Quadratic spline interpolation on uniform meshes

The interpolation problem at uniform mesh points of a quadratic splines(x _i)=f _i,i=0, 1,...,N ands(x ₀)=f₀ is considered. It is known that s–f=O(h ³) and s–f=O(h ²), whereh is the step size, and that these orders cannot be improved. Contrary to recently published results we prove that superconvergence cannot occur for any particular point independent off other than mesh points wheres=f by assumption. Best error bounds for some compound formulae approximatingf _i andf _i ⁽³⁾ are also derived.     

Properties of RF sputtered ZnxCd1−xS thin films

Zn _x Cd_1–x S thin films (0x0.20) were prepared using rf sputtering in argon atmosphere and characterized using X-ray diffraction, optical transmission, electrical resistivity and photoconductive decay measurements. The films were found to possess hexagonal structure. The crystallite size and degree of preferential orientation were found to decrease with the increase ofx and to improve upon annealing in vacuum at 250 °C. The transmission edge shifted towards shorter wavelengths with the increase ofx in agreement with the expected shift in the energy band gap. The films were found to exhibit room temperature resistivity in the range 100–1000 cm. The obtained values of long wavelength transmission (70–80%) and minority carrier diffusion length (30 m) are high enough for the application of these films in the field of solar cells.     

Synthesis of condensed systems containing the tetrazole ring by base-catalyzed intramolecular cyclization of quaternary ammonium salts

Quaternary ammonium salts containing propargyl and 3-(2-methyltetrazol-5-yl)propargyl groups undergo base-catalyzed cyclization at room temperature with self heating to form condensed heterocyclic systems containing the tetrazole ring. Heating at 90–92°C for 2 h is necessary to cyclize the allyl analogs of the starting salts.Communication 234 of the series Research on Amines and Ammonium Compounds. For 233, see [1].Institute of Organic Chemistry, National Academy of Sciences of the Republic of Armenia, Erevan 375094. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 390–394, March, 1999.     

Anodic Stripping Voltammetry of Heavy Metals at Nanocrystalline Boron‐Doped Diamond Electrode

Boron‐doped Diamond (BDD) electrode has become one of the important tools for heavy metal detection. By studying some analytical parameters of DPASV method, like deposition time and potential in different electrolyte concentrations (acetate buffer), the conditions for detecting very low metal ion levels (Zn, Cd, Pb, and Cu) could be chosen. Diluted electrolyte (0.01 M buffer) was one of the factors favoring low detection and quantification limits, but its quantification range is short in comparison to more concentrated media. For ?1.7 V deposition potential, the detection of single metal at ppb levels was reached in 60 s deposition time. Understanding different metal‐metal interactions shows the limits to the simultaneous determination of heavy metals at BDD. Quantification was possible for the simultaneous determination of Zn, Cd and Pb despite the overlapping of Zn and Cd peaks. The performance of the BDD was compared with that of another C‐based solid electrode: the glassy carbon electrode (without mercury plating). A lower base line current, wider potential range, higher sensitivity (3 to 5 times higher than GC) and longevity of the material were noticed for the BDD.     

Development of the FTIR properties of nano-structure silica gel doped with different rare earth elements,prepared by sol-gel route

Structural characteristics of pure silica gel (silica-xerogel, SiO₂) and silica gel doped with some rare earth elements (REEs) such as, praseodymium Pr³⁺, and Europium Eu³⁺, Erbium Er³⁺ and Holmium Ho³⁺ ions, with different concentrations ranging from 1 up to 6%, in the form of monolith materials were prepared by sol-gel technique, Using tetra-ethoxysilane as precursor materials, which are of particular interest for sol-gel integrated optics applications. Some structural features of sol-gel derived monolith are analyzed, namely the structure of nano-particle momolith samples, based on X-ray diffraction (XRD) and Fourier Transform Infrared (FTIR). We show that the XRD spectra of α-crystobalite are obtained for the pure samples at 1100°C and even by doping with the four REEs ions.     

Ylures sans sel,evolution en phosphoranes et equilibre ylure ⇌ phosphorane : I Synthese et structure

Synthesis of new salt-free ylids $\text{9}$,$\text{12}$ to $\text{16}$, $\text{19}$, $\text{20}$, $\text{22}$, $\text{27}$ and $\text{29}$ and phoiphoranes $\text{10}$, $\text{17}$, $\text{18}$, $\text{21}$, $\text{23}$, $\text{30}$ to $\text{33}$ by addition of a trivalent phosphorus compound (phosphites and amino-phosphines ) $\text{1}$ to $\text{7}$ with dimethyl acetylencedicartboxylate in presence of a protic trapping reagent are described. The results are consistent with trapping of carbanionic species. In relation with the. cyclic of acyclic structure of the triivalent phosphorus compound and the protic trapping reagent ie : methanol, phenol, carboxylic acid, etc.., several pathways are involved. Clearly), three phenomena are shown : one can obtain an ylid via a phosphorane or conversely a phosphorane via an ylid or an equilibrium Phoiphorane ? ylid. Results are dealing with thermodynamic or kinetically controlled reactions.     

Heterocycles from carbohydrate precursors. Part XIX. The X-ray crystal structure determination of the reaction product of 4-(2-acetoxyethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methylhydrazine

X-ray crystallographic data show that the product obtained in the reaction of 4-(2-acetoxy-ethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methyl-hydrazine is the bicyclic compound 2,6-dimethyl-3,4-dioxo-2,3,4,6,7,8-hexahydropyridazino-[4,3-c]pyridazine 4-(p-bromophenylhydrazone) ( 10 ) and not as originally suggested 1-methyl-3-(1-methylpyrazolin-3-yl)-4,5-pyrazoledione 4-(p-bromophenylhydrazone) ( 8 ).