Thursday 29 May 2014

The rose days are over but still I remember its delight

This season's rose days are over. But I still remember the splendid figures in my mind.
Why the roses are so special? I have not the answer. What I can only say is that rose tells us the time passing or the life's importance as like we need in our times, so to speak, affection.

Rhododendron flower has bloomed after rose season

In the garden white rhododendron has bloomed after white rose season.
Surely we have a tiny heaven in the garden since we had cultivated the soil.


Photos taken at 29 May 2014

Monday 26 May 2014

The temple of ravine, pre-modern architecture of Tokyo

We went to Itsukaichi Ravine, west area of Tokyo at 14 May, where deep green forest was near the Akigawa River. From Itsukaichi some 15 minute walk to the temple. All was calm and solemn in the precincts.

The main gate of Kotokuji Temple,Itsukaichi, Tokyo

The main hall of Kotokuji Temple

 The veranda of main hall

 The temple window and the board of telling the meal time

The Akigawa River and the Ravine
All photos taken at 14 May 2014


Distance Theory Historical Review


Sekinan Research Field of Language

Distance Theory
Historical Review 


TANAKA Akio
 

         


Memory
The Time of Quantum
The Time of WANG Guowei
The Time of Language
The Time of Wittgenstein
From Distance to Pseudo-Kobayashi-Distance

Intuitive Concept

On Time Property Inherent in Characters
Quantum Theory for Language
Distance Theory 
Prague Theory
Quantum
Quantization of Language
Discreteness of Language
Distance
Distance of Word
Orbit of Word
Dimension
Dimension of Word

Connection

Connection of Words 
Hyperbolicity
Reflection of Word 
Boundary of Words



                                                                           Tokyo
                                                                 February 11, 2012
                             
                                                  Sekinan Research Field of Language



  

Salute, this year's rose season

The rose season soon ends this year's fabulous time. Salute, good bye to the next year. Many people has seen the tiny garden's lovely white roses and a few red roses probably with love.













Sunday 25 May 2014

The Murayama Dam, the place if the heaven falls on the earth

I love the Murayama Dam for its calmness,spread to the far mountains and clear high sky. Ever on father's back I went and now with wife. All at ease.






Mitake Ravine, West end of Tokyo

Yesterday  we went to the Mitake Ravine to see its fine landscape and the Tama River's coolness. The hiker and one-day campers were so many to make lunch or barbecue. We ate the light lunch at the river front while birds were flying and catching their foods from the river.





Saturday 24 May 2014

Word construction and its dimension / 4 September 2013

TANAKA Akio

Tokyo
4 September 2013

1.
Here language means language model that is described by mathematics.
2.
Description is done by arithmetic geometry.
3.
Language model has not any relationship with natural language.
4.
Language model adopts the themes derived from some phenomena of natural language.
5.
The model dealt here is related with the next two themes.
(1) Parts and whole at the construction of word.
(2) Dimension of word constructed from parts to whole.
6.
(Theorem)
The next and are regular closed immersion of codimension cd
XYYZ
Here is  given Cartesian diagram of the next scheme.
X'i'Y' j'→Z'
↓         ↓        ↓
XiY j Z
At this time the next equality sign is set up.
(j O i)! = i! O j! : CHr(Z') → CHr–c–d(X')
7.
Consideration
Here  i is supposed to be one meaning minimum and j is the another one meaning minimum.
Also X is supposed to be old word and Z is supposed to be constructed new word and Y is supposed to be internal word that is located between X and Z.
(1) The whole of word is constructed from the parts of word.
(2) The dimension of new word has lower dimension than the old word. The new word's dimension's decrease is equal to the r minus the sum of codimensions of i and j.
      That is to say, the dimension of  new word decreases than the dimension of old word. The degree of decrease is related with the codimensions of additional meanings.
♦ Here ends the paper.

Zoho sites of SRFL Sekinan Research Field of Language

Zoho sites of SRFL show the mathematical approach to clear description for language essential parts.
The URL is the next.


