01008nam0 2200277 450 00001846320081030111405.0084933987120081030d1998----km-y0itay50------baengUSy-------001yyFundamental number theory with applicationsRichard A. MollinBoca Raton ; New York1998XII, 439 p.24 cm<<The >>CRC press series on discrete mathematics and its applications2001<<The >>CRC press series on discrete mathematics and its applicationsFundamental number theory with applications33172NumeriTeoriaApplicazioni512.720Algebra. Teoria dei numeriMollin,Richard A.<1947- >65944ITUNIPARTHENOPE20081030RICAUNIMARC000018463M 512.7/2M 1669DSA2008Fundamental number theory with applications33172UNIPARTHENOPE05640nam 2200745Ia 450 991079225490332120230607230543.097866119987901-281-99879-60-19-156508-30-19-955644-X(CKB)2560000000298393(EBL)431105(OCoLC)320958687(SSID)ssj0000115304(PQKBManifestationID)11132045(PQKBTitleCode)TC0000115304(PQKBWorkID)10008345(PQKB)10853492(StDuBDS)EDZ0000076462(MiAaPQ)EBC431105(Au-PeEL)EBL431105(CaPaEBR)ebr10358346(CaONFJC)MIL199879(MiAaPQ)EBC7036444(Au-PeEL)EBL7036444(EXLCZ)99256000000029839320020107d2002 uy 0engur|n|---|||||txtccrBrownian motion[electronic resource] fluctuations, dynamics, and applications /Robert M. MazoOxford Clarendon Press20021 online resource (302 p.)Oxford science publicationsInternational series of monographs on physics ;112Description based upon print version of record.0-19-851567-7 0-19-170562-4 Includes bibliographical references (p. 271-284) and index.Contents; 1 Historical Background; 1.1 Robert Brown; 1.2 Between Brown and Einstein; 1.3 Albert Einstein; 1.4 Marian von Smoluchowski; 1.5 Molecular Reality; 1.6 The Scope of this Book; 2 Probability Theory; 2.1 Probability; 2.2 Conditional Probability and Independence; 2.3 Random Variables and Probability Distributions; 2.4 Expectations and Particular Distributions; 2.5 Characteristic Function; Sums of Random Variables; 2.6 Conclusion; 3 Stochastic Processes; 3.1 Stochastic Processes; 3.2 Distribution Functions; 3.3 Classification of Stochastic Processes; 3.4 The Fokker-Planck Equation3.5 Some Special Processes3.6 Calculus of Stochastic Processes; 3.7 Fourier Analysis of Random Processes; 3.8 White Noise; 3.9 Conclusion; 4 Einstein-Smoluchowski Theory; 4.1 What is Brownian Motion?; 4.2 Smoluchowski's Theory; 4.3 Smoluchowski Theory Continued; 4.4 Einstein's Theory; 4.5 Diffusion Coefficient and Friction Constant; 4.6 The Langevin Theory; 5 Stochastic Differential Equations and Integrals; 5.1 The Langevin Equation Revisited; 5.2 Stochastic Differential Equations; 5.3 Which Rule Should Be Used?; 5.4 Some Examples; 6 Functional Integrals; 6.1 Functional Integrals6.2 The Wiener Integral6.3 Wiener Measure; 6.4 The Feynman-Kac Formula; 6.5 Feynman Path Integrals; 6.6 Evaluation of Wiener Integrals; 6.7 Applications of Functional Integrals; 7 Some Important Special Cases; 7.1 Several Cases of Interest; 7.2 The Free Particle; 7.3 The Distribution of Displacements; 7.4 The Harmonically Bound Particle; 7.5 A Particle in a Constant Force Field; 7.6 The Uniaxial Rotor; 7.7 An Equation for the Distribution of Displacements; 7.8 Discussion; 8 The Smoluchowski Equation; 8.1 The Kramers-Klein Equation; 8.2 The Smoluchowski Equation8.3 Elimination of Fast Variables8.4 The Smoluchowski Equation Continued; 8.5 Passage over Potential Barriers; 8.6 Concluding Remarks; 9 Random Walk; 9.1 The Random Walk; 9.2 The One-Dimensional Pearson Walk; 9.3 The Biased Random Walk; 9.4 The Persistent Walk; 9.5 Boundaries and First Passage Times; 9.6 Random Remarks on Random Walks; 10 Statistical Mechanics; 10.1 Molecular Distribution Functions; 10.2 The Liouville Equation; 10.3 Projection Operators-The Zwanzig Equation; 10.4 Projection Operators-The Mori Equation; 10.5 Concluding Remarks11 Stochastic Equations from a Statistical Mechanical Viewpoint11.1 The Langevin Equation A Heuristic View; 11.2 The Fokker-Planck Equation-A Heuristic View; 11.3 What is Wrong with these Derivations?; 11.4 Eliminating Fast Processes; 11.5 The Distribution Function; 11.6 Discussion; 12 Two Exactly Treatable Models; 12.1 Two Illustrative Examples; 12.2 Brownian Motion in a Dilute Gas; 12.3 Discussion; 12.4 The Particle Bound to a Lattice; 12.5 The One-Dimensional Case; 12.6 Discussion; 13 Brownian Motion and Noise; 13.1 Limits on Measurement; 13.2 Oscillations of a Fiber13.3 A Pneumatic ExampleBrownian motion- the incessant motion of small particles suspended in a fluid- is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. - ;Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statisticaInternational series of monographs on physics (Oxford, England) ;112.Oxford science publications.Brownian motion processesMarkov processesBrownian motion processes.Markov processes.530.42530.475Mazo Robert M66678MiAaPQMiAaPQMiAaPQBOOK9910792254903321Brownian motion377517UNINA