The logic of quantum systems with diagonal singularities

The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not the conventional logic of Hilbert space, because only finite combinations of prepositions are allowed.     

57Fe Mössbauer study of amorphous and nanocrystalline Fe73.5Nb3Cu1Si13.5B9 after neutron irradiation

⁵⁷Fe Mössbauer spectroscopy is used to study neutron irradiation induced changes in the short-range order of Fe_73.5Nb₃Cu₁Si_13.5B₉ alloy. The samples are investigated in both amorphous and nanocrystalline states. Neutron irradiation leads to an increase of the standard deviation of a hyperfine field distribution (HFD), implying rearrangement of the atoms towards disordering. Simultaneously, changes in the average value of the hyperfine field and a net magnetic moment position occur as a consequence of a spin reorientation, atom mixing and microscopic stress centres which are introduced by neutron irradiation.     

Low-temperature transport properties of UCu5

The electrical resistivity (T) and the thermal conductivity (T) have been measured for UCu₅ in the temperature range between 0.02 and 20 K. Two distinct anomalies in (T) are due to previously established phase transitions at approximately 15 and 1 K, respectively. They indicate considerable changes in the electronic structure of this compound, implying sizeable truncations of the Fermi surface with decreasing temperature at both transitions. In almost the entire covered temperature range the thermal conductivity is dominated by phonon contributions. Its temperature dependence is fairly well reproduced by a calculation considering phonon scattering by electrons and by point defects. At very low temperatures, asT approaches 0 K, the Wiedemann-Franz law _e L ₀ T, where _e is the electronic part of (T) andL ₀ is the Lorenz number, is almost perfectly fulfilled.     

Photoluminescence of Anisotropically etched silicon

Visible room-temperature luminescence of Anisotropically Chemically Etched (ACE) silicon under spontaneous chemical surface modification in HNO₃:HF solution is reported. The material is investigated by SEM, AES, IR transmission and Raman scattering methods.     

Pulsed-laser photolysis of Mn2(CO)10: A time-resolved fluorescence study

Mn₂(CO)₁₀ was photolysed in the gas phase by the XeCl-excimer laser with fluence in the range 25–300 mJ/cm² and a dye laser. The UV/VIS emission of the products was probed on a nanosecond time scale. The emission from excited states of metal atoms was detected only. The Mn atoms are predominantly formed in their ground statea ⁶ S _{2 1/2}. The absorption of one photon and the subsequent relaxation process leads to the formation ofz ⁶ P _J ⁰ (J = 11/2, 21/2, 31/2) states and emission of photons at a wavelength of 403 nm. The formation of the excited statese ⁸ D _{5 1/2},z ⁶ F _{4 1/2} ⁰ ande ⁶ D _{4 1/2} and the subsequent emission observed at wavelengths of 357, 383 and 446 nm requires the absorption of two photons by the ground-state Mn atoms. In addition, transition from thea ⁶ D _j (J = 11/2, 21/2) lower states were observed in the wavelength-resolved Laser-Induced Fluorescence (LIF) spectra.     

Thermal and mechanical coupling between successive pulses in KrF-excimer-laser ablation of polyimide

Multiple-shot effects in laser processing and ablation of polyimide are examined and are found to be the dominant phenomena for processes involving several hundreds or thousands of pulses. For fluences less than 260 mJ/cm², it was found that it is impossible to cut through 75 m polyimide foils for an arbitrarily large number of excimer pulses even though this fluence is more than ten times the single-shot ablation threshold. The halt in etching is due to the formation, over a number of shots, of a robust carbon matrix with a deep surface roughness which is also responsible for laser-induced electrical conductivity. The effect of thermal coupling between successive shots is shown to be a dominant factor in determining the electrical properties of the carbon layer. Differences in electrical conductivity of up to 12 orders of magnitude were found for only small differences in repetition rate. Transmission electron microscopy revealed the changes in microstructure responsible for the dramatic differences in electrical properties.     

Spectral properties of operators of the theory of harmonic potential

We classify the points of the spectrum of the operatorsB andB ^* of the theory of harmonic potential on a smooth closed surfaceS ³. These operators give the direct value onS of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators inL ₂ (S). We prove that the half-interval [–2, 2) is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operatorsB andB ^* on ellipsoidal surfaces.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.This research was partially supported by the Russian Foundation for Basic Research.     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

Bifurcation of controllability regions in a plane by separatrix splitting

For a nonlinear controlled dynamic system of the form where u(t) is a bounded piecewise-continuous control and m u(t) n, the article studies bifurcations (qualitative changes) of controllability (reachability) regions due to merging and subsequent splitting of separatrices of the equilibrium states of auxiliary autonomous systems. Conditions for continuous and discontinuous changes of the controllability (reachability) regions are established. Bifurcations of controllability regions of Duffing equations are considered as an illustration.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 70–81, 1993.