Friday 7 December 2018

What is signal? A mathematical model of nerve 6 December Edition



What is signal?

A mathematical model of nerve

For father and mother

TANAKA Akio

Tokyo
21 November 2018-6 December 2018


0.

This short paper would finally write on signal through the relation between language and nerve, for which using mathematical method at the way.
This paper's one of kernels is energy which is naturally accepted at the side of verve, but at the side of language, it may be not accepted widely till now.
In this paper, I probably do not refer to the language's energy, that has been written several times in the papers before.
If necessary refer to the next essays.

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Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.


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1. Language

Next definition for language shows my simple image to language and energy.


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Language and Spacetime 

Language
Definition for the Child who Lost the World 

0 The world spreads around the human being.
1 Language divides the world.
2 Language connects the world.
3 Language bends the world.
4 Language stretches the world.
5 Language shrinks the world.
6 Language extinguishes the world.
7 Language creates the world.
8 Language gives despair.
9 Language gives hope.
10 Language is pasting on spacetime with energy.
Postscript
[Referential note / November 29, 2007]
For Authentication of Solidity 
[Definition added / November 3, 2008]
Definition 10, the part of <with energy> is newly added.
Tokyo March 3, 2007
Tokyo November 3, 2008 Added


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2. Human sense

On language and human sense, I ever wrote simply at the next paper.


Macro Time and Micro time

TANAKA Akio
24 July 2013
atbankofdam



1. Through natural language, in human being, occurred the electrical signal by eye or ear. These complex situations are beyond this paper’s limits.
2. Language is a physical object as signal and its transmission. At this circumstances, language must be recognised to be the existence that has finite time.
3. An apple on the desk gradually becomes rotten by passing the time very after the crop in the orchard. #0
4. Like an apple, language has passing physical time in oneself.
5. Language is metamorphosed  by the time progressing.  #1
6. Language includes the outer world from human being to universe. At this declaration, I recall Blaise Pascal’s Pensées. XXXIII. PROOFS OF JESUS CHRIST 308 The infinite distance between body and mind symbolizes the infinitely more infinite distance between mind and charity, for charity is supernatural.(Translated by A.J. Krailsheimer, 1966) #2
7. Language’s time goes freely from the present to the future or the present to the past. #3
8. Language symbolises the time from finiteness to infinity. #4
9. Human being recognises this vast language world perfectly. #5

References
#0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan Research Field of Language
#1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos
#2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966.
#3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory / December 16, 2006 / Sekinan Research Field of Language
#4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos
#5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos

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3. Signal

Signal Goes to meaning.
Traffic signal shows Go, Attention and Stop to people by three colour lights
Morse code sends a message by short and long signals.
Signal has structure that resembles language.
Morse code can regards as a written language.
What is signal's peculiarity?
It depends on signal's generation that has simple on-off phenomenon.
This phenomenon combines with the other on-off phenomena and become complex structure that has meaning like language.
Signal seems a primordial form of language.


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4. Nerve

Is nerve signal?
I have any knowledge on physiological nerve.
So at this paper I prepare a mathematical model of nerve comparative with signals.
At mathematical model, on-off system is not simply fit with the expression of mathematical space.
Here on-off system is arranged for more simple form.
I ever wrote a paper below.


The paper is a very intuitive one but there are some hints on signal.
Now I need one chapter for my new trial paper.
The chapter is " 6. Basic principle of quantum theory"
The original text is the following.

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６　量子理論の基本原理
　量子理論は、伝統的には実辞とされる陽性量子が1階層で進行することが基本である。したがってある種の量子群すなわち文において、陰性量子が冒頭に立つときには、その前に陽性量子または量子群が省略されたと考えることができる。
陰性量子が陽性量子の進行方向に変化を与えて、新しい階層に移行させることは、陰性量子が受けている被圧迫エネルギーによるとしたが、より正確には、以下のように説明できる。
一般に断定の虚辞とされる「也」は、その実辞としての意味は現代においては不分明であり、陽性量子としてはほぼ消滅したと考えることができる。その代わりに陰性量子としての虚辞機能が台頭して現在に至るが、その機能を細分すれば、断定、主題提示、呼びかけ、詠嘆、疑問、反語等の極めて多様である。
たとえば、「回也不愚」（『論語』為政篇）においては、「回」という人物が、（階層が変わり）孔子の心中において、（また階層が変わり）否定される存在であり、（さらに階層が変わり）「おろかものの類」が提示される。」
「階層が変わる」ということは、「回」という人物が、「也」と出現によって実在の人物から、孔子の心中における考察対象へと変換されたことを意味し、さらにその考察対象が「不」によって抹消されることを意味し、さらに新しく「愚」という概念が登場することを意味する。
すなわち陰性量子は、陽性量子が有する言語世界への直接的な意味を行うのではなく、実辞としてはもはや空白となった自らの領域へ、陽性量子を導くjことによって、一種の真空無重力の状態を現前させ、その方位を転換することであると仮定する。その転換に必要とされるエネルギーは、領域が受けている被圧迫のエネルギーから生ずるものと仮定する。　

