# Yang–Baxter Equations, Computational Methods and Applications

## Abstract

**:**

## 1. Introduction

## 2. Yang–Baxter Equations

**Definition 2.1.**

**Remark 2.2.**

**Remark 2.3.**

## 3. The Set-Theoretical Yang–Baxter Equation

**Definition 3.1.**

**Theorem 3.2.**

**Proof.**

**Theorem 3.3.**

**Proof.**

**Remark 3.4.**

## 4. Transcendental Numbers and Applications

**Theorem 4.1.**

**Proof.**

**Remark 4.2.**

**Remark 4.3.**

## 5. The Yang–Baxter Equations in Informatics

The maipart of another sorting algorithm, related to the left-hand side of (2), is given below (see [1]).intm, aux; m=L;while(m) {for(int i=1; i≤L-1; i++)if(s[L-i] ≥ s[L+1-i]) { aux = s[L+1-i]; s[L+1-i] = s[L-i]; s[L-i] = aux; } m - -; }

if(s[i]≥s[j]) { aux=s[i]; s[i]=s[j]; s[j]=aux; }

## 6. Non-Associative Algebras and Their Unifications

**Definition 6.1.**

**Remark 6.2.**

**Remark 6.3.**

**Theorem 6.4.**

**Proof.**

**Remark 6.5.**

**Theorem 6.6.**

**Remark 6.7.**

**Theorem 6.8.**

## 7. Conclusions and Further Implications

## Conflicts of Interest

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Nichita, F.F.
Yang–Baxter Equations, Computational Methods and Applications. *Axioms* **2015**, *4*, 423-435.
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Yang–Baxter Equations, Computational Methods and Applications. *Axioms*. 2015; 4(4):423-435.
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2015. "Yang–Baxter Equations, Computational Methods and Applications" *Axioms* 4, no. 4: 423-435.
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