Rajkumar, Rahul; Weisbart, David Components and exit times of Brownian motion in two or more \(p\)-adic dimensions. (English) Zbl 07823634 J. Fourier Anal. Appl. 29, No. 6, Paper No. 75, 28 p. (2023). MSC: 60-XX 35-XX PDFBibTeX XMLCite \textit{R. Rajkumar} and \textit{D. Weisbart}, J. Fourier Anal. Appl. 29, No. 6, Paper No. 75, 28 p. (2023; Zbl 07823634) Full Text: DOI arXiv OA License
Mukhamedov, Farrukh; Khakimov, Otabek \(p\)-adic phase transitions for countable state Potts model. (English) Zbl 07784854 Math. Methods Appl. Sci. 46, No. 13, 14104-14119 (2023). MSC: 82Bxx 82Cxx PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{O. Khakimov}, Math. Methods Appl. Sci. 46, No. 13, 14104--14119 (2023; Zbl 07784854) Full Text: DOI
Bikulov, A. Kh.; Zubarev, A. P. Oscillations in \(p\)-adic diffusion processes and simulation of the conformational dynamics of protein. (English) Zbl 07778256 \(p\)-Adic Numbers Ultrametric Anal. Appl. 15, No. 3, 169-186 (2023). MSC: 82Cxx 82Dxx 82Bxx PDFBibTeX XMLCite \textit{A. Kh. Bikulov} and \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 15, No. 3, 169--186 (2023; Zbl 07778256) Full Text: DOI arXiv
Sarfraz, Naqash; Gürbüz, Ferit Weak and strong boundedness for \(p\)-adic fractional Hausdorff operator and its commutator. (English) Zbl 07773901 Int. J. Nonlinear Sci. Numer. Simul. 24, No. 6, 2281-2292 (2023). MSC: 42B35 26D15 46B25 47G10 PDFBibTeX XMLCite \textit{N. Sarfraz} and \textit{F. Gürbüz}, Int. J. Nonlinear Sci. Numer. Simul. 24, No. 6, 2281--2292 (2023; Zbl 07773901) Full Text: DOI arXiv
Rahmatullaev, Muzaffar; Tukhtabaev, Akbarkhuja Some non-periodic \(p\)-adic generalized Gibbs measures for the Ising model on a Cayley tree of order \(k\). (English) Zbl 07749836 Math. Phys. Anal. Geom. 26, No. 3, Paper No. 22, 23 p. (2023). Reviewer: Sergey Ludkovsky (Moskva) MSC: 82B20 82B26 60D99 37P20 26E30 05C90 PDFBibTeX XMLCite \textit{M. Rahmatullaev} and \textit{A. Tukhtabaev}, Math. Phys. Anal. Geom. 26, No. 3, Paper No. 22, 23 p. (2023; Zbl 07749836) Full Text: DOI
Mukhamedov, F. M.; Rahmatullaev, M. M.; Tukhtabaev, A. M.; Mamadjonov, R. The \(p\)-adic Ising model in an external field on a Cayley tree: periodic Gibbs measures. (English. Russian original) Zbl 1521.82005 Theor. Math. Phys. 216, No. 2, 1238-1253 (2023); translation from Teor. Mat. Fiz. 216, No. 2, 383-400 (2023). MSC: 82B20 82B28 82B26 82B27 82B41 PDFBibTeX XMLCite \textit{F. M. Mukhamedov} et al., Theor. Math. Phys. 216, No. 2, 1238--1253 (2023; Zbl 1521.82005); translation from Teor. Mat. Fiz. 216, No. 2, 383--400 (2023) Full Text: DOI
Franchini, Simone Replica symmetry breaking without replicas. (English) Zbl 1515.82155 Ann. Phys. 450, Article ID 169220, 35 p. (2023). MSC: 82D30 60F10 PDFBibTeX XMLCite \textit{S. Franchini}, Ann. Phys. 450, Article ID 169220, 35 p. (2023; Zbl 1515.82155) Full Text: DOI arXiv
Bikulov, A. Kh.; Zubarev, A. P. The sojourn time problem for a \(p\)-adic random walk and its applications. (English) Zbl 1515.60126 \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 4, 265-278 (2022). MSC: 60G50 26E30 PDFBibTeX XMLCite \textit{A. Kh. Bikulov} and \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 4, 265--278 (2022; Zbl 1515.60126) Full Text: DOI arXiv
Rahmatullaev, Muzaffar; Tukhtabaev, Akbarkhuja On periodic \(p\)-adic generalized Gibbs measures for Ising model on a Cayley tree. (English) Zbl 1508.37054 Lett. Math. Phys. 112, No. 6, Paper No. 112, 18 p. (2022). MSC: 37E25 39A60 82B20 PDFBibTeX XMLCite \textit{M. Rahmatullaev} and \textit{A. Tukhtabaev}, Lett. Math. Phys. 112, No. 6, Paper No. 112, 18 p. (2022; Zbl 1508.37054) Full Text: DOI
