Trace and determinant in algebras associated with the yang-baxter equation

1987 ◽  
Vol 21 (3) ◽  
pp. 239-240
Author(s):  
D. I. Gurevich
Keyword(s):  
Baxter Equation

Solution of the deformed Schwarzschild metric by the Yang-Baxter equation

2019 ◽  
Vol 96 (4) ◽  
pp. 8-14
Author(s):  
A. Meirambay ◽  
◽  
K.K. Yerzhanov ◽  
Keyword(s):  
Baxter Equation ◽  
Schwarzschild Metric

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

Ore extensions of quasitriangular Hopf group coalgebras

2014 ◽  
Vol 13 (06) ◽  
pp. 1450016 ◽  
Author(s):  
Daowei Lu ◽  
Dingguo Wang
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Baxter Equation ◽  
Ore Extension ◽  
Ore Extensions ◽  
Necessary And Sufficient

In this paper, we mainly consider some special Ore extension of quasitriangular Hopf group coalgebra, and give the necessary and sufficient conditions when the Ore extension of quasitriangular Hopf group coalgebras will preserve the same quasitriangular structure. Furthermore, in the two examples given at the end, we construct new solutions of Yang–Baxter equation of Hopf group coalgebras version.

scholarly journals On the Yang–Baxter equation and left nilpotent left braces

2017 ◽  
Vol 221 (4) ◽  
pp. 751-756 ◽  
Author(s):  
Ferran Cedó ◽  
Tatiana Gateva-Ivanova ◽  
Agata Smoktunowicz
Keyword(s):  
Baxter Equation

A New Representation of Birman-Wenzl Algebra and Solution of Yang-Baxter Equation

1993 ◽  
Vol 20 (2) ◽  
pp. 195-200
Author(s):  
Lu-yu Wang ◽  
Jim-Hui Dai ◽  
Jun Zhang
Keyword(s):  
Baxter Equation

scholarly journals Solutions of the Yang–Baxter equation: Descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

2011 ◽  
Vol 847 (2) ◽  
pp. 387-412 ◽  
Author(s):  
P.E. Finch ◽  
K.A. Dancer ◽  
P.S. Isaac ◽  
J. Links
Keyword(s):  
Dihedral Group ◽  
Group Algebras ◽  
Baxter Equation ◽  
Vertex Model

Contact Angle of Nepenthes alata Slippery Zone: Results from Measurement and Model Analysis

2021 ◽  
pp. 1-7
Author(s):  
Lixin Wang ◽  
Pan Pan ◽  
Shixing Yan ◽  
Shiyun Dong
Keyword(s):  
Contact Angle ◽  
Hierarchical Structures ◽  
Model Analysis ◽  
Contact Angle Measurement ◽  
Angle Measurement ◽  
Structure Characteristic ◽  
Baxter Equation ◽  
Measured Contact Angle ◽  
The Relationship ◽  
Contact Angle Analysis

The slippery zone of Nepenthes alata depends on its highly evolved morphology and structure to show remarkable superhydrophobicity, which has gradually become a biomimetic prototype for developing superhydrophobic materials. However, the mechanism governing this phenomenon has not been fully revealed through model analysis. In this paper, the superhydrophobicity of slippery zone is studied by contact angle measurement, morphology/structure examination and model analysis. The slippery zone causes ultrapure water droplet to produce a considerably high contact angle (155.11–158.30°), and has a micro-nano scale hierarchical structures consisting of lunate cells and wax coverings. According to the Cassie-Baxter equation and a self-defined infiltration coefficient, a model was established to analyze the effect of structure characteristic on the contact angle. Analysis result showed that the calculated contact angle (154.67–159.49°) was highly consistent with the measured contact angle, indicating that the established model can quantitatively characterize the relationship between the contact angle and the structure characteristic. Our study provides some evidences to further reveal the superhydrophobic mechanism of Nepenthes alata slippery zone, as well as inspires the biomimetic development of superhydrophobic surfaces.

scholarly journals Constructing Hopf braces

2019 ◽  
Vol 30 (02) ◽  
pp. 1850089 ◽  
Author(s):  
A. L. Agore
Keyword(s):  
Hopf Algebras ◽  
Baxter Equation ◽  
Matched Pairs

We investigate Hopf braces, a concept recently introduced by Angiono, Galindo and Vendramin [I. Angiono, C. Galindo and L. Vendramin, Hopf braces and Yang–Baxter operators, Proc. Amer. Math. Soc. 145 (2017) 1981–1995] in connection to the quantum Yang–Baxter equation. More precisely, we propose two methods for constructing Hopf braces. The first one uses matched pairs of Hopf algebras while the second one relies on category-theoretic tools.

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