Open AccessOn the HN-integration of spatial (integral) derivatives of multivector fields with singularities in RN
Author(s) -
Branko Saric
Publication year - 2017
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1708433s
Subject(s) - mathematics , multivector , pure mathematics , bijection , gravitational singularity , rectangle , manifold (fluid mechanics) , mathematical analysis , algebra over a field , discrete mathematics , geometry , mechanical engineering , current algebra , jordan algebra , engineering
A method of spatial (integral) differentiation of multivector fields in an N -dimensional manifold M, into which a hyper-rectangle [a,b] is mapped by a bijective smooth map r : [a,b] ? M, has been introduced. For a class of discontinuous multivector fields a new concept of a residual field as well as the concept of total HN integrability have been defined. Finally, this led naturally to an extension of Cauchy?s residue theorem in M.