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.
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]
Tokyo June 15, 2008
[Reference December 22, 2008]
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