منابع مشابه
In Praise of an Elementary Identity of Euler
We survey the applications of an elementary identity used by Euler in one of his proofs of the Pentagonal Number Theorem. Using a suitably reformulated version of this identity that we call Euler’s Telescoping Lemma, we give alternate proofs of all the key summation theorems for terminating Hypergeometric Series and Basic Hypergeometric Series, including the terminating Binomial Theorem, the Ch...
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Let G be a median graph on n vertices and m edges and let k be the number of equivalence classes of the Djoković’s relation Θ defined on the edge-set of G. Then 2n − m − k ≤ 2. Moreover, 2n − m − k = 2 if and only if G is cube-free. A median graph is a connected graph such that, for every triple of vertices u, v, w, there is a unique vertex x lying on a geodesic (i.e. shortest path) between eac...
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Identity (1) below resulted from our investigation in [21] of chip-firing games on complete graphs K n , for n ≥ 1; see, e.g., [2] for antecedents. The left side expresses the sum of the probabilities of a game experiencing firing sequences of each possible length ℓ = 0, 1,. .. , n. This note gives a combinatorial proof that these probabilities sum to unity. We first manipulate n − 1 n + 1 + n ...
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Idsardi and Raimy 2000 (I&R) propose that the representations posited by a learner are constrained by economy considerations. If a child hears a string like the Temiar continuative [sglOg], two possibilities are available while building the underlying representation of the string. Either the two segments [g] perceived in the string correspond to different tokens of the same type, or they corres...
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A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., Vol. 1, pp. 92-112(2008)] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1999
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700033190