scholarly journals The Toda molecule equation and the $\varepsilon$-algorithm

1998 ◽  
Vol 67 (224) ◽  
pp. 1565-1576 ◽  
Author(s):  
Atsushi Nagai ◽  
Tetsuji Tokihiro ◽  
Junkichi Satsuma
Keyword(s):  
Molecule Equation

Ultra-discrete Toda molecule equation

1998 ◽  
Vol 244 (5) ◽  
pp. 383-388 ◽  
Author(s):  
A. Nagai ◽  
T. Tokihiro ◽  
J. Satsuma
Keyword(s):  
Molecule Equation

scholarly journals MATRIX MODELS OF TWO-DIMENSIONAL GRAVITY AND DISCRETE TODA THEORY

1996 ◽  
Vol 11 (22) ◽  
pp. 1797-1806 ◽  
Author(s):  
MASATO HISAKADO ◽  
MIKI WADATI
Keyword(s):  
Discrete Time ◽  
Matrix Model ◽  
Scaling Limit ◽  
Toda Chain ◽  
Partition Functions ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Molecule Equation

Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

Soliton cellular automaton, Toda molecule equation and sorting algorithm

1999 ◽  
Vol 255 (4-6) ◽  
pp. 265-271 ◽  
Author(s):  
A. Nagai ◽  
D. Takahashi ◽  
T. Tokihiro
Keyword(s):  
Cellular Automaton ◽  
Sorting Algorithm ◽  
Molecule Equation
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