Weisbart, David Estimates of certain exit probabilities for \(p\)-adic Brownian bridges. (English) Zbl 1507.60051 J. Theor. Probab. 35, No. 3, 1878-1897 (2022). MSC: 60G22 60B15 PDFBibTeX XMLCite \textit{D. Weisbart}, J. Theor. Probab. 35, No. 3, 1878--1897 (2022; Zbl 1507.60051) Full Text: DOI arXiv
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V. Giorgio Parisi: the Nobel Prize in Physics 2021. (English) Zbl 1489.01023 \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 1, 81-83 (2022). MSC: 01A70 82-03 PDFBibTeX XMLCite \textit{B. Dragovich} et al., \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 1, 81--83 (2022; Zbl 1489.01023) Full Text: DOI
Mukhamedov, Farrukh; Khakimov, Otabek Chaos in \(p\)-adic statistical lattice models: Potts model. (English) Zbl 1504.30064 Zúñiga-Galindo, W. A. (ed.) et al., Advances in non-Archimedean analysis and applications. The \(p\)-adic methodology in STEAM-H. Cham: Springer. STEAM-H, Sci. Technol. Eng. Agric. Math. Health, 115-165 (2021). MSC: 30G06 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{O. Khakimov}, in: Advances in non-Archimedean analysis and applications. The \(p\)-adic methodology in STEAM-H. Cham: Springer. 115--165 (2021; Zbl 1504.30064) Full Text: DOI
Bikulov, A. Kh.; Zubarev, A. P. Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin. (English) Zbl 1515.92037 Physica A 583, Article ID 126280, 19 p. (2021). MSC: 92C45 35S05 35Q92 60J76 82C44 PDFBibTeX XMLCite \textit{A. Kh. Bikulov} and \textit{A. P. Zubarev}, Physica A 583, Article ID 126280, 19 p. (2021; Zbl 1515.92037) Full Text: DOI arXiv
Tukhtabaev, Akbarkhuja On \(G_2\)-periodic quasi Gibbs measures of \(p\)-adic Potts model on a Cayley tree. (English) Zbl 1477.82006 \(p\)-Adic Numbers Ultrametric Anal. Appl. 13, No. 4, 291-307 (2021). MSC: 82B20 46S10 82B26 05C05 60K35 PDFBibTeX XMLCite \textit{A. Tukhtabaev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 13, No. 4, 291--307 (2021; Zbl 1477.82006) Full Text: DOI
Weisbart, David On infinitesimal generators and Feynman-Kac integrals of adelic diffusion. (English) Zbl 1480.60003 J. Math. Phys. 62, No. 10, Article ID 103504, 22 p. (2021). MSC: 60B05 60J60 11R56 PDFBibTeX XMLCite \textit{D. Weisbart}, J. Math. Phys. 62, No. 10, Article ID 103504, 22 p. (2021; Zbl 1480.60003) Full Text: DOI arXiv
Sarfraz, Naqash; Aslam, Muhammad; Jarad, Fahd Boundedness for commutators of rough \(p\)-adic Hardy operator on \(p\)-adic central Morrey spaces. (English) Zbl 1485.42032 J. Funct. Spaces 2021, Article ID 4886197, 5 p. (2021). MSC: 42B20 42B25 42B35 42B30 46S10 46E30 PDFBibTeX XMLCite \textit{N. Sarfraz} et al., J. Funct. Spaces 2021, Article ID 4886197, 5 p. (2021; Zbl 1485.42032) Full Text: DOI
Hussain, Amjad; Sarfraz, Naqash; Khan, Ilyas; Alqahtani, Aisha M. Estimates for commutators of bilinear fractional \(p\)-adic Hardy operator on Herz-type spaces. (English) Zbl 1480.42029 J. Funct. Spaces 2021, Article ID 6615604, 7 p. (2021). Reviewer: Michael Perelmuter (Kyïv) MSC: 42B25 42B35 42B30 47S10 26A33 PDFBibTeX XMLCite \textit{A. Hussain} et al., J. Funct. Spaces 2021, Article ID 6615604, 7 p. (2021; Zbl 1480.42029) Full Text: DOI
Ny, A. Le; Liao, L.; Rozikov, U. A. \(p\)-adic boundary laws and Markov chains on trees. (English) Zbl 1462.82015 Lett. Math. Phys. 110, No. 10, 2725-2741 (2020). Reviewer: Hasan Akin (Gaziantep) MSC: 82B26 46S10 12J12 60K35 60J20 05C05 PDFBibTeX XMLCite \textit{A. Le Ny} et al., Lett. Math. Phys. 110, No. 10, 2725--2741 (2020; Zbl 1462.82015) Full Text: DOI arXiv
Kozyrev, Sergei V. Learning problem for functional programming and model of biological evolution. (English) Zbl 1447.92288 \(p\)-Adic Numbers Ultrametric Anal. Appl. 12, No. 2, 112-122 (2020). MSC: 92D15 92D10 68T05 PDFBibTeX XMLCite \textit{S. V. Kozyrev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 12, No. 2, 112--122 (2020; Zbl 1447.92288) Full Text: DOI