The garden hedge rose towards the sky
19 May 2014

Friday 23 May 2014

sekinanArchive

sekinanArchive is the data house of papers, essays and photos from 2003 related with theoretical language study.

sekinanArchive

The archive of
SRFL Sekinan Research Field of Language

Chronicle
Dedication
Dictionary
File
Site
Zoho

Tokyo
13 April 2014
Sekinan Research Field of Language

Symmetry and Infinity. For Climber OKADA Noboru

For Climber OKADA Noboru and His West Hodaka in Snow
From early Work

TANAKA Akio
               
                         

Symmetry and Infinity
Grammar <Language World, Real World>
Freedom and String <World, Anti-World>
Distance <Real Language, Mirror Language>
Sentence <Finiteness, Infinity>
[Snowy Dawn Tokyo February 3, 2008]



                                                              Tokyo
                                                      19 April 2014

                                    Sekinan Research Field of Language

Wednesday 21 May 2014

sekinanpaper, latest papers of SRFL

sekinanpaper shows the latest papers on language at SRFL.


The pond of Murayama Dam, Sayama Hills, Tokyo
Photo taken at 19 May 2014

Reversion Conjecture Revised

Reversion Conjecture is the utmost paper of SRFL Sekinan Research Field of Language.
The paper's URL is the next


The pond and the iris in the Murayama Dam Park
Photo taken at 19 May 2014

Tuesday 20 May 2014

Simplification of Reversion Conjecture

Reversion conjecture is simplified by Kerz-Saito's theorem, 2012.

Kerz, M., Saito, S.: Cohomological Hasse principle and motivic cohomology of arithmetic schemes. 2012

Interpretation of Reversion conjecture

According to Reversion conjecture, language has a standstill point in itself.
Here it means that every word has standstill point and every word has a proper distance from the standstill point. This distance constructs word's proper meaning and grammar.

Refer to the next.
Distance Theory 2004 / 5 May 2004
Reversion Theory 2004 / 27 September 2004

New starting point on language, Reversion conjecture

Reversion conjecture may become the new starting point on language, especially on language universals.
Reversion conjecture has the preparatory thinking by algebraic geometry.
Refer to the next.





Reversion Conjecture

Reversion Conjecture

Conjecture for reversion of language

TANAKA Akio

Conjecture for reversion of language
14/10/2013 11:21
Conjecture for reversion of language
Language has a standstill point in itself.

[Explanation]
This conjecture’s intuition is prepared at the paper, Reversion Theory 2004 at Sekinan Research Field of Language.
This conjecture’s mathematical basis is given by Kato conjecture 1986. The conjecture is said to be given cohomological Hasse principle at unramified number theory.

[References]
News. hillssouthroad
News
Reversion Theory 2004
14/10/2013 11:10
Kato conjecture 1986 
13/10/2013 23:07
K. KATO, 1986 
12/10/2013 19:52
Read more: http://hillssouthroad.webnode.com/

                                                                         Tokyo
                                                                    1 May 2014
                                                Sekinan Research Field of Language

Monday 19 May 2014

At Bank of Dam Again

Sekinan Research Field of Language

At Bank of Dam Again 

TANAKA Akio 





               
                         
At bank of dam we conversed with friends on many innocent themes in our youth days. Long time ago the place was the sight of the fireworks, for which father took me and elder sister to see in the summer night. When returning home you perfectly slept soundly at father's back, the sister said to me later.
After some thirty years after, we came again with the family to play in the fallen leaves at the bank of dam. Children were rolling down at the slope of the bank wearing golden leaves on the clothes.
And after half a century we have come again at the bank with wife protecting leg's slight pains each other.




Water Intake Tower of Murayama Dam

Murayama Dam is located at the west Sayama hills of Tokyo. I have come here frequently since in my child days, the first being carried on father's back. Today with my wife took lunch at the bench facing at the pond near the Dam. Wind was so cool and the air fresh, birds and frogs were singing by their best songs.

