66,929 research outputs found
The Tur\'{a}n number and probabilistic combinatorics
In this short expository article, we describe a mathematical tool called the
probabilistic method, and illustrate its elegance and beauty through proving a
few well-known results. Particularly, we give an unconventional probabilistic
proof of a classical theorem concerning the Tur\'{a}n number .
Surprisingly, this proof cannot be found in existing literature.Comment: 5 pages; to appear in Amer. Math. Monthly 201
Tau Electroweak Couplings
We review world-average measurements of the tau lepton electroweak couplings,
in both decay (including Michel parameters) and in production ( and W^-\to\tau^-\nubar_\tau). We review the searches for
anomalous weak and EM dipole couplings. Finally, we present the status of
several other tau lepton studies: searches for lepton flavor violating decays,
neutrino oscillations, and tau neutrino mass limits.Comment: 12 pages, 16 figures; talk presented at Heavy Flavours 8,
Southampton, UK, 199
Perturbation expansions at large order: Results for scalar field theories revisited
The question of the asymptotic form of the perturbation expansion in scalar
field theories is reconsidered. Renewed interest in the computation of terms in
the epsilon-expansion, used to calculate critical exponents, has been
frustrated by the differing and incompatible results for the high-order
behaviour of the perturbation expansion reported in the literature. We identify
the sources of the errors made in earlier papers, correct them, and obtain a
consistent set of results. We focus on phi^4 theory, since this has been the
most studied and is the most widely used, but we also briefly discuss analogous
results for phi^N theory, with N>4. This reexamination of the structure of
perturbation expansions raises issues concerning the renormalisation of
non-perturbative effects and the nature of the Feynman diagrams at large order,
which we discuss.Comment: 14 page
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Number of Pages: 2Integrative BiologyGeological Science
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