scholarly journals On the HN-integration of spatial (integral) derivatives of multivector fields with singularities in RN

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2433-2439
Author(s):  
Branko Saric
Keyword(s):  
Dimensional Manifold ◽  
Residue Theorem ◽  
Residual Field ◽  
Smooth Map ◽  
Derivatives Of

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.

MULTIVECTOR AND EXTENSOR FIELDS ON SMOOTH MANIFOLDS

2007 ◽  
Vol 04 (06) ◽  
pp. 965-985 ◽  
Author(s):  
A. M. MOYA ◽  
V. V. FERNÁNDEZ ◽  
W. A. RODRIGUES
Keyword(s):  
Differential Geometry ◽  
Vector Space ◽  
Vector Fields ◽  
Dimensional Manifold ◽  
Smooth Vector ◽  
Local Chart ◽  
Arbitrary Topology ◽  
Key Concepts ◽  
Derivatives Of ◽  
Canonical Vector

The main objective of this paper (second in a series of four) is to show how the Clifford and extensor algebras methods introduced in a previous paper of the series are indeed powerful tools for performing sophisticated calculations appearing in the study of the differential geometry of a n-dimensional manifold M of arbitrary topology, supporting a metric field g (of given signature (p,q)) and an arbitrary connection ∇. Specifically, we deal here with the theory of multivector and extensor fields on M. Our approach does not suffer the problems of earlier attempts which are restricted to vector manifolds. It is based on the existence of canonical algebraic structures over the canonical (vector) space associated to a local chart (Uo, ϕo) of a given atlas of M. The key concepts of a-directional ordinary derivatives of multivector and extensor fields are defined and their properties studied. Also, we recall the Lie algebra of smooth vector fields in our formalism, the concept of Hestenes derivatives and present some illustrative applications.

Physical Properties of TCNQ Salts with N-Methyl Derivatives of Pyridine

1982 ◽  
Vol 85 (1) ◽  
pp. 257-263 ◽  
Author(s):  
A. Graja ◽  
M. Przybylski ◽  
B. Butka ◽  
R. Swietlik
Keyword(s):  
Physical Properties ◽  
Methyl Derivatives ◽  
Derivatives Of

Diorganyl Derivatives of Tellurium(IV) (σ-Telluranes of R 2 TeX 2 Type)

2002 ◽  
Vol 23 (2) ◽  
pp. 125-207 ◽  
Author(s):  
Igor D. Sadekov ◽  
Alexander V. Zakharov ◽  
Alexander A. Maksimenko
Keyword(s):  
Derivatives Of

Hindered rotation around the amide bond in a series of derivatives of 2-acetamidothiophenes

1991 ◽  
Vol 88 ◽  
pp. 689-707 ◽  
Author(s):  
P Andriamadio ◽  
D Nicole ◽  
A Cartier ◽  
M Wierzbicki ◽  
G Kirsch
Keyword(s):  
Amide Bond ◽  
Hindered Rotation ◽  
Derivatives Of
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