Is it possible to find a formula expressing the Nielsen number N( f ) by the numbers N( ̃ f ) where ̃ f runs the set of all lifts? Such a formula seems very desirable since the difficulty of computing the Nielsen number often depends on the size of the fundamental group. Since π1 ̃ X ⊂ π1X , the computation of N( ̃ f ) may be simpler. We will translate this problem to algebra. The main result of th...

PLENARIES R IS FOR RURAL: PHONOLOGICALLY CONSTRUCTING THE RURAL OTHER IN SOUTHERN ENGLAND ........................................................................................................................................................................ 5 DAVID BRITAIN CHRONOTOPES OF DIALECT STYLE ................................................................................................

We consider the Froggatt-Nielsen (FN) mechanism reproducing the observed mass hierarchies and mixing angles for quarks and leptons. The large νμ-ντ mixing suggested from recent Superkamiokande experiments on the atmospheric neutrinos implies lopsided FN U(1) charges for the lepton doublets. There are two possible charge assignments to generate the large νμ-ντ mixing. We point out that the two m...

It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa models with unbroken flavour and chiral symmetries and no doubling of the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is avoided, bec...

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Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst Nielsen polylogarithms, both generic and at special arguments including the sixth roots of unity. The relations are explicitly exhibited in the case of low weights. All of this work relies heavily on symbolic and numeric computation. For use in applications all results are implemented and acces...

The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of single-valued maps. If the fibration is orientable, the pro...