Sekinan Table: SRFL Paper Cell Theory and other information

Sunday 30 August 2020

SRFL Paper Cell Theory and other information

PAPER

Cell Theory　
Continuation of Quantum Theory for Language
From Cell to Manifold For LEIBNIZ and JAKOBSON

TANAKA Akio

1
Cell is defined by the following.
n-dimensional ball Dn　has interior that consists of cells. Cell is expressed by Dn – δDn and notated to en that has no boundary.
δ is boundary operator.　
Homomorphism of Dn is notated to ēn.ēn – δēn = en
2
Set of no- boundary-cells becomes cell complex.
3
Some figures are expressed by cell. hn is attaching map.
n-dimensional sphere Sn = ē0 ∪hn ēn
n-dimensional ball Dn = ( ē0 ∪hn-1 ēn ) ∪ ēn
Torus T2 = ( ē0 ∪h1 ( ē0 ∪ēn ) )∪h2 ē2
3
Grassmann manifold is defined by the following.
Grassmann manifold GR(m, n) is all of n-dimensional linear subspaces in m-dimensional real vector space.
S1 = GR( 2, 1 )
4
Canonical vector bundle γ is defined by the following. E is all space. π is projection.
γ= ( E, π, GR(m, n) )
5
Here from JAKOBSON Roman ESSAIS DE LINGUISTIQUE GÉNÉRALE, <semantic minimum> is presented.
Now <semantic minimum> is expressed by cell ē3.
6
<Word> is expressed by D2.
7
<Sentence> is expressed by Grassmann manifold’s canonical vector bundle γ1 ( GR(3, 1) ).

Tokyo
June 2, 2007
Sekinan Research Field of Language
http://www.sekinan.org

[Reference note / December 23, 2008]
Time of Word / sekinan.wiki.zoho.com

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