Critical circle maps near bifurcation

We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than 1/3. Moreover, the rotation number is a Hölder continuous function of the parameter.Partially supported by KBN grant Iteracje i Fraktale #210909101.Partially supported by NSF Grant #DMS-9206793 and the Sloan Research Fellowship.     

V. Thioanalogues of sparteine lactams. (+)-2-Thiono-17-oxosparteine and (+)-2,17-dithionosparteine

The X-ray and spectroscopic results clearly indicate that the (+)-2-thiono-17-oxosparteine (1) and (+)-2,17-ditihionosparteine (2) are conformationally rigid. In order to analyze deviations of lactam/thiolactam groups from planarity induced by ring constraints, the Dunitz-Winkler approach has been used. The lactam and thiolactam groups are close to planarity, only the lactam group in one of the two independent molecules of 1 is markedly non-planar. The bond angles in the thiolactam and lactam groups are highly diverse. Rings A and C adopt a distorted sofa conformation in both compounds. The distortions in the molecules of 2 as compared with those in the related monothiolactams correspond to the unusual chemical shifts of H5(eq), H5(ax) and H11, as well as to the extremely low J_5ax-6 and extremely large J_5eq-6 coupling constants. Also chemical shifts show a similar regularity being extremely high and low for C2 and C17, respectively.     

Loss of isocyanic acid from the internal oxadiazole ring of protonated molecules of some 2,5-diaryl-1,3,4-oxadiazoles

The fragmentation pattern of some protonated 2,5-diaryl-1,3,4-oxadiazoles is discussed. An unusual decomposition consisting of elimination of the isocyanic acid molecule from the internal oxadiazole ring was found. This fragmentation pathway was deduced on the basis of B/E linked scan mass spectra of metastable ions with liquid secondary ion mass spectrometry as the ionization method and also of low-energy CID mass spectra where electrospray was used as the ionization technique. High resolution measurements were also performed.     

Die Massenspektren der Pyrrolidide einiger aliphatisch-alicyclischer Carbonsäuren

The mass spectra of the pyrrolidides of some long-chain carboxylic acids with alicyclic residues attached to their ω-end are discussed and compared with the spectra of the corresponding esters. Fragmentation triggered by the pyrrolidide group generates a series of peaks, which clearly exhibits the size and the structure of the carbon chain.     

Shape of the proton potential in an intramolecular hydrogen-bonded system. Part II

The crystals of 5,5′-dibromo-3-diethylaminomethyl-2,2′-biphenol N-oxide were studied by X-ray and FT-IR spectroscopy. Within this molecule two short OHO intramolecular hydrogen bonds are formed. The NO?H⁺?O⁻ bond between the OH and the N-oxide groups is very strong, of 2.419(7) Å between the oxygen atoms. The proton potential of this hydrogen bond is flat, broad and has probably no barrier—consequently it could not be located from X-ray diffraction data. The other hydrogen bond formed between two hydroxyl groups appears asymmetrical from FT-IR spectra, and shows also relatively limited proton polarizability. The molecular conformation is non-planar, due to strong overcrowding effect between the oxygen atoms involved in the hydrogen bonds.     

Crystal Structures of 1,5,9,18,22,26-Hexaaza[11.11]-p-cyclophane Adducts; Two-dimensional Supramolecular Networks

Two newly identified supramolecular structures arise from self-assembly of the macrocyclic 1,5,9,18,22,26- hexaaza[11.11]-p-cyclophane salts with o-nitrophenol (C₂₈H₅₀N₆)⁴⁺·4(C₆H₄NO₂O)⁻ (1) and with HCl (C₂₈H₅₂N₆)⁶⁺·6Cl^-·4H₂O (2). In both cases two-dimensional supramolecular sheets are formed.     

Electron scattering on C6F6 and SF6 molecules

Total absolute cross sections for electron scattering on hexafluorobenzene, C₆F₆, and sulfur hexafluoride, SF₆, molecules, have been measured as a function of impact energy from 0.6 to 250 eV. The total cross section for C₆F₆ exhibits a very broad peak stretching from 10 to 100 eV with some weak features near 9.5 and 15 eV superimposed on the peak. Apart from the well-known low-energy resonant structures in the SF6 total cross section function, a new weak resonant feature close to 25 eV has been noticed in the present experiment, in accordance with earlier theoretical calculations.     

Trace analysis of metals in plant samples with inductively coupled plasma – mass spectrometry

An analytical method for the quantitative determination of Al, Ti, V, Cr, Co, Ni, Cu, Zn, Mo, Cd, Ti and Pb in plant samples by ICP-MS has been developed. Spectral interferences, plant matrix effects, precision and accuracy are discussed. Results are demonstrated for selected samples concerned with the mass balance of heavy metals after utilization of non-food vegetable materials in a power plant. Received: 7 January 1997 / Revised: 2 June 1997 / Accepted: 18 June 1997     

The First Reaction of Dimethoxycarbene with an Imine Moiety

The nucleophilic dimethoxycarbene (DMC; 2 ) generated by thermal decomposition of 2,5‐dihydro‐1,3,4‐oxadiazole derivative 1 in boiling toluene reacts smoothly with N‐(9H‐fluoren‐9‐ylidene)‐4‐methylbenzenesulfonamide ( 7b ) to yield carbonimidoate derivative 10 . A multi‐step reaction pathway, initiated by the attack of DMC onto the C?N bond and followed by the migration of the sulfonyl group (or via a sulfinate anion) is proposed to explain the formation of the final product. In contrast to the formal ketimine 7b , N‐benzylidene‐4‐methylbenzenesulfonamide ( 7a ), a formal aldimine, does not react with DMC under comparable conditions.     

Preparation and Characterization of a Lignin Modified Electrode

Alkali lignin undergoes strong adsorption on polycrystalline gold electrodes. Subsequent oxidation in a sulfuric acid solution leads to a restructured redox‐active polymer that shows features characteristic for surface confined species. Surface coverage of up to 4.40×10^?10 mol cm^?2 may be obtained depending on the adsorption time or lignin concentration in the adsorption solution. Using Laviron's approach the electron‐transfer rate constant and the transfer coefficient were found to be 8.9 s^?1 and 0.35, respectively. The formal potential of the redox couple shifted negatively with pH at a rate of ca. 60 mV/pH unit, suggesting a 2 e/2 H⁺ reaction. The redox couple was also found to be a good mediator for electrochemical ascorbic acid oxidation in neutral phosphate buffer with ca. 250 mV reduction of the oxidation overpotential.