On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Composition of particles emitted at largep T and medium angles inpp,dd, andαα collisions at the CERN intersecting storage rings

The relative yields of kaons and protons compared with the yield of pions at highp _T and polar angles θ away from 90° (in the range from 10° to 45°) are presented forpp, dd, and αα interactions at a centre-of-mass energy \(\sqrt {s_{NN} } = 31\) GeV per nucleon-nucleon collision. The measured particle ratios depend on the atomic mass numberA of the beam particles and on θ. TheA dependence of the ratios becomes stronger for largerp _T and is more pronounced at smaller polar angles.     

High-p T αα andαp interactions

Properties of secondaries associated with a high-p _T charged trigger particle (3<p _T <5 GeV/c) were studied for αp and αα interactions at c.m. energies \(\sqrt s = 88\) GeV and 125 GeV, respectively. Thep _T distributions of secondaries in the away-jet and trigger-jet regions were compared with those for high-p _{T pp} interactions. No statistically significant differences were seen, except at lowp _T . Momentum and angular distributions of spectator and leading protons were studied as a function of charge and rapidity of the trigger hadron. The observed correlations between trigger charge and number of spectator protons provide evidence of valence quark contributions to the trigger jet.     

Revaluation of the correlation of isomer shift with Np-O bond length in various neptunyl(V and VI) compounds

Summary The correlations of isomer shifts in various neptunyl(V and VI) compounds with crystallographic structures were revaluated. A linear correlation between the isomer shifts of neptunyl(VI) compounds and Np-O bond lengths of neptunyl group has been demonstrated. On the other hand, it has been evidenced that the isomer shifts of neptunyl(V) compounds are correlated much stronger with the mean Np-O distances in the crystals than the lengths in neptunyl(V) group.     

Synthetic studies on cyathins: enantioselective total synthesis of (+)-allocyathin B2

[reaction: see text] The enantioselective total synthesis of (+)-allocyathin B(2) has been achieved. Our approach features a convergent enantioselective construction of the 5-6-7 tricyclic core system using the originally developed chiral building blocks via asymmetric catalysis, the intramolecular aldol reaction in high yield, successful samarium diiodide-mediated ring expansion, and a newly developed double-bond installation method.     

NMR and MO Studies on the Molecular Structure of a Fluoranthene-Benzene Complex

Summary. Fluoranthene (FA) forms a 1:1 van der Waals complex with benzene in cyclohexane. The ¹H NMR spectrum of this complex shows that the FA moiety in the complex state has five kinds of hydrogen atoms and that the ¹H NMR peaks assigned to the protons attached to the naphthalene skeleton are largely shifted to higher magnetic field on complex formation with benzene. These observations indicate that the complex takes the structure of C_S symmetry, in which the benzene molecule mainly interacts with the electronic system localized on the naphthalene moiety of FA. The present ab initio calculations reproduce well the ¹H NMR spectral shifts mentioned above and the experimentally predicted C_S structure of the complex. According to the PPP calculations for the electronic absorption spectral changes on the complex formation, the FA-benzene complex is considered to take a sandwich type structure.     

Magnetic structure of graphite ribbon

Anoble mechanism of spin polarization is proposed for finite graphite sheet with edge. For graphite ribbon with zigzag edge, there appear peculiar ‘edge states’. These localized states comprise nearly flat band at the Fermi level, which easily causes magnetic instability. Magnetic structure is suggested from Hartree-Fock analysis of the Hubbard model, where huge magnetic moments are induced at around both of edges by weak HubbardU and are coupled antiferromagnetically with each other.     

Photophysics of aromatic molecules with low-lying pi sigma* states: excitation-energy dependence of fluorescence in jet-cooled aromatic nitriles

Excitation-energy dependence of fluorescence intensity and fluorescence lifetime has been measured for 4-dimethylaminobenzonitrile (DMABN), 4-aminobenzonitrile (ABN), 4-diisopropylaminobenzonitrile (DIABN), and 1-naphthonitrile (NN) in a supersonic free jet. In all cases, the fluorescence yield decreases rather dramatically, whereas the fluorescence lifetime decreases only moderately for S1 (pi pi*, L(b)) excess vibrational energy exceeding about 1000 cm(-1). This is confirmed by comparison of the normalized fluorescence excitation spectrum with the absorption spectrum of the compound in the vapor phase. The result indicates that the strong decrease in the relative fluorescence yield at higher energies is due mostly to a decrease in the radiative decay rate of the emitting state. Comparison of the experimental results with the TDDFT potential energy curves for excited states strongly suggests that the decrease in the radiative decay rate of the aminobenzonitriles at higher energies is due to the crossing of the pi pi* singlet state by the lower-lying pi sigma*(C[triple bond]N) singlet state of very small radiative decay rate. The threshold energy for the fluorescence "break-off" is in good agreement with the computed energy barrier for the pi pi*/pi sigma* crossing. For NN, on the other hand, the observed decrease is in fluorescence yield at higher excitation energies can best be attributed to the crossing of the pi pi* singlet state by the pi sigma* triplet state.