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 分数维动力学 国内英文版
 电子书价格：14元 如何计算价格 作　　者：（俄罗斯）塔拉索夫著 出 版 社： 出版年份：2010 年 ISBN：9787040294736 页数：505 页 支持介质： 图书格式说明及阅读软件下载 分享到： 图书封面及目录 Part Ⅰ Fraction？l Continuous Models of Fractal Distributions1 Fractional Integration and Fractals 1.1 Riemann-Liouville fractional integrals 1.2 Liouville fractional integrals 1.3 Riesz fractional integrals 1.4 Metric and measure spaces 1.5 Hausdorff measure 1.6 Hausdorff dimension and fractals 1.7 Box-counting dimension 1.8 Mass dimension of fractal systems 1.9 Elementary models of fractal distributions 1.10 Functions and integrals on fractals 1.11 Properties of integrals on fractals 1.12 Integration over non-integer-dimensional space 1.13 Multi-variable integration on fractals 1.14 Mass distribution on fractals 1.15 Density of states in Euclidean space 1.16 Fractional integral and measure on the real axis 1.17 Fractional integral and mass on the real axis 1.18 Mass of fractal media 1.19 Electric charge of fractal distribution 1.20 Probability on fractals 1.21 Fractal distribution of particles References2 Hydrodynamics of Fractal Media 2.1 Introduction 2.2 Equation of balance of mass 2.3 Total time derivative of fractional integral 2.4 Equation of continuity for fractal media 2.5 Fractional integral equation of balance of momentum 2.6 Differential equations of balance of momentum 2.7 Fractional integral equation of balance of energy 2.8 Differential equation of balance of energy 2.9 Euler's equations for fractal media 2.10 Navier-Stokes equations for fractal media 2.11 Equilibrium equation for fractal media 2.12 Bernoulli integral for fractal media 2.13 Sound waves in fractal media 2.14 One-dimensional wave equation in fractal media 2.15 Conclusion References 3 Fractal Rigid Body Dynamics 3.1 Introduction 3.2 Fractional equation for moment of inertia 3.3 Moment of inertia of fractal rigid body ball 3.4 Moment of inertia for fractal rigid body cylinder 3.5 Equations of motion for fractal rigid body 3.6 Pendulum with fractal rigid body 3.7 Fractal rigid body rolling down an inclined plane 3.8 Conclusion References4 Electrodynamics of Fractal Distributions of Charges and Fields 4.1 Introduction 4.2 Electric charge of fractal distribution 4.3 Electric current for fractal distribution 4.4 Gauss'theorem for fractal distribution 4.5 Stokes'theorem for fractal distribution 4.6 Charge conservation for fractal distribution 4.7 Coulomb's and Biot-Savart laws for fractal distribution 4.8 Gauss'law for fractal distribution 4.9 Ampere's law for fractal distribution 4.10 Integral Maxwell equations for fractal distribution 4.11 Fractal distribution as an effective medium 4.12 Electric multipole expansion for fractal distribution 4.13 Electric dipole moment of fractal distribution 4.14 Electric quadrupole moment of fractal distribution 4.15 Magnetohydrodynamics of fractal distribution 4.16 Stationary states in magnetohydrodynamics of fractal distributions 4.17 Conclusion References 5 Ginzburg-Landau Equation for Fractal Media 5.1 Introduction 5.2 Fractional generalization of free energy functional 5.3 Ginzburg-Landau equation from free energy functional 5.4 Fractional equations from variational equation 5.5 Conclusion References 6 Fokker-Planck Equation for Fractal Distributions of Probability 6.1 Introduction 6.2 Fractional equation for average values 6.3 Fractional Chapman-Kolmogorov equation 6.4 Fokker-Planck equation for fractal distribution 6.5 Stationary solutions of generalized Fokker-Planck equation 6.6 Conclusion References 7 Statistical Mechanics of Fractal Phase Space Distributions 7.1 Introduction 7.2 Fractal distribution in phase space 7.3 Fractional phase volume for configuration space 7.4 Fractional phase volume for phase space 7.5 Fractional generalization of normalization condition 7.6 Continuity equation for fractal distribution in configuration space 7.7 Continuity equation for fractal distribution in phase space 7.8 Fractional average values for configuration space 7.9 Fractional average values for phase space 7.10 Generalized Liouville equation 7.11 Reduced distribution functions 7.12 Conclusion ReferencesPart Ⅱ Fractional Dynamics and Long-Range Interactions8 Fractional Dynamics of Media with Long-Range Interaction 8.1 Introduction 8.2 Equations of lattice vibrations and dispersion law 8.3 Equations of motion for interacting particles 8.4 Transform operation for discrete models 8.5 Fourier series transform of equations of motion 8.6 Alpha-interaction of particles 8.7 Fractional spatial derivatives 8.8 Riesz fractional derivatives and integrals 8.9 Continuous limits of discrete equations 8.10 Linear nearest-neighbor interaction 8.11 Linear integer long-range alpha-interaction 8.12 Linear fractional long-range alpha-interaction 8.13 Fractional reaction-diffusion equation 8.14 Nonlinear long-range alpha-interaction 8.15 Fractional 3-dimensional lattice equation 8.16 Fractional derivatives from dispersion law 8.17 Fractal long-range interaction 8.18 Fractal dispersion law 8.19 Grünwald-Letnikov-Riesz long-range interaction 8.20 