Antoniouk, Alexandra V.; Khrennikov, Andrei Yu.; Kochubei, Anatoly N. Multidimensional nonlinear pseudo-differential evolution equation with \(p\)-adic spatial variables. (English) Zbl 1454.35423 J. Pseudo-Differ. Oper. Appl. 11, No. 1, 311-343 (2020). Reviewer: Manuel Cruz-López (Guanajuato) MSC: 35S10 47J35 11S80 60J25 76S05 35K65 35R11 PDFBibTeX XMLCite \textit{A. V. Antoniouk} et al., J. Pseudo-Differ. Oper. Appl. 11, No. 1, 311--343 (2020; Zbl 1454.35423) Full Text: DOI arXiv
Bakken, Erik; Weisbart, David \(p\)-adic Brownian motion as a limit of discrete time random walks. (English) Zbl 07068255 Commun. Math. Phys. 369, No. 2, 371-402 (2019). MSC: 47Bxx 60Gxx PDFBibTeX XMLCite \textit{E. Bakken} and \textit{D. Weisbart}, Commun. Math. Phys. 369, No. 2, 371--402 (2019; Zbl 07068255) Full Text: DOI
Kozyrev, S. V. Biology as a constructive physics. (English) Zbl 1419.92022 \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 4, 305-311 (2018). MSC: 92D15 82B99 PDFBibTeX XMLCite \textit{S. V. Kozyrev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 4, 305--311 (2018; Zbl 1419.92022) Full Text: DOI arXiv
Zúñiga-Galindo, W. A. Non-Archimedean replicator dynamics and Eigen’s paradox. (English) Zbl 1411.92228 J. Phys. A, Math. Theor. 51, No. 50, Article ID 505601, 26 p. (2018). MSC: 92D15 11S80 35S10 PDFBibTeX XMLCite \textit{W. A. Zúñiga-Galindo}, J. Phys. A, Math. Theor. 51, No. 50, Article ID 505601, 26 p. (2018; Zbl 1411.92228) Full Text: DOI arXiv
Bikulov, A. Kh.; Zubarev, A. P. Model of \(p\)-adic random walk in a potential. (English) Zbl 1402.60052 \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 2, 130-150 (2018). MSC: 60G50 82B41 PDFBibTeX XMLCite \textit{A. Kh. Bikulov} and \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 2, 130--150 (2018; Zbl 1402.60052) Full Text: DOI arXiv
Zúñiga-Galindo, W. A. Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems. (English) Zbl 1397.80009 Nonlinearity 31, No. 6, 2590-2616 (2018). Reviewer: Aleksey Syromyasov (Saransk) MSC: 80A99 11S80 12J12 45K05 46S10 60J60 82B41 PDFBibTeX XMLCite \textit{W. A. Zúñiga-Galindo}, Nonlinearity 31, No. 6, 2590--2616 (2018; Zbl 1397.80009) Full Text: DOI arXiv
Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia; de Jesús Correa, María Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management. (English) Zbl 1404.81028 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 375, No. 2106, Article ID 20160398, 23 p. (2017). MSC: 81P15 62P35 PDFBibTeX XMLCite \textit{M. Á. Lozada Aguilar} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 375, No. 2106, Article ID 20160398, 23 p. (2017; Zbl 1404.81028) Full Text: DOI
Oleschko, K.; Khrennikov, Andrei Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity. (English) Zbl 1382.92112 Russ. J. Math. Phys. 24, No. 4, 505-516 (2017). MSC: 92C35 76Z05 35R02 PDFBibTeX XMLCite \textit{K. Oleschko} and \textit{A. Khrennikov}, Russ. J. Math. Phys. 24, No. 4, 505--516 (2017; Zbl 1382.92112) Full Text: DOI
Oleschko, K.; Khrennikov, A. Yu. Applications of \(p\)-adics to geophysics: linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions. (English. Russian original) Zbl 1387.86020 Theor. Math. Phys. 190, No. 1, 154-163 (2017); translation from Teor. Mat. Fiz. 190, No. 1, 179-190 (2017). MSC: 86A05 86A99 60J60 76T20 76B45 PDFBibTeX XMLCite \textit{K. Oleschko} and \textit{A. Yu. Khrennikov}, Theor. Math. Phys. 190, No. 1, 154--163 (2017; Zbl 1387.86020); translation from Teor. Mat. Fiz. 190, No. 1, 179--190 (2017) Full Text: DOI
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V.; Zelenov, E. I. \(p\)-adic mathematical physics: the first 30 years. (English) Zbl 1394.81009 \(p\)-Adic Numbers Ultrametric Anal. Appl. 9, No. 2, 87-121 (2017). Reviewer: Diana Maimut (Bucharest) MSC: 81-03 81T30 11F33 83F05 92D20 PDFBibTeX XMLCite \textit{B. Dragovich} et al., \(p\)-Adic Numbers Ultrametric Anal. Appl. 9, No. 2, 87--121 (2017; Zbl 1394.81009) Full Text: DOI arXiv
