Wednesday, 29 July 2015

Sekinan Study Paper Tokyo 2015

Sekinan Study Paper 

Tokyo
2015 


Study result of 
Sekinan Library
Sekinan Research Field of Language 
Zoho 

Sekinan Study Paper is the paper site of Sekinan Library and Sekinan Research Field of Language.
Sekinan Library was founded at Tachikawa, Tokyo in 1986 for the study of language.
In 2003, for the specialized study of language universals, Sekinan Research Field of Language was added at Hakuba, Nagano.  
Blog for Paper
Blog for News
Picture
The summer of Kirigamine Highlands, Nagano, Japan.
 I have stayed and written the early time papers at the lodge nearby.

Friday, 24 July 2015

Infinite Loop Space Language Word as Infinite loop Space

Infinite Loop Space Language

Word as Infinite loop Space

TANAKA Akio

1. 
Result of D. G. Quillen by Annals of Mathematics, 96 (1972).
Algebraic K theory over commutative ring R.
 is classifying space of   .
Quillen showed that  is infinite loop space.

2.
Interpretationof Quillen's result.
Meaning of word is expressed by .
Word is expressed by .
Saying in other words. 
Word is expressed by high dimensional algebraic K group over commutative ring R.
Conclution at the present.
Word has meaning that is expressed by infinite loop space.
Word has parameter that is expressed by commutative ring.
Word has dimension that belongs to albegraic K group.

Tokyo
6 December 2012
Sekinan Research Field of Language

Infinite Loop Space language Contents

Infinite Loop Space language


Word as Infinite Loop Space

Tokyo
24 July 2015 Reprint

Thursday, 23 July 2015

Dual Language Duality of Language


Dual Language

Duality of Language

TANAKA Akio

1. Theorem(Poincaré duality)
For oriented compact n-dimension topological manifold M,
biliear form

is exact,
 and  become dual space each other.
2. Interpretation
Word := MBoundary of language := pDual language :=  and Language := 
3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.

Tokyo
25 May 2012
Sekinan Research Field of Language

Birational Language Elements of Word

Birational Language

Elements of Word

TANAKA Akio

1, Proposition
Weighted projective space  is birationally equivalent with projective space  .
2. Proposition
Weighted hyperplane  is isomorphic to Weighted projective space  .
3. Proposition
Weighted projective space  is one-to-one correspondent with quotient space  .
Here G is finite Abellian group to ptrojective space .
 .
4. Definition
The next  is hyperplane defined by equation  .
 .
Here coordinate system  of linear space V is called homogenious coordinate system of projective space  .
5. Interpretation
Language:= projective space  .
Word:=Weighted hyperplane  .
Elements of word:=coordinate system  of linear space V .
6. Conclution
When elements of word is given at linear space, language is defined at projective space using birational equivalence.


Tokyo
April 26, 2012
Sekinan Reserach Field of Language

Birational Language, Dual Language Contents

Genealogical Tree Fourth Edition

Genealogical Tree 

TANAKA Akio

Tokyo
18 July 2015 First Edition
23 July 2015 Fourth Edition
Sekinan Study
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Genealogical Tree 

Manuscript of Quantum Theory for Language
|
On Time Property Inherent in Characters
|
Quantum Theory for Language
|                                                |
Distance Theory                      Property of Quantum
|                                                 |
Prague Theory                        Quantification of Quantum
|
Reversion Theory
|
Mirror Theory
|
Mirror Language
|
Guarantee of Language
|
Actual Language and Imaginary Language
|
Direction
|
Uniformity
|
Changeability
|
Individuality
|
Time
|
Fixation
|
Grammar
|
Substantiality
|
Frame
|
Recognition
|
Ideogram
|
Conversation
|
Descriptiveness
|
Lineation
|
System
|
Automaton
|
Vector

|
Cell Theory
     |
     From Cell to Manifold <For LEIBNIZ and JAKOBSON>     
     Conifold as Word     
     Projective Space as Scheme for Word Order 
     |
Algebraic Linguistics
     |     
     Sentence versus Word
     Deep Fissure between Word and Sentence
     |

