10th for KARCEVSKIJ Sergej
1
Word
has meaning.
2
Meaning
consists of semantic minimum.
Semantic
minimum is the term that is used by JACOBSON Roman, ESSAIS DE LINGUISTIQUE GÉNÉRALE, 1973.
Semantic
minimum is abbreviated to SM.
3
Word
generates sentence.
4
Language
consists of semantic meaning, word and sentence.
5
Language
is in space.
Space
is considered as n-dimensional
complex space.
n-dimensional
complex space is notated to Cn.
Point
of Cn is expressed by z.
Open
set of Cn is expressed by Ω.
Ω is
proto-meaning minimum.
6
Language
has distance.
z∈Cn
|
z | = ( | z1|2 + … + | zn|2 ) 1/2
|
z | is proto-distance.
7
Set
of all the nonnegative integers is expressed by Z+.
For
every point a of Ω, power series that is convergent to complex valued function f over a neighborhood of a is called Pa.
Pa (z) =
∑α∈Zn+ cα(z – a)α, cα∈C
When
there is Pa (z), f is called holomorphic function.
Holomorphic
function is C∞ class.
When
complex adjoint z ↦ 
is holomorphic, f is called
antiholomorphic.
Set
of all the holomorphic functions over Ω is
expressed by A (Ω).
A (Ω) is proto-word.
8
All
the holomorphic functions are the solution of Cauchy-Riemann equation.
Cauchy-Riemann
equation is simultaneous differential equation.
= 0, j
= 1, …, n
Cauchy-Riemann
equation is proto-sentence.
[References]
Reversion
Analysis Theory / Tokyo June 8, 2008
Reversion
Analysis Theory 2 / Tokyo June 12, 2008
Tokyo June 15, 2008
Sekinan
Research Field of Language
[Reference December 22,
2008]