In this paper, we investigate metric properties and dispersive effects of strongly mixing transformations on general metric spaces endowed with a probability measure; in particular, we investigate their connections with the theory of generalized (α-harmonic) diameters on general metric spaces. We first show that the known result by R. E. Rice ([Aequationes Math. 17(1978), 104-108], Theorem 2) (motivated by some physical phenomena and offer some clarifications of these phenomena), which is a substantial improvement of Theorems 1 and 2 due to T. Erber, B. Schweizer and A. Sklar [Comm. Math. Phys., 29 (1973), 311 – 317], can be generalized in such a way that this result remains valid when "ordinary diameter" is replaced by "α-harmonic diameter of any finite order". Next we show that  "ordinary essential diameter" in the mentioned Rice's result can be replaced by the" essential α-harmonic diameter  of any finite order". These  results also complement the previous results (on dynamical systems with discrete time and/or generalised diameters) of N. Faried and M. Fathey, H. Fatkic, E. B. Saff, S. Sekulovic and V.  Zakharyuta.

Multi-core processors offer a growing potential of parallelism but pose a challenge of program development for achieving high performance in applications. This pape r presents a comparison of the five parallel programming models for implementing parallel programs in C++ on multi -core computer systems. The models under consideration are Intel®'s Thread Building Blocks (TBB), OpenMPI, Intel®'s Cilk™ Plus, OpenMP and Pthreads. For demonstration purposes multiple parallel implementations of an algorithm for matrix multiplication suitable for parallelization were created. The main goal of this paper is a comprehensive comparison of chosen models with respect to the following criteria: performance and coding effort required.