An Introduction to Isomorphic Mathematical Analysis System
Abstract
This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame, dual-variable-isomorphic function, and isomorphic coordinate system. More concepts are introduced to constitute the whole IMAS framework. This IMAS attempts to provide current MA with new implements, which include isomorphic frame, thereby effectively putting the MA to work as well in some unevenly distributed coordinate spaces, realized by the isomorphic coordinate system. With these implements, many existing MA concepts are extended and incorporated into the new IMAS.
Cite
@article{arxiv.2312.05350,
title = {An Introduction to Isomorphic Mathematical Analysis System},
author = {Yuan Liu},
journal= {arXiv preprint arXiv:2312.05350},
year = {2024}
}
Comments
60 pages. Keywords: Isomorphic frame; DVI function; Isomorphic coordinate system; Dual-variable-isomorphic convex function; Isomorphic mean of a function; Dual-isomorphic derivative; Isomorphic integral; Elastic mean of a function; Elastic integral; Geometrical meaning of Cauchy mean value theorem; Theory of isomorphic mathematical analysis system (TIMAS). arXiv admin note: substantial text overlap with arXiv:2308.06500