Hyperbolic Language Connection of Words
Connection of Words
0.
[Preface]
From Distance to Pseudo-Kobayashi-Distance
1.
C is complex plane.
is unit disk which center is the origin of C.
z, w are the two points of .
Hyperbolic distance 
between z and w are defined by the next.
, 
.
2.
M is complex manifold.
x, y are arbitrary points of M.
fv is finite sequence of regular curve.
Point zv is 
.
, 
.
.
{ 
} is called regular chain.
Kobayashi pseudodistance dM is defined by the next.
.
3.
[Interpretation on 2.]
:= Meaning minimum of word.
dM := Distance of word.
M:= Word.
4.
[Definition]
When dM becomes distance function, M is called Kobayashi hyperbolic.
When dM becomes complete distance, M is called complete Kobayashi hyperbolic.
5.
When M = is satisfied at dM , dM is equel to Poincaré distance.
6.
X is complex maifold.
M is contained in X as relative compact.
7.
[Definition]
What embedding 
is hyperbolic embedding is defined by the next.
M is KObayashi hyperbolic.
Arbitrary boundary points 
.
.
.
8.
[Theorem,Kwack 1969]
When M ishyperbolicly embedding in X,
What arbitrary regular map 
\{0} 
is regularly connected to 
.
9.
[Interpretation on 6,7,8,9]
X:= Language.
M:= Word.
:= Distance of word.
:= Connection of words.
10.
[Conjecture, Kobayashi]
(i) If d is 
, degree d's general hypersurface X of 
is Kobayashi hyperbolic.
(ii)If d is 
, \ 
is hyperbolicly embedded in .
11.
[Interpretation on 10.]
X:= Language.
d:= Hierarchy of language.
12.
[References]
<On meaning minimum of word>
From Cell to Manifold / Cell Theory / Tokyo June 2, 2007
Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008
<On distance of word>
Distance Theory /Tokyo May 5, 2004
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008
<On connection of words>
Quantum Theory for Language / Tokyo January 15, 2004
<On hyperbolicity>
Reflection of Word / Complex Manifold Deformation Theory / Tokyo December 7, 2008
Boundary of Words / Topological Group language Theory / Tokyo February 12, 2009
13
[History]
Distance of language Historical Review
14.
[Appendix]
The Time of Language / Tokyo January 10, 2012
Tokyo
February 3, 2012
At the Last Wintry Day of Classical Calendar in Japan
Sekinan Research Field of Language