Discrete Orthogonality of the Malmquist Takenaka System of the Upper Half Plane and Rational Interpolation

In the representation of non periodic signals the use of special rational orthogonal systems is more efficient. One of these bases is the Malmquist–Takenaka system for the upper half plane. We will prove the discrete orthogonality of this system. Based on the discretization we introduce a new rational interpolation operator and we will study the properties of this operator. A finite sampling theorem for a special subset of non periodic analytic signals will be presented.     

Vapour—liquid equilibrium in binary mixtures formed by benzene or cyclohexane with 1-chloropropane or 1-chlorobutane

The vapour—liquid equilibria (VLE) for the binary systems formed by 1-chloropropane with benzene and cyclohexane at 308.15 K and 318.15 K, and for systems formed by 1-chlorobutane with the same hydrocarbons at 308.22 K, 328.27 K and 348.31 K have been determined by a total pressure ebulliometric method. The accuracy of these results was proved by comparing the heat of mixing data calculated from these VLE results with those obtained by direct measurements (Amaya, 1961; Grolier et al., 1973). The experimental data and the results of correlation by means of the Redlich—Kister equation are given. The systems with benzene were found to be nearly ideal, while those with cyclohexane exhibit positive deviations (G^E = 220–260 J mole^?1 for an equimolar mixture). New vapour pressure versus temperature data for 1-chlorobutane are reported.     

Julius Petersen annotated bibliography

This is the first comprehensive bibliography of Julius Petersen's papers and books, covering not only his mathematical works, but also his contributions to economics, social science, physics and education.     

Metal-metal bond or isolated metal centers? Interaction of Hg(CN)2 with square planar transition metal cyanides

Three adducts have been prepared from Hg(CN)(2) and square planar M(II)(CN)(4)(2)(-) transition metal cyanides (M = Pt, Pd, or Ni, with d(8) electron shell) as solids. The structure of the compounds K(2)PtHg(CN)(6).2H(2)O (1), Na(2)PdHg(CN)(6).2H(2)O (2), and K(2)NiHg(CN)(6).2H(2)O (3) have been studied by single-crystal X-ray diffraction, XPS, Raman spectroscopy, and luminescence spectroscopy in the solid state. The structure of K(2)PtHg(CN)(6).2H(2)O consists of one-dimensional wires. No CN(-) bridges occur between the heterometallic centers. The wires are strictly linear, and the Pt(II) and Hg(II) centers alternate. The distance d(Hg)(-)(Pt) is relatively short, 3.460 A. Time-resolved luminescence spectra indicate that Hg(CN)(2) units incorporated into the structure act as electron traps and shorten the lifetime of both the short-lived and longer-lived exited states in 1 compared to K(2)[Pt(CN)(4)].2H(2)O. The structures of Na(2)PdHg(CN)(6).2H(2)O and K(2)NiHg(CN)(6).2H(2)O can be considered as double salts; the lack of heterometallophilic interaction between the remote Hg(II) and Pd(II) atoms, d(Hg)(-)(Pd) = 4.92 A, and Hg(II) and Ni(II) atoms, d(Hg)(-)(Ni) = 4.61 A, is apparent. Electron binding energy values of the metallic centers measured by XPS show that there is no electron transfer between the metal ions in the three adducts. In solution, experimental findings clearly indicate the lack of metal-metal bond formation in all studied Hg(II)-CN(-)-M(II)(CN)(4)(2)(-) systems (M = Pt, Pd, or Ni).     

