The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

Polymer-supported and polymeric chiral guanidines: Preparation and application to the asymmetric Michael reaction of iminoacetate with methyl vinyl ketone

Summary Polymer-supported and polymeric chiral guanidines carrying an imidazolidine skeleton are designed as polymer-based base catalysts. Thus, (R)-2-[(S)-1-hydroxymethyl-2-phenylethylimino]-4-phenylimidazolidine was newly prepared from (R)-phenylglycine as the key functional unit of these guanidines. Application of the polymer-based chiral guanidines to the asymmetric Michael reaction of t-butyl diphenyliminoacetate with MVK led to expected asymmetric induction in the Michael adduct with moderate enantioselectivity in the use of the latter polymeric chiral guanidines.     

Advances in organic synthesis using polymer-supported reagents and scavengers under microwave irradiation

Summary Microwave-assisted and polymer-supported organic syntheses have emerged independently as versatile tools for rapid generation of organic molecules. Chemists are increasingly looking for a combination of both techniques for efficient organic synthesis. This review covers the recent literature on organic synthesis using microwave heating in conjunction with polymer-supported reagents and scavengers.     

Temperature dependent structural and optical properties of nanocrystallineCdO thin films deposited by sol–gel process

Nanocrystallites of cadmium oxide (CdO) thin films were deposited by sol–gel dip coating technique on glass and Si substrates. XRD and TEM diffraction patterns confirmed the nanocrystalline cubic CdO phase formation. TEM micrograph of the film revealed the manifestation of nano CdO phase with average particle size lying in the range 1.6–9.3 nm. UV–Vis spectrophotometric measurement showed high transparency (nearly 75% in the wavelength range 500–800 nm) of the film with a direct allowed bandgap lying in the range 2.86–3.69 eV. Particle size has also been calculated from the shift of bandgap with that of bulk value for the films for which the particles sizes are comparable to Bohr exitonic radius. The particle size increases with the increase in annealing temperature and also the intensity of XRD peaks increases which implies that better crystallinity takes place at higher temperature.This revised version was published online in August 2005 with a corrected issue number.     

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.     

Intranuclear-Cascade model calculation of photofission probabilities for actinide nuclei

We have calculated the fission probabilities for ²³⁷Np, ^{233, 235, 238}U, ²³²Th, and ^natPb following the absorption of photons with energies from 68 MeV to 3.77 GeV using the RELDIS Monte Carlo code. This code implements the cascade-evaporation-fission model of intermediate-energy photonuclear reactions. It includes multiparticle production in photoreactions on intranuclear nucleons, pre-equilibrium emission, and the statistical decay of excited residual nuclei via competition of evaporation, fission, and multifragmentation processes. The calculations show that in the GeV energy region the fission process is not solely responsible for the entire total photoabsorption cross-section, even for the actinides. The fission probabilities are 80-95% for ²³³U, ²³⁵U, and ²³⁷Np, 70-80% for ²³⁸U, and only 55-70% for ²³²Th. This is because certain residual nuclei that are created by deep photospallation at GeV photon energies have relatively low fission probabilities. The results of those model calculations are in reasonable agreement (at the 10% level) with recent experimental data on relative photofission cross-sections for ²³⁷Np and ^{233, 235, 238}U (but not for ²³²Th or ^natPb) from the Saskatchewan and Jefferson Laboratories over a very wide range in photon energy. Using our calculated fission probabilities plus the total photoabsorption cross-sections per nucleon, estimated from previous cross-section data for nuclei from C to Pb, we can infer absolute photofission cross-sections for the actinide nuclei and compare them with the SAL and JLab results. The resulting discrepancies, however, clearly demonstrate the need for direct measurement of the total photoabsorption cross-sections for the heavy actinides.     

Large momenta fluctuations of charm quarks in the Quark-Gluon Plasma<Superscript>⋆</Superscript>

We show that large fluctuations of D-mesons kinetic-energy (or momentum) distributions might be a signature of a phase transition to the Quark-Gluon Plasma (QGP). In particular, a jump in the variance of the momenta or kinetic energy, as a function of a control parameter (temperature or Fermi energy at finite baryon densities) might be a signature for a first-order phase transition to the QGP. This behavior is completely consistent with the order parameter defined for a system of interacting quarks both at zero temperature (and finite baryon densities) or at finite temperatures which shows a jump in correspondence with a first-order phase transition to the QGP. The J/Ψ displays exactly the same behavior of the order parameter and of the variance of the D-mesons. We discuss implications for relativistic heavy-ion collisions within the framework of a transport model and possible hints for experimental search.     

Elastic scattering via quark structure of nucleons

In the framework of the Glauber multiple-scattering theory, the elastic collisions of proton-proton (pp) at the center-of-mass energies = 23.5, 30.7, 44.7, and 52.8 GeV and alpha-proton (p) at = 88 and 89 GeV are analyzed by considering the quark structure of their constituents. The differential cross-section containing the full multiple-scattering series between their quarks is calculated using Gaussian forms for the quark density and quark-quark (QQ) scattering amplitudes. The results obtained from the quark model and the conventional nucleon model are compared with the experimental data. The comparison shows that the nucleon model reproduces the experimental data more satisfactorily than the quark model, and both approaches have limited success in describing the data at such energies. The agreement with the experimental data is improved by the inclusion of the phase variation.