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Upper estimate of martingale dimension for self-similar fractals
We study upper estimates of the martingale dimension of diffusion
processes associated with strong local Dirichlet forms. By applying a general
strategy to self-similar Dirichlet forms on self-similar fractals, we prove
that for natural diffusions on post-critically finite self-similar sets
and that is dominated by the spectral dimension for the Brownian motion
on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc
The liquid Miscibility Gap and the Distribution of Silver Between Speiss and Metallic Lead in the Pb-Fe-As, Pb-Cu-As and Pb-Fe-Cu-As System at 1200℃
The liquid miscibility gap and the distribution of silver between speiss and metallic lead for the Pb-Fe-Cu-As quarternary system have been determined at 1200℃. The miscibility gap in the Pb-Fe-As system covered a wide composition range. Molten lead containing a small amount of arsenic equilibrated with the speiss which consisted of iron arsenide with a small quantity of dissolved lead. The miscibility gap in the Pb-Cu-As system was also determined. In this system, the solubility of lead in speiss had a minimum with increasing arsenic content. In the quarternary system, the region of immiscibility was found to be distributed between the above, two, ternary systems on a pseudoternary phase diagram and was dependent on the cu/Fe+Cu ratio in speiss. The arsenic content in molten lead increased sharply beyond a definite quantity of arsenic in speiss. The behaviour of the distribution ratio of silver, K_, defined as wt.% Ag in speiss/wt.% Ag in metallic lead was summarized as follows : (1) In the Pb-Fe-As system, the values for K_ were low when the arsenic content in speiss was below 40% ; but above this range, the values increased sharply. (2) In the Pb-Cu-As system, K_ was around 1.2 for all speiss compositions investigated. (3) In the Pb-Fe-Cu-As system, the value of K_ was distributed between those obtained for the two ternary systems. The distribution ratios of silver derived from practical data agreed well with present work. From these results, a pyrometallurgical process in which lead and precious metals are recovered as bullion and in which arsenic is fixed and discarded as iron arsenide speiss can be proposed
Fuel Hydrogen Retention of Plasma Facing Material and Its Removal by Inert Gas Glow Discharges
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