Nonlinear Sciences / Nlin.SI

All posts under category "Nonlinear Sciences / Nlin.SI"

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Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

: ๋ณธ ๋…ผ๋ฌธ์€ ๊ตฌ์กฐ ์ตœ์ ํ™” ๋ถ„์•ผ์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š” ๋ผ๊ทธ๋ž‘์ฃผ ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃจ๋ฉฐ, ํŠนํžˆ ๊ทธ๋ฆฐํž ๋ถ€๋Ÿฌ์ง ๋ฌธ์ œ์— ๋Œ€ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ๋ฒ•์„ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์–‡์€ ํƒ„์„ฑ ๋ง‰๋Œ€์˜ ์ตœ์  ํ˜•ํƒœ๋ฅผ ์ฐพ๋Š”๋ฐ ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๋ผ๊ทธ๋ž‘์ฃผ ๊ฐ€์„ค์ด ์‹ค์ œ๋กœ ์œ ํšจํ•จ์„ ์ฆ๋ช…ํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. 1. ์„œ๋ก  ์„œ๋ก ์—์„œ๋Š” ๋ณธ ๋…ผ๋ฌธ์˜ ์ฃผ์š” ๋ชฉํ‘œ์™€ ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ์„ ์„ค๋ช…ํ•ฉ๋‹ˆ๋‹ค. ๊ตฌ์กฐ ์ตœ์ ํ™” ๊ณผํ•™์—์„œ ์ค‘์š”ํ•œ ๋ฌธ์ œ ์ค‘ ํ•˜๋‚˜์ธ ๊ทธ๋ฆฐํž ๋ถ€๋Ÿฌ์ง ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃจ๋ฉฐ, ์ด ๋ฌธ์ œ๋Š” ์–‡์€ ํƒ„์„ฑ ๋ง‰๋Œ€๊ฐ€ ํŠน์ • ๋ชจ๋ฉ˜ํŠธ ํ•˜์ค‘์— ๋Œ€ํ•ด ์–ด๋–ป๊ฒŒ ํœ˜์–ด์ง€๋Š”์ง€๋ฅผ ๋ถ„์„ํ•˜๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ๋ผ๊ทธ๋ž‘์ฃผ

MATH-PH Mathematics Nonlinear Sciences
A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension

A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension

์ด ๋…ผ๋ฌธ์€ ๊ณ ์ „ ํ†ตํ•ฉ ๊ฐ€๋Šฅํ•œ ์‹œ์Šคํ…œ์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜๋ฉด์„œ ํŠนํžˆ Korteweg de Vries (KdV) ๋ฐฉ์ •์‹๊ณผ Harry Dym (HD) ๋ฐฉ์ •์‹์„ ์ค‘์‹ฌ์œผ๋กœ ์ƒˆ๋กœ์šด N 2 ์ดˆ๋Œ€์นญ HD ๋ฐฉ์ •์‹์„ ๋ฐœ๊ฒฌํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. ์ด๋“ค ๋ฐฉ์ •์‹์€ ์ˆ˜์‹ญ ๋…„ ๋™์•ˆ ๋‹ค์–‘ํ•œ ํ™•์žฅ์ด ์ด๋ฃจ์–ด์ ธ ์™”์œผ๋ฉฐ, ํŠนํžˆ ์ˆ˜ํผ ๋Œ€์นญ ํ™•์žฅ์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๊ฐ€ ํ™œ๋ฐœํ–ˆ์Šต๋‹ˆ๋‹ค. 1. ๊ณ ์ „ ํ†ตํ•ฉ ๊ฐ€๋Šฅํ•œ ์‹œ์Šคํ…œ๊ณผ ์ˆ˜ํผ ๋Œ€์นญํ™” ๊ณ ์ „ ํ†ตํ•ฉ ๊ฐ€๋Šฅํ•œ ์‹œ์Šคํ…œ์€ ์†”๋ฆฌํ†ค ๋ฐฉ์ •์‹์œผ๋กœ ์•Œ๋ ค์ ธ ์žˆ์œผ๋ฉฐ, ์ด๋“ค ๋ฐฉ์ •์‹์€ ๋‹ค์–‘ํ•œ ํ™•์žฅ์ด ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ ์ˆ˜ํผ ๋Œ€์นญ ํ™•์žฅ์„ ํ†ตํ•ด ์ƒˆ๋กœ์šด ๋ณด์† ํ•„๋“œ๊ฐ€ ๋„์ž…๋˜๊ฑฐ๋‚˜ ๊ธฐ