Mukhamedov, Farrukh; Khakimov, Otabek Phase transition and chaos: \(p\)-adic Potts model on a Cayley tree. (English) Zbl 1355.37106 Chaos Solitons Fractals 87, 190-196 (2016). MSC: 37N20 46S10 39A70 47S10 60K35 82B20 82B26 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{O. Khakimov}, Chaos Solitons Fractals 87, 190--196 (2016; Zbl 1355.37106) Full Text: DOI
Mukhamedov, F.; Khakimov, O. On periodic Gibbs measures of \(p\)-adic Potts model on a Cayley tree. (English) Zbl 1356.82022 \(p\)-Adic Numbers Ultrametric Anal. Appl. 8, No. 3, 225-235 (2016). Reviewer: Guy Jumarie (Montréal) MSC: 82C20 82B30 26E30 05C05 82C26 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{O. Khakimov}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 8, No. 3, 225--235 (2016; Zbl 1356.82022) Full Text: DOI
Sizova, O. M. Ultrametric diffusion in a strong centrally symmetric field. (Russian. English summary) Zbl 1424.60090 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 19, No. 1, 87-104 (2015). MSC: 60J60 60J80 PDFBibTeX XMLCite \textit{O. M. Sizova}, Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 19, No. 1, 87--104 (2015; Zbl 1424.60090) Full Text: DOI MNR
Kozyrev, S. V. Ultrametricity in the theory of complex systems. (English. Russian original) Zbl 1342.93018 Theor. Math. Phys. 185, No. 2, 1665-1677 (2015); translation from Teor. Mat. Fiz. 185, No. 2, 346-360 (2015). MSC: 93A15 93A13 94C15 92D10 PDFBibTeX XMLCite \textit{S. V. Kozyrev}, Theor. Math. Phys. 185, No. 2, 1665--1677 (2015; Zbl 1342.93018); translation from Teor. Mat. Fiz. 185, No. 2, 346--360 (2015) Full Text: DOI
Mukhamedov, Farrukh Renormalization method in \(p\)-adic \(\lambda\)-model on the Cayley tree. (English) Zbl 1334.82046 Int. J. Theor. Phys. 54, No. 10, 3577-3595 (2015). Reviewer: Dominik Strzałka (Rzeszów) MSC: 82C28 82C26 05C05 PDFBibTeX XMLCite \textit{F. Mukhamedov}, Int. J. Theor. Phys. 54, No. 10, 3577--3595 (2015; Zbl 1334.82046) Full Text: DOI arXiv
Bikulov, A. Kh.; Zubarev, A. P. Application of \(p\)-adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into \(\mathbb{Q}_p\). (English) Zbl 1323.60098 \(p\)-Adic Numbers Ultrametric Anal. Appl. 7, No. 2, 121-132 (2015). MSC: 60J25 60G10 26E30 35S05 PDFBibTeX XMLCite \textit{A. Kh. Bikulov} and \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 7, No. 2, 121--132 (2015; Zbl 1323.60098) Full Text: DOI arXiv
Khrennikov, Andrei; Kozyrev, Sergei; Månsson, Alf Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift. (English) Zbl 1323.82037 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, No. 2, Article ID 1550013, 16 p. (2015). MSC: 82C44 45J05 35K57 92C37 PDFBibTeX XMLCite \textit{A. Khrennikov} et al., Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, No. 2, Article ID 1550013, 16 p. (2015; Zbl 1323.82037) Full Text: DOI arXiv
Mukhamedov, Farrukh; Dogan, Mutlay On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions. (English) Zbl 1321.82020 Rep. Math. Phys. 75, No. 1, 25-46 (2015). Reviewer: Guy Jumarie (Montréal) MSC: 82B26 46S10 12J12 39A70 47H10 60K35 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{M. Dogan}, Rep. Math. Phys. 75, No. 1, 25--46 (2015; Zbl 1321.82020) Full Text: DOI
Mukhamedov, Farrukh; Dogan, Mutlay; Akin, Hasan Phase transition for the \(p\)-adic Ising – vannimenus model on the Cayley tree. (English) Zbl 1456.82160 J. Stat. Mech. Theory Exp. 2014, No. 10, Paper No. P10031, 21 p. (2014). MSC: 82B20 05C05 82B23 82B26 82B28 PDFBibTeX XMLCite \textit{F. Mukhamedov} et al., J. Stat. Mech. Theory Exp. 2014, No. 10, Paper No. P10031, 21 p. (2014; Zbl 1456.82160) Full Text: DOI
