Displaying similar documents to “Eigenvaluations”

Functions on adjacent vertex degrees of trees with given degree sequence

Hua Wang (2014)

Open Mathematics

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In this note we consider a discrete symmetric function f(x, y) where f ( x , a ) + f ( y , b ) ⩾ f ( y , a ) + f ( x , b ) f o r a n y x ⩾ y a n d a ⩾ b , associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as ∑ u v ∈ E ( T ) f ( d e g ( u ) , d e g ( v ) ) , are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal...

Brolin's theorem for curves in two complex dimensions

Charles Favre, Mattias Jonsson (2003)

Annales de l’institut Fourier

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Given a holomorphic mapping f : ℙ 2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d - n f n * S converges to the Green current as n → ∞ . We also conjecture necessary condition for the same convergence.