Edit Profile (opens in new tab) Rozikov, Utkir A. Compute Distance To: Compute Author ID: rozikov.utkir-a Published as: Rozikov, U. A.; Rozikov, Utkir A.; Rozikov, Utkir; Rozikov, U. External Links: Math-Net.Ru Documents Indexed: 151 Publications since 1996, including 2 Books 1 Contribution as Editor Reviewing Activity: 381 Reviews Co-Authors: 67 Co-Authors with 124 Joint Publications 986 Co-Co-Authors all top 5 Co-Authors 23 single-authored 15 Mukhamedov, Farruh Maksutovich 14 Ganikhodjaev, Nasir Nabievich 11 Ladra González, Manuel 11 Omirov, Bakhrom A. 7 Rahmatullaev, Muzaffar 7 Sattarov, Iskandar A. 6 Haydarov, Farhod Halimjonovich 5 Casas Miras, José Manuel 5 Gandolfo, Daniel 4 Botirov, Golibjon I. 4 Külske, Christof 4 Ruiz, Jean 3 Eshkabilov, Yusup Khalbaevich 3 Suhov, Yurii Mikhailovich 3 Zada, Akbar 3 Zhamilov, U. U. 2 Akin, Hasan 2 Albeverio, Sergio A. 2 Boxonov, Zafar Saydimahmudovich 2 Dzhumadil’daev, Askar Serkulovich 2 Ishankulov, Farruh T. 2 Jamilov, Uygun U. 2 Khakimov, Otabek N. 2 Khamraev, A. Yu. 2 Le Ny, Arnaud 2 Mendes, José F. F. 2 Murodov, Sherzod Normonovich 2 Shoyimardonov, Sobirjon K. 2 Shoyusupov, Sh. A. 2 Usmonov, J. B. 2 Velasco, Maria Victoria 2 Xudayarov, S. S. 1 Absalamov, Akmal T. 1 Bogachev, Leonid V. 1 Cassandro, Marzio 1 Castaños, Octavio 1 Diyorov, A. M. 1 Eshkobilov, Yusup Kh. 1 Ganikhodzhaev, Rasul N. 1 Hardin, A. J. M. 1 Henning, Florian 1 Ibragimov, Zair 1 Imomkulov, A. N. 1 Karimov, M. M. 1 Khaidarov, F. Kh. 1 Khamraev, Murod 1 Labra, Alicia 1 Levenberg, Norman jun. 1 Luna, A. R. 1 Madgoziev, G. T. 1 Mamurov, B. J. 1 Martin, James Benedict 1 Merola, Immacolata 1 Nazarov, Kh. A. 1 Normatov, É. P. 1 Pah, Chin Hee 1 Picco, Pierre 1 Rakhmatullaev, A. M. 1 Sadullaev, Azimbaĭ Sadullaevich 1 Sayitova, M. 1 Shamsiddinov, N. B. 1 Temir, Seyit 1 Tugyonov, Zohid T. 1 Tulenbaev, K. M. 1 Uǧuz, Selman 1 Varro, Richard 1 Yam, S. all top 5 Serials 25 Theoretical and Mathematical Physics 11 Journal of Statistical Physics 8 Lobachevskii Journal of Mathematics 6 Linear Algebra and its Applications 5 Mathematical Notes 5 Uzbek Mathematical Journal 4 Letters in Mathematical Physics 4 Mathematical Physics, Analysis and Geometry 4 Markov Processes and Related Fields 4 Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 3 Journal of Algebra 3 Uzbekskiĭ Matematicheskiĭ Zhurnal 3 Qualitative Theory of Dynamical Systems 3 Journal of Statistical Mechanics: Theory and Experiment 3 International Journal of Biomathematics 3 Journal of Applied Nonlinear Dynamics 2 Journal of Mathematical Biology 2 Linear and Multilinear Algebra 2 Ukraïns’kyĭ Matematychnyĭ Zhurnal 2 Reviews in Mathematical Physics 2 Queueing Systems 2 Algebra Colloquium 2 Sbornik: Mathematics 2 Doklady Akademii Nauk Respubliki Uzbekistan. Matematika, Tekhnicheskie Nauki, Estestvoznanie 2 TWMS Journal of Pure and Applied Mathematics 2 Discontinuity, Nonlinearity, and Complexity 1 Communications in Algebra 1 Communications in Mathematical Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Reports on Mathematical Physics 1 Russian Mathematical Surveys 1 Ukrainian Mathematical Journal 1 Chaos, Solitons and Fractals 1 Osaka Journal of Mathematics 1 Results in Mathematics 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Stochastic Analysis and Applications 1 International Journal of Mathematics 1 Random Structures & Algorithms 1 Indagationes Mathematicae. New Series 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Difference Equations and Applications 1 Electronic Journal of Probability 1 Izvestiya: Mathematics 1 Doklady Mathematics 1 Methods of Functional Analysis and Topology 1 Regular and Chaotic Dynamics 1 Journal of Nonlinear Mathematical Physics 1 Nonlinear Dynamics and Systems Theory 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Central European Journal of Mathematics 1 International Journal of Geometric Methods in Modern Physics 1 