27 research outputs found
From polygons and symbols to polylogarithmic functions
Full text linkWe present a review of the symbol map, a mathematical tool that can be useful
in simplifying expressions among multiple polylogarithms, and recall its main
properties. A recipe is given for how to obtain the symbol of a multiple
polylogarithm in terms of the combinatorial properties of an associated rooted
decorated polygon. We also outline a systematic approach to constructing a
function corresponding to a given symbol, and illustrate it in the particular
case of harmonic polylogarithms up to weight four. Furthermore, part of the
ambiguity of this process is highlighted by exhibiting a family of non-trivial
elements in the kernel of the symbol map for arbitrary weight.Comment: 75 pages. Mathematica files with the expression of all HPLs up to
weight 4 in terms of the spanning set are include
3D modeling of the laterites on top of the Koniambo Massif, New Caledonia: refinement of the per descensum lateritic model for nickel mineralization
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Multistage crack seal vein and hydrothermal Ni enrichment in serpentinized ultramafic rocks (Koniambo massif, New Caledonia)
No full textUranium metallogenesis of the peraluminous leucogranite from the Pontivy-Rostrenen magmatic complex (French Armorican Variscan belt): the result of long-term oxidized hydrothermal alteration during strike-slip deformation
No full textComparative study of two canal obturation techniques by image analysis and EDS microanalysis
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First case series of robotic radical cystoprostatectomy, bilateral pelvic lymphadenectomy, and urinary diversion with the da Vinci S system
No full textMetallogenesis of the French Massif Central: Time-Space Relationships Between Ore Deposition and Tectono-Magmatic Events
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