Read more: https://srfl-lab.webnode.com/products/manuscript-of-quantum-theory-for-language-with-preface-note-and-note-2-2003-2018/

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At this chapter, the most important concept is positive quantum and negative quantum.
Negative quantum changed to positive quantum by energy.
At the linear space, quantum changes positive to negative and also negative to positive.
By this model, on-off phenomena are mapped at the linear space's quanta's situation.
In the models, quantum is led from V.G.Drinfel'd and M.Jinbo's Quantum group originated in 1985.

Reference
JIMBO Michio. Quantum group and Yang-Baxter equation. Maruzen Shuppan. Tokyo. 2012


5. Method

Manuscript of Quantum Theory for Language written in spring 2003 was roughly designed at a days I was in  hospital by pneumonia half a month in October 2002, when I always saw the river and the mountains west end of Tokyo. I was the very  reviewing life time for my research work.
My poor study was restricted in a narrow field of Chinese classical linguistics mainly developed in the late Qing dynasty the latter half of the 19th century,represented by DUAN Yucai, WANG Niansun, WANG Yingzhi, my favourite WANG Guowei and so forth.
So I determined that my approach to language was only in it and it was the most intimate for me at that time and probably herein after considering my tiny accumulation of study.
Next essay shortly showed the situation in 2002.


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1970s' dream, writing clear description on language universals by mathematics
From The Days of Ideogram

​​​4. Time property in characters
In Autumn 2002 I got pneumonia and was hospitalized about 2 weeks, where I thought of 1970s' dream, writing clear description on language universals by mathematics. The theme was as hard as ever. So, at the bed I thought the basis of language from the side of Chinese character’s classical approach which had vast heritage till Qing dynasty. I directed my attention to the character's figure which had compound meanings containing time elements continuing from Yin dynasty's hieroglyphic characters left on bones and tortoise carapaces some 2400 years ago. I thought that Chinese characters had containing time and its structure could be written by geometric approach once I had abandoned for difficulty. After leaving hospital, I wrote a paper titled On Time Property Inherent in Characters*3-1.

Read more: http://srfl-paper.webnode.com/news/the-days-of-ideogram/


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6. Quantum group

I think that language's foundation is in word.
Recently I started the new approach to word that has more simply at form and more wide-range-covered at usage.
Trial paper is the next.

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Quantum Group Language   
Word Indexed and Word Synthesized 
TANAKA Akio
1.
Word Synthesized is the word that is synthesized meanings in a word by arithmetic or algebraic  geometrical method.
For detailed refer to the next.
Arithmetic Geometry Language 2013
Algebraic Geometry Language 2014

2.
Word Indexed is the word that has index in a word, by which meanings are separated in a word at waiting situation. In a word meanings are combined by algebraic axioms and theorems starting from group theory.
Word Indexed seems to be more simply structure than Word Synthesized.
Word indexed basis is at the below.
Kac-Moody Lie Algebra Note 1 Kac-Moody Lie Algebra 2008
Kac-Moody Lie Algebra Note 2 Quantum Group  2008
The details of Word Indexed will be shown the papers after this.
3.
Meanings contained in Word Indexed is deeply related with quantization and discreteness.
Refer to the next.
Floer Homology Language Note 7 Quantization of Language 2009
Floer Homology Language Note 8 Discreteness of Language 2009

4.
All the basis of Word Indexed is generated at the next.
Manuscript of Quantum Theory for Language  2003 




Reference
Kac-Moody Lie Algebra  2008
Theory 2003-2016  2018
Genealogical Tree of Sekinan's Paper 7th Edition  2015-2018




This paper is unfinished.


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Chinese belongs to the isolated language.
In Chinese one character has one meaning and becomes a word in classical usage. Modern Chinese has many words that contain two or over two characters for one meaning, but basically almost all the characters have still classical one-character-one-meaning usage at the root of language.
Shuowenjezi Zhu written by DUAN Yucai typically shows some 2,000 year history of characters and their meanings.
Modern Chinese precisely said by Hanyu is one language of the over 50 languages officially recognized at the research, and I only know several language's grammars by the field work by linguists.