Conclusion References9 Fractional Ginzburg-Landau Equation 9.1 Introduction 9.2 Particular solution of fractional Ginzburg-Landau equation 9.3 Stability of plane-wave solution 9.4 Forced fractional equation 9.5 Conclusion References10 Psi-Series Approach to Fractional Equations 10.1 Introduction 10.2 Singular behavior of fractional equation 10.3 Resonance terms of fractional equation 10.4 Psi-series for fractional equation of rational order 10.5 Next to singular behavior 10.6 Conclusion ReferencesPart Ⅲ Fractional Spatial Dynamics11 Fractional Vector Calculus 11.1 Introduction 11.2 Generalization of vector calculus 11.3 Fundamental theorem of fractional calculus 11.4 Fractional differential vector operators 11.5 Fractional integral vector operations 11.6 Fractional Green's formula 11.7 Fractional Stokes'formula 11.8 Fractional Gauss'formula 11.9 Conclusion References12 Fractional Exterior Calculus and Fractional Differential Forms 12.1 Introduction 12.2 Differential forms of integer order 12.3 Fractional exterior derivative 12.4 Fractional differential forms 12.5 Hodge star operator 12.6 Vector operations by differential forms 12.7 Fractional Maxwell's equations in terms of fractional forms 12.8 Caputo derivative in electrodynamics 12.9 Fractional nonlocal Maxwell's equations 12.10 Fractional waves 12.11 Conclusion References13 Fractional Dynamical Systems 13.1 Introduction 13.2 Fractional generalization of gradient systems 13.3 Examples of fractional gradient systems 13.4 Hamiltonian dynamical systems 13.5 Fractional generalization of Hamiltonian systems 13.6 Conclusion References14 Fractional Calculus of Variations in Dynamics 14.1 Introduction 14.2 Hamilton's equations and variations of integer order 14.3 Fractional variations and Hamilton's equations 14.4 Lagrange's equations and variations of integer order 14.5 Fractional variations and Lagrange's equations 14.6 Helmholtz conditions and non-Lagrangian equations 14.7 Fractional variations and non-Hamiltonian systems 14.8 Fractional stability 14.9 Conclusion References15 Fractional Statistical Mechanics 15.1 Introduction 15.2 Liouville equation with fractional derivatives 15.3 Bogolyubov equation with fractional derivatives 15.4 Vlasov equation with fractional derivatives 15.5 Fokker-Planck equation with fractional derivatives 15.6 Conclusion ReferencesPart Ⅳ Fractional Temporal Dynamics16 Fractional Temporal Electrodynamics 16.1 Introduction 16.2 Universal response laws 16.3 Linear electrodynamics of medium 16.4 Fractional equations for laws of universal response 16.5 Fractional equations of the Curie-von Schweidler law 16.6 Fractional Gauss'laws for electric field 16.7 Universal fractional equation for electric field 16.8 Universal fractional equation for magnetic field 16.9 Fractional damping of magnetic field 16.10 Conclusion References17 Fractional Nonholonomic Dynamics 17.1 Introduction 17.2 Nonholonomic dynamics 17.3 Fractional temporal derivatives 17.4 Fractional dynamics with nonholonomic constraints 17.5 Constraints with fractional derivatives 17.6 Equations of motion with fractional nonholonomic constraints 17.7 Example of fractional nonholonomic constraints 17.8 Fractional conditional extremum 17.9 Hamilton's approach to fractional nonholonomic constraints 17.10 Conclusion References 18 Fractional Dynamics and Discrete Maps with Memory 18.1 Introduction 18.2 Discrete maps without memory 18.3 Caputo and Riemann-Liouville fractional derivatives 18.4 Fractional derivative in the kicked term and discrete maps 18.5 Fractional derivative in the kicked term and dissipative discrete maps 18.6 Fractional equation with higher order derivatives and discrete map 18.7 Fractional generalization of universal map for 1＜α≤2 18.8 Fractional universal map for α＞2 18.9 Riemann-Liouville derivative and universal map with memory 18.10 Caputo fractional derivative and universal map with memory 18.11 Fractional kicked damped rotator map 18.12 Fractional dissipative standard map 18.13 Fractional Hénon map 18.14 Conclusion ReferencesPart Ⅴ Fractional Quantum Dynamics19 Fractional Dynamics of Hamiltonian Quantum Systems 19.1 Introduction 19.2 Fractional power of derivative and Heisenberg equation 19.3 Properties of fractional dynamics 19.4 Fractional quantum dynamics of free particle 19.5 Fractional quantum dynamics of harmonic oscillator 19.6 Conclusion References20 Fractional Dynamics of Open Quantum Systems 20.1 Introduction 20.2 Fractional power of superoperator 20.3 Fractional equation for quantum observables 20.4 Fractional dynamical semigroup 20.5 Fractional equation for quantum states 20.6 Fractional non-Markovian quantum dynamics 20.7 Fractional equations for quantum oscillator with friction 20.8 Quantum self-reproducing and self-cloning 20.9 Conclusion References21 Quantum Analogs of Fractional Derivatives 21.1 Introduction 21.2 Weyl quantization of differential operators 21.3 Quantization of Riemann-Liouville fractional derivatives 21.4 Quantization of Liouville fractional derivative 21.5 Quantization of nondifferentiable functions 21.6 Conclusion ReferencesIndex