Nonlinear Sciences
Comment on 'The separation of variables and bifurcations of first integrals in one problem of D.N.Goryachev' by Pavel E. Ryabov (Archive:1102.2588v1)

Comment on 'The separation of variables and bifurcations of first integrals in one problem of D.N.Goryachev' by Pavel E. Ryabov (Archive:1102.2588v1)

: ๋ณธ ๋…ผ๋ฌธ์€ Goryachev ์‹œ์Šคํ…œ์— ๋Œ€ํ•œ ๋ณ€์ˆ˜ ๋ถ„๋ฆฌ์™€ ์ฒซ ๋ฒˆ์งธ ํ†ตํ•ฉ์˜ ๋ถ„๊ธฐ๋ฅผ ๋‹ค๋ฃจ๋ฉฐ, ํŠนํžˆ ๊ฒŒ์˜ค๋ฉ”ํŠธ๋ฆญ ์นผ๋ผ๋ชจํ”„ ๋ฐฉ๋ฒ•์ด ์ ์šฉ๋  ๋•Œ ๋น„์ปค๋„ '์ƒˆ๋กœ์šด ๋ณ€์ˆ˜ ๋ถ„๋ฆฌ'๊ฐ€ ๋ฐœ์ƒํ•œ๋‹ค๋Š” ๊ฒƒ์„ ์ฆ๋ช…ํ•œ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” Goryachev ์‹œ์Šคํ…œ์„ ์„ค๋ช…ํ•˜๊ธฐ ์œ„ํ•ด ๊ฐ์šด๋™๋Ÿ‰ ๋ฒกํ„ฐ M๊ณผ ํฌ์•„์†ก ๋ฒกํ„ฐ ฮฑ๋ฅผ ์‚ฌ์šฉํ•˜๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด eโˆ—(3) ๋ฆฌ ํฌ์•„์†ก ๋ธŒ๋ž˜ํ‚ท๊ณผ ์—ฐ๊ด€๋œ ํฌ์•„์†ก ๋ธŒ๋ž˜ํ‚ท์„ ์ •์˜ํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์ ‘๊ทผ๋ฒ•์€ Goryachev ์‹œ์Šคํ…œ์˜ ๋™์—ญํ•™์  ํŠน์„ฑ์„ ์ดํ•ดํ•˜๋Š” ๋ฐ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•œ๋‹ค. ๋…ผ๋ฌธ์—์„œ ์ €์ž๋Š” ๋‘ ๋ณด์กด๋Ÿ‰ H์™€ K ์‚ฌ์ด์˜ ์ƒํ˜ธ์ž‘์šฉ์„ ๋ถ„์„ํ•˜๊ณ , ์ด๋“ค ๊ฐ„์˜ ๊ด€

