The Newton filtration and d-determination of bifurcation problems related to C~0 contact equivalence

In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

High spin chemistry underlying organic molecular magnetism: Topological symmetry rule as the first principle of spin alignment in organic open-shell systems of π-conjugation and their ions

This review paper deals with an overview of molecule-based magnetism as a rapidly developing interdisciplinary field, topological symmetry rule as the first principle of spin alignment in organic open-shell systems in the ground state, the proposal of organic through-bond 1D and 2D ferro- and superparamagnets and the detection of the first organic high-spin molecule, m-phenylenebis(phenylmethylene) in the quintet ground state (S = 2), followed by extended organic high-spin systems with π-conjugation such as aromatic hydrocarbons having S = 3, 4, 5. The paper also describes a theoretical approach to the understanding of electronic spin structures of organic high-spin molecules by invoking both Heisenberg and Hubbard model Hamiltonians, weakly interacting intramolecular high-spin systems from both experimental and theoretical sides, the spin density distribution of the first organic high-spin molecule in terms of electron- nuclear multiple resonance spectroscopy and the detection and characterization of ionic high-spin hydrocarbons, emphasizing the establishment of high spin chemistry underlying organic molecular magnetism.     

High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 μm atmospheric window

The absorption spectrum of natural water vapour around 1.5 μm has been recorded with a typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹ by using a CW-cavity ring down spectroscopy set up based on fibred DFB lasers. A series of 31 DFB lasers has allowed a full coverage of the 6130.8-6748.5 cm⁻¹ (1.63-1.48 μm) region corresponding to the H transparency band of the atmosphere. The line parameters (wavenumber and intensity) of a total of 5190 lines, including 4247 lines of water vapor, were derived by a one by one fit of the lines to a Voigt profile. Different isotopologues of water (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O) present in natural abundance in the sample contribute to the spectrum. For the main isotopologue, H₂¹⁶O, 2130 lines were measured with line intensities as weak as 10⁻²⁹ cm/molecule while only 926 lines (including a proportion of 30% inaccurate calculated lines) with a minimum intensity of 3 × 10⁻²⁷ cm/molecule are provided by the HITRAN and GEISA databases. Our comparison in the whole 5750-7965 cm⁻¹ region, has also evidenced that an error in the process of conversion of the intensity units from cm⁻²/atm to cm⁻¹/(molecule × cm⁻²) at 296 K, has led to H₂¹⁶O line intensities values listed in the HITRAN-2000 database, systematically 8 % below the original FTS values. The rovibrational assignment was performed on the basis of the ab initio calculations by Schwenke and Partridge with a subsequent refinement and validation using the Ritz combination principle together with all previously measured water transitions relevant to this study. This procedure allowed determining 172, 139, 71, and 115 new energy levels for the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O isotopologues, respectively. The results are compared with the available databases and discussed in regard of previous investigations by Fourier transform spectroscopy. The spectrum analysis has showed that most of the transitions which cannot be assigned to water are very weak and are due to impurities such as carbon dioxide and ammonia, leaving only about 3% of the observed transitions unassigned. The interest of a detailed knowledge of water absorption for trace detectors developed in the 1.5 μm range is underlined: for instance HDO contributes significantly to the considered spectrum while no HDO line parameters are provided by the HITRAN database.     

First measurement of the helicity-dependent γ p?pη differential cross-section

The helicity dependence of the γ p↦pη reaction has been measured for the first time at a center-of-mass angle θ^* _η = 70^° in the photon energy range from 780 MeV to 790 MeV. The experiment, performed at the Mainz microtron MAMI, used a 4π-detector system, a circularly polarized, tagged photon beam, and a longitudinally polarized frozen-spin target. The helicity 3/2 cross-section is found to be small and the results for helicity 1/2 agree with predictions from the MAID analysis. Received: 19 December 2002 / Accepted: 10 March 2003 / Published online: 20 May 2003     

LIPSCHITZ STABILITY OF GENERAL CONTROL SYSTEMS Ⅱ.IN TERMS OF TWO MEASURES

1IntroductionStabilityintermsoftwomeasures,thisconceptenableustounifyava-rietyofstabilityconceptsandtoofferageneralandunifiedframeworkforinvestigationofstabilitytheory.AndtheoriginalLiapunovtheoremshavebeenextended,generalizedandweakenedinvariousaspects[3…     

Ethylene polymerization by novel Ziegler–Natta‐type catalysts obtained in situ by the oxidative addition of 8‐hydroxyquinoline‐based ligands to bis(1,5‐cyclooctadiene)nickel(0) and methylaluminoxane

Novel catalytic systems, prepared in situ by the oxidative addition of 8‐hydroxyquinoline ligands to bis(1,5‐cyclooctadiene)nickel(0) and activated by methylaluminoxane, were studied in ethylene polymerization. When 8‐hydroxyquinoline was employed, only oligomeric products were obtained. On the contrary, 5,7‐dinitro‐8‐hydroxyquinoline gave linear polyethylene (PE), but with a modest activity. For the catalyst based on 5‐nitro‐8‐hydroxyquinoline, the productivity was largely dependent on the content of free trimethylaluminum (TMA) present in the commercial aluminoxane. The progressive optimization of the TMA/oligomeric methylaluminoxane ratio increased the productivity, which reached 700 kg of PE/(mol of Ni × h), by an order of magnitude. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 200–206, 2006     

Semilinear Differential Inclusions in Separable Banach Spaces

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Likelihood estimation of soft-core interaction potentials for Gibbsian point patterns

The likelihood method is developed for the analysis of socalled regular point patterns. Approximating the normalizing factor of Gibbs canonical distribution, we simultaneously estimate two parameters, one for the scale and the other which measures the softness (or hardness), of repulsive interactions between points. The approximations are useful up to a considerably high density. Some real data are analyzed to illustrate the utility of the parameters for characterizing the regular point pattern.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

The elimination of fast variables in complex chemical reactions. III. Mesoscopic level (irreducible case)

The master equation for a complex chemical reaction cannot always be reduced to a simpler master equation, even if there are fast and slow individual reaction steps. Nevertheless the elimination of intermediates can be carried out with the help of the-expansion. This is illustrated with a well-known complex reaction: the dissociation of N₂O₅. It is shown that the intrinsic fluctuations in the N₂O₅ decay are larger than those implied by the master equation suggested by the macroscopic rate law.