Chaos : Poincaré Seminar 2010 / / edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau |
Edizione | [1st ed. 2013.] |
Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 |
Descrizione fisica | 1 online resource (281 p.) |
Disciplina |
003.857
515.39 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Dynamics
Ergodic theory Number theory Quantum field theory String theory Statistical physics Dynamical systems Dynamical Systems and Ergodic Theory Number Theory Quantum Field Theories, String Theory Complex Systems Statistical Physics and Dynamical Systems |
ISBN | 3-0348-0697-3 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Foreword -- 1 Étienne Ghys, The Lorenz Attractor, a Paradigm for Chaos -- 2 Stéphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows -- 3 Uzy Smilansky, Discrete Graphs - A Paradigm Model for Quantum Chaos -- 4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann ζ-function -- 5 Hans-Jürgen Stöckmann, Chaos in Microwave Resonators -- 6 Stéphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates -- 7 Jacques Laskar, Is the Solar System Stable?. |
Record Nr. | UNINA-9910437864003321 |
Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Dirac Matter / / edited by Bertrand Duplantier, Vincent Rivasseau, Jean-Nöel Fuchs |
Edizione | [1st ed. 2017.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 |
Descrizione fisica | 1 online resource (XII, 129 p. 45 illus., 44 illus. in color.) |
Disciplina | 530.15 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Mathematical physics
Condensed matter Mathematical Physics Condensed Matter Physics |
ISBN | 3-319-32536-1 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Philip Kim: Graphene and Relativistic Quantum Physics -- Mark Goerbig and Gilles Montambaux : Dirac Fermions in Condensed Matter and Beyond -- Chuan Li, Sophie Guéron, Hélène Bouchiat : Quantum Transport in Graphene : Impurity Scattering as a Probe of the Dirac Spectrum.-Laurent Lévy : Experimental Signatures of Topological Insulators -- David Carpentier :Topology of Bands in Solids: From Insulators to Dirac Matter. |
Record Nr. | UNINA-9910163008303321 |
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
The H Boson / / edited by Costas Bachas, Bertrand Duplantier, Vincent Rivasseau |
Edizione | [1st ed. 2017.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 |
Descrizione fisica | 1 online resource (XII, 133 p. 74 illus., 62 illus. in color.) |
Disciplina | 539.721 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Mathematical physics
Elementary particles (Physics) Quantum field theory Mathematical Physics Theoretical, Mathematical and Computational Physics Elementary Particles, Quantum Field Theory |
ISBN | 3-319-57409-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNINA-9910254310503321 |
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Henri Poincaré, 1912–2012 : Poincaré Seminar 2012 / / edited by Bertrand Duplantier, Vincent Rivasseau |
Edizione | [1st ed. 2015.] |
Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2015 |
Descrizione fisica | 1 online resource (246 p.) |
Disciplina | 530.15 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Dynamics
Ergodic theory Probabilities Mathematical physics Physics Dynamical Systems and Ergodic Theory Probability Theory and Stochastic Processes Mathematical Physics History and Philosophical Foundations of Physics |
Soggetto genere / forma | Conference proceedings. |
ISBN | 3-0348-0834-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Foreword -- 1 Olivier Darrigol - Poincaré's light -- 2 Alain Chenciner - Poincaré and the three-body problem -- 3 Laurent Mazliak: Poincaré's odds -- 4 François Béguin - Henri Poincare and the uniformisation of Riemann surfaces -- 5 Philippe Worms, Harmony and chaos. On the figure of Henri Poincare. |
Record Nr. | UNINA-9910299775503321 |
Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2015 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Information theory : Poincare Seminar 2018 / / Bertrand Duplantier, Vincent Rivasseau, editors |
Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
Descrizione fisica | 1 online resource (222 pages) |
Disciplina | 003.54 |
Collana | Progress in mathematical physics |
Soggetto topico |
Information theory
Tecnologia de la informació |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-030-81480-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Contents -- Foreword -- Thermodynamics and Information Theory -- 1. Introduction -- 2. Thermodynamics: A Brief Review -- 2.1. The Two Principles of Thermodynamics -- 2.2. Molecular Theory of Heat and the Framework of Statistical Mechanics -- 2.3. Brownian Motion: Equilibrium Is Dynamical -- 2.4. Universality of Brownian Motion: Feynman's Ratchet and Pawl -- 2.4.1. Application to molecular motors -- 3. Equilibrium and Non-equilibrium Dynamics -- 3.1. Markovian Dynamics -- 3.2. Connection to Thermodynamics -- 3.3. Time-Reversal Invariance and Detailed Balance -- 3.4. Physical Iinterpretation of Detailed Balance -- 3.5. Entropy Production in Markovian Systems -- 4. The Gallavotti{Cohen Fluctuation Theorem for Markovian Thermodynamics -- 4.1. Generalised Detailed Balance -- 4.2. Time Reversal and the Gallavotti{Cohen Symmetry -- 5. Non-equilibrium Work Identities -- 5.1. Jarzynski's Work Theorem -- 5.2. Crooks' Relation -- 6. Information Theory -- 7. Thermodynamics and Information: The Maxwell Demon -- 8. Conclusion -- Appendix A. Large Deviations and Cumulant Generating Functions -- Appendix B. Proof of the Jarzynski Formula for Hamiltonian Dynamics -- Acknowledgments -- References -- This is IT: A Primer on Shannon's Entropy and Information -- 1. Shannon's Life as a Child -- 2. A Noble Prize Laureate -- 3. Intelligence or Information? -- 4. Probabilistic, not Semantic -- 5. The Celebrated 1948 Paper -- 6. Shannon, not Weaver -- 7. Shannon, not Wiener -- 8. Shannon's Bandwagon -- 9. An Axiomatic Approach to Entropy -- 10. Units of Information -- 11. H or ^Eta? -- 12. No One Knows What Entropy Really Is -- 13. How Does Entropy Arise Naturally? -- 14. Shannon's Source Coding Theorem -- 15. Continuous Entropy -- 16. Change of Variable in the Entropy -- 17. Discrete vs. Continuous Entropy -- 18. Most Beautiful Equation -- 19. Entropy Power.
20. A Fundamental Information Inequality -- 21. The MaxEnt Principle -- 22. Relative Entropy or Divergence -- 23. Generalized Entropies and Divergences -- 24. How Does Relative Entropy Arise Naturally? -- 25. Cherno Information -- 26. Fisher Information -- 27. Kolmogorov Information -- 28. Shannon's Mutual Information -- 29. Conditional Entropy or Equivocation -- 30. Knowledge Reduces Uncertainty - Mixing Increases Entropy -- 31. A Suggestive Venn Diagram -- 32. Shannon's Channel Coding Theorem -- 33. Shannon's Capacity Formula -- 34. The Entropy Power Inequality and a Saddle Point Property -- 35. MaxEnt vs. MinEnt Principles -- 36. A Simple Proof of the Entropy Power Inequality -- 37. Conclusion -- References -- Landauer's Bound and Maxwell's Demon -- 1. Introduction -- 1.1. Maxwell's Demon and Szilard's Engine -- 1.2. Landauer's Principle and Bennett's Resolution -- 2. Experimental Implementations -- 2.1. Experiments on Maxwell's Demon -- 2.1.1. The Szilard engine: work production from information -- 2.1.2. The autonomous Maxwell demon improves cooling -- 2.2. Experiments on Landauer's Principle -- 2.3. Other Experiments on the Physics of Information -- 3. Extensions to the Quantum Regime -- 3.1. Experiments on Quantum Maxwell's Demon -- 3.1. Experiments on Quantum Maxwell's Demon -- 3.2. Experiments on Quantum Landauer's Principle -- 4. Applications -- Appendix A. Stochastic Thermodynamics and Information Energy Cost -- A.1. Estimate the Free Energy Difference from Work Fluctuations -- A.2. Landauer Bound and the Jarzynski Equality -- A.2.1. Experimental test of the generalized Jarzynski equality -- Appendix B. Set-up Used in the Experiment Presented in Section 2.2 -- B.1. The One-Bit Memory System -- B.2. Heat Measurements -- References -- Verification of Quantum Computation: An Overview of Existing Approaches -- 1. Introduction. 