Annals of Functional Analysis 1 Springer Proceedings in Mathematics & Statistics 1 Journal of Algebra and Related Topics all top 5 Fields 75 Statistical mechanics, structure of matter (82-XX) 49 Probability theory and stochastic processes (60-XX) 38 Dynamical systems and ergodic theory (37-XX) 30 Combinatorics (05-XX) 26 Biology and other natural sciences (92-XX) 21 Nonassociative rings and algebras (17-XX) 13 Functional analysis (46-XX) 9 Operator theory (47-XX) 7 Field theory and polynomials (12-XX) 6 Number theory (11-XX) 5 Group theory and generalizations (20-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functions of a complex variable (30-XX) 3 Potential theory (31-XX) 3 Quantum theory (81-XX) 2 Associative rings and algebras (16-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 122 Publications have been cited 1,316 times in 362 Documents Cited by ▼ Year ▼ Gibbs measures on Cayley trees. Zbl 1278.82002Rozikov, Utkir A. 86 2013 Quadratic stochastic operators and processes: results and open problems. Zbl 1242.60067Ganikhodzhaev, Rasul; Mukhamedov, Farrukh; Rozikov, Utkir 78 2011 Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree. Zbl 0964.82504Ganikhodzhaev, N. N.; Rozikov, U. A. 57 1997 On Gibbs measures of \(p\)-adic Potts model on the Cayley tree. Zbl 1161.82311Mukhamedov, Farruh M.; Rozikov, Utkir A. 37 2004 On evolution algebras. Zbl 1367.17026Casas, J. M.; Ladra, M.; Omirov, B. A.; Rozikov, U. A. 35 2014 A hard-core model on a Cayley tree: an example of a loss network. Zbl 1139.90338Suhov, Y.; Rozikov, U. A. 33 2004 Partition structures of the group representation of the Cayley tree into cosets by finite-index normal subgroups and their applications to the description of periodic Gibbs distributions. Zbl 0978.82506Rozikov, U. A. 32 1997 The Potts model with countable set of spin values on a Cayley tree. Zbl 1101.82003Ganikhodjaev, N. N.; Rozikov, U. A. 30 2006 On inhomogeneous \(p\)-adic Potts model on a Cayley tree. Zbl 1096.82007Mukhamedov, Farrukh; Rozikov, Utkir 28 2005 Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree. Zbl 1298.82022Külske, C.; Rozikov, U. A.; Khakimov, R. M. 26 2014 On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. Zbl 1061.82007Mukhamedov, Farruh; Rozikov, Utkir 26 2004 The dynamics of strictly non-Volterra quadratic stochastic operators on the 2-simplex. Zbl 1194.47077Zhamilov, U. U.; Rozikov, U. A. 25 2009 \(F\)-quadratic stochastic operators. Zbl 1167.92023Rozikov, U. A.; Zhamilov, U. U. 25 2008 A chain of evolution algebras. Zbl 1220.17026Casas, J. M.; Ladra, M.; Rozikov, U. A. 23 2011 Evolution algebra of a bisexual population. Zbl 1293.17041Ladra, M.; Rozikov, U. A. 21 2013 Gibbs measures for SOS models on a Cayley tree. Zbl 1106.60081Rozikov, U. A.; Suhov, Y. M. 20 2006 A three state hard-core model on a Cayley tree. Zbl 1171.82308Martin, James; Rozikov, Utkir; Suhov, Yuri 19 2005 Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree. Zbl 1157.82311Rozikov, U. A.; Rakhmatullaev, M. M. 18 2008 On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. II. Zbl 1071.82017Mukhamedov, Farruh; Rozikov, Utkir 17 2005 Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model. Zbl 0957.82007Rozikov, U. A. 17 1999 An evolution algebra in population genetics. Zbl 1292.17030Labra, A.; Ladra, M.; Rozikov, U. A. 17 2014 Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree. Zbl 1180.82034Rozikov, U. A.; Rakhmatullaev, M. M. 17 2009 On rational \(p\)-adic dynamical systems. Zbl 1053.37022Mukhamedov, Farruh; Rozikov, Utkir 17 2004 On Ising model with four competing interactions on Cayley tree. Zbl 1185.60112Ganikhodjaev, N. N.; Rozikov, U. A. 16 2009 On nilpotent index and dibaricity of evolution algebras. Zbl 1343.17021Casas, J. M.; Ladra, Manuel; Omirov, B. A.; Rozikov, U. A. 16 2013 Evolution algebras generated by Gibbs measures. Zbl 1260.46031Rozikov, U. A.; Tian, J. P. 