Log in

Relevant bibliographies by topics / Ito equation / Books

To see the other types of publications on this topic, follow the link: Ito equation.

Books on the topic 'Ito equation'

Author: Grafiati

Published: 30 May 2022

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 books for your research on the topic 'Ito equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse books on a wide variety of disciplines and organise your bibliography correctly.

1

Chung, Kai Lai. Introduction to stochastic integration. 2nd ed. Birkhäuser, 1990.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

Full text

Abstract:

The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existe

APA, Harvard, Vancouver, ISO, and other styles

3

Stuart, Charles A. Bifurcation into spectral gaps. Société mathématique de Belgique, 1995.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

4

Billings, S. A. Mapping nonlinear integro-differential equations into the frequency domain. University of Sheffield, Dept. of Control Engineering, 1989.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

5

Zhukova, Galina. Differential equations. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072180.

Full text

Abstract:

The textbook presents the theory of ordinary differential equations constituting the subject of the discipline "Differential equations". Studied topics: differential equations of first, second, arbitrary order; differential equations; integration of initial and boundary value problems; stability theory of solutions of differential equations and systems. Introduced the basic concepts, proven properties of differential equations and systems. The article presents methods of analysis and solutions. We consider the applications of the obtained results, which are illustrated on a large number of spe

APA, Harvard, Vancouver, ISO, and other styles

6

Esther, Muia, Robert H. Ebert Program on Critical Issues in Reproductive Health and Population., and Population Council. East and Southern Africa Regional Office., eds. Integrating men into the reproductive health equation: Acceptability and feasibility in Kenya. Population Council, 2000.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

7

Pollock, Marcia (Marcia Kay), 1942-2011, ed. Putting God back into Einstein's equations: Energy of the soul. Shechinah Third Temple, Inc., 2012.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

8

Sinha, N. Inclusion of chemical kinetics into beam-warming based PNS model for hypersonic propulsion applications. AIAA, 1987.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

9

Kudinov, Igor', Anton Eremin, Konstantin Trubicyn, Vitaliy Zhukov, and Vasiliy Tkachev. Vibrations of solids, liquids and gases taking into account local disequilibrium. INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1859642.

Full text

Abstract:

The monograph presents the results of the development and research of new mathematical models of the processes of vibrations of solids, liquids and gases, taking into account local disequilibrium. To derive differential equations, the Navier—Stokes equations, Newton's second law and modified formulas of the classical empirical laws of Fourier, Hooke, Newton are used, which take into account the velocities and accelerations of the driving forces (gradients of the corresponding quantities) and their consequences (heat flow, normal and tangential stresses). The conditions for the occurrence of sh

APA, Harvard, Vancouver, ISO, and other styles

10

Hartley, T. T. Insights into the fractional order initial value problem via semi-infinite systems. National Aeronautics and Space Administration, Lewis Research Center, 1998.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

11

Ikeda, Nobuyuki. Stochastic differential equations and diffusion processes. 2nd ed. North-Holland Pub. Co., 1989.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

12

Umarov, Sabir, Marjorie G. Hahn, and Kei Kobayashi. Beyond the Triangle : Brownian Motion, Ito Calculus, and Fokker-Planck Equation: Fractional Generalizations. World Scientific Publishing Co Pte Ltd, 2018.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

13

Bray, William O. Journey into Partial Differential Equations. Jones & Bartlett Learning, LLC, 2012.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

14

Escudier, Marcel. Basic equations of viscous-fluid flow. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0015.

Full text

Abstract:

In this chapter it is shown that application of the momentum-conservation equation (Newton’s second law of motion) to an infinitesimal cube of fluid leads to Cauchy’s partial differential equations, which govern the flow of any fluid satisfying the continuum hypothesis. Any fluid flow must also satisfy the continuity equation, another partial differential equation, which is derived from the mass-conservation equation. It is shown that distortion of a flowing fluid can be split into elongational distortion and angular distortion or shear strain. For a Newtonian fluid, the normal and shear stres

APA, Harvard, Vancouver, ISO, and other styles

15

A Journey Into Partial Differential Equations. Jones & Bartlett Publishers, 2010.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

16

Rajeev, S. G. Euler’s Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0002.

