Friday 19 December 2014

Energy and Distance in Language / 31 August 2008

Energy and Distance in Language
Energy Distance Theory

Note 1
Energy and Distance

TANAKA Akio

1
Curvein 3-dimensional Euclidian space   : [0, 1] → 3
Longitudeof   ) = dt
2
Surface   S
Curvecombines and in   l
Coordinateof     φ → S
Coordinateof   2
φ = ( φ , φ , φ )
φ )
φ )
3
Curvein   : [0, 1] → 3
Curveon   )
Ω )= { : [0,1] → (0) = (1 ) = }
∈ Ω )
)= φ ) )
( 0 )= 0
( 1 ) = 1
) = dt     dt
ij isRiemann metric.
4
Longitudeis defined by the next.
x, xˑ     dt
5
Energyis defined by the next.
x, xˑ   =   ∑ I,j i,j )) xˑ xˑ dt
6
x, xˑ ≥ ( x, xˑ ) ) 2
7
Theorem
For ∈ Ω ), the nexttwo are equivalent.
(i) akesminimum value at .
(ii) takes minimum value at .
8
What longitudeis the minimum in curve is equivalent what energy is the minimum in curve.
9
Longitude is corresponded with distancein Distance Theory.

[References]
Distance Theory / Tokyo May 4, 2004
Property of Quantum / Tokyo May 21, 2004  
Mirror Theory / Tokyo June 5, 2004
Mirror Language / Tokyo June 10, 2004
Guarantee of Language / Tokyo June 12, 2004
Reversion Theory / Tokyo September 27, 2004

Tokyo August 31, 2008

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