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286
Alexander Burstein’s Lovely Combinatorial Proof of John Noonan’s Beautiful Theorem that the number of npermutations that contain the Pattern 321 Exactly Once Equals (3/n)(2n)!/((n3)!(n+3)!)
"... Alex Burstein[1] gave a lovely combinatorial proof of John Noonan’s[2] lovely theorem that the number of npermutations that contain the pattern 321 exactly once equals 3 2n n n+3 ..."
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Alex Burstein[1] gave a lovely combinatorial proof of John Noonan’s[2] lovely theorem that the number of npermutations that contain the pattern 321 exactly once equals 3 2n n n+3
The SkolemAbouzaïd’s theorem in the singular case
, 2014
"... Let F (X,Y) ∈ Q[X,Y] be a Qirreducible polynomial. In 1929 Skolem [8] proved the following beautiful theorem: Theorem 1.1 (Skolem) Assume that F (0, 0) = 0. (1) ..."
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Let F (X,Y) ∈ Q[X,Y] be a Qirreducible polynomial. In 1929 Skolem [8] proved the following beautiful theorem: Theorem 1.1 (Skolem) Assume that F (0, 0) = 0. (1)
An English translation of Bertrand’s theorem
, 2008
"... A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English. PACS: 45.50.Dd; 45.00.Pk 1 ..."
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Cited by 2 (0 self)
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A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English. PACS: 45.50.Dd; 45.00.Pk 1
An Algorithmic Proof Theory for Hypergeometric (ordinary and ``$q$'') Multisum/integral Identities
, 1991
"... this paper we show that these fast algorithms can be extended to the much larger class of multisum terminating hypergeometric (or equivalently, binomial coefficient) identities, to constant term identities of DysonMacdonald type, to MehtaDyson type integrals, and more generally, to identities inv ..."
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Cited by 189 (17 self)
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the same for single and multi (terminating) qhypergeometric identities, with continuous and/or discrete variables. Here we describe these algorithms in general, and prove their validity. The validity is an immediate consequence of what we call "The fundamental theorem of hypergeometric summation
Proof of the Riemannian Penrose inequality using the positive mass theorem
 MR MR1908823 (2004j:53046) MATHEMATICAL GENERAL RELATIVITY 73
"... We prove the Riemannian Penrose Conjecture, an important case of a conjecture [41] made by Roger Penrose in 1973, by defining a new flow of metrics. This flow of metrics stays inside the class of asymptotically flat Riemannian 3manifolds with nonnegative scalar curvature which contain minimal sphe ..."
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Cited by 119 (14 self)
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) and hence the mass contributed by the black holes in each of the metrics in the flow is constant, and then use the Positive Mass Theorem to show that the total mass of the metrics is nonincreasing. Then since the total mass equals the mass of the black hole in a Schwarzschild metric, the Riemannian Penrose
Variational theory for the total scalar curvature functional for Riemannian metrics and related topics
 in Topics in Calculus of Variations (Montecatini
, 1987
"... The contents of this paper correspond roughly to that of the author's lecture series given at Montecatini in July 1987. This paper is divided into five sections. In the first we present he EinsteinHilbert variationM problem on the space of Riemannian metrics on a compact closed manifold M. We ..."
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Cited by 177 (2 self)
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compute the first and secol~d variation and observe the distinction which arises between conformal directions and their orthogonal complements. We discuss variational characterizations of constant curvalure m trics, and give a proof of 0bata's uniqueness theorem. Much of the material in this section
MICHA̷L MISIUREWICZ 1. Interval Combinatorial Dynamics has its roots in Sharkovsky’s Theorem. This
"... beautiful theorem describes the possible sets of periods of all cycles of a continuous map of an interval (or the real line) into itself. Here by a cycle I mean a periodic orbit, and by a period its minimal period. Consider the following Sharkovsky’s ordering <s of the set N of natural numbers: ..."
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beautiful theorem describes the possible sets of periods of all cycles of a continuous map of an interval (or the real line) into itself. Here by a cycle I mean a periodic orbit, and by a period its minimal period. Consider the following Sharkovsky’s ordering <s of the set N of natural numbers:
An end theorem for stratified spaces
"... We show that a tame ended stratified space X is the interior of a compact stratified space if and only if a Ktheoretic obstruction γ∗(X) vanishes. The obstruction γ ∗ (X) is a localization of Quinn’s mapping cylinder neighborhood obstruction. The main results are Theorem 1.6 and Theorem 1.7 below. ..."
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. In particular, this explains when a Gmanifold is the interior of a compact Gmanifold with boundary. Our methods include a new transversality theorem, Corollary 1.17. 1 Main Results, Background and Definitions. 1.1. A beautiful theorem of geometric topology characterizes those topological manifolds which can
Why beautiful people are more intelligent
, 2004
"... Empirical studies demonstrate that individuals perceive physically attractive others to be more intelligent than physically unattractive others. While most researchers dismiss this perception as a ‘‘bias’ ’ or ‘‘stereotype,’ ’ we contend that individuals have this perception because beautiful people ..."
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than lowerstatus men. (3) Intelligence is heritable. (4) Beauty is heritable. If all four assumptions are empirically true, then the conclusion that beautiful people are more intelligent is logically true, making it a proven theorem. We present empirical evidence for each of the four assumptions
Results 1  10
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286