Full text

Abstract:

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure). Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant. In this limit, Euler’s equations have scale invariance in addi

APA, Harvard, Vancouver, ISO, and other styles

17

Cantor, Brian. The Equations of Materials. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851875.001.0001.

Full text

Abstract:

This book describes some of the important equations of materials and the scientists who derived them. It is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. It is meant to be readable and enjoyable, a primer rather than a textbook, covering only a limited number of topics and not trying to be comprehensive. It is pitched at the level of a final year school student or a first year undergraduate who has been studying the physical sciences and is thinking of specialising

APA, Harvard, Vancouver, ISO, and other styles

18

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

Full text

Abstract:

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equ

APA, Harvard, Vancouver, ISO, and other styles

19

Rajeev, S. G. Hamiltonian Systems Based on a Lie Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0010.

Full text

Abstract:

There is a remarkable analogy between Euler’s equations for a rigid body and his equations for an ideal fluid. The unifying idea is that of a Lie algebra with an inner product, which is not invariant, on it. The concepts of a vector space, Lie algebra, and inner product are reviewed. A hamiltonian dynamical system is derived from each metric Lie algebra. The Virasoro algebra (famous in string theory) is shown to lead to the KdV equation; and in a limiting case, to the Burgers equation for shocks. A hamiltonian formalism for two-dimensional Euler equations is then developed in detail. A discret

APA, Harvard, Vancouver, ISO, and other styles

20

Mann, Peter. Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0027.

Full text

Abstract:

In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, spacetime variations), resulting in the Noether condition. Quasisymmetries and spontaneous symmetry breaking are discussed, as well as local symmetry and global symmetry. Following these definitions, Noether’s first theorem and Noether’s second theorem are developed. The classical Schrödinger field is investigated and the key equations of classical mechanics are summarised into a single Lagrangian.

APA, Harvard, Vancouver, ISO, and other styles

21

Deruelle, Nathalie, and Jean-Philippe Uzan. Self-gravitating fluids. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0015.

Full text

Abstract:

This chapter briefly describes ‘perfect fluids’. These are characterized by their mass density ρ‎(t, xⁱ), pressure p(t, ⁱ), and velocity field v(t, ⁱ). The motion and equilibrium configurations of these fluids are determined by the equation of state, for example, p = p(ρ‎) for a barotropic fluid, and by the gravitational potential U(t, ⁱ) created at a point ⁱ by other fluid elements. The chapter shows that, given an equation of state, the equations of the problem to be solved are the continuity equation, the Euler equation, and the Poisson equation. It then considers static models with spheric

APA, Harvard, Vancouver, ISO, and other styles

22

Rajeev, S. G. Finite Difference Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0014.

Full text

Abstract:

This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by functions of difference operators. Padé approximants (Fornberg) give a unifying principle for deriving the various stencils used by numericists. Boundary value problems for the Poisson equation and initial value problems for the diffusion equation are solved using FDM. Numerical instability of explicit schemes are explained physically and implicit schemes introduced. A discrete version of theClebsch f

APA, Harvard, Vancouver, ISO, and other styles

23

Mann, Peter. Virtual Work & d’Alembert’s Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0013.

Full text

Abstract:

This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a d

APA, Harvard, Vancouver, ISO, and other styles

24

Succi, Sauro. Model Boltzmann Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0008.

Full text

Abstract:

This chapter deals with simplified models of the Boltzmann equation, aimed at reducing its mathematical complexity, while still retaining the most salient physical features. As observed many times in this book, the Boltzmann equation is all but an easy equation to solve. The situation surely improves by moving to its linearized version, but even then, a lot of painstaking labor is usually involved in deriving special solutions for the problem at hand. In order to ease this state of affairs, in the mid-fifties, stylized models of the Boltzmann equations were formulated, with the main intent of

APA, Harvard, Vancouver, ISO, and other styles

25

Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

Full text

Abstract:

Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is n

APA, Harvard, Vancouver, ISO, and other styles

26

Prussing, John E. Rocket Trajectories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198811084.003.0003.

Full text

Abstract:

rocket trajectories, including equations of motion are treated. High- and low-thrust engines are analysed, including constant-specific-impulse and variable-specific-impulse engines. The equation of motion of a spacecraft which is thrusting in a gravitational field determines its trajectory.

