Best Approximation and Perturbation Property in Hilbert Spaces

We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.The authors thank the referees for valuable suggestions.K.F. Ng - This author was partially supported by Grant A0324638 from the National Natural Science Foundation of China and Grants (2001) 01GY051-66 and SZD0406 from Sichuan Province. Y.R. He -This author was supported by a Direct Grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong.     

Three-dimensional visualization of diffusion flame shapes under acoustic excitation using stereoscopic imaging and reconstruction technique

Stereoscopic imaging and reconstruction technique is introduced to reconstruct the flame structures that are subject to acoustic excitation. The laminar diffusion flame under investigation was created in a cylindrical tube and excited by a loudspeaker. Stereo images were taken at a shutter speed of 1/10000^th second using a ‘stereo camera’ and the depth cue of the flame structures along the camera viewing direction were then computed using machine vision methodology. By visualizing the computed three-dimensional flame models, as well as judging the corresponding attribute such as surface gradient, the understanding of the flame and acoustic wave interaction could be improved.     

Application of the ray tracing method in studying tracks in SSNTDs

The ray tracing method was applied to study etched tracks from α-particles in CR-39 solid-state nuclear track detectors. The transmission mode of a microscope operation was simulated. A track was considered as a set of small triangular elements, and the brightness of all elements was calculated systematically through the entire track to create the final image. Preliminary results are given for α-particle tracks in the CR-39 detector for initial energies of 4 and 4.5 MeV, and incident angles of 40 and 90°, respectively. Total reflection, as well as the slope of a surface element in the track wall, were identified as the main factors that affect the brightness of that element. At this stage, comparisons with experimental results can be made in terms of the average grey levels for the entire tracks.     

Properties of a local pairing model of high-Tc superconductivity

A simulation technique is used to study the properties of the “hole modulated hopping” model introduced by Hirsch. The superconducting order parameter, energy gap and pair size have been determined for a range of particle densities and temperatures in the neighbourhood of the superconducting phase transition. Results are consistent with the interpretation of the superconducting transition to be Bose-like at low hole densities and BCS-like at high hole densities, with a crossover near the T_c maximum in the T_c versus hole density curve. This behaviour is related to the existence of small non-overlapping pairs at low hole densities and large strongly interpenetrating pairs at hole densities above the T_c maximum.     

On strongly jump traceable reals

In this paper we show that there is no minimal bound for jump traceability. In particular, there is no single order function such that strong jump traceability is equivalent to jump traceability for that order. The uniformity of the proof method allows us to adapt the technique to showing that the index set of the c.e. strongly jump traceables is -complete.     

Nucleon currents between highly excited nuclei: (II). Influence of the relative motion

A finite-temperature Thomas-Fermi method has been used to study the nucleon flux between two hot semi-infinite slabs of nuclear matter in arbitrary relative motion. As an application, we estimate the imaginary part of the optical potential associated with nucléon transfer at the strong absorption radius. Analytical fits to the exact results are given for head-on and tangential collisions at zero temperature.     

Fission of medium mass elements induced by 126 MeV 14N ions

Ni, Se, Mo, Ag, Ho and Au targets were bombarded by 126 MeV ¹⁴N ions in order to study compound nucleus fission. The large angular momentum brought in by the projectile implies much greater fission probabilities than those obtained when the same compound nuclei are created with light projectiles. We employed two surface-barrier detectors. The results obtained are fission cross sections, angular correlations and kinetic energy and mass distributions. Fissilities are found to decrease exponentially with the ratio Z²/A of the fissioning nucleus until Z²/A = 19 (molybdenum) and then to increase again for lower Z²/A. The calculations of fissilities performed with the fission barrier of Myers and Swiatecki, and including angular momentum effects in evaporation-fission competition, gives the same variation of fissilities as the experimental one, but the results obtained are lower than the experimental values. The total kinetic energies measured are higher than the predictions of the liquid drop model by around 10 MeV (Nix). The shapes of the mass distributions indicate that the value of x_BG (Businaro-Gallone point) is lower than 0.4 (silver).