On a question of H. Kraljević

In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented.     

The interactive fixed charge inhomogeneous flows optimization problem

An optimization problem of interactive inhomogenous flows (Steiner multicommodity network flow problem) is formulated. The problem's main characteristic is a fixed charge change when combining multicommodity communications. In this paper we propose a method for solving this problem which, in order to restrict the search on the feasible domain, reduces the original problem to a concave programming problem in the form: min {f(x)|xX} wheref:ⁿ is a concave function, andX ₀ ⁿ is a flow polytope defined by network transportation constraints. For practical large-scale problems arising from planning transportation networks on inhomogeneous surfaces defined by a digital model, a method of local optimization over a flow polytope vertex set is proposed, which is far more effective in comparison with the Gallo and Sodini method under polytope strong degeneracy conditions.     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

The Fermi doublet V2−V3 + V4 of CH3CN as a probe of molecular interactions

The Fermi doublet V₂?V₃ + V₄ of CH₃CN in basic, inert and acidic solvents has been studied by IR and Raman spectroscopy. The values of W, the Fermi coupling coefficient, obtained from IR spectra varies with the nature of the solvent while W evaluated from Raman data remains constant at 12.5 ± 0.5 cm^?1. The similar effects of Bronsted and Lewis acids on the band frequencies and intensities is evidence that the CN group complexes with acids via the N atom “n” electron pair and not the π bond.     

Simultane Ionen-Chromatographie von Kationen und Anionen mit Komplexonen als Elutionsmittel und selektiver UV-Detektion

Summary The complexones EDTA, DCTA and EGTA were investigated as eluting agents at various pH-values for the simultaneous separation of 9 cations and 6 anions using ion chromatography on a silica gel based anion exchanger (Nucleosil 10-Anion II). 1,2-Diaminocyclohexanetetraacetic acid (DCTA) proved to be the best eluting agent. UV spectrophotometry was used for both direct and indirect detection of the anions and anionic metal complexes and a detailed study was carried out with respect to selectivity of detection. This was facilitated by referring to the UV absorption spectra of the anions and metal complexes involved. By choice of a suitable wavelength between 203 and 270 nm and taking into account pH effects, a number of selective determinations were possible. Examples include Pb and Cu in the presence of excess of Ca and Mg as well as nitrate, nitrite and bromide in a large excess of chloride and sulphate. Some examples of detection limits are (g/l) nitrate 2, Fe(III) 3, Cu 9 and Pb 12 (sample volume 20 l, direct UV-detection). The Chromatographie behaviour of Fe(II) and Fe(III) was studied and discussed. Drinking water was analysed for chloride, nitrate and sulphate as well as Ca and Mg using DCTA in the eluent. Complete analyses can be carried out in less than 15 min.

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Herrn Prof. Dr. R. Neeb zum 60. Geburtstag gewidmet     

Novel chemical modifications at the 4-position of chromones. Synthesis and reactivity of 4H-chromene-4-spiro-5′-isoxazolines and related compounds

Reactions of chromones with dilithiooximes proceed via nucleophilic 1,2-addition to give, on acidification, 4H-chromene-4-spiro-5′-isoxazoline derivatives in high yields. On treatment with concentrated H₂SO₄ the isoxazoline ring of this novel spiroannulated heterocyclic system opens to give α,β-unsaturated oximes, which undergo nitrosation, bromination, and the Beckmann rearrangement to the corresponding spiroisoxazolines and α,β-unsaturated amides, respectively. The latter can be obtained directly by the Beckmann rearrangement of 4H-chromene-4-spiro-5′-isoxazolines.     

Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

Summary. In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.     

Ba(SbF(6))(2).5XeF(2): first xenon(II) compound with barium. Synthesis,vibrational spectra,and crystal structure

The reaction between Ba(SbF(6))(2) and excess XeF(2) in anhydrous HF at room temperature yields the white solid Ba(SbF(6))(2).5XeF(2) after the excess XeF(2) and the solvent have been removed under vacuum. Ba(SbF(6))(2).5XeF(2) crystallizes in the monoclinic space group C2/m, with a = 13.599(6) A, b = 12.086(4) A, c = 9.732(5) A, beta = 134.305(6) degrees, V = 1144.7 (8) A(3), and Z = 2. The coordination sphere of each barium atom consists of 12 fluorine atoms. The structure consists of alternating layers of Ba(SbF(6))(2).XeF(2) and 4 XeF(2) molecules. The Ba atoms in the Ba(SbF(6))(2).XeF(2) layer are in a nearly rhombic-net array and are linked with trans F-bridging ligands of SbF(6)(-). A XeF(2) molecule is placed in the center of each rhombus of the Ba(2+) array so that its symmetry axis is perpendicular to the plane of the Ba(SbF(6))(2).XeF(2) layer. This layer is linked to its neighbors by a layer of centrosymmetric XeF(2) molecules. Raman spectra are in accord with all XeF(2) molecules being symmetrical.