Hausdorff dimension of Moran sets with increasing spacing

For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.     

Super-stationary set, subword problem and the complexity

Let Ω⊂{0,1}^N be a nonempty closed set with N={0,1,2,…}. For N={N₀<N₁<N₂<?}⊂N and ω∈{0,1}^N, define ω[N]∈{0,1}^N by and

     

Numeration systems,fractals and stochastic processes

A numeration system Ω is a compactification of the set of real numbers keeping the actions of addition and positive multiplication in a natural way. That is, Ω is a compact metrizable space with #Ω≥2 to which ℝ acts additively andG acts multiplicatively satisfying the distributive law, whereG is a nontrivial closed multiplicative subgroup of ℝ₊. Moreover, the additive action is minimal and uniquely ergodic with 0-topological entropy, while the multiplication by λ has |log λ|-topological entropy attained uniquely by the unique invariant probability measure under the additive action. We construct Ω as above as a colored tiling space corresponding to a weighted substitution. This framework contains especially the substitution dynamical systems and β-transformation systems with periodic expansion of 1, both of which have discreteG. It also contains systems withG=ℝ₊. We study α-homogeneous cocycles on it with respect to the addition. They are interesting from the point of view of fractal functions or sets as well as self-similar processes. We obtain the zeta-functions of Ω with respect to the multiplication.     

Absorption cross sections for antiprotons on carbon, aluminum and copper at 485 and 597 MeV/c

Absorption cross sections for antiprotons on C, Al and Cu have been measured by a transmission method at 485 and 597 MeV/c. Nuclei are shown to be black to antiprotons at these momenta. Using the available data up to 280 GeV/c, the momentum dependence of the absorption cross sections is investigated. Empirically, a simple expression σ_abs = γ(p/p₀)^−β, with β and γ constants and p₀ = 1 GeV/c, gives a good account of the data in a remarkably wide momentum range, 0.5–280 GeV/c.     

Minimal cocycles with the scaling property and substitutions

‘Fractal’ functions are formulated as a minimal cocycle on a topological dynamics which admits nontrivial scaling transformations. In this paper, it is proved that if in addition it admits a continuous family of scaling transformations, then itscapacity is not ino(N ²). We define minimal cocycles with nontrivial scaling transformations coming from substitutions on a finite alphabet which are proved to have capacityO(N), so that they admit only a discrete family of scaling transformations. We also construct one which has capacityO(N ²) and admit a continuous family of scaling transformations. Supported by C.N.R.S.(U.R.A 225); Partially supported by the Japan Society for the Promotion of Science.     

Theoretical models for deuteron photodisintegration in the energy range between 250 MeV and 800 MeV

Two theoretical models of γd → pn are developed to study the differential cross-section and'the proton polarization data in a coherent way. The first model is an extension of conventional diagrammatic summations of Born terms and isobar excitation terms. The second model is novel in that the isobar excitation terms are replaced by experimentally determined _γN → N_π helicity amplitudes. The second model allows us to extend to higher energies with the introduction of only one arbitrary parameter. The differential cross-section data are fairly well reproduced in the whole energy range, while the proton polarization data are very far removed from the calculations.