Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...

A simple proof is presented for the min-max theorem of Lovv asz on cacti. Instead of using the result of Lovv asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem.

This paper is devoted to the completeness issue of RMLCI | the relative modal logic with composition and intersection | a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally deenable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper \Complete axiomatization of a ...

A vanishing theorem is proved for`-adic cohomology with compact support on a singular aane complete intersection. As an application, it is shown that for an aane complete intersection deened over a nite eld of q elements, the reciprocal \poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibility of the poles o...

A theorem of Picard type is proved for entire holomorphic mappings into projective varieties. This theorem has local nature in the sense that the existence of Julia directions can be proved under natural additional assumptions. An example is given which shows that Borel’s theorem on holomorphic curves omitting hyperplanes has no such local counterpart. Let P be complex projective space of dimen...

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}~= 1, of jump discontinuities. Let S be the smallest closed set which satisfies: (i) S is a union of forward characteristics. (ii) S contains all the forward characteristics from the points {xi}~= 1" (iii) if two fo...

This short note gives an alternative proof of the M-convex intersection theorem, which is one of the central results in discrete convex analysis. This note is intended to provide a direct simpler proof accessible to nonexperts. 1 M-Convex Intersection Theorem The M-convex intersection theorem [3, Theorem 8.17] reads as follows, where V is a nonempty finite set, and Z and R are the sets of integ...