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[en] The K-property of cylindric billiards give on the 4-torus is established. These billiards are neither open-quotes orthogonal,close quotes where general necessary and sufficient conditions were obtained by D.Szasz, nor isomorphic to hard-ball systems, where the connecting path formula of N. Simanyi is a hand
[en] The Hughes-Drever experiment has shown inertial mass to be isotropic to approximately 10-23, which presents difficulties for Machian theories of inertia, according to which nearby bodies such as the sun or the galaxy should produce anisotropies. However, if inertial influence is propagated in the same way as light, the presence of a nearby body causes a change in the apparent position of distant objects which effectively renormalizes the background contribution to inertia, making it anisotropic. To first order al least, this induced effective anisotropy can cancel the anisotropy due to the local body
[en] Summary and conclusion: (1) Multiplicity - PHOBOS have performed complete charged particle multiplicity measurements for Au+Au, Cu+Cu, d+Au, and p+p collisions, System size dependence, and 'Complete' pseudorapidity distributions; 'Universality' compared to elementary e+e- collisions; and (2) Midrapidity multiplicity - Factorization of centrality and energy dependencies; (3) Limiting fragmentation - extended longitudinal scaling - Seen for Au+Au, Cu+Cu, and d+Au, Also observed in flow observables; (4) Total charged particle multiplicity - Nch/Npart constant with centrality, (5) Future - Finish up many analysis and reviews.
[en] In a paper dedicated to unifying martingales and ergodic averages, Kachurovskii introduced certain unifying discrete-time martingale ergodic and ergodic martingale processes, for which he proved convergence theorems and established maximal and dominant inequalities. Our purpose in this article is to obtain similar results for such processes with continuous time. In addition, the results are used to assert convergence of yet another unifying process relating to Rota's approach to unification of martingales and Abel ergodic averages. Bibliography: 13 titles.
[en] The generalization of a configuration averaging to a system displaying irreversible effects is suggested. The properties of the ''pathological'' equilibrium state at low temperatures are determined and discussed. (author). 16 refs, 3 figs
[en] In the ergodic regime, several methods efficiently estimate the temporal scaling of time series characterized by long-range power-law correlations by converting them into diffusion processes. However, in the condition of ergodicity breakdown, the same methods give ambiguous results. We show that in such regime, two different scaling behaviors emerge depending on the age of the windows used for the estimation. We explain the ambiguity of the estimation methods by the different influence of the two scaling behaviors on each method. Our results suggest that aging drastically alters the scaling properties of non-ergodic processes.
[en] We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann–Sinai ergodic hypothesis. (paper)
[en] A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element to the inertia of a particle experiencing an acceleration from rest is proportional to , where is the angle between the line connecting and and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass.
[en] We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of the initially invariant subintervals occurs and forces the subsystems to merge into one system that has exactly one invariant density. We prove that the invariant density of the perturbed system converges in the L1-norm to a particular convex combination of the invariant densities of the intermittent map. In particular, we show that the ratio of the weights in the combination is equal to the limit of the ratio of the measures of the holes
[en] In this article, we show that on certain Gatzouras–Lalley carpets, more than one ergodic measure exists with full Hausdorff dimensions. This gives a negative answer to a conjecture of Gatzouras and Peres (1997 Ergod. Theory Dyn. Syst. 17 147–67.)