A trace theorem for Dirichlet forms on fractals

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field.     

An effective synthesis of N,N-dimethylamides from carboxylic acids and a new route from N,N-dimethylamides to 1,2-diaryl-1,2-diketones

Carboxylic acids were heated at 150 °C in DMF in the presence of 1.25 equiv of thionyl chloride to give corresponding N,N-dimethylamides in good yields. Tandem chlorination and amidation reactions occurred in the one-pot procedure. Dicarboxylic acids needed prolonged reaction time to produce bisamides in good yields. Some benzamides were efficiently converted into corresponding 1,2-diaryl-1,2-diketones (benzils) under acyloin condensation conditions in the presence of 4,4′-di-tert-butylbiphenyl (DBB) in THF. Ultrasonic irradiation effectively accelerates the reaction, but it is not critical. However, the presence of DBB is fatal to the reaction. Although a few synthetic methods for benzils from benzoic acids have been reported so far, this method is one of the most convenient and highly reproducible procedures.     

Reduced crystallization time of YBCO in a fluorine-free MOD process using uv-lamp irradiation

We have studied the crystallization time dependence of the epitaxial YBCO films (t = 0.8 μm) grown on CeO₂-buffered SrTiO₃ substrates by fluorine-free metal–organic deposition using uv-lamp irradiation (uv-MOD). As increasing the time (T₀) for heat treatment at the reaction temperature (760 °C) from 0 to 90 min, J_c and the YBCO 0 0 l XRD intensity are steeply increased and reach their maximum values at T₀ = 10 min. This suggests that the heat treatment required for YBCO crystallization is significantly shortened in uv-MOD compared to conventional all-pyrolytic F-free MOD processes, which consume T₀ = 90–150 min for crystallizing 0.4–0.5-μm-thick films. Scanning electron microscope measurement revealed a drastic change in surface morphology between T₀ = 8 and 10 min, showing a good correspondence to the J_c and XRD data which suggest that the epitaxial growth reaches the film surface at the very early stage in the heat treatment.     

Investigation of void formation beneath thin AlN layers by decomposition of sapphire substrates for self-separation of thick AlN layers grown by HVPE

Void formation at the interface between thick AlN layers and (0 0 0 1) sapphire substrates was investigated to form a predefined separation point of the thick AlN layers for the preparation of freestanding AlN substrates by hydride vapor phase epitaxy (HVPE). By heating 50–200 nm thick intermediate AlN layers above 1400 °C in a gas flow containing H₂ and NH₃, voids were formed beneath the AlN layers by the decomposition reaction of sapphire with hydrogen diffusing to the interface. The volume of the sapphire decomposed at the interface increased as the temperature and time of the heat treatment was increased and as the thickness of the AlN layer decreased. Thick AlN layers subsequently grown at 1450 °C after the formation of voids beneath the intermediate AlN layer with a thickness of 100 nm or above self-separated from the sapphire substrates during post-growth cooling with the aid of voids. The 79 μm thick freestanding AlN substrate obtained using a 200 nm thick intermediate AlN layer had a flat surface with no pits, high optical transparency at wavelengths above 208.1 nm, and a dislocation density of 1.5×10⁸ cm⁻².     

Anatomy of a laminar starting thermal plume at high Prandtl number

We present an experimental study of the dynamics of a plume generated from a small heat source in a high Prandtl number fluid with a strongly temperature-dependent viscosity. The velocity field was determined with particle image velocimetry, while the temperature field was measured using differential interferometry and thermochromic liquid crystals. The combination of these different techniques run simultaneously allows us to identify the different stages of plume development, and to compare the positions of key-features of the velocity field (centers of rotation, maximum vorticity locations, stagnation points) respective to the plume thermal anomaly, for Prandtl numbers greater than 10³. We further show that the thermal structure of the plume stem is well predicted by the constant viscosity model of Batchelor (Q J R Met Soc 80: 339–358, 1954) for viscosity ratios up to 50.     

Electrolytic reduction of Tc(VII) in nitric acid solution using glassy carbon electrode

Electroreduction of Tc(VII) was studied in nitric acid solution using glassy carbon electrode. The electroreduction was conducted at a constant potential –300 mV (vs. Ag/AgCl) with a potentiostat. It was found that the difference of the Tc concentration in the solutions before and after the electrolysis was negligibly small. This means that there were almost no TcO₂ or Tc deposited on the carbon fiber electrode during the electroreduction. Absorption spectra and distribution coefficients obtained by ion-exchange analysis indicated that Tc(VII) was reduced to Tc(IV).This work was financed by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) under the framework of The Development of Innovative Nuclear Technologies.     

Transition density estimates for Brownian motion on affine nested fractals

A class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals. For these fractals estimates on the transition density for the Brownian motion are obtained using the associated Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtain the off-diagonal bound. The approach differs from previous treatments as it uses only the Dirichlet form and no estimates on the resolvent. The bounds obtained are expressed in terms of an intrinsic metric on the fractal.     

Developmental changes of poly(ADP-ribose) polymerase expression in Sarcophaga peregrina

To elucidate the physiological role of poly(ADP-ribose) polymerase (PARP), we studied the levels of PARP mRNA and protein during the developmental stages of Sarcophaga peregrina. PARP mRNA expression changed remarkably throughout the developmental stages. The level of PARP mRNA (the molecular ratio of PARP mRNA to the total RNA) was highest in unfertilized eggs and that of PARP protein (the molecular ratio of PARP protein to the total protein of the crude extract) was high in unfertilized and fertilized eggs and in 1st instar larvae. During the embryogenesis period, the levels of PARP mRNA and protein gradually decreased. The levels of PARP mRNA during larval and pupal periods became less than about 5% of that in unfertilized eggs. After the emergence of adult flies, the levels of PARP mRNA and protein increased both in female and male flies. PARP activity normalized with the total amount of protein in the crude extract changed in parallel to the level of PARP protein throughout the developmental stages. The biological significance of the drastic change of mRNA and protein levels of PARP still remains to be clarified.     

Synthetic studies of carzinophilin. Part 1: Synthesis of 2-methylidene-1-azabicyclo[3.1.0]hexane systems related to carzinophilin

Synthesis of the model compounds of carzinophilin carrying 2-methylidene-1-aza-bicyclo[3.1.0]hexane systems was achieved. Formation of malonylidenes or N-acyl-glycinylidenepyrrolidines was carried out by utilizing Eschenmoser's sulfide contraction or Herdeis's condensation between the 2-methylthio-Δ¹-pyrrolone derivatives and ethyl nitroacetate, respectively. The 1-azabicyclo-[3.1.0]hexane systems were constructed by base-promoted aziridine formation.