Mukhamedov, Farrukh On the strong phase transition for the one-dimensional countable state \(p\)-adic Potts model. (English) Zbl 1456.82159 J. Stat. Mech. Theory Exp. 2014, No. 1, Paper No. P01007, 23 p. (2014). MSC: 82B20 PDFBibTeX XMLCite \textit{F. Mukhamedov}, J. Stat. Mech. Theory Exp. 2014, No. 1, Paper No. P01007, 23 p. (2014; Zbl 1456.82159) Full Text: DOI
Zubarev, A. P. On stochastic generation of ultrametrics in high-dimensional Euclidean spaces. (English) Zbl 1315.60020 \(p\)-Adic Numbers Ultrametric Anal. Appl. 6, No. 2, 155-165 (2014). MSC: 60D05 54E35 82D30 PDFBibTeX XMLCite \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 6, No. 2, 155--165 (2014; Zbl 1315.60020) Full Text: DOI arXiv
Sizova, O. M. A method for solving the \(p\)-adic Kolmogorov-Feller equation for an ultrametric random walk in an axially symmetric external field. (English. Russian original) Zbl 1441.60071 J. Math. Sci., New York 203, No. 6, 884-891 (2014); translation from Fundam. Prikl. Mat. 18, No. 2, 197-207 (2013). MSC: 60J99 35R09 82C41 PDFBibTeX XMLCite \textit{O. M. Sizova}, J. Math. Sci., New York 203, No. 6, 884--891 (2014; Zbl 1441.60071); translation from Fundam. Prikl. Mat. 18, No. 2, 197--207 (2013) Full Text: DOI
Avetisov, V. A.; Bikulov, A. Kh.; Zubarev, A. P. Ultrametric random walk and dynamics of protein molecules. (English. Russian original) Zbl 1311.60040 Proc. Steklov Inst. Math. 285, 3-25 (2014); translation from Tr. Mat. Inst. Steklova 285, 9-32 (2014). Reviewer: Ivan Křivý (Ostrava) MSC: 60G18 92C40 92C45 PDFBibTeX XMLCite \textit{V. A. Avetisov} et al., Proc. Steklov Inst. Math. 285, 3--25 (2014; Zbl 1311.60040); translation from Tr. Mat. Inst. Steklova 285, 9--32 (2014) Full Text: DOI
Mukhamedov, Farrukh; Akın, Hasan Phase transitions for \(p\)-adic Potts model on the Cayley tree of order three. (English) Zbl 1456.82825 J. Stat. Mech. Theory Exp. 2013, No. 7, Paper No. P07014, 30 p. (2013). MSC: 82C40 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{H. Akın}, J. Stat. Mech. Theory Exp. 2013, No. 7, Paper No. P07014, 30 p. (2013; Zbl 1456.82825) Full Text: DOI arXiv
Torba, S. M.; Zúñiga-Galindo, W. A. Parabolic type equations and Markov stochastic processes on adeles. (English) Zbl 1333.35126 J. Fourier Anal. Appl. 19, No. 4, 792-835 (2013). Reviewer: Cristina Pérez-García (Santander) MSC: 35K90 60J25 35S10 47S10 35K08 35R60 PDFBibTeX XMLCite \textit{S. M. Torba} and \textit{W. A. Zúñiga-Galindo}, J. Fourier Anal. Appl. 19, No. 4, 792--835 (2013; Zbl 1333.35126) Full Text: DOI arXiv
Mukhamedov, F.; Akin, H. The \(p\)-adic Potts model on the Cayley tree of order three. (English. Russian original) Zbl 1286.82004 Theor. Math. Phys. 176, No. 3, 1267-1279 (2013); translation from Teor. Mat. Fiz. 176, No. 3, 513-529 (2013). MSC: 82B20 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{H. Akin}, Theor. Math. Phys. 176, No. 3, 1267--1279 (2013; Zbl 1286.82004); translation from Teor. Mat. Fiz. 176, No. 3, 513--529 (2013) Full Text: DOI
Mukhamedov, Farrukh On dynamical systems and phase transitions for \(q + 1\)-state \(p\)-adic Potts model on the Cayley tree. (English) Zbl 1280.46047 Math. Phys. Anal. Geom. 16, No. 1, 49-87 (2013). Reviewer: Hasan Akin (Gaziantep) MSC: 46S10 82B26 82B20 37N20 PDFBibTeX XMLCite \textit{F. Mukhamedov}, Math. Phys. Anal. Geom. 16, No. 1, 49--87 (2013; Zbl 1280.46047) Full Text: DOI arXiv
Mukhamedov, Farrukh Existence of \(p\)-adic quasi Gibbs measure for countable state Potts model on the Cayley tree. (English) Zbl 1281.46062 J. Inequal. Appl. 2012, Paper No. 104, 12 p. (2012). MSC: 46S10 82B26 12J12 PDFBibTeX XMLCite \textit{F. Mukhamedov}, J. Inequal. Appl. 2012, Paper No. 104, 12 p. (2012; Zbl 1281.46062) Full Text: DOI arXiv
