From f9621c44c83196a63d8b57bf2c3530f9aa024629 Mon Sep 17 00:00:00 2001 From: oskar Date: Mon, 30 Mar 2026 01:37:13 +0200 Subject: [PATCH] device-56.home 2026-3-30:1:37:13 --- .../demo_théorème_du_début.excalidraw.md | 106 ++++++++++-------- .../demo_théorème_du_début.excalidraw.svg | 4 +- ...ur non spécialistes – suite look-and-say.md | 8 +- désintégration audioactive.md | 37 +++++- 4 files changed, 98 insertions(+), 57 deletions(-) diff --git a/Excalidraw/demo_théorème_du_début.excalidraw.md b/Excalidraw/demo_théorème_du_début.excalidraw.md index 973167b6..fb563540 100644 --- a/Excalidraw/demo_théorème_du_début.excalidraw.md +++ b/Excalidraw/demo_théorème_du_début.excalidraw.md @@ -36,6 +36,8 @@ ffd8bbb1f258e27c8d6d0cb5386c5dbe927d4d91: $$\left. \begin{array}[c] \\ \\ \\ \\ \end{array} \right\}$$ +0c26d0c5c9ca46fff3834a4156bbfcf1899051c6: $$[n^{1}$$ + %% ## Drawing ```compressed-json @@ -47,102 +49,108 @@ KYB2AcgYYYTlie0KsfWeAAZ5ip4xseX1082CyAoSdW5liu11hJmEiq+5048K5bKQIQjKaTcCpJU5TVYJ 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a/Mathématiques pour non spécialistes – suite look-and-say.md +++ b/Mathématiques pour non spécialistes – suite look-and-say.md @@ -75,7 +75,7 @@ Après 2 jours, on ne peut plus avoir : + apparition d'un $\geq 4$ car $x^4$ impossible (thm. J1) + $3X3$ $=\begin{cases},3X,3y \longleftarrow X^3y^3 {\,\color{red}\Large \times } \text{ (thm. J1)} \\ 3,X3, {\,\color{red}\Large \times } \text{ (thm. J1)}\end{cases}$ --- +--- ## Théorème du début Le début arrivera toujours sur l'un de ces cycles : @@ -101,4 +101,8 @@ Le début arrivera toujours sur l'un de ces cycles : -- ### Théorème du début — Démonstration -![[attachments/Capture d’écran 2026-03-29 à 22.50.04.png]] \ No newline at end of file +![[attachments/Capture d’écran 2026-03-29 à 22.50.04.png]] + + +-- +### Théorème du début — Démonstration \ No newline at end of file diff --git a/désintégration audioactive.md b/désintégration audioactive.md index c78f55ed..6b56dc07 100644 --- a/désintégration audioactive.md +++ b/désintégration audioactive.md @@ -192,18 +192,47 @@ header-auto-numbering: > > - $[1^{3}2^{2}$ ou, plus généralement $[1^{3}$ > > - $[2^{1}X^{\leq 2}$ > > - $[2^{3}$ -> > - $[3^{1}X^{1}$ que l'on restreint à $[3^{1}(\neq 1)^{1}$ pour que les cas soient bien disjoints +> > - $[3^{1}X^{1}$ que l'on restreint à $[3^{1}(\neq 1)^{1}$ pour éviter la superposition avec un autre cas > > - $[3^{1}(\leq 2)^{2}$ > > - $[3^{2}(\leq 2)^{\leq 3}$ qui est l'une de ces deux possibilités : -> > - $[3^{1}1^{\leq 3}$ -> > - $[3^{1}2^{\leq 3}$ +> > - $[3^{2}1^{\leq 3}$ +> > - $[3^{2}2^{\leq 3}$ +> > - $[n^{1}$ +> > > > De là, on observe que toutes les possibilités convergent vers l'un des cycles donnés : > > ![[demo_théorème_du_début.excalidraw]] > > > > Par ailleurs, si $R$ commence par $[22$ : > > - si $R = [22]$ la preuve est trivialle > > - sinon on considère un $R'$ tel que $R = [22 \cdot R'$, et on utilise l'argument précédent pour montrer que $R'$ arrive sur le cycle $[1^{1}X^{1} \longrightarrow [1^{3} \longrightarrow [3^{1}X^{\neq 3}$ -> > [[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=186&rect=12,345,377,408|schéma original de Conway p.186]] +> > --- +> > +> > On peut modifier cette liste : +> > - en assimilant $[3^{1}X^{1}$ et $[3^{1}(\leq 2)^{2}$ aux deux cas $[3^{1}X^{3}$, $[3^{1}X^{\leq 2}$ +> > - en assimilant $[3^{2}(\leq 2)^{\leq 3}$ aux cas $[3^{2}X^{3}$, $[3^{2}X^{\leq 2}$ +> > - en assimilant $[1^{3}2^{2}$ et $[1^{3}X^{1}$ au seul cas $[1^{3}$ +> > - en séparant $[1^{2}2^{\leq 3}$ en $[1^{2}X^{1}$ (qui est déjà listé), $[1^{2}2^{2}$ et $[1^{2}2^{3}$ +> > - en séparant $[2^{1} X^{\leq 2}$ en $[2^{1}X^{2}$ et $[2^{1}X^{\neq 2}$ +> > - en ajoutant $[1^{1}3^{2}$ +> > Cela nous donne la liste suivante : +> > - $[1^{1}] = [1^{1}X^{0}$ +> > - $[1^{1}X^{1}$ +> > - $[1^{1}2^{2}$ +> > - $[1^{1}3^{2}$ +> > - $[1^{2}2^{2}$ +> > - $[1^{2}2^{3}$ +> > - $[1^{3}$ +> > - $[2^{1}X^{2}$ +> > - $[2^{1}X^{\neq 2}$ +> > - $[2^{3}$ +> > - $[3^{1}X^{3}$ +> > - $[3^{1}X^{\leq 2}$ +> > - $[3^{2}X^{3}$ +> > - $[3^{2}X^{\leq 2}$ +> > - $[n^{1}$ +> > +> > Cela nous permet d'atteindre le schéma original de Conway : +> > ![[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=186&rect=12,345,377,408|schéma original de Conway p.186]]