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On some generalizations of the classical Riemann problem
Author(s) -
Dmitrieva I.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701128
Subject(s) - mathematics , pure mathematics , riemann sphere , riemann hypothesis , constructive , class (philosophy) , algebraic number , noncommutative geometry , riemann surface , riemann problem , sequence (biology) , matrix (chemical analysis) , order (exchange) , boundary (topology) , boundary value problem , mathematical analysis , genetics , materials science , process (computing) , finance , artificial intelligence , biology , computer science , economics , composite material , operating system
The special class of the homogeneous vector boundary Riemann problems on the finite sequence of algebraic surfaces is investigated completely. Its coefficients are the noncommutative permutative matrices of the arbitrary but not prime order, and boundary conditions are given on the system of open contours. The constructive solution procedure and definite structure of the canonical solution matrix are obtained and present some generalizations of the classical Riemann problem. Simultaneously the corresponding class of algebraic equations for the appropriate covering surfaces is formed explicitly too. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)