The water intake tower of the Sayama Hills, Tokyo

Also refer to the next.

sekinanfresh, new top page of SRFL

sekinanfresh is the new top page of the language research site SRFL.
The URL is the next.

Photo taken at 16 May 2014

Saturday 17 May 2014

Mini-climbing roses at the arch.

Mini-climbing roses are now in their best at the arch.



For their best , some ten years needed

After some ten years, the roses are now blooming their best style.


Flower in the garden, verbena

At the hedge' pot, verbena has bloomed today after rather long preparation. 16 May 2014


Friday 16 May 2014

Rose of Today 16 May 2014

White rose, "Fresh Snow" has bloomed at the hedge this early summer. I have love  this rose 15 years.


Also refer to the next




Pinterest, SRFLPhoto Flower and Woodwork

SRFLPhoto is the photo site of SRFL Sekinan Research Field of Language.

SRFLNews: The language research site, SRFLTheory renewed

Thursday 15 May 2014

Rose season, early summer delight

Rose season has come again in the garden. I have waited the time after long one year passing. The season's highlight only keeps one week or so. The early summer always passes rapidly. So probably we all love this flower.



Three photos have been taken at 15 May 2014

Also refer to the next

Tuesday 13 May 2014

Preparation for Description on Language

Preparation for Description on Language  

TANAKA Akio

               
                         

For clear description on meaning, word and language, mathematical method is essentially inevitable for me after long wandering about traditional way of study on language, especially through the vast heritage of the Linguistic Circle of Prague.
Minute description has gotten under way using the mathematics, in my part, particularly of algebraic geometry. The foundation and decision to adopt mathematics became actualizing between 2003and 2008. Definitive style was found at a group papers of Complex Manifold Deformation Theory 2008-2009.
After this CMDT papers, my standpoint of study has never wavered any more.
Here I show the preparation styles to reach the CMDT and the CMDT papers that made the firm base of description at the next.
Subsequent papers of CMDT are shown at the Zoho sites that has been the main place of my study till now.

1.

                                                                  Tokyo
                                                         13 May 2014
                                       Sekinan Research Field of Language

One starting point of descriptive way for language study




1
Complex n-dimensional open ball is presented. Abbreviation is n open ball. The notation is B aR )
> 0
Open set { zCn | | z-| < R }
2
Open set of Cn     Ω
Map fromΩ to open set of CnΩ’     F = (f1, f2, …, f)
Element of F     fj
When fis normal function over Ω, F is called holomorphic map.
Composition of holomorphic map is also holomorphic map.
3
Set of all the holomorphic functions over Ω     A (Ω )
(Ω  1/ f (Ω  -1(0) )
Holomorphic map that has holomorphic inverse map is called biholomorphic map
When there exists biholomorphic function from Ω to Ω is called biholomorphic equivalent.
Bijective holomorphic map is biholomorphic.
Biholomorphic map from Ω to Ω is called holomorphic automorphism that becomes group by product as composition.
The group is called holomorphic automorphism group. The notation is Aut Ω.
4
Each n open ball is holomorphic equivalent.
B ( (0,0, …, 0 ) is notated as B n.
5
All the locally 2 powered integrable functions     L2loc (Ω)
(Ω ) = {f  L2loc (Ω) | ∂f /∂ = 0, = 0, 1, …, n }
6
n open ball     B (aR ) ⊆ Ω
Volume element of B (aR )     dS
Vol ( B (aR ) ) : = B (aR )dS = 2πnR2n-1/(n-1)!
(Ω ) is closed subspace on topology of L2convergence .
(Ω ) and (Ω )is separable.
7
Domain     Ω
Point     a
Ω
ζ
(∂B)n
For arbitrary zΩ and ζ(∂B)nwhen (a1+ζ1(z1-a1), …, an+ζn(zn-an) ) Ω is satisfied, Ω is called Reinhardt domain centered by a.
For arbitrary zΩ and ζ∂Bn, when (a1+ζ1(z1-a1), …, an+ζn(zn-an) ) Ω is satisfied, Ω is complete Reinhardt domain centered by a.
n open balB (aR ) is complete Reinhardt domain.
8
n dimensional complex ball that has center 0    D = n   
D’s logarithm image log D is defined by the next.
log = {x(R{-∞})n ex : = (ex1, …, exn) D }
When dialog image is convex, D is logarithm convex.
Outer point of D     a
Monomial ma(z)  
supzD | ma(z) | < ma(a) = 1
Word, meaning element and distance are defined by the next at simplified level.
Word : = n ( = complete Reinhardt domain centered by 0 )  
Meaning element : = a ( = Outer point of D)
Distance : = supzD | ma(z) | of monomial ma(z)
9
Word, meaning element and distance are considered in connection with Cauchy-Riemann equation.