Nonlinear Sciences
Size Effect of Diagonal Random Matrices

Size Effect of Diagonal Random Matrices

1. ๋ฌด์ž‘์œ„ ํ–‰๋ ฌ ์ด๋ก ์˜ ๋ฐฐ๊ฒฝ ๋ฌด์ž‘์œ„ ํ–‰๋ ฌ ์ด๋ก ์€ ํ˜ผ๋ž€์Šค๋Ÿฌ์šด ์–‘์ž ์‹œ์Šคํ…œ์˜ ์ŠคํŽ™ํŠธ๋Ÿผ ํ†ต๊ณ„์  ํŠน์„ฑ์„ ์„ค๋ช…ํ•˜๋Š” ์ค‘์š”ํ•œ ๋„๊ตฌ์ด๋‹ค. ํŠนํžˆ, ์‹œ๊ฐ„ ๋ฐ˜์ „ ๋ถˆ๋ณ€ ์–‘์ž ์‹œ์Šคํ…œ์€ ํšŒ์ „ ๋Œ€์นญ์„ ๊ฐ€์งˆ ๋•Œ ๊ฐ€์šฐ์Šค ์ง๊ต ์ง‘ํ•ฉ(GOE)์˜ ๋ฌด์ž‘์œ„ ํ–‰๋ ฌ๋กœ ํ‘œํ˜„๋œ๋‹ค. ์ด๋Š” ํ˜ผ๋ž€์Šค๋Ÿฌ์šด ์‹œ์Šคํ…œ์—์„œ ์ˆ˜์ค€ ์ƒ๊ด€ ๊ด€๊ณ„๋ฅผ ์„ค๋ช…ํ•˜๋Š” ๋ฐ ์‚ฌ์šฉ๋˜๋ฉฐ, N์ด ๋ฌดํ•œ๋Œ€๋กœ ์ ‘๊ทผํ•  ๋•Œ ๊ฐ€์žฅ ํฅ๋ฏธ๋กœ์šด ๊ฒฐ๊ณผ๊ฐ€ ์–ป์–ด์ง„๋‹ค. 2. ๋Œ€๊ฐ ๋ฌด์ž‘์œ„ ํ–‰๋ ฌ์˜ ํŠน์„ฑ ๋…ผ๋ฌธ์€ N์ฐจ์› ๋Œ€๊ฐ ๋ฌด์ž‘์œ„ ํ–‰๋ ฌ์˜ ๊ณ ์œ ๊ฐ’ ํ†ต๊ณ„ํ•™์„ ๋ถ„์„ํ•œ๋‹ค. ํŠนํžˆ, ์ˆ˜์ค€ ๊ฐ„ ๊ฐ„๊ฒฉ(NNS) ๋ถ„ํฌ์™€ ๋ถ„์‚ฐ ฮฃยฒ๋ฅผ ํ†ตํ•ด ๋‹จ๊ธฐ ๋ฐ ์žฅ๊ธฐ ์ƒ๊ด€ ๊ด€๊ณ„๋ฅผ

Nonlinear Sciences Condensed Matter
A Class of Special Solutions for the Ultradiscrete Painleve II Equation

A Class of Special Solutions for the Ultradiscrete Painleve II Equation

: ๋ณธ ๋…ผ๋ฌธ์€ ํŒŒ์ธ๋ ˆ๋ธŒ II ๋ฐฉ์ •์‹์˜ ์ดˆ๊ณ ๊ธ‰ ์ด์‚ฐํ™”๋œ ํ˜•ํƒœ๋ฅผ ์—ฐ๊ตฌํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด ์–ป์–ด์ง€๋Š” ํŠน๋ณ„ํ•œ ํ•ด์— ๋Œ€ํ•ด ์‹ฌ๋„ ์žˆ๊ฒŒ ๋ถ„์„ํ•œ๋‹ค. ํŠนํžˆ, q ์ฐจ๋ถ„ ์œ ์‚ฌํ˜• ์—์–ด๋ฆฌ ๋ฐฉ์ •์‹์„ ๊ธฐ๋ฐ˜์œผ๋กœ udPII (์ดˆ๊ณ ๊ธ‰ ์ด์‚ฐํ™” ํŒŒ์ธ๋ ˆ๋ธŒ II) ๋ฐฉ์ •์‹์˜ ํŠน์ˆ˜ํ•ด๋ฅผ ๊ตฌ์ถ•ํ•˜๊ณ  ๊ทธ ์„ฑ์งˆ์„ ํƒ๊ตฌํ•œ๋‹ค. ์ดˆ๊ณผ ์ด์‚ฐํ™”์™€ p ์ดˆ๊ณผ ์ด์‚ฐํ™” ์ดˆ๊ณผ ์ด์‚ฐํ™”๋Š” ์ฃผ์–ด์ง„ ์ฐจ๋ถ„ ๋ฐฉ์ •์‹์„ ์…€ ์˜คํ† ๋งˆํ†ค์œผ๋กœ ๋ณ€ํ™˜ํ•˜๋Š” ๊ณผ์ •์ด๋‹ค. ์ด ๊ณผ์ •์—์„œ ์ข…์† ๋ณ€์ˆ˜ x<sub>n</sub> ์€ ์ด์‚ฐ ๊ฐ’์„ ๊ฐ€์ง€๊ฒŒ ๋˜๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ์›๋ž˜์˜ ๋ฏธ๋ถ„ ๋ฐฉ์ •์‹์ด ์กฐ๊ฐ ์„ ํ˜• ๋ฐฉ์ •์‹์œผ๋กœ ๊ทผ์‚ฌ๋œ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ '์Œ์˜ ๋ฌธ์ œ'๋กœ

