We study the divided power structures over a product of operads with distributive law. give systematic method to characterise algebras such from algebra coming each factor operads. operadic derivation, as well $p$-level in characteristic $p$, and Poisson 3.

Quantification of conservative forces in multifrequency atomic force microscopy requires solving the general equations theory expressed terms virials interaction. Power law expressions are commonly utilized when dealing with electrostatic, ferroelectric, magnetic, or long range (van der Waals) forces. Here, we discuss modeled power laws (n), where exponent n covers = 2–5, and employ to explore ...

Power laws, such as Zipf s law, and exponential relations, leading to straight lines in logarithmic or semi-logarithmic scales, are presented in a unified setting. It is shown that the class of size-frequency power laws is larger than the class of rank-frequency power laws. Their ubiquity in all fields of science is illustrated.

In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and it...