CHINO Eiichi and Golden Prague
June 30, 2015
CHINO Eiichi and Golden Prague
TANAKA Akio
C also died early, who had taught me Russian and linguistics. He loved
the old city that had the beautiful towers and bridges.
the old city that had the beautiful towers and bridges.
In C‘s many works there was the essay “The Moon of Carpathians”. He wrote
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached “Golden Prague”. Prague, it was his youth itself.
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached “Golden Prague”. Prague, it was his youth itself.
Now I cannot hear his voice telling the various anecdotes on languages,
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as “the genius of linguistics”.
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as “the genius of linguistics”.
[References]
Time of Word
June 30, 2015
Conjecture A
5 Time of Word
Conjecture
Word has time.
[View¶]
¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains
and vigorous port towns at dawn.
1
Kähler manifold X
Kähler form w
A certain constant c
Cohomology class of w 2πc1(X)
c1(X)>0
Kähler metric g
Real C∞ function f
∫X (ef– 1)wn = 0
Ric(w) –w = 
f
f
2
Monge-Ampère equation
(Equation 1)
Use continuity method
(Equation 1-2)
Kähler form w’ = w + 
f
f
Ric(w‘) = tw‘ + (1-t)w‘
δ>0
I = {
}
}
3
is differential over t.
is differential over t.
Ding’s functional Fw
4
(Lemma)
There exists constant that is unrelated with t.
When utis the solution of equation 1-2, the next is satisfied.
Fw(ut)
C
C
5
Proper of Ding’s functional is defined by the next.
Arbitrary constant K
Point sequence of arbitrary P(X, w)K {ui}
(Theorem)
When Fw is proper, there exists Kähler-Einstein metric.
[Impression¶]
¶ Impression is developed from the view.
1
If word is expressed by u , language is expressed by Fw and comprehension of human
being is expressed by C, what language is totally comprehended by human being is
guaranteed.
Refere to the next paper.
#![]()
Guarantee of Language
2
If language is expressed by being properly generated, distance of language is expressed by
Kähler-Einstein metric and time of language is expressed by t, all the situation of language
is basically expressed by (Equation1-2).
Refer to the next paper.
#![]()
Distance Theory
3
If inherent time of word is expressed by t‘s [δ, 1], dynamism of meaning minimum is
mathematically formulated by Monge-Ampère equation.
Refer to the next papers.
#1<For inherent time>
#2<For meaningminimum>
#3<For meaning minimum’s finiteness>
Tokyo January 1, 2009
Amplitude of Meaning Minimum
June 30, 2015
Conjecture A
4 Amplitude of Meaning Minimum
Conjecture
Meaning minimum has finite amplitude.
[View*]
*Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains
and vigorous port towns at dawn.
1
Bounded domain of Rm Ω
C∞ function defined in Ω u, F
u, F satisfy the next equation.
F(D2u) = Ψ
D2u is hessian matrix of u.
F is C∞ function over Rm×m .
Open set that includes range of D2u U
U satisfies the next.
(i) Constant λ, Λ 
(ii) F is concave.
2
(Theorem)
Sphere that has radius 2R in Ω B2R
Sphere that has same center with B2R and has radius σR in Ω BσR
Amplitude of D2u ampD2u
ampBσRD2u = supBσRD2u – infBσRD2u
0<σ<1
C and e are constant that is determined by dimension m and 
.
.
ampBσRD2u
Cσe(ampBRD2u + 
supB2R|D
| + 
supB2R |D2
| )
Cσe(ampBRD2u + supB2R|D| + supB2R |D2| )
[Impression]
1 Meaning minimum is the smallest meaning unit of word. Refer to the reference ![]()
#2 and ![]()
#2′.
2 If meaning minimum of word is expressed by BσR, it has finite amplitude in adequate
domain.
[References 1 On meaning minimum]
#1 ![]()
Holomorphic Meaning Theory / 10th for KARCEVSKIJ Sergej
#2 ![]()
Word and Meaning Minimum
#2′ ![]()
From Cell to Manifold
#3 ![]()
Geometry of Word
[References 2 On generation of word]
#4 ![]()
Growth of Word
#5 ![]()
Generation Theorem
#6 ![]()
Deep Fissure between Word and Sentence
#7 ![]()
Tomita’s Fundamental Theorem
#8 ![]()
Borchers’ Theorem
#9 ![]()
Finiteness in Infinity on Language
#10 ![]()
Properly Infinite
#11 ![]()
Purely Infinite
[References 3 on distance and mirror on word]
#12 ![]()
Distance Theory / Tokyo May 5, 2004 / Sekian Linguistic Field
#13 ![]()
Quantification of Quantum / Tokyo May 29, 2004 / Sekinan Linguistic Field
#14 ![]()
Mirror Theory / Tokyo June 5, 2004 / Sekinan Linguistic Field
#15 ![]()
Mirror Language / Tokyo June 10, 2004 / Sekinan Linguistic Field
#16 ![]()
Reversion Theory / Tokyo September 27, 2004 / Sekinan Linguistic Field
#17 ![]()
Mirror Theory Group / Tokyo December 9, 2008 / Sekinan Linguistic Field
To be continued
Tokyo December 17, 2008
[References 4 / December 23, 2008 / on time of word]
#18 ![]()
Time of Word / Tokyo December 23, 2008 / sekinan.wiki.zoho.com
Homology Structure of Word
June 30, 2015
Note6
Homology Structure of Word
§ 1
1
Compact manifold in small diameter M
Inner product space h (M)
Map h (M) 
k→ h (M)
k→ h (M)
2
A model and B model by Witten, E.
