## Tirozzi, Brunello

Compute Distance To:
 Author ID: tirozzi.brunello Published as: Tirozzi, B.; Tirozzi, Brunello
 Documents Indexed: 95 Publications since 1977, including 2 Books 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 56 Co-Authors with 79 Joint Publications 1,371 Co-Co-Authors
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### Co-Authors

 1 single-authored 32 Dobrokhotov, Sergei Yurievich 17 Shcherbina, Mariya 10 Feng, Jianfeng 7 Nazaikinskii, Vladimir E. 6 Albeverio, Sergio A. 4 Bianchi, Daniela 4 Reutskiy, Sergiy Yu 4 Shafarevich, Andreĭ Igorevich 3 Ferraro, Enrico 3 Khrennikov, Andreĭ Yur’evich 3 Klevin, A. I. 3 Rotundo, Giulia 3 Sergeev, Sergeĭ Alekseevich 2 Abundo, Mario 2 Agliari, Elena 2 Anikin, A. Yu. 2 Barra, Adriano 2 Campanino, Massimo 2 Lifits, S. A. 2 Minenkov, Dmitrii S. 2 Pastur, Leonid Andreevich 2 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 2 Semenov, E. S. 2 Tudorovskii, T. Ya. 1 Alladio, F. 1 Brown, David 1 Bruschi, Antonella 1 Buratti, P. 1 Calogero, Raffaele A. 1 Capocaccia, D. 1 Cardinali, Alessandro 1 Cassandro, Marzio 1 Corsini, Stefano 1 De Smedt, Stany 1 Del Grosso, Gabriella 1 Dobrushin, Roland L’vovich 1 Doria, Serena 1 Dorotheyev, E. A. 1 Gawȩdzki, Krzysztof 1 Grushin, V. V. 1 Krüger, Norbert 1 Kupiainen, Antti 1 Lifits, Sergei 1 Limongiello, Alessandro 1 Marasco, Addolorata 1 Marchetti, Cristina 1 Marie, Helene 1 Mele, Giovanni 1 Micozzi, P. 1 Migliore, Michele 1 Minasyan, V. B. 1 Morusci, Sara 1 Nekrasov, R. V. 1 Olivieri, Enzo 1 Pittalis, Stefano 1 Pontrelli, Giuseppe 1 Puca, Silvia 1 Rossoni, Enrico 1 Scacciatelli, E. 1 Semënov, Evgeniĭ Mikhaĭlovich 1 Sinitsyn, S. O. 1 Tartaglia, Giangaetano 1 Tavani, Flavia 1 Tolchennikov, Anton A. 1 Vargas, Carlos A. 1 Wei, Gang 1 You, Gongqiang 1 Zegarlinski, Boguslaw 1 Zucchi, R.
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### Serials

 14 Russian Journal of Mathematical Physics 6 Communications in Mathematical Physics 6 Mathematical and Computer Modelling 6 Journal of Physics A: Mathematical and General 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 Theoretical and Mathematical Physics 4 Doklady Mathematics 4 Markov Processes and Related Fields 3 Computers & Mathematics with Applications 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Helvetica Physica Acta 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Doklady Akademii Nauk 2 Computer Assisted Mechanics and Engineering Sciences 2 Communications on Pure and Applied Analysis 1 International Journal of Modern Physics B 1 Biological Cybernetics 1 Journal of Engineering Mathematics 1 Prikladnaya Matematika i Mekhanika 1 Bollettino della Unione Matemàtica Italiana. Serie VI. C. Analisi Funzionale e Applicazioni 1 Bollettino della Unione Matemàtica Italiana. Serie VI. A 1 Bollettino della Unione Matemàtica Italiana. Serie VI. B 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Journal of Computational Neuroscience 1 International Journal of Theoretical and Applied Finance 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of Statistical Mechanics: Theory and Experiment 1 Series on Advances in Mathematics for Applied Sciences 1 Modeling and Simulation in Science, Engineering and Technology
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### Fields