APA, Harvard, Vancouver, ISO, and other styles

27

Succi, Sauro. Approach to Equilibrium, the H-Theorem and Irreversibility. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0003.

Full text

Abstract:

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underl

APA, Harvard, Vancouver, ISO, and other styles

28

Morawetz, Klaus. Approximations for the Selfenergy. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0010.

Full text

Abstract:

The systematic expansion of the selfenergy is presented with the help of the closure relation of chapter 7. Besides Hartree–Fock leading to meanfield kinetic equations, the random phase approximation (RPA) is shown to result into the Lennard–Balescu kinetic equation, and the ladder approximation into the Beth–Uehling–Uhlenbeck kinetic equation. The deficiencies of the ladder approximation are explored compared to the exact T-matrix by missing maximally crossed diagrams. The T-matrix provides the Bethe–Salpeter equation for the two-particle correlation functions. Vertex corrections to the RPA a

APA, Harvard, Vancouver, ISO, and other styles

29

Rajeev, S. G. Viscous Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0005.

Full text

Abstract:

Here some solutions of Navier–Stokes equations are found.The flow of a fluid along a pipe (Poisseuille flow) and that between two rotating cylinders (Couette flow) are the simplest. In the limit of large viscosity (small Reynolds number) the equations become linear: Stokes equations. Flow past a sphere is solved in detail. It is used to calculate the drag on a sphere, a classic formula of Stokes. An exact solution of the Navier–Stokes equation describing a dissipating vortex is also found. It is seen that viscosity cannot be ignored at the boundary or at the core of vortices.

APA, Harvard, Vancouver, ISO, and other styles

30

Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.

Full text

Abstract:

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechan

APA, Harvard, Vancouver, ISO, and other styles

31

Morawetz, Klaus. Nonequilibrium Quantum Hydrodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0015.

Full text

Abstract:

The balance equations resulting from the nonlocal kinetic equation are derived. They show besides the Landau-like quasiparticle contributions explicit two-particle correlated parts which can be interpreted as molecular contributions. It looks like as if two particles form a short-living molecule. All observables like density, momentum and energy are found as a conserving system of balance equations where the correlated parts are in agreement with the forms obtained when calculating the reduced density matrix with the extended quasiparticle functional. Therefore the nonlocal kinetic equation fo

APA, Harvard, Vancouver, ISO, and other styles

32

Mann, Peter. Vector Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0034.

Full text

Abstract:

This chapter gives a non-technical overview of differential equations from across mathematical physics, with particular attention to those used in the book. It is a common trend in physics and nature, or perhaps just the way numbers and calculus come together, that, to describe the evolution of things, most theories use a differential equation of low order. This chapter is useful for those with no prior knowledge of the differential equations and explains the concepts required for a basic exposition of classical mechanics. It discusses separable differential equations, boundary conditions and

APA, Harvard, Vancouver, ISO, and other styles

33

Deruelle, Nathalie, and Jean-Philippe Uzan. The Kerr solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0048.

Full text

Abstract:

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals.

APA, Harvard, Vancouver, ISO, and other styles

34

Sogge, Christopher D. A review: The Laplacian and the d’Alembertian. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0001.

Full text

Abstract:

This chapter reviews the Laplacian and the d'Alembertian. It begins with a brief discussion on the solution of wave equation both in Euclidean space and on manifolds and how this knowledge can be used to derive properties of eigenfunctions on Riemannian manifolds. A key step in understanding properties of solutions of wave equations on manifolds is to compute the types of distributions that include the fundamental solution of the wave operator in Minkowski space (d'Alembertian), with a specific function for the Euclidean Laplacian on Rn. The chapter also reviews another equation involving the

APA, Harvard, Vancouver, ISO, and other styles

35

Succi, Sauro. Stochastic Particle Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0009.

Full text

Abstract:

Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical devel

APA, Harvard, Vancouver, ISO, and other styles

36

Deruelle, Nathalie, and Jean-Philippe Uzan. The Maxwell equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0030.

Full text

Abstract:

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge

APA, Harvard, Vancouver, ISO, and other styles

37

Deruelle, Nathalie, and Jean-Philippe Uzan. Conservation laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0045.

