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

Unauthorized Practice of Law—Limited Practice of Law for Real Estate Closing Officers?—Hagan & Van Kamp, P.S. v. Kassler Escrow, Inc., 96 Wn. 2d 443, 635 P.2d 730 (1981)

In 1979, the Washington legislature enacted RCW chapter 19.62, which authorized certain laypersons to prepare documents and instruments relating to real estate transactions. The statute was passed in response to the Washington Supreme Court\u27s decision in Washington State Bar Association v. Great Western Union Federal Savings and Loan Association. In Great Western, the court held that laypersons who received compensation for the preparation of legal documents were engaged in the unauthorized practice of law. The legislature\u27s response, authorizing the activities prohibited in Great Western, raised questions regarding the scope of legislative and judicial power to define and regulate the practice of law. This Note examines the doctrine of inherent judicial power to regulate the practice of law, as developed by the Washington court, and discusses the relation of this doctrine to the preparation of real estate documents. It recommends that the Washington Supreme Court adopt a limited practice rule or some other guideline to regulate competent lay preparation of real estate documents. Adoption of such a rule would allow the court to maintain its integrity, while best serving and protecting the public

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

Digital Video in the Classroom: Communication Skills for Future Natural Resource Professionals

The Natural Resource Communications course in Oregon State University’s College of Forestry is designed to provide students with the skills to be effective members of a resource organization and techniques for working in the public arena. The course focuses on teamwork and group dynamics, meeting management skills, public relations, interpretation, and public education and outreach. The course has been incorporating student digital video production as a capstone experience synthesizing these skills into a tangible product

How populist attitudes scales fail to capture support for populists in power

Populist attitudes are generally measured in surveys through three necessary and non-compensatory elements of populism, namely anti-elitism, people-centrism, and Manicheanism. Using Comparative Study of Electoral Systems Module 5 (2016-2020) data for 30 countries, we evaluate whether this approach explains voting for populist parties across countries in Asia, Europe and the Americas. We show that the existing scales of populist attitudes effectively explain voting for populists in countries where populist leaders and parties are in opposition but fail to explain voting for populist parties in countries where they are in power. We argue that current approaches assume "the elite" to mean "politicians", thus failing to capture attitudes towards "non-political elites" often targeted by populists in office - in particular, journalists, academics/experts, bureaucrats, and corporate business leaders. The results reveal limits to the usefulness of existing survey batteries in cross-national studies of populism and emphasize the need to develop approaches that are more generalizable across political and national contexts

Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces

This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on particular fractals and further less regular cases as well. The proof is based on a new chaining argument and it is free of volume growth assumptions

On the role of shake-off in single-photon double ionization

The role of shake-off for double ionization of atoms by a single photon with finite energy has become the subject of debate. In this letter, we attempt to clarify the meaning of shake-off at low photon energies by comparing different formulations appearing in the literature and by suggesting a working definition. Moreover, we elaborate on the foundation and justification of a mixed quantum-classical ansatz for the calculation of single-photon double ionization