Pointed minimal sets and $S$-regularity

counterexamples in a−minimal sets

several tables have been given due to a − minimal sets. our main aim in this paper is tocomplete these tables by employing several examples.

On the Regularity of Critical and Minimal Sets of a Free Interface Problem

We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to give a short proof of a partial regularity proved by Fan Hua Lin in [8], and to study the possible shapes of conical sets which are critical points.

Finite Dimensional Pointed Hopf Algebras over S

Minimal Sets and Varieties

The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have...

Minimal closed sets and maximal closed sets

Some properties of minimal open sets and maximal open sets are studied in [1, 2]. In this paper, we define dual concepts of them, namely, maximal closed set and minimal closed set. These four types of subsets appear in finite spaces, for example. More generally, minimal open sets and maximal closed sets appear in locally finite spaces such as the digital line. Minimal closed sets and maximal op...