x = 3.42 Mg m^–3. The structure of the title compound is one-dimensional consisting of infinite chains made of face sharing CdBr₆ octahedra. The methylammonium groups are situated in the space between chains. The cations and anions are joined by hydrogen bonding.     

Quantum Effect on the Energy Levels of Eu2+ Doped K2Ca2(SO4)3 Nanoparticles

Quantum confinement effect on the energy levels of Eu²⁺ doped K₂Ca₂(SO₄)₃ nanoparticles has been observed. The broad photoluminescence (PL) emission band of Eu²⁺ doped K₂Ca₂(SO₄)₃ microcrystalline sample observed at ～436 nm is found to split into two narrow well resolved bands, located at 422 and 445 nm in the nanostructure form of this material. This has been attributed to the reduction in the crystal field strength of the nanomaterials, which results in widening the energy band gap and splitting the broad 4f⁶5d energy level of Eu²⁺. Energy band gap values of the micro and nanocrystalline K₂Ca₂(SO₄)₃ samples were also determined by measuring the UV–visible absorption spectra. These values are 3.34 and 3.44 eV for the micro and nanocrystalline samples, respectively. These remarkable results suggest that activators having wide emission bands might be subjected to weak crystal strength via nanostructure materials to modify their electronic transitions. This might prove a powerful technique for producing new-advanced materials for use in the fields of solid state lasers and optoelectronic devises.