Avetisov, Vladik Avanesovich; Bikulov, Al’bert Khakimovich; Zubarev, Aleksandr Petrovich Mathematical modeling of molecular “nano-machines”. (Russian. English summary) Zbl 1449.82018 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 2011, No. 1(22), 9-15 (2011). MSC: 82D80 82D60 92-08 PDFBibTeX XMLCite \textit{V. A. Avetisov} et al., Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 2011, No. 1(22), 9--15 (2011; Zbl 1449.82018) Full Text: DOI MNR
Kozyrev, S. V. Methods and applications of ultrametric and \(p\)-adic analysis: from wavelet theory to biophysics. (English. Russian original) Zbl 1298.42038 Proc. Steklov Inst. Math. 274, Suppl. 1, S1-S84 (2011); translation from Sovrem. Probl. Mat. 12, 5-168 (2008). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 42C40 11Z05 11S80 35S05 43A70 47G30 82C44 92C05 92D10 PDFBibTeX XMLCite \textit{S. V. Kozyrev}, Proc. Steklov Inst. Math. 274, S1--S84 (2011; Zbl 1298.42038); translation from Sovrem. Probl. Mat. 12, 5--168 (2008) Full Text: DOI
Dolgopolov, Mikhail V.; Zubarev, Alexander P. Some aspects of \(m\)-adic analysis and its applications to \(m\)-adic stochastic processes. (English) Zbl 1268.60076 \(p\)-Adic Numbers Ultrametric Anal. Appl. 3, No. 1, 39-51 (2011). MSC: 60G99 46N30 46S10 PDFBibTeX XMLCite \textit{M. V. Dolgopolov} and \textit{A. P. Zubarev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 3, No. 1, 39--51 (2011; Zbl 1268.60076) Full Text: DOI arXiv
Kozyrev, S. V.; Khrennikov, A. Yu. \(p\)-adic integral operators in wavelet bases. (English. Russian original) Zbl 1250.42093 Dokl. Math. 83, No. 2, 209-212 (2011); translation from Dokl. Akad. Nauk 437, No. 4, 457-461 (2011). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 42C40 11S80 47G10 PDFBibTeX XMLCite \textit{S. V. Kozyrev} and \textit{A. Yu. Khrennikov}, Dokl. Math. 83, No. 2, 209--212 (2011; Zbl 1250.42093); translation from Dokl. Akad. Nauk 437, No. 4, 457--461 (2011) Full Text: DOI
Gutkin, B.; Osipov, V. A. Spectral problem of block-rectangular hierarchical matrices. (English) Zbl 1218.82025 J. Stat. Phys. 143, No. 1, 72-87 (2011). Reviewer: Dominik Strzałka (Rzeszów) MSC: 82D30 82D99 15B99 PDFBibTeX XMLCite \textit{B. Gutkin} and \textit{V. A. Osipov}, J. Stat. Phys. 143, No. 1, 72--87 (2011; Zbl 1218.82025) Full Text: DOI arXiv
Albeverio, S.; Khrennikov, A. Yu.; Shelkovich, V. M. The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory. (English) Zbl 1218.47071 J. Math. Anal. Appl. 375, No. 1, 82-98 (2011). Reviewer: Hartmut Fuehr (Aachen) MSC: 47G30 42C40 46S10 47J35 35S11 PDFBibTeX XMLCite \textit{S. Albeverio} et al., J. Math. Anal. Appl. 375, No. 1, 82--98 (2011; Zbl 1218.47071) Full Text: DOI
Bradley, Patrick Erik From image processing to topological modelling with \(p\)-adic numbers. (English) Zbl 1260.94008 \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 4, 293-304 (2010). MSC: 94A08 55U15 11S99 68T45 PDFBibTeX XMLCite \textit{P. E. Bradley}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 4, 293--304 (2010; Zbl 1260.94008) Full Text: DOI
Mukhamedov, Farrukh On \(p\)-adic quasi Gibbs measures for \(q+1\)-state Potts model on the Cayley tree. (English) Zbl 1268.82007 \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 3, 241-251 (2010). MSC: 82B20 60K35 PDFBibTeX XMLCite \textit{F. Mukhamedov}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 3, 241--251 (2010; Zbl 1268.82007) Full Text: DOI
King, Emily J.; Skopina, Maria A. Quincunx multiresolution analysis for \(L^2(\mathbb Q^2_2)\). (English) Zbl 1273.42036 \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 3, 222-231 (2010). Reviewer: Stamatis Koumandos (Nicosia) MSC: 42C40 11S80 PDFBibTeX XMLCite \textit{E. J. King} and \textit{M. A. Skopina}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 3, 222--231 (2010; Zbl 1273.42036) Full Text: DOI