15 2011 On dynamics of \(\ell\)-Volterra quadratic stochastic operators. Zbl 1342.92199Rozikov, U. A.; Zada, A. 15 2010 A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree. Zbl 1149.82008Rozikov, U. A. 14 2006 Periodic Gibbs measures for the Potts model on the Cayley tree. Zbl 1286.82006Rozikov, U. A.; Khakimov, R. M. 14 2013 Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Zbl 1252.82026Eshkabilov, Y. K.; Haydarov, F. H.; Rozikov, U. A. 14 2012 Dynamics of two-dimensional evolution algebras. Zbl 1297.37011Rozikov, U. A.; Murodov, Sh. N. 14 2013 Existence of a phase transition for the Potts \(p\)-adic model on the set \(\mathbb{Z}\). Zbl 1031.82013Ganikhodzhaev, N. N.; Mukhamedov, F. M.; Rozikov, U. A. 14 2002 \(p\)-adic \((2,1)\)-rational dynamical systems. Zbl 1302.37056Albeverio, S.; Rozikov, U. A.; Sattarov, I. A. 14 2013 On \(q\)-component models on Cayley tree: contour method. Zbl 1076.82509Rozikov, U. A. 13 2005 Volterra quadratic stochastic operators of a two-sex population. Zbl 1232.47060Rozikov, U. A.; Zhamilov, U. U. 13 2011 On models with uncountable set of spin values on a Cayley tree: integral equations. Zbl 1252.82034Rozikov, Utkir A.; Eshkobilov, Yusup Kh. 13 2010 On \(p\)-adic Gibbs measures for hard core model on a Cayley tree. Zbl 1281.82006Gandolfo, Daniel; Rozikov, Utkir A.; Ruiz, Jean 12 2012 On cubic operators defined on finite-dimensional simplexes. Zbl 1075.37540Rozikov, U. A.; Khamraev, A. Yu. 12 2004 On quadratic stochastic operators generated by Gibbs distributions. Zbl 1164.37309Ganikhodzhaev, N. N.; Rozikov, U. A. 12 2006 Fertile HC models with three states on a Cayley tree. Zbl 1157.82312Rozikov, U. A.; Shoyusupov, Sh. A. 12 2008 \(p\)-adic Gibbs measures and Markov random fields on countable graphs. Zbl 1286.82013Rozikov, U. A.; Khakimov, O. N. 11 2013 On non-Volterra quadratic stochastic operators generated by a product measure. Zbl 1161.37365Rozikov, U. A.; Shamsiddinov, N. B. 11 2009 A contour method on Cayley trees. Zbl 1214.82020Rozikov, U. A. 11 2008 On the uniqueness of Gibbs measures for \(p\)-adic nonhomogeneous \({\lambda}\)-model on the Cayley tree. Zbl 1065.46057Khamraev, Murod; Mukhamedov, Farruh; Rozikov, Utkir 11 2004 Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Zbl 1277.82008Eshkabilov, Yu. Kh.; Haydarov, F. H.; Rozikov, U. A. 11 2013 On a nonlinear \(p\)-adic dynamical system. Zbl 1347.37148Rozikov, U. A.; Sattarov, I. A. 11 2014 Description of all translation-invariant \(p\)-adic Gibbs measures for the Potts model on a Cayley tree. Zbl 1332.82018Rozikov, U. A.; Khakimov, O. N. 10 2015 On construction and a class of non-Volterra cubic stochastic operators. Zbl 1322.37018Rozikov, U. A.; Khamraev, A. Yu. 10 2014 Dibaric and evolution algebras in biology. Zbl 1370.17034Ladra, M.; Omirov, B. A.; Rozikov, U. A. 10 2014 Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree. Zbl 1368.05068Külske, Christof; Rozikov, Utkir A. 10 2017 One-dimensional Ising models with long range interactions: cluster expansion, phase-separating point. Zbl 1297.82006Cassandro, Marzio; Merola, Immacolata; Picco, Pierre; Rozikov, Utkir 9 2014 On real chains of evolution algebras. Zbl 1361.17030Omirov, B. A.; Rozikov, U. A.; Tulenbayev, K. M. 9 2015 Phase transitions for a model with uncountable set of spin values on a Cayley tree. Zbl 1276.05060Eshkabilov, Yu. Kh.; Rozikov, U. A.; Botirov, G. I. 8 2013 Gibbs measures for the SOS model with four states on a Cayley tree. Zbl 1177.82031Rozikov, U. A.; Shoyusupov, Sh. A. 8 2006 A description of harmonic functions via properties of the group representation of the Cayley tree. Zbl 1187.43005Normatov, É. P.; Rozikov, U. A. 8 2006 Chain of evolution algebras of “chicken” population. Zbl 1288.17023Rozikov, U. A.; Murodov, Sh. N. 8 2014 On free energies of the Ising model on the Cayley tree. Zbl 1273.82013Gandolfo, D.; Rakhmatullaev, M. M.; Rozikov, U. A.; Ruiz, J. 