National Minority Languages in China   2004


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National Minority Languages in China





Zhongguo Shaoshu Minzu Yuyan Jianzhi Congshu

Minzu Chubanshe

1 Buyi yu jianzhi    YU Cuirong edited    1980   
2 Dongbu yugu yu jianzhi    ZHAONA Situ edited    1981
3 Dulong yu jianzhi    SUN Hongkai edited    1982
4 Donsiang yu jianzhi    LIU Zhaoxiong edted    1981
5 Gelaoyu jianzhi    HE Jiashan edited   1983
6 Maonan yu jianzhi    LIANG MIin edited    1980
7 Menggu yu jianzhi    DAO Bu edited    1983
8 Li yu jianzhi    OUYANG Jueya  ZHENG Taiqing edited    1980
9 Pumi yu jianzhi    LU Shaozun edited    1983
10 Qiang yu jianzhi    SUN Hongkai edited    1981
11 Mulao yu jianzhi    WANG Jin  ZHENG Guoqiao edited    1980
12 Tai yu jianzhi    YU Cuirong  LUO Meizhen edited    1980
13 Tuzu yu jainzhi     ZHAONA Situ edited    1981
14 Wa yu jianzhi    Zhou Zhizhi  YAN Qixiang edited    1984
15 Yaozu yuyan jianzhi    MAO Zongwu  MENG Chaoji  ZHENG Zongze    edited    1982

       

Guojia minwei minzu wenti 5 zhong congshu zhi 1
Zhongguo Shaoshu Minzu Yuyan Jianzhi Congshu

Minzu Chubanshe

16 Achang yu jianzhi    DAI Qingxia  SUI Zhichao edited    1985
17 Bulang yu jianzhi    LI Daoyong  NIE Xiizhen  QIU Efeng edited    1986
18 Chaoxian yu jianzhi    XUAN Dewu  JIN Xiangyuan  ZHAO Xi edited    1985
19 Cuonamen yu jianzhi    LU Shaozun edited    1986
20 Deang yu jianzhi    CHEN Xiangmu WANG Jingliu LEI Yongliang edited   1986
21 Elunchun yu jianzhi    HU Zengyi edited    1986
22 Ewenke yu jianzhi    HU Zengyi  CHAO Ke edited    1986
23 Gaoshanzu yuyan jianzhi (Ameisi yu)     HE Rufen  ZENG Siqi  TIAn Zhongshan  LIN Dengxian edited    1986
24 Gaoshanzu yuyan jianzhi (Bunen yu)     HE Rufen  ZENG Siqi  LI Wensu  LIN Qingchun edited    1986
25 Gaoshanzu yuyan jianzhi (Peiwan yu)    CHEN Kang  MA rongsheng edited    1986
26 Heni yu jianzhi    LI Yongsui  WANG Ersong edited    1986
27 Hesake yu jianzhi    GENG Shimin  LI Zengxiang edited    1985
28 Heze yu jianzhi    AN Jun edited    1986
29 Jing yu jianzhi    OUYANG Jueya  CHENG Fang  YU Cuirong edited    1984
30 Jinuo yu jianzhi    GAI Xingzhi edited    1986
31 Keerkezi yu jianzhi    HU Shenhua edited    1986
32 Lahu yu jianzhi    CHANG Hongen  mainly edited
33 Lisu yu jianzhi     CHU Lin  MU Yuzhang  GAI Xingzhi edited    1986
34 Luoba zu yuyian jianzhi (Bengni-Bogaer yu)    OUYANG Jueya edited    1985
35 Naxi yu jianzhi    HE Jiren JIANG Zhu yi edited    1985  
36 Nu zu yuyan jianzhi (Nuban yu)    SUN Hongkai  LIU Lu edited    1986
37 Cangluo menba yu jianzhi    ZHANG Jichuan edited     1986
38 Sala yu    LIN Lianyu edited    1985
39 She yu jianzhi    MAO zongwu  MENG Chaoji edited    1986
40 Xibu yugu yu jianzhi    CHEN Zongzhen LEI Xuanchun edited    1985
41 Tajike yu jianzhi    GAO erjiang edited    1985
42Tayaer yu jianzhi     CHEN Zongzhen  YI Liqian edited    1986
43 Tujia yu jianzhi    TIAN Desheng  HE Tianzhen deng edited    1986
44 Weiwuer yu    ZHAO Xiangru  SHU Zhining edited    1985
45 Wuzubieke yu jianzhi   CHENG Shiliang  ABUTURE Heman edited    1987
46 Xibo yu jianzhi    LI Shulan  ZHONG Qian edited    1986
47 Yi yu jianzhi    CHEN Shilin  BIAN Shiming  LI Xiuqing dited    1985



TOKYO
December 31, 2004


Read more: https://geometrization-language.webnode.com/news/national-minority-languages-in-china/


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 Xixiayu is a very interesting for me resembling the Hanyu and in the late 20th century the language was deciphered by Japanese linguist NISHIDA Tatsuo.



