Wednesday, 23 May 2018
Imaginary Language Hyperbolic Space Language 2011
Imaginary Language
Hyperbolic Space Language
TANAKA Akio
September 5, 2011
TANAKA Akio
September 5, 2011
[Preparation]
3 dimensional hyperbolic space H3
Spherical surface at infinity Sx
Ideal simplex that has vertexes on Sx Σ
Internal angles of triangle that is projected to plane z = 0
Internal angles of ideal simplex α, β,γ
Internal angles except α, β,γ α1, β1,γ1
Volume of ideal simplex V
<Theorem>
V (Σ) = Λ(α) +Λ(β)+Λ(γ)
V (Σ) = Λ(α) +Λ(β)+Λ(γ)
[Interpretation]
Language model is expressed by V (Σ).
Language model is expressed by V (Σ).
Word is expressed by Σ.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Imaginary Language Volume of Language 2011
[Preparation]
Volume of orthogonal hyperbolic simplex V(Σ(α, β, γ))
Schläfli function S(α,β,γ)
Schläfli function S(α,β,γ)
<Theorem>
V(Σ(α, β, γ)) =
V(Σ(α, β, γ)) =

[Interpretation]
Language model is made by hyperbolic simplex.
Language model contains imaginary part.
Language model is made by hyperbolic simplex.
Language model contains imaginary part.
This paper has been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of langauge
All rights reserved.
© 2011 by The Sekinan Research Field of langauge
Stabe and Unstable of Language For the Supposition of KARCEVSKIJ Sergej 2011
Stabe and Unstable of Language
For the Supposition of KARCEVSKIJ Sergej
The papers on thise site have been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Time of WANG Guowei 2011
Time of WANG Guowei
The papers on this site have been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Notes for KARCEVSKIJ Sergej 2011
Notes for KARCEVSKIJ Sergej
The papers on this site have been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Subscribe to:
Posts (Atom)