Distance Theory Algebraically Supplemented
     |
     Bend     
     Distance <Direct Succession of Distance Theory>
     S3 and Hoph Map 
     |
Noncommutative Distance Theory
     |
     Groupoid     C*-Algebra
     Point Space     Atiyah’s Axiomatic System
     Kontsevich Invariant
      |
Clifford Algebra
      |
     From Super Space to Quantization
     Anti-automorphism
     Anti-self-dual Form
     Dirac Operator
     TOMONAGA's Super Multi-time Theory 
     Periodicity
     Creation Operator and Annihilation Operator
     Meaning Product 
     |
Kac-Moody Lie Algebra 

     |
     Kac-Moody Lie Algebra
     Quantum Group
     Finiteness in Infinity on Language
     |
Operator Algebra

     |
     Differential Operator and Symbol
     <One Paper lost>
     Self-adjoint and Symmetry 
     Frame Operator             
     Order of Word     
     Grammar     
     Recognition
     |
von Neumann Algebra
     |

     von Neumann Algebra 1
      Measure
     Tensor Product
     Compact Operator 

     von Neumann Algebra 2
     Generation Theorem
     von Neumann Algebra 3
     Properly Infinite
     Purely Infinite
     von Neumann Algebra 4
     Tomita's Fundamental Theorem
     Borchers' Theorem
     Relation between Word and Sentence
     |
Functional Analysis
     |
     Functional Analysis 
     Baire's Category Theorem
     Equality and Inequality
     Space
     Functional
     Finiteness of Vocabulary
     Distance at Hypersurface     
     Functional Analysis 2
     Pre-Hilbert Space and Hilbert Space
     Orthogonal Decomposition
     Generation of Word
      |
Reversion Analysis Theory
      |
      

      Reversion Analysis Theory      
      Reversion Analysis Theory 2
      |
Holomorphic Meaning Theory
      |

      Holomorphic Meaning Theory
      Holomorphic Meaning Theory 2
      |
Stochastic Meaning Theory
      |

      Stochastic Meaning Theory      
      Stochastic Meaning Theory 2
      Stochastic Meaning Theory 3
      Stochastic Meaning Theory 4
      Stochastic Meaning Theory 5
      

      Stochastic Meaning Theory Conjecture 1
      Stochastic Meaning Theory Conjecture 2 

      |
Energy Distance Theory
      |

      Energy and Distance
      Heat and Diffusion
      Energy and Functional
      Finsler Manifold and Distance
      Word and Meaning Minimum

      Geometry of Word  
      |
Complex Manifold Deformation Theory
      |

      Distance of Word
      Reflection of Word
      Uniqueness of Word
      Amplitude of Meaning Minimum
      Time of Word
      Orbit of Word

      Map between Words
      Understandability of Language

     |
Language Manifold Theory
     |
     Moser's Theorem
     |
Topological Group Language Theory

     |
     Word Problem of Word-hyperbolic Group 
     From Finiteness to Infinity on Language
     

     Boundary of Words 
     |
Symplectic Language Theory
     |

     Symplectic Topological Existence Theorem     
     Gromov-Witten Invariant     
     Mirror Symmetry Conjecture on Rational Curve     
     Isomorphism of Map Sequence     
     Generating Function  (Text lost)   
     Homological Mirror Symmetry Conjecture by KONTSEVICH
    Structure of Meaning

    On Structure
    |
Floer Homology Language
    |
    Potential of Language
   Supersymmetric Harmonic Oscillator
   Grothendieck Group
   Reversibility of Language
   Homology Generation of Language
   Homology Structure of Word
   Quantization of Language
   Discreteness of Language
   |
Proto Algebraic Geometry Language   
   |   
   Language, Word, Distance, Meaning and Meaning Minimum
   |

Imaginary Language
   |
Projective Space Model
   |
   Vector Bundle Model
   | 
   |
    |
Hyperbolic Language
   |
   |
Grassmann Language
   |
   Grassmann Language
   Grassmann Language 
   |
   Grassmann Language 2 
   Elements of Word
   |
   |    
   Parts and Whole (AGL Preface)     
   Dimension of Language (AGL 1)       
   Synthesis of Meaning and Transition of Dimension (AGL 2)       
   Birth of Word, Synthesis of Meaning and Dimension of New Word (AGL 3)  
   Dimension Conjecture at Synthesis of Meaning (AGL 4)                   
   |
Three conjectures for dimension, synthesis and reversion with root and supplement
   |
At least three elements for language universals
   |
   Disposition of Language
   Distance of Word
   Flow of Language
   Papers for Language Dimension, In chronological order
   Preparation for the energy of language

............................................................................................................................................

The Tree is unfinished.
Arranged by Sekinan Study