Kozyrev, Sergei V. Dynamics on rugged landscapes of energy and ultrametric diffusion. (English) Zbl 1253.82040 \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 2, 122-132 (2010). MSC: 82B41 60J60 PDFBibTeX XMLCite \textit{S. V. Kozyrev}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 2, 122--132 (2010; Zbl 1253.82040) Full Text: DOI
Bikulov, Albert Kh. Problem of the first passage time for \(p\)-adic diffusion. (English) Zbl 1255.60010 \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 2, 89-99 (2010). Reviewer: Michael Voit (Dortmund) MSC: 60B15 60J60 60J75 PDFBibTeX XMLCite \textit{A. Kh. Bikulov}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 2, No. 2, 89--99 (2010; Zbl 1255.60010) Full Text: DOI
Kozyrev, S. V.; Khrennikov, A. Yu. 2-adic numbers in genetics and Rumer’s symmetry. (English. Russian original) Zbl 1402.92299 Dokl. Math. 81, No. 1, 128-130 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 430, No. 1, 32-34 (2010). MSC: 92D10 PDFBibTeX XMLCite \textit{S. V. Kozyrev} and \textit{A. Yu. Khrennikov}, Dokl. Math. 81, No. 1, 128--130 (2010; Zbl 1402.92299); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 430, No. 1, 32--34 (2010) Full Text: DOI
Khrennikov, A. Yu.; Shelkovich, V. M. Non-Haar \(p\)-adic wavelets and their application to pseudo-differential operators and equations. (English) Zbl 1184.46066 Appl. Comput. Harmon. Anal. 28, No. 1, 1-23 (2010). Reviewer: Cristina Pérez-García (Santander) MSC: 46S10 47S10 42C40 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{V. M. Shelkovich}, Appl. Comput. Harmon. Anal. 28, No. 1, 1--23 (2010; Zbl 1184.46066) Full Text: DOI arXiv
Khrennikov, Andrei Yu.; Kozyrev, S. V. 2-adic clustering of the PAM matrix. (English) Zbl 1403.92071 J. Theor. Biol. 261, No. 3, 396-406 (2009). MSC: 92C40 62P10 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{S. V. Kozyrev}, J. Theor. Biol. 261, No. 3, 396--406 (2009; Zbl 1403.92071) Full Text: DOI HAL
Khrennikov, Andrei Yu. Gene expression from polynomial dynamics in the 2-adic information space. (English) Zbl 1198.37144 Chaos Solitons Fractals 42, No. 1, 341-347 (2009). MSC: 37N40 92D10 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov}, Chaos Solitons Fractals 42, No. 1, 341--347 (2009; Zbl 1198.37144) Full Text: DOI arXiv
Dragovich, B.; Dragovich, A. Yu. A \(p\)-adic model of DNA sequence and genetic code. (English) Zbl 1187.92039 \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 1, 34-41 (2009). MSC: 92C40 92D10 92-08 PDFBibTeX XMLCite \textit{B. Dragovich} and \textit{A. Yu. Dragovich}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 1, 34--41 (2009; Zbl 1187.92039) Full Text: DOI arXiv
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V. On \(p\)-adic mathematical physics. (English) Zbl 1187.81004 \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 1, 1-17 (2009). Reviewer: Olaf Ninnemann (Berlin) MSC: 81-02 81Q65 00A69 11S80 12J25 PDFBibTeX XMLCite \textit{B. Dragovich} et al., \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 1, 1--17 (2009; Zbl 1187.81004) Full Text: DOI arXiv
Mukhamedov, Farrukh On the existence of generalized Gibbs measures for the one-dimensional \(p\)-adic countable state Potts model. (English. Russian original) Zbl 1187.82027 Proc. Steklov Inst. Math. 265, 165-176 (2009); translation from Tr. Mat. Inst. Steklova 265, 177-188 (2009). Reviewer: Dominik Strzałka (Rzeszów) MSC: 82B20 11E95 11S82 PDFBibTeX XMLCite \textit{F. Mukhamedov}, Proc. Steklov Inst. Math. 265, 165--176 (2009; Zbl 1187.82027); translation from Tr. Mat. Inst. Steklova 265, 177--188 (2009) Full Text: DOI arXiv
