-
Previous Article
Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems
- NACO Home
- This Issue
-
Next Article
An adaptive wavelet method and its analysis for parabolic equations
Solutions of the Yang-Baxter matrix equation for an idempotent
1. | Department of Mathematics, The Univeristy of Southern Mississippi, Hattiesburg, MS 39406-5045, United States |
2. | Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045 |
3. | Department of Mathematics, The Univeristy of New Haven, West Haven, CT 06516, United States |
4. | Department of mathematics and Statistics, The University of Missouri - Kansas City, Kansas City, MO 64110-2499, United States |
References:
[1] |
R. Baxter, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain II eqivalence to a generalized ice-type lattice model, Ann Phys., 76 (1973), 25-47.
doi: 10.1016/0003-4916(73)90440-5. |
[2] |
A. Cibotarica, "An Examination of the Yang-Baxter Equation,'' Master thesis, University of Southern Mississippi in Hattiesberg, 2011. |
[3] |
J. Ding and N. Rhee, A nontrivial solution to a stochastic matrix equation, East Asia J. Applied Math., 2 (2012), 277-284. |
[4] |
F. Felix, "Nonlinear Equations, Quantum Groups and Duality Theorems: A Primer on the Yang-Baxter Equation," VDM Verlag, 2009. |
[5] |
M. Jimbo, "Introduction to the Yang-Baxter equation,'' Braid Group, Knot Theory and Statistical Physics II, World Scientific, (1994), 153-176. |
[6] |
C. N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta function interaction, Phys. Rev. Lett., 19 (1967), 1312-1315.
doi: 10.1103/PhysRevLett.19.1312. |
[7] |
C. N. Yang and M. L. Ge, "Braid Group, Knot Theory and Statistical Physics II,'' World Scientific, 1994. |
show all references
References:
[1] |
R. Baxter, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain II eqivalence to a generalized ice-type lattice model, Ann Phys., 76 (1973), 25-47.
doi: 10.1016/0003-4916(73)90440-5. |
[2] |
A. Cibotarica, "An Examination of the Yang-Baxter Equation,'' Master thesis, University of Southern Mississippi in Hattiesberg, 2011. |
[3] |
J. Ding and N. Rhee, A nontrivial solution to a stochastic matrix equation, East Asia J. Applied Math., 2 (2012), 277-284. |
[4] |
F. Felix, "Nonlinear Equations, Quantum Groups and Duality Theorems: A Primer on the Yang-Baxter Equation," VDM Verlag, 2009. |
[5] |
M. Jimbo, "Introduction to the Yang-Baxter equation,'' Braid Group, Knot Theory and Statistical Physics II, World Scientific, (1994), 153-176. |
[6] |
C. N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta function interaction, Phys. Rev. Lett., 19 (1967), 1312-1315.
doi: 10.1103/PhysRevLett.19.1312. |
[7] |
C. N. Yang and M. L. Ge, "Braid Group, Knot Theory and Statistical Physics II,'' World Scientific, 1994. |
[1] |
Sigve Hovda. Closed-form expression for the inverse of a class of tridiagonal matrices. Numerical Algebra, Control and Optimization, 2016, 6 (4) : 437-445. doi: 10.3934/naco.2016019 |
[2] |
Eric Bedford, Kyounghee Kim. Degree growth of matrix inversion: Birational maps of symmetric, cyclic matrices. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 977-1013. doi: 10.3934/dcds.2008.21.977 |
[3] |
Zenonas Navickas, Rasa Smidtaite, Alfonsas Vainoras, Minvydas Ragulskis. The logistic map of matrices. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 927-944. doi: 10.3934/dcdsb.2011.16.927 |
[4] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems and Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[5] |
Björn Gebhard. A note concerning a property of symplectic matrices. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2135-2137. doi: 10.3934/cpaa.2018101 |
[6] |
Janusz Mierczyński. Averaging in random systems of nonnegative matrices. Conference Publications, 2015, 2015 (special) : 835-840. doi: 10.3934/proc.2015.0835 |
[7] |
Jim Wiseman. Symbolic dynamics from signed matrices. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 621-638. doi: 10.3934/dcds.2004.11.621 |
[8] |
Akbar Mahmoodi Rishakani, Seyed Mojtaba Dehnavi, Mohmmadreza Mirzaee Shamsabad, Nasour Bagheri. Cryptographic properties of cyclic binary matrices. Advances in Mathematics of Communications, 2021, 15 (2) : 311-327. doi: 10.3934/amc.2020068 |
[9] |
Delio Mugnolo. Dynamical systems associated with adjacency matrices. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 1945-1973. doi: 10.3934/dcdsb.2018190 |
[10] |
El Mustapha Ait Ben Hassi, Mohamed Fadili, Lahcen Maniar. Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix. Mathematical Control and Related Fields, 2020, 10 (3) : 623-642. doi: 10.3934/mcrf.2020013 |
[11] |
Chinmay Kumar Giri. Index-proper nonnegative splittings of matrices. Numerical Algebra, Control and Optimization, 2016, 6 (2) : 103-113. doi: 10.3934/naco.2016002 |
[12] |
Ferenc Szöllősi. On quaternary complex Hadamard matrices of small orders. Advances in Mathematics of Communications, 2011, 5 (2) : 309-315. doi: 10.3934/amc.2011.5.309 |
[13] |
Barbara A. Shipman. Compactified isospectral sets of complex tridiagonal Hessenberg matrices. Conference Publications, 2003, 2003 (Special) : 788-797. doi: 10.3934/proc.2003.2003.788 |
[14] |
David Damanik, Jake Fillman, Milivoje Lukic, William Yessen. Characterizations of uniform hyperbolicity and spectra of CMV matrices. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1009-1023. doi: 10.3934/dcdss.2016039 |
[15] |
B. Cantó, C. Coll, E. Sánchez. The problem of global identifiability for systems with tridiagonal matrices. Conference Publications, 2011, 2011 (Special) : 250-257. doi: 10.3934/proc.2011.2011.250 |
[16] |
Riccardo Aragona, Alessio Meneghetti. Type-preserving matrices and security of block ciphers. Advances in Mathematics of Communications, 2019, 13 (2) : 235-251. doi: 10.3934/amc.2019016 |
[17] |
Imen Bhouri, Houssem Tlili. On the multifractal formalism for Bernoulli products of invertible matrices. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1129-1145. doi: 10.3934/dcds.2009.24.1129 |
[18] |
Leonid Golinskii, Mikhail Kudryavtsev. An inverse spectral theory for finite CMV matrices. Inverse Problems and Imaging, 2010, 4 (1) : 93-110. doi: 10.3934/ipi.2010.4.93 |
[19] |
Shengtian Yang, Thomas Honold. Good random matrices over finite fields. Advances in Mathematics of Communications, 2012, 6 (2) : 203-227. doi: 10.3934/amc.2012.6.203 |
[20] |
Steve Limburg, David Grant, Mahesh K. Varanasi. Higher genus universally decodable matrices (UDMG). Advances in Mathematics of Communications, 2014, 8 (3) : 257-270. doi: 10.3934/amc.2014.8.257 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]