8 2013 An introduction to mathematical billiards. Zbl 1417.37028Rozikov, Utkir A. 7 2019 Random walks in random media on a Cayley tree. Zbl 0998.60044Rozikov, U. A. 7 2001 Gibbs measures on Cayley trees: results and open problems. Zbl 1268.60122Rozikov, Utkir A. 7 2013 Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree. Zbl 1311.82005Rozikov, U. A.; Haydarov, F. H. 7 2015 Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. Zbl 1357.82023Kuelske, C.; Rozikov, U. A. 7 2015 On disordered phase in the ferromagnetic Potts model on the Bethe lattice. Zbl 0980.82006Ganikodhjaev, Nasir; Rozikov, Utkir 6 2000 Description of periodic \(p\)-harmonic functions on Cayley tree. Zbl 1188.31004Rozikov, Utkir A.; Ishankulov, Farruh T. 6 2010 A new set of limiting Gibbs measures for the Ising model on a Cayley tree. Zbl 1211.82010Akin, H.; Rozikov, U. A.; Temir, S. 6 2011 Representability of trees and some of their applications. Zbl 1028.82008Rozikov, U. A. 6 2002 Potts model with competing interactions on the Cayley tree: The contour method. Zbl 1157.82308Botirov, G. I.; Rozikov, U. A. 6 2007 On phase transitions for \(p\)-adic Potts model with competing interactions on a Cayley tree. Zbl 1152.82309Mukhamedov, F. M.; Rozikov, U. A.; Mendes, J. F. F. 6 2006 Constrained evolution algebras and dynamical systems of a bisexual population. Zbl 1382.17022Dzhumadil’daev, A.; Omirov, B. A.; Rozikov, U. A. 6 2016 Ocean ecosystem discrete time dynamics generated by \(\ell\)-Volterra operators. Zbl 07036869Rozikov, U. A.; Shoyimardonov, S. K. 5 2019 Solvability criteria for the equation \(x^q=a\) in the field of \(p\)-adic numbers. Zbl 1296.11157Casas, J. M.; Omirov, B. A.; Rozikov, U. A. 5 2014 The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model. Zbl 1282.82017Rozikov, U. A.; Khakimov, R. M. 5 2012 New phase transitions of the Ising model on Cayley trees. Zbl 1292.82005Gandolfo, D.; Haydarov, F. H.; Rozikov, U. A.; Ruiz, J. 5 2013 On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field. Zbl 1457.82114Bogachev, Leonid V.; Rozikov, Utkir A. 5 2019 Four competing interactions for models with an uncountable set of spin values on a Cayley tree. Zbl 1387.82015Rozikov, U. A.; Haydarov, F. H. 5 2017 Tree-hierarchy of DNA and distribution of Holliday junctions. Zbl 1383.92060Rozikov, U. A. 5 2017 \(p\)-adic dynamical systems of (2,2)-rational functions with unique fixed point. Zbl 1380.37155Rozikov, U. A.; Sattarov, I. A. 4 2017 Description of limit Gibbs measures for \(\lambda\)-models on Bethe lattices. Zbl 1071.82523Rozikov, U. A. 4 1998 On a class of evolution algebras of “chicken” population. Zbl 1339.17022Dzhumadil’daev, A.; Omirov, B. A.; Rozikov, U. A. 4 2014 On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree. Zbl 1121.82014Mukhamedov, Farrukh; Rozikov, Utkir; Mendes, José F. F. 4 2007 Countably periodic Gibbs measures of the Ising model on the Cayley tree. Zbl 1031.82016Rozikov, U. A. 4 2002 Gibbs measures for the fertile three-state hard-core models on a Cayley tree. Zbl 1369.82010Rozikov, U. A.; Khakimov, R. M. 4 2015 On \(l\)-Volterra quadratic stochastic operators. Zbl 1263.47073Rozikov, U. A.; Zada, A. 4 2009 Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees. Zbl 1376.82027Gandolfo, D.; Rahmatullaev, M. M.; Rozikov, U. A. 4 2017 A discrete-time dynamical system and an evolution algebra of mosquito population. Zbl 1409.92210Rozikov, U. A.; Velasco, M. V. 3 2019 Gradient Gibbs measures for the SOS model with countable values on a Cayley tree. Zbl 1431.82014Henning, Florian; Külske, Christof; Le Ny, Arnaud; Rozikov, Utkir A. 3 2019 A polynomial \(p\)-adic dynamical system. Zbl 1294.37033Mukhamedov, F. M.; Rozikov, U. A. 3 2012 Periodic Gibbs measures for the Ising model with competing interactions. Zbl 1178.82019Nazarov, Kh. A.; Rozikov, U. A. 3 2003 Flow of finite-dimensional algebras. Zbl 