Another passway to mathematics

Another passway to mathematics 

02jan13

In some 40 years I had concerned with mathematics to which I only had read several books as if it is  the books of arts, for example, the verses of Chinese classics that are always obscure to understand by my Chinese ability. On the Tang Dynasty’s famous poet, DU fu’s work I had not clearly understood, probably till now. But the works are all pleasant in its own way. As like them mathematics I had read some books and papers. Definitely  I could not make DU Fu-like work. But I liked DU Fu so much. And I also cannot understand mathematics anymore, but also like it. If there be not valuation that is usual done at school, more people maybe like it as same as they read poems putted before them. Mathematicians are put to study stern logics for its long history while the poets make poems that need severe rules of rhythm and meaning. That is all, for my standpoint on mathematics or Chinese classics,or my life.

Read Andre Martinet

Read Andre Martinet 

21jan13

Reread Andre Martinet’s ELEMENTS DE LINGUISTIQUE GENERALE, 1970. When I was a student in 1970s, the book was already determined the established reputation. Now at rereading, I confirmed that one of his most concerned thing was the amalgamation of moneme, which is still radically never solved . But by his approach or any other similar approached researchers, Martinet-like style of studying is very difficult to progress. I have taken the another way to think on the themes influenced from KARCEVSKIJ Sergej (the early example ;Holomorphic meaning Theory 2008 ) by using the mathematical methods, especially algebraic geometry.

Recent result on the relation between characters and time in language is shown below.
Time of WANG Guowei, 2011, sekinanmetria 

Tokyo
16 July 2012

On WANG Guowei, refer to the next.

The Time of WANG Guowei

Tokyo

21 January 2013 added

SAITO Kohei, painter and tender teachr on art and life

SAITO Kohei, painter and tender teachr on art and life 

08jan13

Long time ago of my age 20s, when I talked with SAITO Kohei age 40s, painter of my colleague at high school, I asked him, “Which painter do you like best?”

He immediately answered “It’s Grunewald, do you know the painter?” At that time I did not know on this famous painter anymore. Probably feeling pitiful, soon after he brought me a book on the painter and showed me the famous The Crucifixion.

In those days I was an unskilled  high school teacher and he was also an art teacher of the same school.  He taught me the various things on art, literature and the way of living for researching own precious theme. At that time I had learned writing language mainly focused to Chinese old inscription on tortoise carapaces.

I frequently had visited his art study room and drank coffee being made from him. At one time, he let me take my portraits spending several days. Drawing the portraits, he said that contrary to my image I had a lean face. He was always gentle and took care of me.

Several years later, I left school teacher and again started study at a university to deepen the philological bases. He also stopped teaching at the school and devoted himself  to painting and lived apart from me at Yokohama.

In 2010 I heard the aluminum of the school, he died by disease.  I loved him so much and truly thanked him for his tender and wider kindness to my poor and immature young time.

Tokyo
18 May 2012
8 January 2013 added
Sekinan Research Field of Language

Symbolic Repetition

Symbolic Repetition 

26jan13

Trough some ten year learning I have confirmed that the meaning of word has a certain repetition which I call symbolic repetition for generating the core symbolic meaning of word. I strongly became aware of this repetition’s importance when I saw the Kagura, the traditional village dance performing at the shrine. The theme of the dance was the generation of nation by God from the myth of the ancient Japanese classics. The situation at the play-going is shown at the next.
Sato-kagura, Village Shinto dance, Fuchu, Tokyo / 20 November 2012From now on, I will describe this symbolic repetition using infinite loop space of algebraic K theory. The proto-type of symbolic repetition are already presented at the intuitive style at my early works. The relative papers are shown at the below.
On Time Property Inherent in Characters / 28 March 2003
Quantum Theory for Language / 15 January 2004
Prague Theory / 2 October 2004Loop space as language’s representation is roughly shown at the below.
Loop Time of Character / 15 September 2011

Tokyo
5 December 2012
Sekinan Research Field of Language

Reference added
27 December 2012
Word as Infinite Loop Space / 6 December 2012

Sato-kagura, Dance Permance, at Okunitama-jinja Shrine,
Fuchu, Tokyo, 20 November 2012

Symbolism of Japan, Haiku

Sekinan Research Field of Language

Symbolism of Japan, Haiku 

TANAKA Akio 
4 July 2012



                                        

Haiku is the traditional Japanese literature since the Meiji Period some 140 years ago, the ancestor of which was called Haikai that was began in the Muromachi Period some 500 years ago.

