Small Deviations of Riemann-Liouville Processes In lq Spaces With Respect To Fractal Measures

We investigate Riemann–Liouville processes R_H, with H> 0, and fractional Brownian motions B_H, for 0 < H <1, and study their small deviation properties in the spacesL_q([0, 1], µ). Of special interest here are thin (fractal)measures µ, that is, those that are singular with respectto the Lebesgue measure. We describe the behavior of small deviationprobabilities by numerical quantities of µ, called mixedentropy numbers, characterizing size and regularity of the underlyingmeasure. For the particularly interesting case of self-similarmeasures, the asymptotic behavior of the mixed entropy is evaluatedexplicitly. We also provide two-sided estimates for this quantityin the case of random measures generated by subordinators. While the upper asymptotic bound for the small deviation probabilityis proved by purely probabilistic methods, the lower bound isverified by analytic tools concerning entropy and Kolmogorovnumbers of Riemann–Liouville operators. 2000 MathematicsSubject Classification 60G15 (primary), 47B06, 47G10, 28A80(secondary).     

Electrons Mediate the Gas‐Phase Oxidation of Formic Acid with Ozone

Gas‐phase reactions of CO₃^.? with formic acid are studied using Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometry. Signal loss indicates the release of a free electron, with the formation of neutral reaction products. This is corroborated by adding traces of SF₆ to the reaction gas, which scavenges 38 % of the electrons. Quantum chemical calculations of the reaction potential energy surface provide a reaction path for the formation of neutral carbon dioxide and water as the thermochemically favored products. From the literature, it is known that free electrons in the troposphere attach to O₂, which in turn transfer the electron to O₃. O₃^.? reacts with CO₂ to form CO₃^.?. The reaction reported here formally closes the catalytic cycle for the oxidation of formic acid with ozone, catalyzed by free electrons.     

Photochemical Hydrogen Evolution at Metal Centers Probed with Hydrated Aluminium Cations,Al+(H2O)n,n=1–10

Hydrated aluminium cations have been investigated as a photochemical model system with up to ten water molecules by UV action spectroscopy in a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. Intense photodissociation was observed starting at 4.5 eV for two to eight water molecules with loss of atomic hydrogen, molecular hydrogen and water molecules. Quantum chemical calculations for n=2 reveal that solvation shifts the intense 3s–3p excitations of Al⁺ into the investigated photon energy range below 5.5 eV. During the photochemical relaxation, internal conversion from S₁ to T₂ takes place, and photochemical hydrogen formation starts on the T₂ surface, which passes through a conical intersection, changing to T₁. On this triplet surface, the electron that was excited to the Al 3p orbital is transferred to a coordinated water molecule, which dissociates into a hydroxide ion and a hydrogen atom. If the system remains in the triplet state, this hydrogen radical is lost directly. If the system returns to singlet multiplicity, the reaction may be reversed, with recombination with the hydroxide moiety and electron transfer back to aluminium, resulting in water evaporation. Alternatively, the hydrogen radical can attack the intact water molecule, forming molecular hydrogen and aluminium dihydroxide. Photodissociation is observed for up to n=8. Clusters with n=9 or 10 occur exclusively as HAlOH⁺(H₂O)_n-1 and are transparent in the investigated energy range. For n=4–8, a mixture of Al⁺(H₂O)_n and HAlOH⁺(H₂O)_n-1 is present in the experiment.     

Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators

We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators.     

Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift

The phase and the group velocities are calculated in a three-dimensional neighbourhood of the focus of an aberration-free lens illuminated by a spatially Gaussian beam. The Gouy phase shift caused by the diffraction results in superluminal pulse propagation on the optical axis within the Rayleigh range.     

Comparison of small-angle p and pp elastic scattering at 52.8 GeV center-of-mass energy at the CERN intersecting storage rings

Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001|t|0.06 GeV² for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the p and pp differential cross sections yields the p total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both p and pp. Our results show conclusively that the p total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the p and pp total cross section vanishes at very high energy.     

Nanosecond optical pulse shaping in cadmium-sulfide-selenide glasses

Transmission characteristics of a nonlinear Fabry-Perot interferometer containing Cd(S, Se)-glasses were measured using laser pulses of 10 ns duration. The interferometer functioned as an optical limiter and optical discriminator. Optical bistability has not been observed, probably because of the finite relaxation time of the nonlinear effects.     

Decay of the false vacuum at finite temperature

In this paper we study kinetics of the first-order phase transitions in gauge theories with spontaneous symmetry breaking. A general theory of the decay of the metastable phase (false vacuum) at a finite temperature is developed. A number of concrete examples are considered, which will make it possible to study kinetics of phase transitions in a wide class of theories without complicated computer calculations.