Mathematics Nonlinear Sciences
Integration of Constraint Equations in Problems of a Disc and a Ball Rolling on a Horizontal Plane

Integration of Constraint Equations in Problems of a Disc and a Ball Rolling on a Horizontal Plane

์ด ๋…ผ๋ฌธ์€ ์›ํ˜•๊ณผ ๊ตฌ๊ฐ€ ์ˆ˜ํ‰๋ฉด์—์„œ ๋ฏธ๋„๋Ÿฌ์ง ์—†์ด ๊ตด๋Ÿฌ๊ฐ€๋Š” ๋™์—ญํ•™์  ๋ฌธ์ œ๋ฅผ ์ฒด๊ณ„์ ์œผ๋กœ ๋ถ„์„ํ•˜๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๊ณ ์ „ ์—ญํ•™์˜ ๋ณต์žกํ•œ ๋ฌธ์ œ๋ฅผ ๋‹จ์ˆœํ™”ํ•˜๊ณ  ํ•ด๊ฒฐํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ, ์ž์—ฐ ๋ฐฉ์ •์‹์„ ํ™œ์šฉํ•˜์—ฌ ์ ‘์ด‰ ๊ถค์ ์˜ ๊ณก๋ฅ  ์˜์กด์„ฑ์„ ๋ช…ํ™•ํžˆ ํ‘œํ˜„ํ•จ์œผ๋กœ์จ, ๊ตด๋Ÿฌ๊ฐ€๋Š” ๋™์ž‘์— ๋Œ€ํ•œ ๊นŠ์€ ์ดํ•ด์™€ ์ •๋Ÿ‰์ ์ธ ๋ถ„์„์ด ๊ฐ€๋Šฅํ•ด์ง‘๋‹ˆ๋‹ค. 1. ์›ํ˜•๊ณผ ๊ตฌ์˜ ๊ตด๋Ÿฌ๊ฐ€๋Š” ์šด๋™ ์›ํ˜•๊ณผ ๊ตฌ๊ฐ€ ์ˆ˜ํ‰๋ฉด์—์„œ ๊ตด๋Ÿฌ๊ฐˆ ๋•Œ, ์ด๋“ค์˜ ์›€์ง์ž„์€ ๋น„ํ™€๋ก ์  ์ œ์•ฝ์ด๋ผ๋Š” ๋ณต์žกํ•œ ๋™์—ญํ•™์  ์กฐ๊ฑด์— ์˜ํ•ด ๊ฒฐ์ •๋ฉ๋‹ˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ œ์•ฝ์€ ์ ‘์ด‰์  P์˜ ์œ„์น˜์™€ ์›ํ˜• ๋˜๋Š” ๊ตฌ์˜ ํšŒ์ „๊ฐ ฯ•, ์ „๋‹จ๊ฐ ฯˆ, ๊ทธ