I have made Haiku since age 20s. My Haiku's teacher is SAEKI Shoichi, one of the modern Haiku writers in Japan. SAEKI's teacher is probably ISHIDA Hakyo, famous Haiku writer in the Showa Period. Thus the tradition of the literature has been inherited to me.

One of my youth age's Haiku, at Tokyo, February 1970, is the following.

パンタグラフ冷たい隙間で発光す

Pantagurafu tsumetai sukimade hakkosu

Pantograph
At the coldest clink
Radiates light for me

Symbolism of Japan, Haiku again

Symbolism of Japan, Haiku again 04/09/2013 0 Comments   I think that Haiku is the symbolic literature in Japan.The explanation of details is omitted now. I only introduce the contemporary fact of it. My favourite Hakuest, ISHIDA Akio ever wrote on her husband, ISHIDA Hakyo, one of the most Haikuest of modern Japan. The next is the one. Hi tomoshite Hachijuhachiya wo tuma to ori <Trial translation> Turning on a light the eighty eightth night of the year is with husband <Explanation> The husband Hakyo has long been tuberculosis.The late years are almost at hospital for treatment. The eighty eight day of the year is the the peak period of gathering the fresh green tea's leaves. Famous annual function of the early summer. Probably Hakyo returned home for the lull time of the disease. Tonight was the best day for the two. <Symbolism of Japan> Haiku shows the reality of daily life for the ordinary people by only 17 syllable of Japanese. [Reference] Symbolim of Japan, Haiku. 4 July 2012

sekinanlogos Conjecture

sekinanlogos Conjecture

Conjecture: Author sekinan

• Distance
• Reflection
• UNiqueness
• Amplitude
• Meaning
• Infinite
• Reference

Bibliography 2011 / Algebraic Geometry

Bibliography 2011
Algebraic Geometry

[CLE-KOL1995] Herbert Clemens, Janos Kollar. Current Topics in Complex Algebraic Geometry. Cambridge University Press, Cambridge, 1995.
[COR2007] Alessio Corti. Flips for 3-folds and 4-folds. Oxford University Press, Oxford, 2007.
[HIR2004] HIRONAKA Hesuke. Algebraic Geometry. Kyoto University Press, Kyoto, 2004.
[IIT2001] IITAKA Shigeru. Geometry of Plane Curve. Kyoritsu Shuppan, Tokyo, 2001.
[ISH2000] ISHIDA Masanori. Basis of Algebraic Geometry. Baifukan, Tokyo, 2000
[KAT1998] KATSURA Toshiyuki. Algebraic Geometry Primer. Kyoritsu Shuppan, Tokyo, 1998.
[KAWAGUCHI2011] KAWAGUCHI Shu. Book review MORIWAKI Atsushi : Arakelov Geometry, Sugaku, January 2011. Iwanami Shoten, 2011.
[KAWAMATA2001] KAWAMATA Yujiro. Geometry of Objective Space. Asakura Shoten, Tokyo, 2001.
[KOL-MOR2008] Janos Kollar, MORI Shigefumi.Birational Geometry. Iwanami Shoten, Tokyo, 2008.
[KON2008] KONO Toshitake. Field Theort and Geometry. Iwanami Shoten, Tokyo, 2008.
[KON2009] KONO Toshitake. Geometry of Repeated Integral. Springer-Japan, Tokyo, 2009.
[KON-TAM2008] KONO Akira, TAMAKI Dai. General Cohomology. Iwanami Shoten, Tokyo,2008.
[MORISHITA2009] MORISHITA Masanori. Knot Theory and Prime Number. Springer-Japan, Tokyo, 2009.
[MORIWAKI Atsushi2008] MORIWAKI Atsushi. Arakelov Geometry. Iwanami Shoten, Tokyo, 2008.
[MUK2008] MUKAI Shigeru. Moduli Theory 1. Iwanami Shoten, Tokyo, 2008.
[MUK2008] MUKAI Shigeru. Moduli Theory 2. Iwanami Shoten, Tokyo, 2008.
[NOG2003] NOGUCHI Junjiro. Several Variable Nevanlinna Theory and Diophantine Approximation. Kyoritsu Shuppan, Tokyo, 2003.
[OSH2008] OSHIKA Ken'ichi. Discrete Group. Iwanami Shoten, Tokyo, 2008.
[SAI2009] SAITO Takeshi. Fermat Conjecture. Iwanami Shoten, Tokyo, 2009.
[TANIYAMA1994] TANIYAMA Yutaka. Complete Works of TANIYAMA Yutakaenlarged edition. Nihonhyoronsha, Tokyo, 1994.
[TANIZAKI2002] TANIZAKI Toshiyuki. Lie Algebra and Quantum Group. Kyoritsu Shuppan, Tokyo, 2002.
[UEN2005] UENO Kenji. Algebraic Geometry. Iwanami Shoten, Tokyo, 2005.
[UEN-SHI2008] UENO Kenji, SHIMIZU Yuji. Deformation and Period of Complex Structure. Iwanami Shoten, Tokyo, 2008.

