Sunday 4 August 2019

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


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.
δis boundary operator. 
Homomorphism of Dis notated to ēn.
ēn  - δēen
2 Set of no- boundary-cells becomes cell complex.
3 Some figures are expressed by cell. hn is attaching map.
n-dimensional sphere      S=  ēhn  ēn   
n-dimensional ball          D= ( ēhn-1  ēn ) ∪ ēn
Torus                              T2 = ( ē0  h ēēn ) )∪hē2
3 Grassmann manifold is defined by the following.
Grassmann manifold GR(mn) is all of n-dimensional linear subspaces in m-dimensional real vector space.
                                        S1 = GR2)
4 Canonical vector bundle γ is defined by the following. E is all space. π is projection.
γ= ( EπGR(mn) )
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(31) ).
 
Tokyo June 2, 2007
Sekinan Research Field of Languagewww.sekinan.org
 
[Reference note / December 23, 2008]
 


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