Large inductive dimension of the Smirnov remainder

The purpose of this paper is to investigate the large inductive dimension of the remainder of the Smirnov compactification of the n-dimensional Euclidean space with the usual metric, and give an application of it.Comment: 8 pages, accepted for publication in Houston Journal of Mathematic

Describing the proper n-shape category by using non-continuous functions

In this paper, we describe the proper n-shape category by using non-continuous functions. Moreover, applying non-continuous homotopies, we show that the Cech expansion is a polyhedral expansion in the proper n-homotopy category

The Smirnov remainders of uniformly locally connected proper metric spaces

AbstractThe aim of this paper is to investigate relations between uniform local connectedness and the dimension of the Smirnov remainder. In particular, we devote this paper to calculating the dimension of the Smirnov remainder udRn∖Rn of the n-dimensional Euclidean space (Rn,d) with uniform local connectedness. We show that dimudR∖R=indudR∖R=IndudR∖R=1 if (R,d) is uniformly locally connected. Moreover, we introduce a new concept of “thin” covering spaces, and we have the following: If an infinite covering space (R2,d˜) of a compact 2-manifold is “thin”, then dimud˜R2∖R2=indud˜R2∖R2=Indud˜R2∖R2=2

Slip-weakening distance in dynamic rupture of inslab normal-faulting earthquakes

We estimate the critical slip-weakening distance on in-slab earthquake faults in a subduction zone, by applying a recent approach proposed by us. This approach is to find a relation between the breakdown time of shear stress Tb, the time of peak slip velocity Tpv, and the slip-weakening distance Dc, from the time histories of shear stress, slip and slip velocity at each point on the fault. The previous results show that Dc at Tb can be well approximated by D'c at Tpv for faults even with a heterogeneous stress drop distribution, except at locations near barriers and fault edges. We apply the above method to three large in-slab, normal-faulting earthquakes in the Mexican subduction zone. To do this, we calculate the spatial distribution of slip-velocity functions and final slip from kinematic waveform inversion of strong-motion and teleseismic records, and the stress history and final stress change from dynamic rupture calculations. By integrating the slip-velocity functions obtained from the inversion, from the rupture arrival time to the time of peak slip velocity, we obtain slip D' c at Tpv and then correct it for Dc at Tb through dynamic calculations. We also estimate the lowest resolvable limit and probable errors of Dc from the slip-velocity functions, and its upper bound from a theoretical constraint between the dynamic stress drop and Dc. We found that the slip-weakening distance Dc estimated in the frequency band between 0.05 and 0.5 Hz ranges between 40 and 120 cm on the in-slab fault of the 1999 Oaxaca earthquake (Mw= 7.5). The largest Dc is detected in the central fault and in part of the deeper sections, and Dc in the zone around the hypocentre ranges between 50 and 70 cm. The estimated Dc values appear to be less depth-dependent but are rather more dependent on the local maximum slip. This possible slip dependence might be interpreted by the degree of fault roughness, in addition to stress heterogeneities. The fracture energy G in the central section and in the hypocentral zone are roughly estimated to be of the order of 10–15 and 5–8 MJ m−2, respectively. Both of the estimated Dc and G values are somewhat larger than those on the vertical fault of two recent, shallow strike-slip earthquakes in western Japan