A model M as symplectic structure
B model M as complex structure
3
(A model)
(Definition)
H kA (M) = H k(M;C)
H *A (M) = 
H kA (M)
H kA (M)
Inner product <. , .>A <u, v>A = 
( 
; cup product)
( ; cup product)
mA, 02(u, v) = 
4
(Theorem)
( H *A (M), mA, 02, <. , .>A ) is Frobenius algebra.
5
Oriented 2-dimensional manifold with genus g Σg
6
J (Σg) = {JΣg | Smooth complex structure over Σg }
Integer over 0 k
Different k-number points over Σg z1, …, zk (Gathered points are expressed by 
. )
. )
Diff (Σg, 
) = {ψ : Σg → Σg | ψ(
) = 
, ψ is differential homeomorphism. }
) = {ψ : Σg → Σg | ψ() = , ψ is differential homeomorphism. }
Quotient space M g,k = J (Σg) / Diff (Σg, 
)
)
Rieman surface of genus g with k marked points (Σ, 
)
)
(Σ, 
) 
M g,k
) M g,k
Autmorphism group Aut (Σ, 
) = { ψ : Σ → Σ | ψ is biregular.ψ(
) = 
}
) = { ψ : Σ → Σ | ψ is biregular.ψ() = }
Compactification of M g,k CM g,k
§2
１
Symplectic manifold M
Differential 2-form over M wM
Well-formed almost complex structure with wM JM
β
H2(M; Z)
H2(M; Z)
(
is pseudoholomorphic.)
(Σ,
, φ) 
, φ)
2
[(Σ,
, φ)] 
, φ)]
Evaluation map ev[(Σ,
, φ)]=
, φ)]=
3
Forgetting map fg : 
Enlarged Forgetting map fg : 
3
(Definition)
(Gromov-Witten invariant)
(ev, fg)*
Gromov-Witten invariant is expressed by GWg,k(M, wM; β)
4
(Theorem)
Sumset 
is compact.
is compact.
5
(Associative law)
(Theorem)
[Image]
Meaning minimum of word is identified with 
.
.
Word is identified with 
Commutativity of meaning minimums in word guaranteed by theorem of associative law.
[References]
September 10, 2007
22, 2008
Tokyo December 17, 2008
Tokyo June 16, 2009
[Related Note / June 18, 2009]
Basis of the further study on language – Potential
June 28, 2015
Basis of the further study on language – Potential
Note1
Potential of Language
¶ Prerequisite conditions
1
(Definition)
(Gromov-Witten potential) 
2
(Theorem)
(Witten-Dijkggraaf-Verlinde-Verlinde equation) 
3
(Theorem)
(Structure of Frobenius manifold)
Symplectic manifold (M, wM)
Poincaré duality < . , . >
Product <V1 V2, V3> = V1V2V3( 
)
)
(M, wM) has structure of Frobenius manifold over convergent domain of Gromov-Witten potential.
4
(Theorem)
Mk,β (Q1, …, Qk) = 
N(β) expresses Gromov-Witten potential.
[Image]
When Mk,β (Q1, …, Qk) is identified with language, language has potential N(β).
[Reference]
First designed on
Tokyo April 29, 2009
Newly planned on further visibility
Tokyo June 16, 2009
[Note, 31 March 2015]
This paper was first designed for energy of language. But at that time, I could not write
the proper approach from the concept of energy by mathematical process. So I wrote
the paper through the concept of potential. Probably energy is one of the most fundamental
factors on language.
In 2003 I wrote Quantum Theory for Language , before which I wrote the manuscript focusing
the concept of quantum abstracted from the ideogram of classical Chinese written language.
The last target of manuscript was energy and meaning of quantum that was the ultimate
unit of language.
Refer to the next.
Preparation for the energy of language
June 28, 2015
Preparation for the energy of language
TANAKA Akio
The energy of language seems to be one of the most fundamental theme for the further step-up study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory papers written so far.
How does the language models connect with natural language?
June 27, 2015
How does the language models connect with natural language?
Natural language contains many important factors theoretically abstracted in the long philological studies.
At the contrast the language models made by mathematical description are themselves have not any connections with natural language.
The models by mathematics, which is totally composed from a few premises, contains many theorems and their understructures.
In these underconstructures, natural language’s factors are resembled with mathematical factors.
At the result, some resemblances are compared between mathematical models and natural language.
From these works, some resemblances to language universals may be appeared in the factors of mathematical models modified by natural language.
At the contrast the language models made by mathematical description are themselves have not any connections with natural language.
The models by mathematics, which is totally composed from a few premises, contains many theorems and their understructures.
In these underconstructures, natural language’s factors are resembled with mathematical factors.
At the result, some resemblances are compared between mathematical models and natural language.
From these works, some resemblances to language universals may be appeared in the factors of mathematical models modified by natural language.
7 April 2014
[5 May 2014 Reference added]
True-false problem of the Crete
True-false problem of the Crete
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