Mathematics Nonlinear Sciences
The quadratic WDVV solution $E_8(a_1)$

The quadratic WDVV solution $E_8(a_1)$

์ด ๋…ผ๋ฌธ์€ ๊ณ ์ฐจ์› ๋ฆฌ ๋Œ€์ˆ˜์™€ ํ”„๋กœ๋ฒค๋ฆฌ์šฐ์Šค ๋งŒ๋Œ(Frobenius Manifold) ์‚ฌ์ด์˜ ๊นŠ์€ ๊ด€๊ณ„๋ฅผ ํƒ๊ตฌํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ, Eโ‚ˆ(aโ‚)๋ผ๋Š” ํŠน์ •ํ•œ ๊ฒฝ์šฐ์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” Witten Dijkgraaf Verlinde Verlinde (WDVV) ๋ฐฉ์ •์‹์ด๋ผ๋Š” ์ค‘์š”ํ•œ ํŽธ๋ฏธ๋ถ„ ๋ฐฉ์ •์‹ ์‹œ์Šคํ…œ์˜ ํ•ด๋ฅผ ๊ตฌ์„ฑํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ํƒ๊ตฌํ•ฉ๋‹ˆ๋‹ค. ํ”„๋กœ๋ฒค๋ฆฌ์šฐ์Šค ๋งŒ๋Œ์€ ๋Œ€์ˆ˜์  ๊ตฌ์กฐ์™€ ๊ธฐํ•˜ํ•™์  ๊ตฌ์กฐ๊ฐ€ ๊ฒฐํ•ฉ๋œ ๋ณต์žกํ•œ ์ˆ˜ํ•™์  ๊ฐ์ฒด์ž…๋‹ˆ๋‹ค. ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๊ตฌ์กฐ๊ฐ€ ์–ด๋–ป๊ฒŒ Eโ‚ˆ ๋ฆฌ ๋Œ€์ˆ˜์™€ ์—ฐ๊ฒฐ๋˜๋Š”์ง€, ๊ทธ๋ฆฌ๊ณ  ๊ทธ ์ž ์žฌ ํ•จ์ˆ˜๋Š” ์–ด๋–ค ํ˜•ํƒœ๋ฅผ ๊ฐ€์ง€๋Š”์ง€๋ฅผ ๋ถ„

MATH-PH Mathematics Nonlinear Sciences
Hyperdeterminant and an integrable partial differential equation

Hyperdeterminant and an integrable partial differential equation

๋ณธ ๋…ผ๋ฌธ์€ ํ•˜์ดํผ๊ฒฐ์ •์‹๊ณผ ๋น„์„ ํ˜• ํŽธ๋ฏธ๋ถ„๋ฐฉ์ •์‹ ๊ฐ„์˜ ๊ด€๊ณ„๋ฅผ ํƒ๊ตฌํ•˜๋ฉฐ, ํŠนํžˆ ๋ฐฐํ„ด ๋ฐฉ์ •์‹๊ณผ ์œ ์‚ฌํ•œ ํ˜•ํƒœ์˜ ์ƒˆ๋กœ์šด ๋น„์„ ํ˜• ํŽธ๋ฏธ๋ถ„๋ฐฉ์ •์‹์„ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์ˆ˜ํ•™์  ๊ตฌ์กฐ์™€ ๋ฌผ๋ฆฌํ•™์  ์‘์šฉ ์‚ฌ์ด์˜ ์—ฐ๊ฒฐ์„ ๊ฐ•ํ™”ํ•˜๋Š” ์ค‘์š”ํ•œ ๋‹จ๊ณ„๋กœ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. 1. ํ•˜์ดํผ๊ฒฐ์ •์‹๊ณผ ๋ฐฐํ„ด ๋ฐฉ์ •์‹ ๋ฐฐํ„ด ๋ฐฉ์ •์‹์€ ๋ ˆ๊ทธ๋กœ ๋ณ€ํ™˜์„ ํ†ตํ•ด ์„ ํ˜•ํ™”๋  ์ˆ˜ ์žˆ๋Š” ํŠน์„ฑ์„ ๊ฐ€์ง€๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋Š” ํŒŒ์ธ๋ ˆ๋ฒ  ํ…Œ์ŠคํŠธ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋ถ€๋ถ„ ๋ฏธ๋ถ„๋ฐฉ์ •์‹์˜ ์ ๋ถ„ ๊ฐ€๋Šฅ์„ฑ์„ ์—ฐ๊ตฌํ•˜๋Š” ๋ฐ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•ฉ๋‹ˆ๋‹ค. ๋ฐฐํ„ด ๋ฐฉ์ •์‹์€ ๋‹ค์–‘ํ•œ ๋ฌผ๋ฆฌํ•™์  ํ˜„์ƒ์—์„œ ๋‚˜ํƒ€๋‚˜๋ฉฐ, ํŠนํžˆ ๋น„์„ ํ˜• ํŽธ๋ฏธ๋ถ„๋ฐฉ์ •์‹์˜ ํ•ด์„์— ์žˆ์–ด ํ•ต

