Multilevel contours on bundles of complex planes

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex plane to another. Within a random environment, the behavior of contours and multilevel contours passing through the bundles of complex planes are studied. Further properties of contours by a removal process of the data are studied. The concept of “islands” and “holes” within a bundle is introduced through this article. These all constructions help to understand the dynamics of the set of points of the bundle. Further research on the topics introduced here will be followed up by the author. These include closed approximations of the multilevel contour formations and their removal processes. The ideas and results presented in this article are novel.

Original languageEnglish (US)
Title of host publicationGeometry and Statistics
EditorsFrank Nielsen, Arni S.R. Srinivasa Rao, C.R. Rao
PublisherElsevier B.V.
Pages401-464
Number of pages64
ISBN (Print)9780323913454
DOIs
StatePublished - Jan 2022

Publication series

NameHandbook of Statistics
Volume46
ISSN (Print)0169-7161

Keywords

  • Holomorphism
  • Multilevel complex planes
  • PDEs
  • Randomness
  • Spinning

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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