 30 Partial differential equations (35-XX) 28 Statistical mechanics, structure of matter (82-XX) 24 Fluid mechanics (76-XX) 22 Biology and other natural sciences (92-XX) 19 Probability theory and stochastic processes (60-XX) 11 Computer science (68-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Geophysics (86-XX) 6 Numerical analysis (65-XX) 5 Statistics (62-XX) 5 Quantum theory (81-XX) 4 Systems theory; control (93-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

62 Publications have been cited 428 times in 249 Documents Cited by Year
Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336
Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B.
2008
The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095
Dobrushin, R. L.; Tirozzi, Brunello
1977
Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2007
Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092
Pastur, L.; Shcherbina, M.; Tirozzi, B.
1994
$$p$$-adic dynamical systems. Zbl 0974.37018
Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S.
1998
Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301
Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A.
2009
Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036
Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B.
2011
Localized solutions of one-dimensional non-linear shallow-water equations with velocity $$c=\sqrt x$$. Zbl 1196.35161
Dobrokhotov, S. Yu; Tirozzi, B.
2010
Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2013
Rigorous solution of the Gardner problem. Zbl 1034.82042
Shcherbina, Mariya; Tirozzi, Brunello
2003
Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya.
2006
Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012
Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B.
2013
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055
Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B.
2007
The free energy of a class of Hopfield models. Zbl 1097.82551
Shcherbina, M.; Tirozzi, B.
1993
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107
Shcherbina, Mariya; Tirozzi, Brunello
2012
Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009
Cassandro, M.; Olivieri, E.; Tirozzi, B.
1982
A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082
Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B.
1997
On the replica symmetric equations for the Hopfield model. Zbl 0988.82024
Pastur, L.; Shcherbina, M.; Tirozzi, B.
1999
Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya.
2006
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163
Shcherbina, Mariya; Tirozzi, Brunello
2010
Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003
Albeverio, S.; Tirozzi, B.; Zegarlinski, B.
1992
$$p$$-adic dynamical systems and neural networks. Zbl 1010.82027
Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello
1999
Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074
Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B.
1997
Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163
Scacciatelli, E.; Tirozzi, B.
1992
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054
Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B.
2008
Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello
2013
Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057
Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B.
2011
Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325
Reutskiy, S.; Rossoni, E.; Tirozzi, B.
2003
Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123
Reutskiy, S. Yu.; Tirozzi, B.
1999
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Asymptotics of shallow water equations on the sphere. Zbl 1311.76012
Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A.
2014
Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2005
The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099
Feng, Jianfeng; Tirozzi, Brunello
1995
An introduction to the mathematical theory of neural networks. Zbl 0965.68083
Albeverio, S.; Tirozzi, B.
1997
On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2015
On the critical capacity of the Hopfield model. Zbl 1038.82069
Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello
2001
On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005
Shcherbina, Maria; Tirozzi, Brunello
2002
A note on minimum-variance theory and beyond. Zbl 1048.37073
Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello
2004
Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049
Dobrokhotov, S.; Semenov, E.; Tirozzi, B.
2003
On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530
Dobrokhotov, S. Yu.; Tirozzi, B.
2002
Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003
Dotsenko, V. S.; Tirozzi, B.
1991
Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070
Feng, J. F.; Tirozzi, B.
1997
Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B.
2017
A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307
Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello
2005
Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091
Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello
1979
Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004
Reutskiy, S.; Tirozzi, B.
2007
Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818
Agliari, Elena; Barra, Adriano; Tirozzi, Brunello
2019
Trefftz spectral method for initial-boundary problems. Zbl 0951.65100
Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello
1997
Neural networks and sea time series. Recontruction and extreme-event analysis. Zbl 1094.62121
Tirozzi, Brunello; Puca, Silvia; Pittalis, Stefano; Bruschi, Antonella; Morusci, Sara; Ferraro, Enrico; Corsini, Stefano
2006
Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032
Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello
2016
Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B.
2016
Learning of $$p$$-adic neural networks. Zbl 1078.82521
Khrennikov, Andrei; Tirozzi, Brunello
2000
Generalization and learning error for nonlinear perceptron. Zbl 1168.91512
Shcherbina, M.; Tirozzi, B.
2002
The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026
Abundo, M.; Tirozzi, B.
1984
Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002
Der, R.; Dotsenko, V. S.; Tirozzi, B.
1992
Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063
Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q
2007
Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067
Feng, Jianfeng; Tirozzi, B.; Zucchi, R.
1996
The local central limit theorem for a Gibbs random field. Zbl 0421.60091
Campanino, M.; Capocaccia, D.; Tirozzi, B.
1979
Borel summability of the perturbation series in a hierarchical $$\lambda (\nabla \Phi)^ 4$$ model. Zbl 0587.60099
Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B.
1984
On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109
Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele
2012
Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818
Agliari, Elena; Barra, Adriano; Tirozzi, Brunello
2019
Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B.
2017
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032
Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello
2016
Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B.
2016
On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2015
Asymptotics of shallow water equations on the sphere. Zbl 1311.76012
Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A.
2014
Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2013
Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012
Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B.
2013
Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello
2013
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107
Shcherbina, Mariya; Tirozzi, Brunello
2012
On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109
Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele
2012
Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036
Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B.
2011
Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057
Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B.
2011
Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Localized solutions of one-dimensional non-linear shallow-water equations with velocity $$c=\sqrt x$$. Zbl 1196.35161
Dobrokhotov, S. Yu; Tirozzi, B.
2010
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163
Shcherbina, Mariya; Tirozzi, Brunello
2010
Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B.
2010
Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301
Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A.
2009
Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336
Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B.
2008
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054
Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B.
2008
Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2007
Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055
Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B.
2007
Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004
Reutskiy, S.; Tirozzi, B.
2007
Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063
Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q
2007
Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya.
2006
Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311
Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya.
2006
Neural networks and sea time series. Recontruction and extreme-event analysis. Zbl 1094.62121
Tirozzi, Brunello; Puca, Silvia; Pittalis, Stefano; Bruschi, Antonella; Morusci, Sara; Ferraro, Enrico; Corsini, Stefano
2006
Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506
Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I.
2005
A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307
Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello
2005
A note on minimum-variance theory and beyond. Zbl 1048.37073
Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello
2004
Rigorous solution of the Gardner problem. Zbl 1034.82042
Shcherbina, Mariya; Tirozzi, Brunello
2003
Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325
Reutskiy, S.; Rossoni, E.; Tirozzi, B.
2003
Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049
Dobrokhotov, S.; Semenov, E.; Tirozzi, B.
2003
On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005
Shcherbina, Maria; Tirozzi, Brunello
2002
On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530
Dobrokhotov, S. Yu.; Tirozzi, B.
2002
Generalization and learning error for nonlinear perceptron. Zbl 1168.91512
Shcherbina, M.; Tirozzi, B.
2002
On the critical capacity of the Hopfield model. Zbl 1038.82069
Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello
2001
Learning of $$p$$-adic neural networks. Zbl 1078.82521
Khrennikov, Andrei; Tirozzi, Brunello
2000
On the replica symmetric equations for the Hopfield model. Zbl 0988.82024
Pastur, L.; Shcherbina, M.; Tirozzi, B.
1999
$$p$$-adic dynamical systems and neural networks. Zbl 1010.82027
Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello
1999
Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123
Reutskiy, S. Yu.; Tirozzi, B.
1999
$$p$$-adic dynamical systems. Zbl 0974.37018
Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S.
1998
A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082
Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B.
1997
Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074
Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B.
1997
An introduction to the mathematical theory of neural networks. Zbl 0965.68083
Albeverio, S.; Tirozzi, B.
1997
Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070
Feng, J. F.; Tirozzi, B.
1997
Trefftz spectral method for initial-boundary problems. Zbl 0951.65100
Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello
1997
Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067
Feng, Jianfeng; Tirozzi, B.; Zucchi, R.
1996
The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099
Feng, Jianfeng; Tirozzi, Brunello
1995
The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092
Pastur, L.; Shcherbina, M.; Tirozzi, B.
1994
The free energy of a class of Hopfield models. Zbl 1097.82551
Shcherbina, M.; Tirozzi, B.
1993
Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003
Albeverio, S.; Tirozzi, B.; Zegarlinski, B.
1992
Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163
Scacciatelli, E.; Tirozzi, B.
1992
Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002
Der, R.; Dotsenko, V. S.; Tirozzi, B.
1992
Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003
Dotsenko, V. S.; Tirozzi, B.
1991
The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026
Abundo, M.; Tirozzi, B.
1984
Borel summability of the perturbation series in a hierarchical $$\lambda (\nabla \Phi)^ 4$$ model. Zbl 0587.60099
Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B.
1984
Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009
Cassandro, M.; Olivieri, E.; Tirozzi, B.
1982
Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091
Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello
1979
The local central limit theorem for a Gibbs random field. Zbl 0421.60091
Campanino, M.; Capocaccia, D.; Tirozzi, B.
1979
The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095
Dobrushin, R. L.; Tirozzi, Brunello
1977
all top 5

