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Ronald C. Blakey,Wayne D. Ranneythe “..” This chapter deals with the general case, that is, given an n dimensional random vector X and a collection of n by n matrices, .(.); . ∈ . ⊂ IR, attention is focused on conditions under which (.(.).)(mod 1) converges to a distribution uniform on the unit hypercube, ., as . tends to infinity.统治人类 发表于 2025-3-25 19:12:50
Bivalvia in Ancient Hydrocarbon SeepsThere are many ways of introducing the concept of probability in classical, i.e. deterministic physics. This work is concerned with one approach, known as “the method of arbitrary functions.” To illustrate it consider the following example:存心 发表于 2025-3-25 22:59:17
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https://doi.org/10.1007/978-0-8176-4695-0r of (.)(mod 1) = ((.). (mod 1),..., (.)(mod 1)) is studied in detail in Sect.4.1. A necessary and sufficient condition for weak-star convergence of (.)(mod 1) to a distribution uniform on ., ., as . tends to infinity, is established in Theorem 4.2 (Borel, Hopf, Kallenberg). The random vectorexclamation 发表于 2025-3-26 14:02:27
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https://doi.org/10.1007/978-1-4419-8684-9Generator; Mathematica; Rang; Variation; dynamical systems; ergodic theory; modeling; probability