1.1. Blind Quantum Computing -- 1.1.1. Quantum one-time pad -- 1.1.2. Childs' protocol for blind computation -- 1.1.3. Universal Blind Quantum Computation (UBQC) -- 2. Prepare-and-Send Protocols -- 2.1. Quantum Authentication-Based Veri cation -- 2.1.1. Clifford-QAS VQC -- 2.1.2. Poly-QAS VQC -- 2.2. Trap-Based Verification -- 2.3. Veri cation Based on Repeated Runs -- 2.4. Summary of Prepare-and-Send Protocols -- 3. Receive-and-Measure Protocols -- 3.1. Measurement-only Verification -- 3.2. Post-hoc Verification -- 3.3. Summary of receive-and-measure protocols -- 4. Entanglement-based Protocols -- 4.1. Verification Based on CHSH Rigidity -- 4.1.1. RUV protocol -- 4.1.2. GKW protocol -- 4.1.3. HPDF protocol -- 4.2. Verification Based on Self-testing Graph States -- 4.3. Post-hoc Verifi cation -- 4.3.1. FH protocol -- 4.3.2. NV protocol -- 4.4. Summary of Entanglement-based Protocols -- 5. Outlook -- 5.1. Sub-universal Protocols -- 5.2. Fault Tolerance -- 5.3. Experiments and Implementations -- 6. Conclusions -- 7. Appendix -- 7.1. Quantum Information and Computation -- 7.1.1. Basics of quantum mechanics -- 7.1.2. Density matrices -- 7.1.3. Puri cation -- 7.1.4. CPTP maps -- 7.1.5. Trace distance -- 7.1.6. Quantum computation -- 7.1.7. Bloch sphere -- 7.1.8. Quantum error correction -- 7.2. Measurement-based Quantum Computation -- 7.3. Complexity Theory -- References. |
Record Nr. | UNINA-9910495201503321 |
Cham, Switzerland : , : Birkhäuser, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Information theory : Poincare Seminar 2018 / / Bertrand Duplantier, Vincent Rivasseau, editors |
Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
Descrizione fisica | 1 online resource (222 pages) |
Disciplina | 003.54 |
Collana | Progress in mathematical physics |
Soggetto topico |
Information theory
Tecnologia de la informació |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-030-81480-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Contents -- Foreword -- Thermodynamics and Information Theory -- 1. Introduction -- 2. Thermodynamics: A Brief Review -- 2.1. The Two Principles of Thermodynamics -- 2.2. Molecular Theory of Heat and the Framework of Statistical Mechanics -- 2.3. Brownian Motion: Equilibrium Is Dynamical -- 2.4. Universality of Brownian Motion: Feynman's Ratchet and Pawl -- 2.4.1. Application to molecular motors -- 3. Equilibrium and Non-equilibrium Dynamics -- 3.1. Markovian Dynamics -- 3.2. Connection to Thermodynamics -- 3.3. Time-Reversal Invariance and Detailed Balance -- 3.4. Physical Iinterpretation of Detailed Balance -- 3.5. Entropy Production in Markovian Systems -- 4. The Gallavotti{Cohen Fluctuation Theorem for Markovian Thermodynamics -- 4.1. Generalised Detailed Balance -- 4.2. Time Reversal and the Gallavotti{Cohen Symmetry -- 5. Non-equilibrium Work Identities -- 5.1. Jarzynski's Work Theorem -- 5.2. Crooks' Relation -- 6. Information Theory -- 7. Thermodynamics and Information: The Maxwell Demon -- 8. Conclusion -- Appendix A. Large Deviations and Cumulant Generating Functions -- Appendix B. Proof of the Jarzynski Formula for Hamiltonian Dynamics -- Acknowledgments -- References -- This is IT: A Primer on Shannon's Entropy and Information -- 1. Shannon's Life as a Child -- 2. A Noble Prize Laureate -- 3. Intelligence or Information? -- 4. Probabilistic, not Semantic -- 5. The Celebrated 1948 Paper -- 6. Shannon, not Weaver -- 7. Shannon, not Wiener -- 8. Shannon's Bandwagon -- 9. An Axiomatic Approach to Entropy -- 10. Units of Information -- 11. H or ^Eta? -- 12. No One Knows What Entropy Really Is -- 13. How Does Entropy Arise Naturally? -- 14. Shannon's Source Coding Theorem -- 15. Continuous Entropy -- 16. Change of Variable in the Entropy -- 17. Discrete vs. Continuous Entropy -- 18. Most Beautiful Equation -- 19. Entropy Power.
