We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov Process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decompositi...

Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...

Let V be a possibly singular scheme-theoretic complete intersection subscheme of P over an algebraically closed field of characteristic zero. Using a recent result of Fullwood (“On Milnor classes via invariants of singular subschemes”, Journal of Singularities) we develop an algorithm to compute the Chern-Schwartz-MacPherson class and Euler characteristic of V . This algorithm complements exist...

We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decompositi...

Consider the discrete conditional independence model M given by {X1 ⊥ X2 | X3, X1 ⊥ X3 | X2}. The intersection axiom for conditional independence can be applied with the statements of M as premises to derive the conclusion X1 ⊥ (X2, X3). But the independence axiom only holds in general when X is in the interior of the probability simplex, and it’s a natural question to ask what can be inferred ...

This paper is a follow-up on previous work by the author on subtyping with (set-theoretic) union, intersection and recursive types. Previously, it was shown how types may be encoded as regular tree expressions/set constraints. This gave rise to a sound and complete decision procedure for type inclusion. The result was, however, limited to a rather speciic type language. In the work reported on ...

This paper is a follow-up on previous work by the author on sub-typing with (set-theoretic) union, intersection and recursive types. Previously, it was shown how types may be encoded as regular tree expressions/set constraints. This gave rise to a sound and complete decision procedure for type inclusion. The result was, however, limited to a rather speciic type language. In the work reported on...

In this paper, we define a new concept, called N -group soft intersection action (SI) on a soft set. This new notion gathers soft set theory, set theory and N -group theory together and it shows how a soft set effects on an N -group structure in the mean of intersection and inclusion of sets. We then obtain its basic properties with illustrative examples and derive some analog of classical N -g...