منابع مشابه
Of Minima and Maxima
Let h1, · · · , hn be positive integers. We study new sums m(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 min { r1 h1 , · · · , rn hn } and M(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 max { r1 h1 , · · · , rn hn } , the first of which times h1 · · ·hn is the number of lattice points in a pyramid of dimension n + 1. We show that m(h1, · · · , hn) (h1 − 1) · · · (hn − 1) = 1 + ∑ ∅6 =I⊆{1...
متن کاملAlternating minima and maxima, Nash equilibria and Bounded Arithmetic
We show that the least number principle for strict Σk formulas can be characterized by the existence of alternating minima and maxima of length k. We show simple prenex forms of these formulas whose herbrandizations (by polynomial time functions) are ∀Σ̂1 formulas that characterize ∀Σ̂1 theorems of the levels T k 2 of the Bounded Arithmetic Hierarchy, and we derive from this another characterizat...
متن کاملA stochastic fixed point equation for weighted minima and maxima
Given any finite or countable collection of real numbers Tj , j ∈ J , we find all solutions F to the stochastic fixed point equation W d = inf j∈J TjWj , where W and the Wj , j ∈ J , are independent real-valued random variables with distribution F and d = means equality in distribution. The bulk of the necessary analysis is spent on the case when |J | ≥ 2 and all Tj are (strictly) positive. Non...
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Aims. Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. Methods. We present an updated reconstruction of sunspot number over multiple millennia, from C data by means of a physics-based model, using an updated model...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1893
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500001619