statistical physics – What are applications of Jones polynomial on von von Neumann algebras?

I have read according list of below papers a basic connection between Jones polynomial and statistical mechanics is that the Kauffman bracket or Kauffman polynomial a polynomial invariant of knots is in different special cases the Jones polynomial for knots and the partition function for the Potts model in statistical mechanics. The Jones polynomial and its relations to the Yang-Baxter equations in Statistical mechanics, has been generalized to other invariants of knot theory by Kauffman via the Kauffman bracket .Witten has shown that one can use knot theory in the context of quantum field theory to produce invariants of 3- dimensional manifolds. Michael Atiyah also is using the Jones-Witten theory to explore functional integration in gauge theories and quantization. Now my question here is :

Question
What are applications of Jones polynomial on von von Neumann algebras ? or what the Jones polynomials has to do with von Neumann algebras?

Reference list

[1]:The book “Exactly Solved Models in Statistical Mechanics” by Baxter is a really good source if you are interested in the connection between statistical physics and the work of Jones http://physics.anu.edu.au/theophys/_files/Exactly.pdf

[2]:”Statistical Mechanics and the Jones Polynomial” by Louis Kauffman http://www.maths.ed.ac.uk/~aar/papers/kauffmanjones.pdf

[3]:A good source of information on the connection between QFT and the Jones polynominal is Witten’s paper “Quantum field theory and the Jones polynomial” http://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138

[4]:A brief version: certain algebras arising in Jones’ work also occur in the study of exactly solvable models in statistical mechanics. See here for details:
J.S. Birman, The Work of Vaughan F. R. Jones, in ICM’1990 proceedings:
http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0009.0018.ocr.pdf

soft question – Why is the Dyck language/Dyck paths named after von Dyck?

The Dyck language is defined as the language of balanced parenthesis expressions on the alphabet consisting of the symbols $($ and $)$. For example, $()$ and $()(()())$ are both elements of the Dyck language, but $())($ is not. There is an obvious generalisation of the Dyck language to include several different types of parentheses.

It seems to me that the first time the term “Dyck language” is used to describe this language (and its generalisation) is in (Chomsky, N.; Schützenberger, M. P. The algebraic theory of context-free languages. 1963 Computer programming and formal systems, pp. 118–161). Furthermore, all sources online agree that the “Dyck” in question is Walther von Dyck, who introduced the notion of a group presentation in 1882.

However, in the above paper, I can only see a weak reason as to why this language is named after von Dyck. A paragraph directly following the definition reads: The Dyck Language $D_{2n}$ on the $2n$ letters $x_{pm i} : (1 leq i leq n)$ (…) is a very familiar mathematical object: if $varphi$ is the homomorphism of the free monoid generated by ${ x_{pm i}}$ onto the free group generated by the subset ${ x_i mid i > 0}$ that satisfies identically $(varphi x_i)^{-1} = varphi x_{-i}$, then $D_{2n}$ is the kernel of $varphi$.

This alternate characterisation is obviously related to presentations, and thus has some connection with von Dyck. However, I am uncertain whether this is the full reason as to why it is named after him. Perhaps there is an intermediate study of the Dyck language inbetween the work of von Dyck and Chomsky-Schützenberger which makes this connection stronger? Thus, my question:

Why is the “Dyck language” named after von Dyck?

Of course, the same question might as well be asked about “Dyck paths” in combinatorics, closely related to the Catalan numbers, but it seems to me quite clear that Dyck paths were named after the Dyck language.

Any thoughts would be appreciated!

functional analysis – Projection for a given embedding of von Neumann algebra.

Let $mathcal{M}$ and $mathcal{N}$ be two given von Neumann algebras with faithful states $tau$ and $eta$, respectively. Let $varphi:(mathcal{N},eta)rightarrow(mathcal{M},tau)$ be a $^{*}$-embedding (i.e. an injective $C^{*}$-homomorphism) which preserves the states, i.e. $tau(varphi(x))=eta(x)$ for all $xinmathcal{N}$. Define an $L^2$-inner product on $mathcal{M}$ by $langle a,brangle=tau (ab^*)$ for $a,binmathcal{M}$. Let $L^2(mathcal{M},tau)$ be the completion of $mathcal{M}$ with respect to the corresponding $L^2$-norm. Similarly consider $L^2 (mathcal{N},eta)$. Then for each $x,yinmathcal{N}$, $langlevarphi(x),varphi(y)rangle=tau(varphi(x)varphi(y)^{*})=tau(varphi(xy^{*}))=eta(xy^{*})=langle x,yrangle$ and thus $varphi$ extends to an isometry $varphi:L^{2}(mathcal{N},eta)rightarrow L^{2}(M,tau)$. $mathcal{M}$ and $mathcal{N}$ are Let $P$ be the orthogonal projection of $L^2(mathcal{M},tau)$ onto $varphi (L^2(mathcal{N},eta))$.

Question: Is it true that $P(varphi (x)cdot a)=varphi (x)cdot P(a)$ for each $ainmathcal{M}$ and $xinmathcal{N}$?

Algorithmen – Geben Sie bei einer Liste von Ganzzahlen und einer Ziel-Ganzzahl die Anzahl der Tripletts zurück, deren Produkt die Ziel-Ganzzahl und zwei benachbarte Tripletts sind

Frage: Geben Sie bei einer Liste von Ganzzahlen (möglicherweise negativ) und einer Ziel-Ganzzahl die Anzahl der Tripletts zurück, deren Produkt die Ziel-Ganzzahl ist und zwei der Tripletts benachbart sein müssen.