20. A Fundamental Information Inequality -- 21. The MaxEnt Principle -- 22. Relative Entropy or Divergence -- 23. Generalized Entropies and Divergences -- 24. How Does Relative Entropy Arise Naturally? -- 25. Cherno Information -- 26. Fisher Information -- 27. Kolmogorov Information -- 28. Shannon's Mutual Information -- 29. Conditional Entropy or Equivocation -- 30. Knowledge Reduces Uncertainty - Mixing Increases Entropy -- 31. A Suggestive Venn Diagram -- 32. Shannon's Channel Coding Theorem -- 33. Shannon's Capacity Formula -- 34. The Entropy Power Inequality and a Saddle Point Property -- 35. MaxEnt vs. MinEnt Principles -- 36. A Simple Proof of the Entropy Power Inequality -- 37. Conclusion -- References -- Landauer's Bound and Maxwell's Demon -- 1. Introduction -- 1.1. Maxwell's Demon and Szilard's Engine -- 1.2. Landauer's Principle and Bennett's Resolution -- 2. Experimental Implementations -- 2.1. Experiments on Maxwell's Demon -- 2.1.1. The Szilard engine: work production from information -- 2.1.2. The autonomous Maxwell demon improves cooling -- 2.2. Experiments on Landauer's Principle -- 2.3. Other Experiments on the Physics of Information -- 3. Extensions to the Quantum Regime -- 3.1. Experiments on Quantum Maxwell's Demon -- 3.1. Experiments on Quantum Maxwell's Demon -- 3.2. Experiments on Quantum Landauer's Principle -- 4. Applications -- Appendix A. Stochastic Thermodynamics and Information Energy Cost -- A.1. Estimate the Free Energy Difference from Work Fluctuations -- A.2. Landauer Bound and the Jarzynski Equality -- A.2.1. Experimental test of the generalized Jarzynski equality -- Appendix B. Set-up Used in the Experiment Presented in Section 2.2 -- B.1. The One-Bit Memory System -- B.2. Heat Measurements -- References -- Verification of Quantum Computation: An Overview of Existing Approaches -- 1. Introduction. 1.1. Blind Quantum Computing -- 1.1.1. Quantum one-time pad -- 1.1.2. Childs' protocol for blind computation -- 1.1.3. Universal Blind Quantum Computation (UBQC) -- 2. Prepare-and-Send Protocols -- 2.1. Quantum Authentication-Based Veri cation -- 2.1.1. Clifford-QAS VQC -- 2.1.2. Poly-QAS VQC -- 2.2. Trap-Based Verification -- 2.3. Veri cation Based on Repeated Runs -- 2.4. Summary of Prepare-and-Send Protocols -- 3. Receive-and-Measure Protocols -- 3.1. Measurement-only Verification -- 3.2. Post-hoc Verification -- 3.3. Summary of receive-and-measure protocols -- 4. Entanglement-based Protocols -- 4.1. Verification Based on CHSH Rigidity -- 4.1.1. RUV protocol -- 4.1.2. GKW protocol -- 4.1.3. HPDF protocol -- 4.2. Verification Based on Self-testing Graph States -- 4.3. Post-hoc Verifi cation -- 4.3.1. FH protocol -- 4.3.2. NV protocol -- 4.4. Summary of Entanglement-based Protocols -- 5. Outlook -- 5.1. Sub-universal Protocols -- 5.2. Fault Tolerance -- 5.3. Experiments and Implementations -- 6. Conclusions -- 7. Appendix -- 7.1. Quantum Information and Computation -- 7.1.1. Basics of quantum mechanics -- 7.1.2. Density matrices -- 7.1.3. Puri cation -- 7.1.4. CPTP maps -- 7.1.5. Trace distance -- 7.1.6. Quantum computation -- 7.1.7. Bloch sphere -- 7.1.8. Quantum error correction -- 7.2. Measurement-based Quantum Computation -- 7.3. Complexity Theory -- References. |
Record Nr. | UNISA-996466402803316 |
Cham, Switzerland : , : Birkhäuser, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Niels Bohr, 1913-2013 : Poincaré Seminar 2013 / / edited by Olivier Darrigol, Bertrand Duplantier, Jean-Michel Raimond, Vincent Rivasseau |
Edizione | [1st ed. 2016.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 |
Descrizione fisica | 1 online resource (230 p.) |