1406.17048Ladra, M.; Rozikov, U. A. 3 2017 Dynamical systems generated by a gonosomal evolution operator. Zbl 1349.37090Rozikov, Utkir A.; Varro, Richard 3 2016 Holliday junctions for the Potts model of DNA. Zbl 1403.05153Rozikov, Utkir 3 2018 \(p\)-adic dynamical systems of the function \(\frac{ax}{x^2+a}\). Zbl 1441.37105Rozikov, U. A.; Sattarov, I. A.; Yam, S. 3 2019 A group representation of the Cayley forest and some of its applications. Zbl 1065.82005Ganikhodzhaev, N. N.; Rozikov, U. A. 3 2003 On a class of separable quadratic stochastic operators. Zbl 1267.37057Rozikov, U. A.; Zada, A. 3 2011 Algebras of cubic matrices. Zbl 1369.16030Ladra, M.; Rozikov, U. A. 3 2017 A quasi-strictly non-Volterra quadratic stochastic operator. Zbl 1434.37033Hardin, A. J. M.; Rozikov, U. A. 2 2019 Free energies of the Potts model on a Cayley tree. Zbl 1434.82027Rozikov, U. A.; Rakhmatullaev, M. M. 2 2017 Analytic methods in the theory of quantum quadratic stochastic processes. Zbl 1165.81336Ganikhodjaev, N. N.; Mukhamedov, F. M.; Rozikov, U. A. 2 2000 Nonuniqueness of a Gibbs measure for a model on the Cayley tree. Zbl 1274.82025Rozikov, U. A.; Madgoziev, G. T. 2 2011 Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree. Zbl 1401.82009Rozikov, U. A.; Khakimov, R. M.; Khaidarov, F. Kh. 2 2018 Leslie’s prey-predator model in discrete time. Zbl 1464.92233Rozikov, U. A.; Shoyimardonov, S. K. 2 2020 Dynamical systems of the \(p\)-adic (2, 2)-rational functions with two fixed points. Zbl 1445.37077Rozikov, U. A.; Sattarov, I. A. 1 2020 Dynamics of a population with two equal dominated species. Zbl 1448.37123Rozikov, U. A.; Usmonov, J. B. 1 2020 Quadratic stochastic processes of type \((\sigma|\mu)\). Zbl 07303968Mamurov, B. J.; Rozikov, U. A.; Xudayarov, S. S. 1 2020 An introduction to mathematical billiards. Zbl 1417.37028Rozikov, Utkir A. 7 2019 Ocean ecosystem discrete time dynamics generated by \(\ell\)-Volterra operators. Zbl 07036869Rozikov, U. A.; Shoyimardonov, S. K. 5 2019 On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field. Zbl 1457.82114Bogachev, Leonid V.; Rozikov, Utkir A. 5 2019 A discrete-time dynamical system and an evolution algebra of mosquito population. Zbl 1409.92210Rozikov, U. A.; Velasco, M. V. 3 2019 Gradient Gibbs measures for the SOS model with countable values on a Cayley tree. Zbl 1431.82014Henning, Florian; Külske, Christof; Le Ny, Arnaud; Rozikov, Utkir A. 3 2019 \(p\)-adic dynamical systems of the function \(\frac{ax}{x^2+a}\). Zbl 1441.37105Rozikov, U. A.; Sattarov, I. A.; Yam, S. 3 2019 A quasi-strictly non-Volterra quadratic stochastic operator. Zbl 1434.37033Hardin, A. J. M.; Rozikov, U. A. 2 2019 Markov processes of cubic stochastic matrices: quadratic stochastic processes. Zbl 1481.60143Casas, J. M.; Ladra, M.; Rozikov, U. A. 1 2019 Holliday junctions for the Potts model of DNA. Zbl 1403.05153Rozikov, Utkir 3 2018 Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree. Zbl 1401.82009Rozikov, U. A.; Khakimov, R. M.; Khaidarov, F. Kh. 2 2018 Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree. Zbl 1398.82013Rozikov, U. A.; Botirov, G. I. 1 2018 Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree. Zbl 1368.05068Külske, Christof; Rozikov, Utkir A. 10 2017 Four competing interactions for models with an uncountable set of spin values on a Cayley tree. Zbl 1387.82015Rozikov, U. A.; Haydarov, F. H. 5 2017 Tree-hierarchy of DNA and distribution of Holliday junctions. Zbl 1383.92060Rozikov, U. A. 5 2017 \(p\)-adic dynamical systems of (2,2)-rational functions with unique fixed point. Zbl 1380.37155Rozikov, U. A.; Sattarov, I. A. 4 2017 Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees. Zbl 1376.82027Gandolfo, D.; Rahmatullaev, M. M.; Rozikov, U. A. 4 2017 Flow of finite-dimensional algebras. Zbl 1406.17048Ladra, M.; Rozikov, U. A. 3 2017 Algebras of cubic matrices. Zbl 