نتایج جستجو برای: measure preserving transformation
تعداد نتایج: 606925 فیلتر نتایج به سال:
It is well-known that affine equivalence relations keep nonlineaerity invariant for all Boolean functions. The set of all Boolean functions, Fn, over IF n 2 , is naturally regarded as the 2 n dimensional vector space, IF n 2 . Thus, while analyzing the transformations acting on Fn, S22n , the group of all bijective mappings, defined from IF 2 2 onto itself should be considered. As it is shown i...
This is an earlier, but more general, version of ”An L Ergodic Theorem for Sparse Random Subsequences”. We prove an L ergodic theorem for averages defined by independent random selector variables, in a setting of general measure-preserving group actions. A far more readable version of this paper is in the works.
We first investigate on the asymptotics of the Kolmogorov metric entropy and nonlinear n-widths of approximation spaces on some function classes on manifolds and quasi-metric measure spaces. Secondly, we develop constructive algorithms to represent those functions within a prescribed accuracy. The constructions can be based on either spectral information or scattered samples of the target funct...
Proofs of some recent results of Kriz and Forrest are presented which distinguish between four diierent kinds of \sets of recurrence" arising naturally in connection with topological and measure-preserving dynamical systems. 0. Suppose that (X; ; ; T) is an invertible measure preserving system, that is, (X; ;) is a measure space with (X) = 1 and T : X ! X is a bijection mod 0, with (A) = (TA) =...
We study minimax rates of convergence for nonparametric regression and prediction under a random design with dependent errors. It is shown that dependence among errors in general does not hurt a prediction of the next response. For estimating the regression function, however, dependence may damage the minimax rate of convergence. Under the assumption that the errors are independent of the expla...
We study the asymptotic properties of the conditional empirical process based on b F n (Cjx) = n X t=1 ! n (X t ? x)I fYt2Cg indexed by C 2 C, where f(X t ; Y t); t = 1; : : :; ng are observations from a strong mixing stochas-tic process, f! n (X t ? x)g denote some kernel weights, and C is a class of sets. Under the assumption on the richness of the index class C in terms of metric entropy wit...
A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178–1190]. In the present paper, we first generalize this framework to general compressible flows, thereby solving the donating region problem in full generality. Second, we demonstrate the effic...
We classify the C∞ volume-preserving uniformly quasiconformal Anosov flows, such that E+⊕E− is C∞ and the dimensions of E+ and E− are at least two. Then we deduce a classification of volume-preserving uniformly quasiconformal Anosov flows with smooth distributions.
For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...
We review known results and derive some new ones about the mean free path, Kolmogorov-Sinai entropy and Lyapunov exponents for billiard type dynamical systems. We focus on exact and asymptotic formulas for these quantities. The dynamical systems covered in the paper include periodic Lorentz gas, stadium and its modifications, and the gas of hard balls. Some open questions and numerical observat...
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