Tokyo

December 19, 2011
Sekinan Research Field of Language

Reversibility of Language​

​

sekinanlogoshome 

​

Floer Homology Language 

TANAKA Akio 

     

​

Note4 

Reversibility of Language​

​

​

1​

Banach space   E,F​

Local L1,p class map that satisfies  : R×S1 → M      L1,p(R×S1, M; li, lj)    ​

Banach manifold     L1,p(R×S1, M; li, lj)​

Tangent space at      L1,p(R×S1, *TM)​

Section of E (R×S1, M; li, lj)         sh​

​

2​

N| is zero order operator.​

​

3​

​

4​

2n dimensional manifold     M​

Tangent space     TM​

Map     JM : TM → TM​

JM° JM = -1​

​

5 is elliptic 

operator over closed manifold S1 . is Fredholm operator.​

​

6​

(Theorem) is reversible.​

​

7​

Concept <memory> on <Mirror Theory / Tokyo June 5, 2004> is defined by   .​

​

​

[References]​

Mirror Theory / Tokyo June 5, 2004​

Mirror Language / Tokyo June 10, 2004​

Guarantee of Language / Tokyo June 12, 2004​

​

​

​

Tokyo June 5, 2009​

Sekinan Research Field of Language

Source:https://writer.zoho.com/public/sekinan/FHLNote4ReversibilityOfLanguage

Tomita’s Fundamental Theorem

von Neumann Algebra 4

Note 1

Tomita’s Fundamental Theorem  

TANAKA Akio

[Theorem]

(1) JNJ = N ’

(2) Δ^itNΔ^-it = N,  ∀t ∈R

[Preparation]

<1 von Neumann Algebra>

von Neumann algebra     *subalgebra satisfies A ’’ = A. 

<1-1 *subalgebra> 

Algebra A that has involution*       *algebra

Element of *algebra     A∈A

When A = A*, A is called self-adjoint.

When A *A= AA*, A is called normal.

When A A*= 1, A is called unitary.

Subset of A     B

B * := B*∈B

When B = B*, B is called self-adjoint set.

Subalgebra of A     B

When B is adjoint set, B is called *subalgebra.

<1-2 involution*>

Involution * over algebra A over C is map * that satisfies next condition.

Map * : A∈A ↦ A*∈A

Arbitrary A, B∈A, λ∈C

(i) (A*)* = A

(ii) (A+B)* = A*+B*

(iii) (λA)* =λ^-A*

(iiii) (AB)* = B*A*

<2 Modular operator, modular conjugation>

Δ is called modular operator on x₀.

J is called modular conjugation on x₀.

<2-1 Modular operator>

Δ = R^-1(2I-R), Δ^it = R^-it(2I-R)^it, t ∈R.

Δis unbounded positive self-adjoint operator.

Δ^it is 1 coefficient unitary group.

<2-2 Modular conjugation>

J is adjoint linear isometric operator, J² = I.

<2-3 Symmetric operator>

Objection operator from H_R to K, iK     P, Q

R = P + Q

Polar decomposition of P - Q at H_R     P – Q = JT

T is positive symmetric operator over H_R.

Re<x, Ty> = Re<Tx, y>

T² = (P – Q)²

<2-4 Polar decomposition>

φ∈N_*, ψ∈N_*,+

Partial isometric operator     V∈N

φ = R_Vψ and V*V = s(ψ)

|| φ|| = || ψ ||

ψ is called absolute value ofφ.

φ = R_Vψ is called polar decomposition ofφ.

<2-5 N_* >

Bounded linear functional over N     N_*

To be continued

Tokyo May 3, 2008

Sekinan Research Field of Language

www.sekinan.org

[Postscript August 2, 2008]

<On [Theorem] (1) JNJ = N ’>

Algebraic Linguistics / Linguistic Result / Deep Fissure between Word and Sentence / Tokyo September 10, 2007

von Neumann Algebra 4 / Conjecture 1 / Relation between Word and Sentence / Tokyo May 5, 2008

<For more details>

Case