There is also a correspondence between confinement in QCD the fact that the color field is only different from zero in the interior of hadrons and the behaviour of the usual magnetic field in the theory of type-II superconductors : there the magnetism is confined to the interiour of the Abrikosov flux-line lattice, i . e ., the London penetration depth " & lambda; " of that theory is analogous to the confinement radius " R c " of quantum chromodynamics.
32.
Work of Roger Howe in the 1970s and his papers with Allen Moy on representations of " p "-adic GL ( " n " ) opened a possibility of classifying irreducible admissible representations of reductive groups over local fields in terms of appropriately constructed Hecke algebras . ( Important contributions were also made by Joseph Bernstein and Andrey Zelevinsky . ) These ideas were taken much further in Colin Bushnell and Philip Kutzko's " theory of types ", allowing them to complete the classification in the general linear case.
33.
In his " Introduction " to his 1921 Post places the blame on Russell's notion of apparent variable : " Whereas the complete theory [ of Whitehead and Russell ( 1910, 1912, 1913 ) ] requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a result necessitates the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity, which the authors have chosen to call elementary propositions ".
34.
"' Ramified theory of types : function-orders and argument-types, predicative functions "': When Russell proclaimed " all " classes are useful fictions he solved the problem of the " unit " class, but the " overall " problem did not go away; rather, it arrived in a new form : " It will now be necessary to distinguish ( 1 ) terms, ( 2 ) classes, ( 3 ) classes of classes, and so on " ad infinitum "; we shall have to hold that no member of one set is a member of any other set, and that " x " ? " u " requires that " x " should be of a set of a degree lower by one than the set to which " u " belongs.
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