Irregular Behavior of Solutions for Fisher’s Equation

This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some estimate of the difference of two distinct solutions and a comparison technique. Dedicated to Professor Pavol Brunovsky on his 70th birthday.     

Grow-up rate of solutions for a supercritical semilinear diffusion equation

We study solutions of the Cauchy problem for a supercritical semilinear parabolic equation which converge to a singular steady state from below as t→∞. We show that the grow-up rate of such solutions depends on the spatial decay rate of initial data.     

High-speed counter-current chromatography of apple procyanidins

Apple procyanidins were separated by high-speed counter-current chromatography using a type-J multilayer coil planet centrifuge. Several two-phase solvent systems with a wide range of hydrophobicities from a non-polar hexane system to polar n-butanol systems were evaluated their performance in terms of the partition coefficient and the retention of the phase. The best separation of procyanidins B and C was achieved with a two-phase solvent system composed of n-butanol-methyl tert.-butyl ether-acetonitrile-0.1% trifluoroacetic acid (2:4:3:8) using the lower phase as a mobile at a flow-rate of 1.0 ml/min.     

FLAVIN-PHOTOSENSITIZED MONOMERIZATION OF DIMETHYLTHYMINE CYCLOBUTANE DIMER IN THE PRESENCE OF MAGNESIUM PERCHLORATE

We have investigated the photosensitized monomerization of the cis,syn -cyclobutane dimer of 1,3-di-methylthymine using riboflavin tetraacetate and a 5-deazaflavin derivative as photosensitizer. Although little monomerization of the dimer is induced by photoexcitation of the flavins in the absence of any additives, the flavins can function as an efficient photosensitizer in the presence of magnesium perchlorate. Mechanistic studies involving spectroscopic, quantum-yield and flash-photolysis measurements demonstrated that the photosensitized monomerization exclusively proceeds through electron transfer from the dimer to the triplet flavins complexed with Mg²⁺. The effects of magnesium perchlorate are compared with those on the chloranil-photosensitized monomerization and also with the effects of HClO₄ on the flavin-photosensitized reaction.     

SuperB production,matter stability and gauge hierarchy in SUSY GUTs

We analyze the connections between the problems of the cosmological baryon asymmetry (CBA), matter stability and mass hierarchy in supersymmetric Grand Unified models. We show that the typical delay of the phase transition in supersymmetric theories as well as a natural solution to the triplet-doublet Higgs hierarchy problem imply baryon production after the Grand Unification phase transition which in a wide class of SUSY GUTs takes place atT～10⁹–10¹⁰ GeV. Light Higgs colour triplets as a means of producing the CBA are discussed in detail. An alternative mechanism involving a singlet superfield is proposed leading to striking consequences in proton decay with the appearance of (B+L) conserving modes with a muon and a kaon in the final state:n→μ^? K ⁺,p μ ^2212;π⁺ K ⁺ and a lifetime of 10³¹ years.     

Ionic liquid crystal as a hole transport layer of dye-sensitized solar cells

Use of a new ionic liquid crystal, 1-dodecyl-3-methylimidazolium iodide, and iodine as an electrolyte of dye-sensitized solar cells leads to a high short circuit photocurrent density and a high light-to-electricity conversion efficiency, due to a self-assembled structure of the imidazolium cations, resulting in high conductivity of the electrolyte.     

Naturally massless Higgs doublets in supersymmetric SU(5)

We construct a supersymmetric SU(5) model characterized by: (a) naturally massless doublet Higgs superfields; (b) the natural appearance of “light” coloured triplet Higgses of mass of the order 10¹⁰ GeV, and study proton decay as well as the generation of cosmic baryon asymmetry. We find that an appropriate choice of Higgs sector renders dimension-five operators kinematically irrelevant for the stability of the proton. Proton decay proceeds through Higgs boson exchange in terms of dimension-six operators mainly to ${\overline{v}}_{\mu }{K}^{+},v^{+}{K}^0$.