Disciplina | 510 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Mathematical physics
Elementary particles (Physics) Quantum field theory Physics Mathematical Physics Elementary Particles, Quantum Field Theory History and Philosophical Foundations of Physics |
Soggetto genere / forma | Conference papers and proceedings. |
ISBN | 3-319-14316-6 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Foreword -- Keeping Things Open, Tomas Bohr -- Bohr's Trilogy of 1913, Olivier Darrigol -- The Mind that Created the Bohr atom, John Heilbron -- Bohr's Legacy in Cavity QED, Serge Haroche & Jean-Michel Raimond -- From Einstein, Bohr, Schrödinger to Bell and Feynman: A New Quantum Revolution?, Alain Aspect.- Interacting Cold Rydberg Atoms: A Toy Many-Body System, Antoine Browaeys.- Bohr's Complementarity and Kant's Epistemology, Michel Bitbol & Stefano Osnaghi. |
Record Nr. | UNINA-9910254071503321 |
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Time : Poincaré Seminar 2010 / / edited by Bertrand Duplantier |
Edizione | [1st ed. 2013.] |
Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 |
Descrizione fisica | 1 online resource (219 p.) |
Disciplina | 530.15 |
Collana | Progress in Mathematical Physics |
Soggetto topico |
Dynamics
Ergodic theory Mathematical physics Statistical physics Dynamical systems Quantum physics Probabilities Mechanics Dynamical Systems and Ergodic Theory Mathematical Physics Complex Systems Quantum Physics Probability Theory and Stochastic Processes Classical Mechanics |
ISBN | 3-0348-0359-1 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Foreword -- Time and Relativity, Thibault Damour -- (Ir)reversibility and Entropy, Cédric Villani -- (Ir)réversibilité et entropie, Cédric Villani -- Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale, Christopher Jarzynski -- Time Measurement in the XXIst Century, Christophe Salomon -- Time’s Arrow and Eddington’s Challenge, Huw Price -- Image of Time’s Irreversibility, Catherine de Mitry -- Image de l'irréversibilité du Temps, Catherine de Mitry. |
Record Nr. | UNINA-9910438139203321 |
Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
The universe : PoincareÌ Seminar 2015 / / Bertrand Duplantier, Vincent Rivasseau, editors |
Edizione | [1st ed. 2021.] |
Pubbl/distr/stampa | Cham, Switzerland : , : BirkhaÌuser, , [2021] |
Descrizione fisica | 1 online resource (XII, 147 p.) |
Disciplina | 523.01 |
Collana | Progress in Mathematical Physics |
Soggetto topico | Astrophysics |
ISBN | 3-030-67392-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | The Big-Bang Theory: Construction, Evolution and Status -- The Planck Mission and the Cosmic Microwave Background -- Massive Black Holes: Evidence, Demographics and Cosmic Evolution -- New Worlds Ahead: The Discovery of Exoplanets. . |
Record Nr. | UNINA-9910483041603321 |
Cham, Switzerland : , : BirkhaÌuser, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
The universe : PoincareÌ Seminar 2015 / / Bertrand Duplantier, Vincent Rivasseau, editors |
Edizione | [1st ed. 2021.] |
Pubbl/distr/stampa | Cham, Switzerland : , : BirkhaÌuser, , [2021] |
Descrizione fisica | 1 online resource (XII, 147 p.) |
Disciplina | 523.01 |
Collana | Progress in Mathematical Physics |
Soggetto topico | Astrophysics |
ISBN | 3-030-67392-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | The Big-Bang Theory: Construction, Evolution and Status -- The Planck Mission and the Cosmic Microwave Background -- Massive Black Holes: Evidence, Demographics and Cosmic Evolution -- New Worlds Ahead: The Discovery of Exoplanets. . |
Record Nr. | UNISA-996466565703316 |
Cham, Switzerland : , : BirkhaÌuser, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|