### Cited by 264 Authors

 53 Dobrokhotov, Sergei Yurievich 30 Nazaikinskii, Vladimir E. 29 Tirozzi, Brunello 14 Sergeev, Sergeĭ Alekseevich 14 Shafarevich, Andreĭ Igorevich 12 Tolchennikov, Anton A. 9 Agliari, Elena 9 Khrennikov, Andreĭ Yur’evich 8 Barra, Adriano 7 Minenkov, Dmitrii S. 6 Anikin, A. Yu. 6 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 6 Shcherbina, Mariya 6 Tsvetkova, Anna V. 5 Fachechi, Alberto 5 Grushin, V. V. 5 Maslov, Viktor Pavlovich 5 Rozikov, Utkir A. 4 Allilueva, Anna I. 4 Guerra, Francesco 4 Lozhnikov, D. A. 4 Picco, Pierre 4 Sattarov, Iskandar A. 3 Albeverio, Sergio A. 3 Alemanno, Francesco 3 Bovier, Anton 3 Campanino, Massimo 3 Gayrard, Véronique 3 Huang, Jiaoyang 3 Kaneko, Hiroshi 3 Lebowitz, Joel Louis 3 Mukhamedov, Farruh Maksutovich 3 Scacciatelli, E. 3 Tantari, Daniele 3 Volkov, B. I. 3 Yurova, Ekaterina I. 2 Barbier, Jean 2 Benaych-Georges, Florent 2 Benfatto, Giuseppe 2 Bianchi, Daniela 2 Brezhnev, Yurii V. 2 Bulatov, Vitaliĭ Vasil’evich 2 Capocaccia, D. 2 Cassandro, Marzio 2 Comets, Francis M. 2 Feng, Jianfeng 2 Gallavotti, Giovanni M. 2 Genovese, Giuseppe 2 Guionnet, Alice 2 Gundlach, Volker Matthias 2 Hu, Chinkun 2 Janžura, Martin 2 Kabanikhin, Sergeĭ Igorevich 2 Karwowski, Witold 2 Klevin, A. I. 2 Kozyrev, Sergeĭ Vladimirovich 2 Krivorotko, Olga I. 2 Künsch, Hans Rudolf 2 Landon, Benjamin A. 2 Löwe, Matthias 2 Makrakis, George N. 2 Male, Camille 2 Medvedev, Sergeĭ Borisovich 2 Montanari, Andrea 2 Nicolò, Francesco 2 Olivieri, Enzo 2 Pastur, Leonid Andreevich 2 Petrov, P. N. 2 Petrov, Pavel S. 2 Presutti, Errico 2 Rodríguez Bermúdez, Panters 2 Rozanova, Olga S. 2 Shlosman, Senya B. 2 Valiño Alonso, Baldomero 2 Vargas, Carlos A. 2 Yau, Horng-Tzer 2 Yu, Jui-Ling 1 Abundo, Mario 1 Aihara, Kazuyuki 1 Albanese, Linda 1 Alvarez, Gustavo Benitez 1 Amari, Shun-ichi 1 Anashin, Vladimir Sergeevich 1 Arora, Sumit 1 Axelsson, E. Yurova 1 Beccaria, Matteo 1 Berend, Daniel 1 Berry, Hugues 1 Boldrighini, Carlo 1 Bordenave, Charles 1 Boutillier, Cédric 1 Bradley, Patrick Erik 1 Buckel, Maxwell 1 Calderoni, Paola 1 Calogero, Raffaele A. 1 Cancrini, Nicoletta 1 Chen, Dongqing 1 Cheng, Yu-Chen 1 Chirkunov, Yuriĭ Aleksandrovich 1 Christov, Christo Ivanov ...and 164 more Authors
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### Cited in 73 Serials