1369.16030Ladra, M.; Rozikov, U. A. 3 2017 Free energies of the Potts model on a Cayley tree. Zbl 1434.82027Rozikov, U. A.; Rakhmatullaev, M. M. 2 2017 Construction of a set of \(p\)-adic distributions. Zbl 1387.82028Rozikov, U. A.; Tugyonov, Z. T. 1 2017 On subalgebras of an evolution algebra of a “chicken” population. Zbl 1430.17105Omirov, B. A.; Rozikov, U. A. 1 2017 Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones. Zbl 1457.82087Rahmatullaev, M. M.; Rozikov, U. A. 1 2017 Construction of flows of finite-dimensional algebras. Zbl 1421.17007Ladra, M.; Rozikov, U. A. 1 2017 Constrained evolution algebras and dynamical systems of a bisexual population. Zbl 1382.17022Dzhumadil’daev, A.; Omirov, B. A.; Rozikov, U. A. 6 2016 Dynamical systems generated by a gonosomal evolution operator. Zbl 1349.37090Rozikov, Utkir A.; Varro, Richard 3 2016 Description of all translation-invariant \(p\)-adic Gibbs measures for the Potts model on a Cayley tree. Zbl 1332.82018Rozikov, U. A.; Khakimov, O. N. 10 2015 On real chains of evolution algebras. Zbl 1361.17030Omirov, B. A.; Rozikov, U. A.; Tulenbayev, K. M. 9 2015 Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree. Zbl 1311.82005Rozikov, U. A.; Haydarov, F. H. 7 2015 Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. Zbl 1357.82023Kuelske, C.; Rozikov, U. A. 7 2015 Gibbs measures for the fertile three-state hard-core models on a Cayley tree. Zbl 1369.82010Rozikov, U. A.; Khakimov, R. M. 4 2015 On evolution algebras. Zbl 1367.17026Casas, J. M.; Ladra, M.; Omirov, B. A.; Rozikov, U. A. 35 2014 Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree. Zbl 1298.82022Külske, C.; Rozikov, U. A.; Khakimov, R. M. 26 2014 An evolution algebra in population genetics. Zbl 1292.17030Labra, A.; Ladra, M.; Rozikov, U. A. 17 2014 On a nonlinear \(p\)-adic dynamical system. Zbl 1347.37148Rozikov, U. A.; Sattarov, I. A. 11 2014 On construction and a class of non-Volterra cubic stochastic operators. Zbl 1322.37018Rozikov, U. A.; Khamraev, A. Yu. 10 2014 Dibaric and evolution algebras in biology. Zbl 1370.17034Ladra, M.; Omirov, B. A.; Rozikov, U. A. 10 2014 One-dimensional Ising models with long range interactions: cluster expansion, phase-separating point. Zbl 1297.82006Cassandro, Marzio; Merola, Immacolata; Picco, Pierre; Rozikov, Utkir 9 2014 Chain of evolution algebras of “chicken” population. Zbl 1288.17023Rozikov, U. A.; Murodov, Sh. N. 8 2014 Solvability criteria for the equation \(x^q=a\) in the field of \(p\)-adic numbers. Zbl 1296.11157Casas, J. M.; Omirov, B. A.; Rozikov, U. A. 5 2014 On a class of evolution algebras of “chicken” population. Zbl 1339.17022Dzhumadil’daev, A.; Omirov, B. A.; Rozikov, U. A. 4 2014 Exact solution of a generalized ANNNI model on a Cayley tree. Zbl 1304.82016Rozikov, U. A.; Akin, H.; Uğuz, S. 2 2014 Normal subgroups of finite index for the group representation of the Cayley tree. Zbl 1317.20028Rozikov, U. A.; Haydarov, F. H. 2 2014 Gibbs measures on Cayley trees. Zbl 1278.82002Rozikov, Utkir A. 86 2013 Evolution algebra of a bisexual population. Zbl 1293.17041Ladra, M.; Rozikov, U. A. 21 2013 On nilpotent index and dibaricity of evolution algebras. Zbl 1343.17021Casas, J. M.; Ladra, Manuel; Omirov, B. A.; Rozikov, U. A. 16 2013 Periodic Gibbs measures for the Potts model on the Cayley tree. Zbl 1286.82006Rozikov, U. A.; Khakimov, R. M. 14 2013 Dynamics of two-dimensional evolution algebras. Zbl 1297.37011Rozikov, U. A.; Murodov, Sh. N. 14 2013 \(p\)-adic \((2,1)\)-rational dynamical systems. Zbl 1302.37056Albeverio, S.; Rozikov, U. A.; Sattarov, I. A. 14 2013 \(p\)-adic Gibbs measures and Markov random fields on countable graphs. Zbl 1286.82013Rozikov, U. A.; Khakimov, O. N. 11 2013 Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Zbl 1277.82008Eshkabilov, Yu. Kh.; Haydarov, F. H.; Rozikov, U. A. 11 2013 Phase transitions for a model with uncountable set of spin