Reciprocity sheaves, II

We exhibit an intimate relationship between "reciprocity sheaves" from arXiv:1402.4201 [math.AG] and "modulus sheaves with transfers" from arXiv:1908.02975 [math.AG] and arXiv:1910.14534 [math.AG].Comment: A mistake in arXiv:1511.07124 [math.AG] pointed out by Ayoub has been repaired, so the previous paper is restored with a changed titl

Moon Park: A research and educational facility

Moon Park has been proposed as an International Space Year (ISY) event for international cooperative efforts. Moon Park will serve as a terrestrial demonstration of a prototype lunar base and provide research and educational opportunities. The kind of data that can be obtained in the Moon Park facilities is examined taking the minimum number of lunar base residents as an example

The solar wind structure that caused a large-scale disturbance of the plasma tail of comet Austin

The plasma tail of Comet Austin (1989c1) showed remarkable disturbances because of the solar maximum periods and its orbit. Figure 1 shows photographs of Comet Austin taken in Shibata, Japan, on 29 Apr. 1990 UT, during about 20 minutes with the exposure times of 90 to 120 s. There are two main features in the disturbance; one is many bowed structures, which seem to move tailwards; and the other is a large-scale wavy structure. The bowed structures can be interpreted as arcade structures brushing the surface of both sides of the cometary plasma surrounding the nucleus. We identified thirteen structures of the arcades from each of the five photographs and calculated the relation between the distance of each structure from the cometary nucleus, chi, and the velocity, upsilon. The result is shown. This indicates that the velocity of the structures increases with distance. This is consistent with the result obtained from the observation at the Kiso Observatory

A Note on the Critical Problem for Matroids

Let M be a matroid representable over GF(q) and S be a subset of its ground set. In this note we prove that S is maximal with the property that the critical exponent c(M|S; q) does not exceed k if and only if S is maximal with the property that c(M · S) ≤ k. In addition, we show that, for regular matroids, the corresponding result holds for the chromatic number. © 1984, Academic Press Inc. (London) Limited. All rights reserved