Nonlinear Sciences
Toda tau functions with quantum torus symmetries

Toda tau functions with quantum torus symmetries

: ๋ณธ ๋…ผ๋ฌธ์€ ์œ„์ƒ ๋ฌธ์ž์—ด์˜ ๋…น๋Š” ๊ฒฐ์ • ๋ชจ๋ธ๊ณผ 5์ฐจ์› ๊ฒŒ์ด์ง€ ์ด๋ก  ๊ฐ„์˜ ํ†ตํ•ฉ ๊ฐ€๋Šฅ์„ฑ์„ ํƒ๊ตฌํ•œ๋‹ค. ๋…น๋Š” ๊ฒฐ์ • ๋ชจ๋ธ์€ ๋ฌผ๋ฆฌํ•™์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š” ๋ชจ๋ธ๋กœ, ํŠนํžˆ ์œ„์ƒ ๋ฌธ์ž์—ด๊ณผ ๊ด€๋ จ๋œ ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃจ๋Š”๋ฐ ํ™œ์šฉ๋œ๋‹ค. ๋…ผ๋ฌธ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๋ชจ๋ธ์˜ ๋ถ„ํ•  ํ•จ์ˆ˜๊ฐ€ ํŠน์ • ์™ธ๋ถ€ ์ž ์žฌ๋ ฅ์— ์˜ํ•ด ๋ณ€ํ˜•๋  ๋•Œ Toda ๊ณ„์ธต์˜ ํƒ€์šฐ ํ•จ์ˆ˜์™€ ๋ณธ์งˆ์ ์œผ๋กœ ๋™์ผํ•˜๋‹ค๋Š” ๊ฒƒ์„ ๋ณด์—ฌ์ค€๋‹ค. Toda ๊ณ„์ธต์€ ํ†ต์ƒ์ ์ธ ํŽ˜๋ฅด๋ฏธ์˜จ ์‹œ์Šคํ…œ์—์„œ ํŒŒ์ƒ๋œ ์ค‘์š”ํ•œ ์ˆ˜ํ•™์  ๊ตฌ์กฐ๋กœ, ์ด๋ก  ๋ฌผ๋ฆฌํ•™๊ณผ ์ˆ˜ํ•™์—์„œ ๋„๋ฆฌ ์—ฐ๊ตฌ๋˜๊ณ  ์žˆ๋‹ค. ๋…ผ๋ฌธ์—์„œ๋Š” Toda ํƒ€์šฐ ํ•จ์ˆ˜์™€ ๋ณ€ํ˜•๋œ ๋ถ„ํ•  ํ•จ์ˆ˜ ๊ฐ„์˜ ๊ด€๊ณ„๋ฅผ ์–‘์ž ํ† 

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