Lukierska-Walasek, K.; Topolski, K. Hausdorff dimension and hierarchical system dynamics. (English. Russian original) Zbl 1181.37005 Proc. Steklov Inst. Math. 265, 148-153 (2009); translation from Tr. Mat. Inst. Steklova 265, 159-164 (2009). Reviewer: Igor Andrianov (Köln) MSC: 37A50 PDFBibTeX XMLCite \textit{K. Lukierska-Walasek} and \textit{K. Topolski}, Proc. Steklov Inst. Math. 265, 148--153 (2009; Zbl 1181.37005); translation from Tr. Mat. Inst. Steklova 265, 159--164 (2009) Full Text: DOI arXiv
Khrennikov, Andrei; Mukhamedov, Farrukh On uniqueness of Gibbs measure for \(p\)-adic countable state Potts model on the Cayley tree. (English) Zbl 1185.46051 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5327-5331 (2009). MSC: 46S10 82B26 82B20 PDFBibTeX XMLCite \textit{A. Khrennikov} and \textit{F. Mukhamedov}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5327--5331 (2009; Zbl 1185.46051) Full Text: DOI
Avetisov, V. A.; Zhuravlev, Yu. N. An evolutionary interpretation of the \(p\)-adic ultrametric diffusion equation. (English. Russian original) Zbl 1162.35074 Dokl. Math. 75, No. 3, 453-455 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 414, No. 3, 309-312 (2007). Reviewer: Luigi Rodino (Torino) MSC: 35S05 35K57 35Q92 92E20 PDFBibTeX XMLCite \textit{V. A. Avetisov} and \textit{Yu. N. Zhuravlev}, Dokl. Math. 75, No. 3, 453--455 (2007; Zbl 1162.35074); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 414, No. 3, 309--312 (2007) Full Text: DOI
Fan, Ai-Hua; Li, Ming-Tian; Yao, Jia-Yan; Zhou, Dan Strict ergodicity of affine \(p\)-adic dynamical systems on \(\mathbb Z_p\). (English) Zbl 1121.37010 Adv. Math. 214, No. 2, 666-700 (2007). MSC: 37A45 11S85 37A25 37B05 PDFBibTeX XMLCite \textit{A.-H. Fan} et al., Adv. Math. 214, No. 2, 666--700 (2007; Zbl 1121.37010) Full Text: DOI
Konno, Norio Continuous-time quantum walks on ultrametric spaces. (English) Zbl 1107.81015 Int. J. Quantum Inf. 4, No. 6, 1023-1035 (2006). MSC: 81P68 82C41 05C85 68W05 PDFBibTeX XMLCite \textit{N. Konno}, Int. J. Quantum Inf. 4, No. 6, 1023--1035 (2006; Zbl 1107.81015) Full Text: DOI arXiv
Khrennikov, A. Yu.; Kozyrev, S. V. Ultrametric random field. (English) Zbl 1154.60323 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 2, 199-213 (2006). MSC: 60G15 60G60 60H15 60H40 60J99 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{S. V. Kozyrev}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 2, 199--213 (2006; Zbl 1154.60323) Full Text: DOI arXiv
Khrennikov, A. Yu.; Kozyrev, S. V. \(p\)-adic pseudodifferential operators and analytic continuation of replica matrices. (English) Zbl 1179.47064 Theor. Math. Phys. 144, No. 2, 1166-1170 (2005); translation from Teor. Mat. Fiz. 144, No. 2, 336-341 (2005). MSC: 47S10 47G30 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{S. V. Kozyrev}, Theor. Math. Phys. 144, No. 2, 1166--1170 (2005; Zbl 1179.47064); translation from Teor. Mat. Fiz. 144, No. 2, 336--341 (2005) Full Text: DOI
Kozyrev, S. V.; Osipov, V. Al.; Avetisov, V. A. Nondegenerate ultrametric diffusion. (English) Zbl 1110.60070 J. Math. Phys. 46, No. 6, 063302, 15 p. (2005). MSC: 60J35 47D07 47G10 82C70 82D30 PDFBibTeX XMLCite \textit{S. V. Kozyrev} et al., J. Math. Phys. 46, No. 6, 063302, 15 p. (2005; Zbl 1110.60070) Full Text: DOI arXiv
Khrennikov, A. Yu.; Kozyrev, S. V. Wavelets on ultrametric spaces. (English) Zbl 1079.42028 Appl. Comput. Harmon. Anal. 19, No. 1, 61-76 (2005). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 42C40 46S10 47S10 PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{S. V. Kozyrev}, Appl. Comput. Harmon. Anal. 19, No. 1, 61--76 (2005; Zbl 1079.42028) Full Text: DOI
Khrennikov, Andrei Probabilistic pathway representation of cognitive information. (English) Zbl 1465.92004 J. Theor. Biol. 231, No. 4, 597-613 (2004). MSC: 92B20 91E10 11E95 PDFBibTeX XMLCite \textit{A. Khrennikov}, J. Theor. Biol. 231, No. 4, 597--613 (2004; Zbl 1465.92004) Full Text: DOI arXiv