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.     

Isomorphic electron orbitals for vibronic flexibility in a cyclopropenyl radical molecular device

Summary The vibronic character of this molecular device has been studied using isomorphic electron orbitals. The leading role of the softest vibrational mode for the electron transport process is stressed by the quantum mechanical treatment of the rearrangement operator. The theory was used to investigate the possible function of the soliton valve, which has been suggested as a switching tip. The electronic flexibility of the cyclopropenyl radical with respect to molecular vibrations, which is important for the function of the molecular device, is well characterized by the hardness and softness of the electron structure in terms of the orbital energy-occupation number correlation diagram.     

A quantum chemical study of interchain hopping model of negatively charged solitons in polyacetylene

Phonon-assisted interchain hopping of negatively charged solitons in polyacetylene has been studied using a local chemical reaction model CH + CH₄ → CH₄ + CH. Quantum chemical characteristics of the electron transfer process have been analyzed in terms of the dynamic electron density and the mutual polarization moment. The CH stretching vibrational motion of CH₄, which is a local model of the sp³ defect, has been found to play a significant role for the electron transfer. The excitation of the corresponding vibrational mode of the sp³ defect would promote the interchain hopping of the charged soliton. The electron transfer process has also been studied in terms of the “regional” density functional theory. It has been shown that the driving force of the electron transfer is represented by the regional chemical potentials.     

Hydrothermal Synthesis of Mo-Based Oxide Catalysts and Selective Oxidation of Alkanes

Mo-V-M(=Al, Ga, Bi, Sb and Te)–O mixed oxide catalysts were synthesized hydrothermally for the first time, characterized structurally, and tested for ethane and propane oxidation after activation by various ways. These catalysts were black solids of rod-shaped (fiber like) crystals, which had a layer structure in the direction of fiber axis and a high dimensional arrangement of metal octahedra in the cross-section plane. These fresh crystalline materials became active for catalytic oxidation of alkanes after heat-treatment at 600 °C and subsequent grinding in order to increase exposed plane of the cross-section. The resulting catalysts were very active for an oxidative dehydrogenation of ethane with 80% of the ethylene selectivity in the reaction temperature range of 300 to 400 °C and also showed about 50% selectivity to acrylic acid in the propane oxidation. Multi-functional character which derived from the high dimensional structure of the catalysts and mechanism of the selective alkane oxidation were discussed.     

Second-order perturbational treatment of normal coordinates in the string model for the hydration reaction of formaldehyde

A perturbation theory for normal coordinates of nonadiabatic solvation is presented by means of the “string model” of chemical reactions. The dynamic normal coordinate is introduced for the perturbational treatment of the “intrinsic” normal coordinates that are orthogonal to the reaction path. The reaction is defined as the intrinsic reaction coordinate (IRC ) that is treated as a string. The string is thrown in the external force field that acts as a nonadiabatic source of perturbation. As an application of the present treatment, the effect of a water molecule for hydration reaction of formaldehyde is calculated. A second-order perturbation effect for the enhancement of the reaction rate is found.     

Vibronic interactions and possible electron pairing in the photoinduced excited electronic States in molecular systems: a theoretical study

Electron-phonon interactions in the photoinduced excited electronic states in molecular systems such as phenanthrene-edge-type hydrocarbons are discussed and compared with those in the monoanions and cations. The complete phase patterns difference between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) (the atomic orbitals between two neighboring carbon atoms combined in phase (out of phase) in the HOMO are combined out of phase (in phase) in the LUMO) are the main reason that the C-C stretching modes around 1500 cm(-1) afford much larger electron-phonon coupling constants in the excited electronic states than in the charged electronic states. The frequencies of the vibrational modes that play an essential role in the electron-phonon interactions for the excited electronic states are similar to those for the monoanions and cations in phenanthrene-edge-type hydrocarbons. Possible electron pairing and Bose-Einstein condensation in the photoinduced excited electronic states as well as those in the monoanions and cations in molecular systems such as phenanthrene-edge-type hydrocarbons are also discussed.     

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.