Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ 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 $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

Surface and Depth Profile Analyses by the Ion Induced Light Emission

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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