منابع مشابه
Characteristic Functions and Borel Exceptional Values of E-Valued Meromorphic Functions
and Applied Analysis 3 Let n r, f or n r, ∞̂ denote the number of poles of f z in |z| ≤ r and let n r, a, f denote the number of a-points of f z in |z| ≤ r, counting with multiplicities. Define the volume function associated with E-valued meromorphic function f z by V ( r, ∞̂, f V r, f 1 2π ∫ Cr log ∣∣ ∣ ∣ r ξ ∣∣ ∣ ∣Δ log ∥ ∥f ξ ∥ ∥dx ∧ dy, ξ x iy, V ( r, a, f ) 1 2π ∫ Cr log ∣ ∣ ∣ ∣ r ξ ∣ ∣ ∣ ∣Δ...
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The Borel lemma says that any positive non-decreasing continuous function T satisfies T (r+1/T (r)) ≤ 2T (r) outside of a possible exceptional set of finite linear measure. This lemma plays an important role in the theory of entire and meromorphic functions, where the increasing function T is either the logarithm of the maximum modulus function, or the Nevanlinna characteristic. As a result, ex...
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Let n be a positive integer and λ > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(λ, n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most λ. We call this graph a unit disk random graph. Let λ = c √ lnn/n and let X be the number of isolated points in G(...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1982
ISSN: 0035-7596
DOI: 10.1216/rmj-1982-12-1-197