values on a Cayley tree. Zbl 1276.05060Eshkabilov, Yu. Kh.; Rozikov, U. A.; Botirov, G. I. 8 2013 On free energies of the Ising model on the Cayley tree. Zbl 1273.82013Gandolfo, D.; Rakhmatullaev, M. M.; Rozikov, U. A.; Ruiz, J. 8 2013 Gibbs measures on Cayley trees: results and open problems. Zbl 1268.60122Rozikov, Utkir A. 7 2013 New phase transitions of the Ising model on Cayley trees. Zbl 1292.82005Gandolfo, D.; Haydarov, F. H.; Rozikov, U. A.; Ruiz, J. 5 2013 Classification of \(p\)-adic 6-dimensional filiform Leibniz algebras by solutions of \(x^q=a\). Zbl 1272.17007Ladra, Manuel; Omirov, Bakhrom A.; Rozikov, Utkir A. 2 2013 Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Zbl 1252.82026Eshkabilov, Y. K.; Haydarov, F. H.; Rozikov, U. A. 14 2012 On \(p\)-adic Gibbs measures for hard core model on a Cayley tree. Zbl 1281.82006Gandolfo, Daniel; Rozikov, Utkir A.; Ruiz, Jean 12 2012 The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model. Zbl 1282.82017Rozikov, U. A.; Khakimov, R. M. 5 2012 A polynomial \(p\)-adic dynamical system. Zbl 1294.37033Mukhamedov, F. M.; Rozikov, U. A. 3 2012 Quadratic stochastic operators and processes: results and open problems. Zbl 1242.60067Ganikhodzhaev, Rasul; Mukhamedov, Farrukh; Rozikov, Utkir 78 2011 A chain of evolution algebras. Zbl 1220.17026Casas, J. M.; Ladra, M.; Rozikov, U. A. 23 2011 Evolution algebras generated by Gibbs measures. Zbl 1260.46031Rozikov, U. A.; Tian, J. P. 15 2011 Volterra quadratic stochastic operators of a two-sex population. Zbl 1232.47060Rozikov, U. A.; Zhamilov, U. U. 13 2011 A new set of limiting Gibbs measures for the Ising model on a Cayley tree. Zbl 1211.82010Akin, H.; Rozikov, U. A.; Temir, S. 6 2011 On a class of separable quadratic stochastic operators. Zbl 1267.37057Rozikov, U. A.; Zada, A. 3 2011 Nonuniqueness of a Gibbs measure for a model on the Cayley tree. Zbl 1274.82025Rozikov, U. A.; Madgoziev, G. T. 2 2011 System of recursive equations for the partition functions of 1D models. Zbl 1257.82030Rozikov, U. A. 1 2011 On dynamics of \(\ell\)-Volterra quadratic stochastic operators. Zbl 1342.92199Rozikov, U. A.; Zada, A. 15 2010 On models with uncountable set of spin values on a Cayley tree: integral equations. Zbl 1252.82034Rozikov, Utkir A.; Eshkobilov, Yusup Kh. 13 2010 Description of periodic \(p\)-harmonic functions on Cayley tree. Zbl 1188.31004Rozikov, Utkir A.; Ishankulov, Farruh T. 6 2010 Separable quadratic stochastic operators. Zbl 1304.37033Rozikov, U. A.; Nazir, S. 2 2010 Description of \(p\)-harmonic functions on the Cayley tree. Zbl 1200.35310Rozikov, U. A.; Ishankulov, F. T. 1 2010 The dynamics of strictly non-Volterra quadratic stochastic operators on the 2-simplex. Zbl 1194.47077Zhamilov, U. U.; Rozikov, U. A. 25 2009 Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree. Zbl 1180.82034Rozikov, U. A.; Rakhmatullaev, M. M. 17 2009 On Ising model with four competing interactions on Cayley tree. Zbl 1185.60112Ganikhodjaev, N. N.; Rozikov, U. A. 16 2009 On non-Volterra quadratic stochastic operators generated by a product measure. Zbl 1161.37365Rozikov, U. A.; Shamsiddinov, N. B. 11 2009 On \(l\)-Volterra quadratic stochastic operators. Zbl 1263.47073Rozikov, U. A.; Zada, A. 4 2009 \(F\)-quadratic stochastic operators. Zbl 1167.92023Rozikov, U. A.; Zhamilov, U. U. 25 2008 Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree. Zbl 1157.82311Rozikov, U. A.; Rakhmatullaev, M. M. 18 2008 Fertile HC models with three states on a Cayley tree. Zbl 1157.82312Rozikov, U. A.; Shoyusupov, Sh. A. 12 2008 A contour method on Cayley trees. Zbl 1214.82020Rozikov, U. A. 11 2008 Potts model with competing interactions on the Cayley tree: The contour method. Zbl 1157.82308Botirov, G. I.; Rozikov, U. A. 6 2007 On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree. Zbl 1121.82014Mukhamedov, Farrukh; Rozikov, Utkir; Mendes, José F. F. 4 