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The Days of Decipherment

TANAKA Akio

On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth days, so to say, the days of decipherment.

1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told  at Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered the Linear B.

In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered by NISHIDA Tatsuo (1928-2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki narabini Seikago bunpou no kenkyuu in 1962.
In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team developed largely.

In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the Qing dynasty and I read them almost every day containing the comparison with the western linguistic results. The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin  were the most important for me.

In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda, Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was too much difficult to read on. From the days the long and winding road began to mathematics and its applicable study for language universals.

At the exhibition of ancient Greece I confirmed in particular that the stability of language was  kept by letters and characters from the Linear A and Linear B. 

These language or character's situation especially of ideogram has become my study's foundation.


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These language or character's situation, especially of ideogram has become my study's foundation.
For ideogram, refer to the next papers.


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Ideogram Paper   2005-2018

1. Ideogram 2005

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7.
Quantum group 2

In 2008 I wrote on Quantum group at studying Kac-Moody-Lie Algebra.


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Note 2
Quantum Group
1 <Cartan matrix>
Base field     K
Finite index set     I
Square matrix that has elements by integer     A = ( aij )i, j ∈ I
Matrix that satisfies the next is called Cartan matrix.
i, j ∈ I
(1) aii = 2
(2) aij ≤ 0  ( i ≠j )
(3) aij = 0 ⇔ aji = 0
2 <Symmetrizable>
Cartan matrix     A = (aij)i, j ∈I
Family of positive rational number    {di}i∈I
Arbitrary i, j∈I    diaij = djaji
A is called symmetrizable.
3 <Fundamental root data>
Finite dimension vector space     h
Linearly independent subset of h     {hi}i∈I
Dual space of h     h*= HomK (h, K )
Linearly independent subset of h*     {αi} i∈I
Φ = {h, {hi}i∈I, {αi} i∈I }
Cartan matrix A = {αi(hi)} I, j∈I
Φis called fundamental root data of A that is Cartan matrix.
4 <Standard form>
Symmetrizable Cartan matrix    A = (aij)i, j ∈I
Fundamental root data     {h, {hi}i∈I, {αi} i∈I }
E = αi ⊂h*
Family of positive rational number     {di}i∈I
diaij = djaji
Symmetry bilinear form over E     ( , ) : E×E → K     ( (αi ,αj ) = diaij )
The form is called standard form.
5 <Lattice>
n-dimensional Euclid space    Rn
Linear independent vector     v1, …, vn
Lattice of Rn     m1v1+ … +mnvn     ( m1, …, mn ∈ Z )
Lattice of h     hZ
6 <Integer fundamental root data>
From the upperv3, 4 and 5, the next three components are defined.
(Φ, ( , ), hZ )
When the components satisfy the next, they are called integer fundamental root data.
 i ∈ I
(1)  ∈ Z
(2) αi ( hz ) ⊂ Z
(3) ti :=  hi ∈ hz
7 <Associative algebra>
Vector space over K     A
Bilinear product over K     A×A → A
When A is ring, it is called associative algebra.
8 <Similarity>
Integer     m
t similarity of m    [m]t
[m]t = tm-t-m / t- t-1
Integer   m, n   m≧n≧0
Binomial coefficient     (mn)
t similarity of m!     [m]t! = [m]t! [m-1]t!...[1]t
t similarity of (mn)    [mn]t = [m]t! / [n]t! [m-n]t!
[m0] = [mm]t = 1
8 <Quantum group>
Integer fundamental root data that has Cartan matrix A = ( aij )i, j ∈ I
      Ψ = ((h, {hi}i∈I, {αi} i∈I ), ( , ), hz )
Generating set     {Kh}h∈hz ∪{Ei, Fi}i∈I
Associative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.
(1) khkh’ = kh+h’     ( h, h’∈hZ )
(2) k0 = 1
(3) KhEiK-h = qαi(h)Ei    ( h∈hZ , i∈I )
(4) KhFiK-h = qαi(h)Fi   ( h∈hZ , i∈I )
(5) Ei Fj – FjEi = ij  Ki - Ki-1 / qi – qi-1     ( i , j∈I )
(6) p [1-aijp]qiEi1-aij-pEjEip = 0     ( i , j∈I , i ≠j )
(7) p [1-aijp]qiFi1-aij-pFjFip = 0     ( i , j∈I , i ≠j )
[Note]
Parameter q in K is thinkable in connection with the concept of <jump> at the paper Place where Quantum of Language exists / 27 /.
Refer to the next.



