SRFL News: January 2016

Sunday, 31 January 2016

Direction, SRFL Essay / New way to language universals

Homepage > Direction

Direction

Why is boundary necessary in language?

31/01/2016 14:21

Why is boundary necessary in language? q.v. Boundary of Words / 12 February 2009 TANAKA Akio 1. I have thought on language as a physic existence that has inevitably boundary to the outer world. My question is simple and primitive. I ever wrote about the change of language - If there be...

At least three elements for language universals

30/01/2016 20:37

At least three elements for language universals TANAKA Akio Supposition 1: Three elements for language universals For language universals, now I suppose at least three elements being based from mathematical description. Three elements for language universals...

Preparation for the energy of language

30/01/2016 20:35

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...

Thanks to physics about which I ever dreamt in my future

30/01/2016 20:34

Thanks to physics about which I ever dreamt in my future TANAKA Akio In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse...

Saturday, 30 January 2016

SRFL Essay. New essay site of SRFL

SRFL Essay

Portal
SRFL Lab

Note
SRFL Note

Paper
SRFL Paper

Theory
SRFL Theory

Lead

History of SRFL

30/01/2016 17:46

History SRFL Essay is the essay site of Sekinan Library which was founded in 1986 at Tachikawa, Tokyo. Sekinan Library at first aimed to study ideogram's relationship between figure and meaning mainly using Chinese characters. But the study gradually declined to the essences...

SRFL Paper

Paper 2: Sekinan Zoho

2.

Theory: SRFL Theory

Portal: SRFL Lab

Invitation: Sekinan Archive

Base: Sekinan Library

1. Site History: History of SRFL

Paper History: Genealogical Tree of Sekinan's Paper Sixth Edition

------------------------------------------------------------------------------------------------------------

Tokyo

17 August 2015

Boundary of Words

q.v. Zoho Paper. SIL

Topological Group Language Theory

TANAKA Akio

Preliminary Note 3

Boundary of Words

[Theorem]

Distance space ( X , d)

Gromov product ( y | z ) x

Hyperbolic space X

point sequence { x i

X }

Set of all the { x i

X } S ∞ ( X )

Point sequence of X { y i }

When { y i } is lim i →∞ ( x i | y i ) = 0, { y i } is in S ∞ ( X ).

[Explanation]

Hyperbolicity for general distance space is defined by Gromov product.

Details are below.

Distance space is defied by the next.

Distance space that has basic point x 0 ( X, d )

Arbitrary 3 points of X x, y, z

When ( X, d ) satisfies the next, it is called δ -hyperbolic.

( x | y ) x 0

min{( x | z)x 0 , ( y | z ) x 0 }- δ

When distance space ( X, d ) is δ -hyperbolic for arbitrary base point, X is called δ -hyperbolic.

Here for a certain

, δ -hyperbolic space is abbreviatedly called hyperbolic.

The next condition is equivalent with what ( X, d ) is δ -hyperbolic.

d ( x, y ) + d ( z, w )

max{ d ( x, z ) + d ( y, w ), d ( x, w ) + d ( y, z ) } +2 δ

Distance space X

Arc of X α : [0, λ ] → X

Arbitrary s, t

[0, λ ]

d ( α ( s ), α (t)) = | s-t |

Arc α is called geodesic segment.

Geodesic segment from x to y that is x,y

X is expressed by

When arbitrary 2 points of distance space ( X , d) are combinable by geodesic segment, X is

called geodesic space.

xyz =

is called geodesic triangle.

[Impression]

Word is identified with point sequence { x i

X }.

Language is identified with S ∞ ( X ).

New generated word is identified Point sequence of X , { y i } that has condition lim i →∞ ( x i | y i ) .

The new generated word is also in language, that is to say, S ∞ ( X ).

From the condition lim i →∞ ( x i | y i ), spherical surface is considered as boundary at infinity by

the comparison with Poincaré model.

Spherical surface is considered as the unit of language.

Language's distance and warp is also considered under hyperbolic space.

References are below.

[References]

#1 Quantum Theorey for Language

#2 Distance Theory

#3 Warp Theory

The upper papers and the related papers with the themes are seen at Sekinan Linguistuic

Field .

To be continued

Tokyo February 12, 2009

Sekinan Research Field of Language

Thursday, 28 January 2016

Genealogical Tree of Sekinan's Paper Sixth Edition / 1 September 2015 / SRFL Theory

Genealogical Tree of Sekinan's Paper Sixth Edition

TANAKA Akio

Tokyo
18 July 2015 First Edition
1 September 2015 Sixth Edition

SRFL Theory

_________________________________________________________________________________

Genealogical Tree
Sixth Edition

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
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
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 Arithmetic Geometry Language
|
Language, Word, Distance, Meaning and Meaning Minimum
|
Imagenary Language
|
Volume of Language
Hyperbolic Space Language
   |
Notes for KARCEVSKIJ Sergej
|
Notes for KARCEVSKIJ Sergej, "Du Dualisme asymétrique du signe linguistique"
Description of Language
Structure of Word
Condition of Meaning
|
Time of WANG Guowei
|
Loop Time of Character
Symmetry of Language
|
Stable and Unstable of Language
|
Completion of Language
Meaning Minimum of Language
Additional Meaning in Word
|
Projective Space Model
   |
Vector Bundle Model
   |
Diophantine Language
   |
Finiteness of Words
Dimension of Words
|
Hyperbolic Language
|
Connection of Words
|
Grassmann Language
|
Grassmann Language
Grassmann Language
|
Grassmann Language 2
Elements of Word
|
Birational Language, Dual Language
|
Birational Language
Birational Language
Dual Language
   Duality of Language
|
Infinite Loop Space Language
|
Word as Infinite Loop Space
|
Algebraic Geometry Language
|
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
Three Conjectures
Dimension Decrease Conjecture (Conjecture 1)
Synthesis Conjecture (Conjecture 2)
Reversion Conjecture (Conjecture 3)
|
Supplement
Interpretation of Reversion Conjecture
Simplification of Reversion Conjecture
Reversion Conjecture Revised
|
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

Tags:

Genealogical Tree

Sunday, 31 January 2016

Direction

Saturday, 30 January 2016

PortalSRFL Lab

NoteSRFL Note

PaperSRFL Paper

TheorySRFL Theory

Lead

Tags

2.

1.

Site History: History of SRFL

Tags

Boundary of Words ​

Thursday, 28 January 2016

Tags:

Portal
SRFL Lab

Note
SRFL Note

Paper
SRFL Paper

Theory
SRFL Theory

Boundary of Words