Zum Beispiel, wenn die angegebene Liste ist $ A = (1,2,2,2,4) $ und Ziel $ = 8, $ dann ist die Antwort $ 3 $ wie $ (A (0), A (1), A (4)), (A (1), A (2), A (3)) $ und $ (A (0), A (3), A (4)) $ wenn wir verwenden $ 0 $-basierte Nummerierung.

Ich blieb 3 Stunden bei dieser Frage und konnte sie nicht lösen.

Jeder Hinweis wird geschätzt.

Stellen Sie die SSR-App von Nuxt.js über Azure DevOps Pipelines für den Azure App Service bereit

Haftungsausschluss:
✅Ich habe einen Azure App-Dienst mit einem Linux-Container eingerichtet.
✅Ich habe dies hinzugefügt nuxt.config.js

  server: {
    host: '0.0.0.0'
  }

In Azure DevOps Pipelines kopiere ich diese Dateien nach dem Build:

.nuxt/**
static/**
package.json
nuxt.config.js

dann zippe ich sie als package.zip
In den Protokollen wird angezeigt, dass die Dateien erfolgreich komprimiert wurden, aber wenn ich das Paket entpacke, wird keine der Dateien .nuxt Dateien sind vorhanden. Ich bin auch verwirrt, dass aus irgendeinem Grund in der package.zip alle Build-Dateien in einem Ordner mit dem Namen einfach abgelegt werden a/

Dateien archivieren
Sie können auf dem Foto sehen, dass oben der Ordner 'a' erstellt wird und dass anscheinend alle Dateien zum Archiv hinzugefügt werden.
Wenn ich die package.zip entpacke, sind die folgenden Dateien:
 * package.json
 * nuxt.config.js
 * / statisch

entpackte Dateien

So sieht meine YAML-Datei aus:

trigger:
- master

pool:
  vmImage: 'ubuntu-latest'

steps:
- task: NodeTool@0
  inputs:
    versionSpec: '12.x'
  displayName: 'Install Node.js'

- script: |
    cd src/Web.Nuxt
    npm install
    npm run build
  displayName: 'npm install and build'

- task: CopyFiles@2
  inputs:
    SourceFolder: '$(Build.SourcesDirectory)/src/Web.Nuxt'
    Contents: |
      .nuxt/**
      static/**
      package.json
      nuxt.config.js
    TargetFolder: '$(Build.ArtifactStagingDirectory)'

- task: ArchiveFiles@2
  inputs:
    rootFolderOrFile: '$(Build.ArtifactStagingDirectory)'
    archiveType: 'zip'
    archiveFile: '$(Build.ArtifactStagingDirectory)/package.zip'
    replaceExistingArchive: true

- task: PublishBuildArtifacts@1
  inputs:
    PathtoPublish: '$(Build.ArtifactStagingDirectory)/package.zip'
    ArtifactName: 'drop'
    publishLocation: 'Container'

Jede Hilfe wäre sehr dankbar, die mich wieder auf den Weg zur Bereitstellung einer SSR Next.app mit Azure DevOps Pipelines, Azure App Service und einer Nuxt SSR-App bringen kann. Die Fehlerbehebung war schwierig, da in Azure DevOps Pipelines and Releases angegeben wurde, dass alles erfolgreich war.

Is there a connection between imperative programming and Von Neumann architecture?

I came across a wall with this question in the exercise my teacher gave me. Is there a real connection between the Von Neumann architecture and imperative programming?

I tried googling and finding similar questions, but I couldn't find anything, and the one question I did find was that there should be no connection between the Von Neumann architecture and the programming paradigms.

Any help would be appreciated, I'm new to StackExchange. So if I break any rules, please tell me :]

Einrichten von Jenkins auf Kubernetes – Fehler 403

Ich bin auf einem IaaS Kubernetes k8s auf einer virtuellen Maschine.

Ich habe einen Nginx und einige andere Apps eingerichtet, die gut funktionieren. (Ich kann meine Apps erreichen)

Ich benutze Nginx Ingress Controller.

Wenn ich versuche, Jenkins außerhalb des Knotens zu erreichen, erhalte ich eine leere Antwort, aber die Eingangsprotokolle zeigen eine 403 an

Wenn ich Jenkins innerhalb des Knotens kräusele, kann ich ihn problemlos erreichen

Wenn ich den Jenkins-Container neu starte, kann ich auf den zugreifen Please wait while Jenkins is getting ready to work ... Seite, aber nachdem es fertig ist, bekomme ich wieder eine 403.

Irgendeine Idee, warum das passiert?

Operator theory – support of pendulum elements in a von Neumann algebra

To let $ mathcal M $ be a semifinite from Neumann algebra and $ a $ be an unlimited positive self-proclaimed operator who is connected $ mathcal M $, Accept $ x in mathcal M $ is that $ x $ oscillates with all spectral projections from $ a $ and support from $ x $ is included to support $ a $, Is it true that $ chi _ {(0,1)} (ax) = chi _ {(0,1)} (x) $? This should be true there $ a $ and $ x $ we can just assume that these are functions for which this applies. But I want more concrete evidence.