[References]
<Distance>


Tokyo June 8, 2008

[Postscript June 19]
On holomorphic, refer to the next.

One of the descriptive way for language study, Holomorphic Meaning Theory 2



11th for KARCEVSKIJ Sergej


1
Open set of Cn     Ω
Holomorphic function over Ω     f
Set of all the holomorphic function over Ω     A Ω )
Open set     ⊂ Ω
fU ) is called ’s divisor class at U.
Divisor class is notated by D ( f).
2
n-dimensional polydisk is defined by the next.
Open set {z | | zj-aj | < r,  1j}
n-dimensional polydisk is notated by (ar) (r = (r1, …, rn))
(0, 1) is notated by .
××∆  (Number of ∆ is n.)
(ar) and are biholomorphic equivalent.
Hartogs figure      Tε = {(z1z2 2 | |z1| <ε}
When holomorphic map from Hartogs figure to Ω is always expanded to holomorphic map from ∆ 2 to ΩΩ is called Hartogs pseudo-convex.
3
C is Hartogs pseudo-convex.
Cn is Hartogs pseudo-convex.
Holomorphic open set is Hartogs pseudoconvex.
4
Subharmonic function is defined by the next.
Open set at complex plane     Ω
Semicontinuous function that is valued at [-∞, ∞)     ψ : Ω  [-∞, ∞)
  Ω
ψ(z )  (+ re)
5
Plurisubharmonic function is defined by the next.
Open set at complex plane     Ω
Semicontinuous function that is valued at [-∞, ∞)     ψ : Ω  [-∞, ∞)
(z, ωΩ×Cn
Function     ψ( z+ζω )
When  ψ( z+ζω ) is subharmornic as ζ ‘s function, ψ( z+ζω ) is called plurisubharmonic function.
Set of all the plurisubharmonic functions      PSH (Ω)
6
What Ω is pseudoconvex is defined by the next.
Continuous plurisubharmonic function     ψ : Ω → R
Arbitrary cR
Ωψc : = {zΩ |ψ(z) < c }
Ωψc is relatively compact in Ω .
7
Pseudoconvex open set     Ω
H(ΩZ) = {0}
Open subset of Ω     U
g A(U)
Element of A(U)    f
When V(g) is closed set of Ω, there exists D ( f).g.
8
Locally finite open ball     Bj B (pjRj)
Family of Bj     { B}= 1
Ω = 1 Bj
BV(gØ  B U
gj A(Bj) is defined by the next.
g= g | Bj  (BV(g) ≠ Ø)
g= 1    (BV(g) = Ø) 
gjk A(BjBk) : = gj / gk  (BjBk ≠ Ø)
BjBis convex and simply connected.
gjk has not zero point.
(j, k) has one to one correspond with branch ujk of loggjk
uijk over Bi BjBis defined by the next.
uijk : = uij + ujk+ uki
9
Language is defined by the next.
Meaning minimum : = Bj   
Word : = gjk
Sentence : = uijk

[References]

Tokyo June 19, 2008