From cd25e13a8e3a678c056e1b375d454334a519decb Mon Sep 17 00:00:00 2001 From: oskar Date: Wed, 8 Apr 2026 16:58:48 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-8:16:58:48 --- .../obsidian-excalidraw-plugin/data.json | 4 +- .../obsidian-pandoc-reference-list/data.json | 2 +- .../plugins/obsidian-style-settings/data.json | 2 +- .../demo_théorème_du_début.excalidraw.md | 94 +++++++------- .../demo_théorème_du_début.excalidraw.svg | 4 +- ...tive théorème de la fin cycles.excalidraw.md | 117 ++++++++++++++++++ ...ive théorème de la fin cycles.excalidraw.svg | 2 + désintégration audioactive.md | 18 ++- 8 files changed, 186 insertions(+), 57 deletions(-) create mode 100644 attachments/désintégration audioactive théorème de la fin cycles.excalidraw.md create mode 100644 attachments/désintégration audioactive théorème de la fin cycles.excalidraw.svg diff --git a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json index e6382b63..2f541d96 100644 --- a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json +++ b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json @@ -34,7 +34,7 @@ "allowImageCache": true, "allowImageCacheInScene": true, "displayExportedImageIfAvailable": false, - "previewMatchObsidianTheme": false, + "previewMatchObsidianTheme": true, "width": "400", "height": "", "overrideObsidianFontSize": false, @@ -85,7 +85,7 @@ "iframelyAllowed": true, "pngExportScale": 1, "exportWithTheme": true, - "exportWithBackground": true, + "exportWithBackground": false, "exportPaddingSVG": 10, "exportEmbedScene": false, "keepInSync": true, diff --git a/.obsidian/plugins/obsidian-pandoc-reference-list/data.json b/.obsidian/plugins/obsidian-pandoc-reference-list/data.json index d7a74e48..f365b6cc 100644 --- a/.obsidian/plugins/obsidian-pandoc-reference-list/data.json +++ b/.obsidian/plugins/obsidian-pandoc-reference-list/data.json @@ -5,7 +5,7 @@ { "id": 1, "name": "Ma bibliothèque", - "lastUpdate": 1775571160432 + "lastUpdate": 1775656727556 } ], "renderCitations": true, diff --git a/.obsidian/plugins/obsidian-style-settings/data.json b/.obsidian/plugins/obsidian-style-settings/data.json index 46b11049..4f6a2ea6 100644 --- a/.obsidian/plugins/obsidian-style-settings/data.json +++ b/.obsidian/plugins/obsidian-style-settings/data.json @@ -35,7 +35,7 @@ "minimal-style@@code-background@@dark": "#1E1E1E", "minimal-style@@window-title-off": false, "minimal-style@@code-normal@@dark": "#BCBCBC", - "minimal-style@@image-muted": 0.7, + "minimal-style@@image-muted": 1, "minimal-style@@col-alt": false, "supercharged-links@@f1e2-3136-color": "#008A88", "supercharged-links@@591a-86c0-decoration": "initial", diff --git a/Excalidraw/demo_théorème_du_début.excalidraw.md b/Excalidraw/demo_théorème_du_début.excalidraw.md index e746929f..e4cd2896 100644 --- a/Excalidraw/demo_théorème_du_début.excalidraw.md +++ b/Excalidraw/demo_théorème_du_début.excalidraw.md @@ -61,96 +61,98 @@ 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b/Excalidraw/demo_théorème_du_début.excalidraw.svg @@ -1,2 +1,2 @@ - \ No newline at end of file + \ No newline at end of file diff --git a/attachments/désintégration audioactive théorème de la fin cycles.excalidraw.md b/attachments/désintégration audioactive théorème de la fin cycles.excalidraw.md new file mode 100644 index 00000000..bceaa83d --- /dev/null +++ b/attachments/désintégration audioactive théorème de la fin cycles.excalidraw.md @@ -0,0 +1,117 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' + + +# Excalidraw Data + +## Text Elements +## Embedded Files +04ee9575be008dd3cc75238f0c479af0144df112: $$2\cdot 311322113212221]$$ + +ed2a4c0fc556d90bae7bdf658819eac067a989bb: $$2\cdot 13211322211312113211]$$ + +863e0bb6118d1de2696f04a4f43fab8624a7bd64: $$2\cdot 12322211331222113112211]$$ + +5f0a9eb71a73921b4ed5d95d6d949a915c2fadff: $$2\cdot 1113122113322113111221131221]$$ + +c3bfc2ab24ffe59ccc732dba128a66901fa6c9e3: $$2\cdot 31221132221222112112322211n]$$ + +45a03920105d60d417654042595a9400e51e0dff: $$2\cdot 1311222113321132211221121332211n]$$ + +ca22264e4655342e2d1e39db3f28cc1f519ed819: $$2^2]$$ + +62670f424a7fd99dd2c0a9e49105a9007e1610c8: $$(1)$$ + +acd3990fdc2fa19b40c17d95a96c473a5d002d33: $$(2)$$ + +2e1dd3e45c3cd8ecb31469cdc166428d1a0b5d8a: $$(3)$$ + +%% +## Drawing +```compressed-json 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pourra noter $,12,23,11,$ : les virgules précisent le "parsing", c'est-à-dire la bonne manière de lire la chaîne + - = $\dots 233 \dots \longrightarrow \dots ,12,23, \dots$ mais $122111 \centernot{\longrightarrow} \dots ,12,23,1\dots$ même si $122111 \longrightarrow \dots 12231 \dots$ - $L \longrightarrow L'$ signifie que $L$ est dérivée en $L'$ par désintégration audioactive - On note aussi $L \longrightarrow L' \longrightarrow L'' \longrightarrow \cdots$ pour $L \longrightarrow L'$ et $L' \longrightarrow L''$ et $L'' \longrightarrow \cdots$ - $L_{n}$ est le $n^{\text{ème}}$ *descendant* de $L$ (le résultat de $n$ dérivations de $L$) @@ -36,6 +37,7 @@ header-auto-numbering: - $X$ désigne un chiffre arbitraire (non nul) - = $X^{0}a^{\alpha}b^{\beta}c^{\gamma}$ correspond à $[a^{\alpha}b^{\beta}c^{\gamma}$ - = $a^{\alpha}b^{\beta}c^{\gamma}X^{0}$ correspond à $a^{\alpha}b^{\beta}c^{\gamma}]$ + - = - $\neq n$ désigne n'importe quel chiffre (éventuellement 0) autre que $n$ - = $a^{\alpha}b^{\beta}c^{\gamma}X^{\neq 0}$ signifie $a^{\alpha}b^{\beta}c^{\gamma}$ suivi d'au moins un autre chiffre - = $a^{\alpha}b^{\beta}c^{\gamma} (\neq 2)^{\neq 0}$ signifie que ce dernier chiffre n'est pas un $2$ @@ -65,11 +67,9 @@ header-auto-numbering: > [!definition] Atome > Les **atomes** (ou *éléments*) sont les chaînes qui ne possèdent pas de découpage non trivial. -> - source:: [[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=181&selection=221,11,241,7&color=note|(John Horton Conway, 1987)]] ^def-atome - i toute chaîne est **composée** d'un certain nombre d'éléments. On dit que cette chaîne **comprends** lesdits éléments. - - source:: [[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=181&selection=243,5,260,9&color=note|(John Horton Conway, 1987)]] ## Théorèmes @@ -203,7 +203,7 @@ header-auto-numbering: > > - $[n^{1}$ > > > > De là, on observe que toutes les possibilités convergent vers l'un des cycles donnés : -> > ![[demo_théorème_du_début.excalidraw]] +> > ![[demo_théorème_du_début.excalidraw|700]] > > > > Par ailleurs, si $R$ commence par $[22$ : > > - si $R = [22]$ la preuve est trivialle @@ -235,7 +235,7 @@ header-auto-numbering: > > - $[n^{1}$ > > > > 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]] +> > ![[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&width=800|schéma original de Conway p.186]] ^theoreme-debut > [!proposition]+ théorème du découpage @@ -254,7 +254,15 @@ header-auto-numbering: > [!proposition]+ Théorème de la fin > La fin d'une chaîne finit toujours par atteindre l'un de ces cycles : +> ![[attachments/désintégration audioactive théorème de la fin cycles.excalidraw|950]] > +> > [!démonstration]+ Démonstration +> > - Une chaîne se terminant par $1$ apparaîtra nécessairement dans cette chaîne de dérivations (en effet, tous les cas de chaîne finissant par $1$ y sont présents) : +> > $1^{\geq 3}] \longrightarrow \underbrace{(\neq 2)^{X}1^{1}]}_{\substack{\text{plus général}\\\text{que }(\geq 3)^{X}1^{1}]}} \longrightarrow (\neq 2)^{X}1^{2}] \longrightarrow (\neq 2)^{X}2^{1}1^{1}] \longrightarrow \underbrace{2^{X\neq 2}1^{2}]}_{\substack{\text{fin de}\\(\neq 2)^{X}1^{1}2^{1}1^{2}]}} \longrightarrow 2^{2}1^{1}] \longrightarrow 2^{2}1^{2}] \longrightarrow 2^{3}1^{1}]$ +> > Ce qui montre que toute chaîne se terminant par $1$ finit par atteindre une chaîne se terminant par $2^{3}1^{1}]$. +> > De là, en dérivant cette fin plusieurs fois, on obtient successivement : +> > - +> > -