1,527,463 research outputs found
The Filippov-Wazewski relaxation theorem revisited
The converse statement of the Filippov-Wazewski relaxation theorem is proven, more precisely, two differential inclusions have the same closure of their solution sets if and only if the right-hand sides have the same convex hull. The idea of the proof is examining the contingent derivatives to the attainable sets
The Future of Dams Project: Governance Statement
This governance statement sets out shared principles to guide our work and our relationships with each other on the New England Sustainability Consortium’s Future of Dams project. This is a living document, meant to evolve as our partnership evolves. Rather than offering an exhaustive catalog, this governance statement is meant to serve as a touchstone to prompt important conversations about conduct, conflict resolution, authorship, expectations, data sharing, and assessment
Hitting all maximum cliques with a stable set using lopsided independent transversals
Rabern recently proved that any graph with omega >= (3/4)(Delta+1) contains a
stable set meeting all maximum cliques. We strengthen this result, proving that
such a stable set exists for any graph with omega > (2/3)(Delta+1). This is
tight, i.e. the inequality in the statement must be strict. The proof relies on
finding an independent transversal in a graph partitioned into vertex sets of
unequal size.Comment: 7 pages. v4: Correction to statement of Lemma 8 and clarified proof
Effective uniqueness of Parry measure and exceptional sets in ergodic theory
It is known that hyperbolic dynamical systems admit a unique invariant
probability measure with maximal entropy. We prove an effective version of this
statement and use it to estimate an upper bound for Hausdorff dimension of
exceptional sets arising from dynamics
The right angle to look at orthogonal sets
If X and Y are orthogonal hyperdefinable sets such that X is simple, then any
group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup
N such that G/N is Y-internal; N is unique up to commensurability. In order to
make sense of this statement, local simplicity theory for hyperdefinable sets
is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable
families of commensurable subgroups is shown
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