2007 The Potts model with countable set of spin values on a Cayley tree. Zbl 1101.82003Ganikhodjaev, N. N.; Rozikov, U. A. 30 2006 Gibbs measures for SOS models on a Cayley tree. Zbl 1106.60081Rozikov, U. A.; Suhov, Y. M. 20 2006 A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree. Zbl 1149.82008Rozikov, U. A. 14 2006 On quadratic stochastic operators generated by Gibbs distributions. Zbl 1164.37309Ganikhodzhaev, N. N.; Rozikov, U. A. 12 2006 Gibbs measures for the SOS model with four states on a Cayley tree. Zbl 1177.82031Rozikov, U. A.; Shoyusupov, Sh. A. 8 2006 A description of harmonic functions via properties of the group representation of the Cayley tree. Zbl 1187.43005Normatov, É. P.; Rozikov, U. A. 8 2006 On phase transitions for \(p\)-adic Potts model with competing interactions on a Cayley tree. Zbl 1152.82309Mukhamedov, F. M.; Rozikov, U. A.; Mendes, J. F. F. 6 2006 On \(q\)-component models on the Cayley tree: the general case. Zbl 1456.82096Botirov, G. I.; Rozikov, U. A. 1 2006 On inhomogeneous \(p\)-adic Potts model on a Cayley tree. Zbl 1096.82007Mukhamedov, Farrukh; Rozikov, Utkir 28 2005 A three state hard-core model on a Cayley tree. Zbl 1171.82308Martin, James; Rozikov, Utkir; Suhov, Yuri 19 2005 On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. II. Zbl 1071.82017Mukhamedov, Farruh; Rozikov, Utkir 17 2005 On \(q\)-component models on Cayley tree: contour method. Zbl 1076.82509Rozikov, U. A. 13 2005 On Gibbs measures of \(p\)-adic Potts model on the Cayley tree. Zbl 1161.82311Mukhamedov, Farruh M.; Rozikov, Utkir A. 37 2004 ...and 22 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 250 Authors 97 Rozikov, Utkir A. 75 Mukhamedov, Farruh Maksutovich 21 Jamilov, Uygun U. 21 Rahmatullaev, Muzaffar 20 Khakimov, Otabek N. 19 Ladra González, Manuel 16 Omirov, Bakhrom A. 15 Saburov, Mansoor 14 Haydarov, Farhod Halimjonovich 13 Ganikhodjaev, Nasir Nabievich 12 Botirov, Golibjon I. 9 Qaralleh, Izzat 9 Souissi, Abdessatar 8 Embong, Ahmad Fadillah 8 Paniello, Irene 7 Akin, Hasan 7 Külske, Christof 6 Eshkabilov, Yusup Khalbaevich 6 Sattarov, Iskandar A. 6 Velasco, Maria Victoria 5 Cabrera Casado, Yolanda 5 Endo, Eric Ossami 5 Gandolfo, Daniel 5 Ganikhodzhaev, Rasul N. 5 Khatamov, N. M. 5 Liao, Lingmin 5 Pah, Chin Hee 5 Saburov, Mansur Kh. 5 Siles Molina, Mercedes 5 van Enter, Aernout C. D. 4 Bissacot, Rodrigo 4 Casas Miras, José Manuel 4 Fan, Shilei 4 Murodov, Sherzod Normonovich 4 Pułka, Małgorzata 4 Rasulova, M. A. 4 Ruiz, Jean 3 Accardi, Luigi 3 Ahmad, Mohd Ali Khameini 3 Barhoumi, Abdessatar 3 Bartoszek, Krzysztof 3 El Gheteb, Soueidy 3 Garcia, Ronaldo A. 3 Khamraev, Murod 3 Khrennikov, Andreĭ Yur’evich 3 Khudoyberdiyev, Abror Kh. 3 Le Ny, Arnaud 3 Ouattara, Moussa 3 Pirnapasov, Abror T. 3 Reznik, Dan S. 3 Savadogo, Souleymane 3 Scheutzow, Michael K. R. 3 Shahidi, Farruh 3 Tugyonov, Zohid T. 2 Ahmad, Muhammad Zaini 2 Al-Shutnawi, Basma M. 2 Alsarayreh, Abdelwahab 2 Athreya, Siva R. 2 Ban, Jungchao 2 Bandyopadhyay, Antar 2 Cadavid, Paula 2 Calderón Martín, Antonio Jesús 2 Camacho, Luisa Maria 2 Chang, Chih-Hung 2 Dasgupta, Amites 2 Doğan, Mutlay 2 Dragovich, Branko 2 Dzhumadil’daev, Askar Serkulovich 2 Falcón Ganfornina, Óscar Jesús 2 Falcón Ganfornina, Raúl Manuel 2 Fan, Ai Hua 2 Hu, Yueyun 2 Ishankulov, Farruh T. 2 Jahnel, Benedikt 2 Khaidarov, F. Kh. 2 Koiller, Jair 2 Kozyrev, Sergeĭ Vladimirovich 2 Kurganov, K. A. 2 Labra, Alicia 2 Madgoziev, G. T. 2 Makhammadaliev, M. T. 2 Mendes, José F. F. 2 Mukhitdinov, R. T. 2 Nodirov, Shohruh Dilmurodovich 2 Núñez-Valdés, Juan 2 Picco, Pierre 2 Reinfelds, Andrejs 2 Rodiño Montoya, Mary Luz 2 Rodríguez, Pablo M. 2 Shi, Zhan 2 Shlosman, Senya B. 2 Shoyimardonov, Sobirjon K. 2 Shoyusupov, Sh. A. 2 Suhov, Yurii Mikhailovich 2 Temir, Seyit 2 Volovich, Igor’ Vasil’evich 2 Wang, Yuefei 2 Zada, Akbar 2 Zhamilov, U. 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