This paper is devoted to (discrete) p -adic dynamical systems, an important domain of algebraic and arithmetic dynamics. We consider the following open problem from theory of p -adic dynamical systems. Given continuous function f:Zp→Zpf:Zp→Zp. Let us represent it via special convergent series, namely van der Put series. How can one specify whether this function is measure-preserving or not for an arbitrary p ? In this paper, for any prime p , we present a complete description of all compatible measure-preserving functions in the additive form representation. In addition Blazer Nike we prove the criterion in terms of coefficients with respect to the van der Put basis determining whether a compatible function f:Zp→Zpf:Zp→Zp preserves the Haar measure.
A permeable quartzose sandstone was subjected to full-scale cutting tests under a chisel-type drag pick, in both dry and fully saturated conditions. Contrary to the results observed from disc cutting tests in the same setup with the same rock (Abu Bakar and Gertsch, 2011), saturation actually increased the cutting (drag) and normal (vertical) Basket Nike Blazer forces by 9.9% and 9.4%, respectively. The specific energy Blazer Nike Pas Cher of cutting also was greater in the saturated samples, by 28%. More expectedly, the relation of fracture surface area to specific energy was confirmed through several descriptors of chip size distribution, including the Rosin–Rammler x′ parameter, and the empirical coarseness index. An inverse power relation between coarseness index and specific energy was also confirmed.
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