منابع مشابه
A monotonicity property of Bessel functions
We extend and unify the proof of a result of L. Lorch (Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), 209–216) by showing that the ratio sgn(ν)Jν+1(|ν|)/Jν(|ν|) increases from −∞ to 1 as ν increases from ν0 (= −0.8375 . . .) to ∞. Here ν0 is the largest zero of Jν(|ν|). One approach is based on an expansion of this ratio involving Rayleigh sums. Another is based on a continued fraction repres...
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We propose a general model of local property reconstruction. Suppose we have a function f on domain Γ, which is supposed to have a particular property P, but may not have the property. We would like a procedure which produces a function g that has property P and is close to f (according to some suitable metric). The reconstruction procedure, called a filter, has the following form. The procedur...
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We show that the joint spectral radius of a set of matrices is strictly increasing as a function of the data in the sense that if a set of matrices is contained in the relative interior of the convex hull of an irreducible set of matrices, then the joint spectral radius of the smaller set is strictly smaller than that of the larger set. This observation has some consequences in the theory of ti...
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2013
ISSN: 0167-7152
DOI: 10.1016/j.spl.2013.02.004