413 research outputs found

    A nilpotent IP polynomial multiple recurrence theorem

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    We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

    Simultaneous dense and nondense orbits for commuting maps

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    Form discrete- to continuous-time ergodic theorems

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    We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest

    Rigidity and Non-recurrence along Sequences

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    Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

    Optimization of the self-sufficient thorium fuel cycle for CANDU power reactors

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    The results of optimization calculations for CANDU reactors operating in the thorium cycle are presented in this paper. Calculations were performed to validate the feasibility of operating a heavy-water thermal neutron power reactor in a self-sufficient thorium cycle. Two modes of operation were considered in the paper: the mode of preliminary accumulation of 233U in the reactor itself and the mode of operation in a self-sufficient cycle. For the mode of accumulation of 233U, it was assumed that enriched uranium or plutonium was used as additional fissile material to provide neutrons for 233U production. In the self-sufficient mode of operation, the mass and isotopic composition of heavy nuclei unloaded from the reactor should provide (after the removal of fission products) the value of the multiplication factor of the cell in the following cycle K>1. Additionally, the task was to determine the geometry and composition of the cell for an acceptable burn up of 233U. The results obtained demonstrate that the realization of a self-sufficient thorium mode for a CANDU reactor is possible without using new technologies. The main features of the reactor ensuring a self-sufficient mode of operation are a good neutron balance and moving of fuel through the active core

    Nonconventional Large Deviations Theorems

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    We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation
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