Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation

[1] Abbott, J. C. (1967), Implicational algebras, Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, 11(1):3–23. AbbottJ. C. 1967 Implicational algebras Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie 11 1 3 23 Search in Google Scholar

[2] Baxter, R. J. (1972), Partition Function of the Eight-Vertex Lattice Model, Ann. Phys., 70: 193–228. BaxterR. J. 1972 Partition Function of the Eight-Vertex Lattice Model Ann. Phys. 70 193 228 10.1142/9789812798336_0003 Search in Google Scholar

[3] Baxter, R. J. (1982), Exactly Solved Models in Statical Mechanics, Academy Press, London, UK. BaxterR. J. 1982 Exactly Solved Models in Statical Mechanics Academy Press London, UK Search in Google Scholar

[4] Chajda, I. (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathematics, 8(03): 1550040. ChajdaI. 2015 Basic algebras, logics, trends and applications Asian-European Journal of Mathematics 8 03 1550040 10.1142/S1793557115500400 Search in Google Scholar

[5] Chajda, I. (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium, Mathematica, 44(1):19–23. ChajdaI. 2005 Sheffer operation in ortholattices Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium, Mathematica 44 1 19 23 Search in Google Scholar

[6] Chajda, I. and Kolařík, M. (2009), Interval Basic Algebras, NOVI SAD J. MATH., 39(2). ChajdaI. KolaříkM. 2009 Interval Basic Algebras NOVI SAD J. MATH. 39 2 10.1007/s11083-009-9113-0 Search in Google Scholar

[7] Chajda, I., Hala, R. and Lnger, H. (2019), Operations and structures derived from non-associative MV-algebras, Soft Computing, 23(12):3935–3944. ChajdaI. HalaR. LngerH. 2019 Operations and structures derived from non-associative MV-algebras Soft Computing 23 12 3935 3944 10.1007/s00500-018-3309-4650051131123427 Search in Google Scholar

[8] Nichita, F. F. (2015), Yang-Baxter Equations, Computational Methods and Applications, Axioms, 4:423–435. NichitaF. F. 2015 Yang-Baxter Equations, Computational Methods and Applications Axioms 4 423 435 10.3390/axioms4040423 Search in Google Scholar

[9] Nichita, F. F. (2003), On the set-theoretical Yang-Baxter Equation, Acta Univ. Apulensis Math. Inf., 5:9–100. NichitaF. F. 2003 On the set-theoretical Yang-Baxter Equation Acta Univ. Apulensis Math. Inf. 5 9 100 Search in Google Scholar

[10] Nichita, F. F. (2014), Hopf algebras, Quantum Groups and Yang-Baxter Equations. (Special Issue). Available online: http://www.mdpi.com/journal/axioms/special_issue/hopf_algebras_2014 (accessed on 22 June 2017). NichitaF. F. 2014 Hopf algebras, Quantum Groups and Yang-Baxter Equations. (Special Issue) Available online: http://www.mdpi.com/journal/axioms/special_issue/hopf_algebras_2014 (accessed on 22 June 2017). Search in Google Scholar

[11] Sheffer, H. M. (1913), A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4):481–488. ShefferH. M. 1913 A set of five independent postulates for Boolean algebras, with application to logical constants Transactions of the American Mathematical Society 14 4 481 488 10.1090/S0002-9947-1913-1500960-1 Search in Google Scholar

[12] Jakubik, J. (2006), On intervals and the dual of pseudo MV-algebras, Math. Slovaca, 56:213–221. JakubikJ. 2006 On intervals and the dual of pseudo MV-algebras Math. Slovaca 56 213 221 Search in Google Scholar

[13] Jimbo, M. (1989), Introduction to the Yang-Baxter Equation, Int. J. Mod. Phys., 4(15):3759–3777. JimboM. 1989 Introduction to the Yang-Baxter Equation Int. J. Mod. Phys. 4 15 3759 3777 10.1142/S0217751X89001503 Search in Google Scholar

[14] Jimbo, M. (1990), Yang-Baxter Equation in Integrable Systems, Volume 10, Advanced Series in Mathematical Physics, World Scientific Publishing Co. Inc., Singapore. JimboM. 1990 Yang-Baxter Equation in Integrable Systems 10 Advanced Series in Mathematical Physics, World Scientific Publishing Co. Inc. Singapore 10.1142/1021 Search in Google Scholar

[15] Oner, T., Senturk, I. (2017), The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math., 15:926–935. OnerT. SenturkI. 2017 The Sheffer Stroke Operation Reducts of Basic Algebras Open Math. 15 926 935 10.1515/math-2017-0075 Search in Google Scholar

[16] Oner, T., Katican T. and Ulker, A. (2019), Interval Sheffer Stroke Basic Algebras, TWMS J. Appl. Eng. Math., 9(1):134–141. OnerT. KaticanT. UlkerA. 2019 Interval Sheffer Stroke Basic Algebras TWMS J. Appl. Eng. Math. 9 1 134 141 Search in Google Scholar

[17] Oner, T. and Katican T. (2018), On the Solutions of the Set-Theoretical Yang-Baxter Equations in Wajsberg-Algebras, Axioms, 8:1–13. OnerT. KaticanT. 2018 On the Solutions of the Set-Theoretical Yang-Baxter Equations in Wajsberg-Algebras Axioms 8 1 13 10.3390/axioms7010006 Search in Google Scholar

[18] Oner, T. and Katican T. (2019), On solution to the set-theoretical Yang-Baxter equation via BL-algebras, Bull. Int. Math. Virtual Inst., 9(2):207–217. OnerT. KaticanT. 2019 On solution to the set-theoretical Yang-Baxter equation via BL-algebras Bull. Int. Math. Virtual Inst. 9 2 207 217 Search in Google Scholar

[19] Oner, T. and Kalkan, T. (2019), Yang-Baxter Equations in MTL-Algebras, Bulletin of the International Mathematical Virtual Institute, 9:599–607. OnerT. KalkanT. 2019 Yang-Baxter Equations in MTL-Algebras Bulletin of the International Mathematical Virtual Institute 9 599 607 Search in Google Scholar

[20] Oner, T., Senturk, I. and Oner, G. (2017), An Independent Set of Axioms of MV-Algebras and Solutions of the Set-Theoretical Yang-Baxter Equation, Axioms, 6(3):17. OnerT. SenturkI. OnerG. 2017 An Independent Set of Axioms of MV-Algebras and Solutions of the Set-Theoretical Yang-Baxter Equation Axioms 6 3 17 10.3390/axioms6030017 Search in Google Scholar

[21] Perk, J. H. H. and Y. H. Au, Y. H. (2006), Yang-Baxter Equations, in: Encyclopedia of Mathematical Physics(J.-P. Françoise, G. L. Naber, S. T. Tsou, Eds.) 5, 465–473, Elseiver, Oxford, UK. PerkJ. H. H. Y. H. AuY. H. 2006 Yang-Baxter Equations in: Encyclopedia of Mathematical Physics FrançoiseJ.-P. NaberG. L. TsouS. T. Eds. 5 465 473 Elseiver Oxford, UK 10.1016/B0-12-512666-2/00191-7 Search in Google Scholar

[22] Yang, C. N. (1967), Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction, Phys. Rev. Lett., 19:1312–1315. YangC. N. 1967 Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction Phys. Rev. Lett. 19 1312 1315 10.1103/PhysRevLett.19.1312 Search in Google Scholar