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By iterating the map, one obtains a dynamical system called an "interval exchange transformation".
Many research works have been carried out in the fields of information exchange, transformation, discovery and reuse.
Considering the parallel with cutting or shuffling a deck of cards, one can ask whether an interval exchange transformation can truly mix the subintervals.
What Avila and Forni showed is that almost every interval exchange transformation is weakly mixing; in other words, if one chooses at random an interval exchange transformation, the overwhelmingly likelihood is that, when iterated, it will produce a dynamical system that is weakly mixing.
Bacterial species have mechanisms for gene exchange (transformation, conjugation and transduction), and genetic recombination is believed to play a prominent role in diversifying species by distributing variation and generating new allele combinations [ 11].
This correlation in the data gives rise to an approximate symmetry for the likelihood, L (θ ; X t ) ≈ L (θ ; Φ j, k X t ), where Φ j, k is the exchange transformation j ↔ k.
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Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system.
Consequently, Utah, a state with strong antipathy to paying taxes, received a government windfall "to take care of all of their needs for really the next generation" - Steele describes rebuilt infrastructure, sewer lines, land exchanges, transformation of ski resorts into world-class resorts, etc.
As defined by Merriam-Webster, collisions are "an encounter between particles (such as atoms or molecules) resulting in exchange or transformation of energy".
Gene exchange by transformation were found to occur more frequently between thermophilic T. scotoductus and Meiothermus rather than between the extreme thermophiles.
Infinite dynamic interactions between root exudates, microbial activity, genetic exchange, nutrient transformation, and gradient diffusion are most likely the factors shaping this below-ground world (for review, please see [ 34]).
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