Aroma compound analysis of Piper nigrum and Piper guineense essential oils from Cameroon using solid-phase microextraction-gas chromatography,solid-phase microextraction-gas chromatography-mass spectrometry and olfactometry

Three analytical methods were developed for the determination of toxic compounds in recirculating waters of a paper-recycling industry. Three main groups of compounds were considered: (i) wood extractives originated from the raw material; (ii) biocides added during the production process and (iii) surfactants and other adjuvants present in the formulates of these biocides. Wood extractives considered in this study included fatty and resin acids. They were analysed by liquid-liquid extraction using methyl tert.-butyl ether, followed by gas chromatography-mass spectrometry for previous formation of the respective trimethylsilyl esters. Water samples were also extracted with Oasis HLB (copolymer [poly(divinylbenzene-co-N-vinylpyrrolidone]) solid-phase extraction cartridges of 60 mg and analysed by liquid chromatography-electrospray mass spectrometry for the determination of additives and biocides. Using these two approaches levels up to 15 mg/l for total resin and fatty acids, 5 mg/l for alkylbenzene sulfonates and 2-(thiocyanomethylthio)benzotiazol, 100 microg/l for bisphenol A and 2,2-dibromo-3-nitrilepropionamide, and 300 microg/l for nonylphenol ethoxycarboxylate were detected in process waters at different production treatment stages. These levels are of relevance since poor water quality affects the paper-recycling process, the primary water treatment process and eventually, the environmental water quality.     

Studies of correlation between chemical structure and Rf-value in high performance TLC

Correlation between chemical structure and Rf-values was studied in the case of aniline and its derivatives using high performance TLC and a U-chamber. The characteristic group constants referring to each substituent were determined by chromatographing derivatives with one substituent and aniline in toluene and dibutyl ether respectively. On the basis of these constants the R_M and Rf values of derivatives with more substituents were calculated. Comparing the calculated and measured values good agreement was found.     

Influence of relative configuration of disubstituted cyclopentanes and -hexanes on 13C shifts

(13)C shifts of disubstituted cyclopentane and cyclohexane derivatives were compared in dependence on the relative configuration of the two substituents. A diequatorial substitution correlates with deshielding compared to other substitution patterns. Some novel fluorinated cyclopentanes and -hexanes including their DFT calculation-assisted structure elucidation are described.     

Heterocondensed thiophenes and thiazoles by THORPE‐ZIEGLER cyclization

The syntheses of novel thieno‐pyridones, thiazolo‐pyridones, thiazolo‐pyridines and amino‐ and diamino‐dieno‐pyridines were described. Simultaneously, it was demonstrated that in these compounds and in the related 3‐aminothiophenes the replacement of the methylthio by the morpholino group is possible. The structures were characterized using ¹H‐, ¹³C‐NMR, IR and elemental analysis.     

Molecular structures of the digermanes Me2XGeGeXMe2 (X = Me, Cl, and H): an ab initio study combined with experimental investigation by Raman spectroscopy and gas electron diffraction

Ab initio calculations were carried out to investigate the potential-energy surface for internal rotation of the methylated digermanes hexamethyldigermane Me(3)GeGeMe(3) ( 1), dichlorotetramethyldigermane Me(2)ClGeGeClMe(2) ( 2), and tetramethyldigermane Me(2)HGeGeHMe(2) ( 3). Different basis sets [6-31+G(d), SDD, aug-cc-pVTZ] were employed at the DFT and MP2 levels of theory to optimize structures and to calculate energies and vibrational frequencies. For 1, one minimum representing a staggered structure was located on the potential-energy surface. For 2 and 3, antiperiplanar conformations with C 2 symmetry were found to be the global minima. Additionally, synclinal minima were located for 2 and 3 when certain basis sets were employed. Determination of structural parameters in the gas phase by gas electron diffraction confirmed the computed predictions for all three compounds. For 2 and 3, the ratios of antiperiplanar to synclinal conformer were detected to be 90:10 (328 K) and 72:28 (293 K), respectively, by gas electron diffraction. The experimentally determined GeGe bond lengths in 1, 2, and 3 in the gas phase are 241.4(1), 242.7(2) (averaged for antiperiplanar and synclinal), and 241.7(1) pm (equal for antiperiplanar and synclinal). Only averaged structures were observed, using Raman spectroscopy, for 2 and 3 because the wavenumber differences are small between conformers and there is only a small contribution from the second conformer in each case. For 2, the crystal structure was also determined by X-ray diffraction. An anticlinal structure (with Cl atoms eclipsing the C atoms) was found with a GeGe bond length of 242.1 pm.