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In 2004 I wrote the paper named Place where Quantum of Language exists.


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Place where Quantum of Language Exists
1            Quantum of language is the smallest unit of language.
2            Quantum of language moves linearly on the floor of language.
3            Linear movement is the properties of quantum.
4            Floor of language is on the space of language.
5            The space of language is two dimensions.
6            Two dimensions are horizontal and vertical.
7            Horizontal movement makes word, #1
8            Vertical movement makes sentence. #1
9            The space of language is electrical digitized place.
10        Chinese /jiao shi/ means classroom in English. 
11        /Jiao/ is a quantum of language.
12        /Shi/ is a quantum of language.
13        /Jiao shi/ is a word.
14        /Jiao/ sends a quantum to /shi/ quantum.
15        /Shi/ quantum receives a quantum from /jiao/ quantum.
16        What sends quantum is called positive.
17        What receives quantum is called negative.
18        Quantum has positive energy in original condition.
19        Quantum changes negative in the situation of quanta set.
20        Quantum change occurs in two situations in general.
21        One situation is what quanta stand side by side on a floor and neighboring quanta connect well. #2
22        The other situation is what quanta change oneself by the non-use of quanta meaning in language history progress. #2
23        Word has a positive- negative construction.
24        Positive-negative construction occurs on a floor.
25        Sentence has a positive-positive construction.
26        Positive-positive construction occurs on different floors.
27        The latter quantum transfers on a different floor. This transfer is called <jump>.†
28        Quantum has electrical energy which flows to the electrical zero level.
29        Electrical zero level is a sentence end where quantum of language ideally accord with the real world. #3
30        A floor of language is a non-branches electrical circuit.
31        Word is a non-branch circuit.
32        Sentence is a branch circuit.
33        The meaning of word and sentence is a compound system of electrical signals.
#1 Definition of word and sentence can be seen in the paper “Method of Linguistics” and other papers on the site of Sekinan Research Field of Language /www.sekinan.org/.
#2 Definition of connect well can be seen in the paper of “Quantum Theory for Language Synopsis” and other papers on the site of SRFL.
#3 Definition of sentence end can be seen in the paper “Mirror Theory”, “Mirror Language” and other papers on the site of SRFL.
Tokyo July 18, 2004
Postscript 
[Referential note November 9, 2007]
<Place where Quantum of Language Exists> is related with the next papers on the concept.


________________________________



________________________________


[Referential note February 9, 2008]
† Concept <jump> of /27/ is thinkable in connection with <quantum group’s parameter q> at the paper Kac-Moody Lie Algebra / Quantum Group /.
Refer to the next.


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At this paper, 23-33 is the most important for signal's intuitive image.


23        Word has a positive- negative construction.
24        Positive-negative construction occurs on a floor.
25        Sentence has a positive-positive construction.
26        Positive-positive construction occurs on different floors.
27        The latter quantum transfers on a different floor. This transfer is called <jump>.†
28        Quantum has electrical energy which flows to the electrical zero level.
29        Electrical zero level is a sentence end where quantum of language ideally accord with the real world. #3
30        A floor of language is a non-branches electrical circuit.
31        Word is a non-branch circuit.
32        Sentence is a branch circuit.
33        The meaning of word and sentence is a compound system of electrical signals.



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8.
Quantum group 3

Quantum group is defined by JIMBO Michio as the following.

Definition of quantum group 

Generating element: a, b, c, d
Relation: ba = qab,  ca = qac
              bd = q-1db,  cd = q-1dc
              bc = cb, ad - q-1bc = da - qbc = 1
Coproduct:  Δa   Δb           a     b             a     b
                (            )   = (             ) (χ)  (           )
                  Δc   Δd           c      d              c      d
      Δa = a (x）a + b (x) c

                                             JIMBO Michio                                       
                                             Bussei Kenkyu (1992), 57(5): 628-634


9.
Quantum group 4
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