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Introduction to the Yang-Baxter Equation with Open Problems
Axioms, 2012 The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter’s work.
Florin Nichita
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Classical Yang-Baxter equation from β-supergravity
Journal of High Energy Physics, 2019 Yang-Baxter deformations of superstring σ-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the ...
Ilya Bakhmatov, Edvard T. Musaev
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Yang-Baxter Maps from the Discrete BKP Equation
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation.
Saburo Kakei +2 more
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Experimental realization of the Yang-Baxter Equation via NMR interferometry. [PDF]
Sci Rep, 2016 The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory.
Vind FA +6 more
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Midazolam Dosing During CRRT: A Combined Ex Vivo and Physiologically-Based Pharmacokinetic Approach. [PDF]
CPT Pharmacometrics Syst PharmacolABSTRACT Children supported with continuous renal replacement therapy have high mortality rates ranging from 30% to 70%. The cause of this high mortality is multifactorial and includes ineffective drug dosing and altered drug pharmacokinetics. Changes in drug exposure can result from (1) underlying disease; and (2) direct drug interaction and/or ...
McKnite AM +12 more
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Yang-Baxter maps and the discrete KP hierarchy [PDF]
, 2009 We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with ...
Kakei, S., Willox, R., Nimmo, J.J.C.
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Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]
, 2014 The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Guo, Li +5 more
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All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Complexity, 2020 Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation.
Duanmei Zhou, Jiawen Ding
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Problems on Skew Left Braces [PDF]
Advances in Group Theory and Applications, 2019 Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying involutive solutions to the Yang–Baxter equation.
Leandro Vendramin
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Quantum groups, Yang–Baxter maps and quasi-determinants
Nuclear Physics B, 2018 For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang–Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Zengo Tsuboi
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