 40 Russian Journal of Mathematical Physics 30 Mathematical Notes 24 Journal of Statistical Physics 11 Theoretical and Mathematical Physics 10 Communications in Mathematical Physics 9 Probability Theory and Related Fields 8 Journal of Mathematical Physics 8 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 5 Mathematical and Computer Modelling 5 Doklady Mathematics 5 Proceedings of the Steklov Institute of Mathematics 4 Computational Mathematics and Mathematical Physics 3 Computers & Mathematics with Applications 3 Fluid Dynamics 3 Neural Networks 3 Stochastic Processes and their Applications 3 Journal of Statistical Mechanics: Theory and Experiment 2 Biological Cybernetics 2 Journal of Mathematical Analysis and Applications 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 The Annals of Probability 2 Journal of Number Theory 2 Kybernetika 2 Ergodic Theory and Dynamical Systems 2 Physica D 2 Journal of Theoretical Probability 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Indagationes Mathematicae. New Series 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Nonlinear Analysis. Real World Applications 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 The Journal of Mathematical Neuroscience 1 Applicable Analysis 1 International Journal of Theoretical Physics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Mathematical Methods in the Applied Sciences 1 Physics Reports 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Prikladnaya Matematika i Mekhanika 1 The Annals of Statistics 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Tôhoku Mathematical Journal. Second Series 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Acta Mathematicae Applicatae Sinica. English Series 1 Neural Computation 1 The Annals of Applied Probability 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 St. Petersburg Mathematical Journal 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Chaos 1 New Journal of Physics 1 Annales Henri Poincaré 1 Differential Equations 1 Journal of Mathematical Cryptology 1 Journal of Physics A: Mathematical and Theoretical 1 Random Matrices: Theory and Applications 1 Journal of Applied Analysis and Computation 1 Evolution Equations and Control Theory 1 JAMM. Journal of Advanced Mathematical Modeling 1 Results in Applied Mathematics 1 Water Waves
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### Cited in 43 Fields

 91 Partial differential equations (35-XX) 68 Statistical mechanics, structure of matter (82-XX) 63 Probability theory and stochastic processes (60-XX) 54 Fluid mechanics (76-XX) 30 Dynamical systems and ergodic theory (37-XX) 19 Quantum theory (81-XX) 17 Number theory (11-XX) 16 Biology and other natural sciences (92-XX) 14 Computer science (68-XX) 14 Geophysics (86-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Combinatorics (05-XX) 10 Statistics (62-XX) 9 Numerical analysis (65-XX) 8 Differential geometry (53-XX) 5 Operator theory (47-XX) 4 Field theory and polynomials (12-XX) 4 Functional analysis (46-XX) 4 Optics, electromagnetic theory (78-XX) 3 Measure and integration (28-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Convex and discrete geometry (52-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Difference and functional equations (39-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX)