The most striking incident which has occurred since our last has been a debate on a proposition to repeal the law exiling the Bourbon family.
"Harper's New Monthly Magazine, Volume 2, No. 12, May, 1851." by Various
The general proposition that public honours of some kind are valuable incidents in every country can hardly be disputed.
"British Quarterly Review, American Edition, Volume LIV" by Various
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By Proposition 8.11, there is a δ ′ > 0 such that the event E that any δ ′n vertices of Gn are incident with at most δn/2 edges holds whp.
The phase transition in inhomogeneous random graphs
Proposition 8.11 states that, given ε > 0, there is a δ > 0 such that whp any set of at most δn vertices of Gn is incident with at most εn edges. A very special case of Theorem 11.6 gives an alternative proof of this result (under the more restrictive assumptions of the present section).
The phase transition in inhomogeneous random graphs
We’ve now deﬁned xρ(p) and xρ(q) , so the statement of Theorem 12.9 makes sense. (Here ep (τ ) = eq (τ ) is the number of ends of arcs of T which are incident to p.) Moreover by Proposition 12.25, equations (12.5) and (12.6) hold, and the proof of Theorem 12.9 goes through with minimal modiﬁcations.
Positivity for cluster algebras from surfaces
Proposition 14 holds for charged signed graphs by the results of , so we need only identify L′ -graphs with at least one edge of weight 2: such an edge must be incident at x since all edges in H have weight 1.
Lehmer's conjecture for matrices over the ring of integers of some imaginary quadratic fields
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