Full text

Abstract:

This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ‘charges’, characterizing the system. As already mentioned in the introduction to matter energy–momentum tensors in Chapter 3, the concepts of energy, momentum, and angular momentum are related to the invariance properties of the solutions of the equations of motion under spacetime translations or rotations. The chapter explores these in greater detail. It first turns to isometries and Killing vect

APA, Harvard, Vancouver, ISO, and other styles

38

Horing, Norman J. Morgenstern. Interacting Electron–Hole–Phonon System. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0011.

Full text

Abstract:

Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle s

APA, Harvard, Vancouver, ISO, and other styles

39

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

Full text

Abstract:

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator

APA, Harvard, Vancouver, ISO, and other styles

40

Mann, Peter. The Hamiltonian & Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0014.

Full text

Abstract:

This chapter discusses the Hamiltonian and phase space. Hamilton’s equations can be derived in several ways; this chapter follows two pathways to arrive at the same result, thus giving insight into the motivation for forming these equations. The importance of deriving the same result in several ways is that it shows that, in physics, there are often several mathematical avenues to go down and that approaching a problem with, say, the calculus of variations can be entirely as valid as using a differential equation approach. The chapter extends the arenas of classical mechanics to include the co

APA, Harvard, Vancouver, ISO, and other styles

41

Epstein, Charles L., and Rafe Mazzeo. Maximum Principles and Uniqueness Theorems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0003.

Full text

Abstract:

This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both for the model operators on an open orthant and for the general Kimura diffusion operators on a compact manifold with corners, as well as their elliptic analogues. Of particular note in this regard is a generalization of the Hopf boundary point maximum principle. The chapter first presents maximum principles for the model operators before discussing Kimura diffusion operators on manifolds with corn

APA, Harvard, Vancouver, ISO, and other styles

42

Rajeev, S. G. Boundary Layers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0007.

Full text

Abstract:

It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’

APA, Harvard, Vancouver, ISO, and other styles

43

McDuff, Dusa, and Dietmar Salamon. From classical to modern. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0002.

Full text

Abstract:

The first chapter develops the basic concepts of symplectic topology from the vantage point of classical mechanics. It starts with an introduction to the Euler–Lagrange equation and shows how the Legendre transformation leads to Hamilton’s equations, symplectic forms, symplectomorphisms, and the symplectic action. It ends with a brief overview of some modern results in the subject on the symplectic topology of Euclidean space, such as the Weinstein conjecture and the Gromov nonsqueezing theorem.

APA, Harvard, Vancouver, ISO, and other styles

44

Horing, Norman J. Morgenstern. Q. M. Pictures; Heisenberg Equation; Linear Response; Superoperators and Non-Markovian Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0003.

Full text

Abstract:

Three fundamental and equivalent mathematical frameworks (“pictures”) in which quantum theory can be lodged are exhibited and their relations and relative advantages/disadvantages are discussed: (1) The Schrödinger picture considers the dynamical development of the overall system state vector as a function of time relative to a fixed complete set of time-independent basis eigenstates; (2) The Heisenberg picture (convenient for the use of Green’s functions) embeds the dynamical development of the system in a time-dependent counter-rotation of the complete set of basis eigenstates relative to th

APA, Harvard, Vancouver, ISO, and other styles

45

Morawetz, Klaus. Quantum Kinetic Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0009.

Full text

Abstract:

The gradient approximations of the Kadanoff and Baym equations are derived up to first order. The off-shell motions responsible for the satellites are shown to ensure causality. The cancellation of off-shell motions from the drift and correlation part of the reduced density provides a precursor of the kinetic equation for the quasiparticle distribution which leads to a functional between reduced and quasiparticle distribution, named the extended quasiparticle picture. Virial corrections appear as internal gradients in the selfenergy and therefore in the considered processes. With this extended

APA, Harvard, Vancouver, ISO, and other styles

46

Kanzieper, Eugene. Painlevé transcendents. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.9.

Full text

Abstract:

This article discusses the history and modern theory of Painlevé transcendents, with particular emphasis on the Riemann–Hilbert method. In random matrix theory (RMT), the Painlevé equations describe either the eigenvalue distribution functions in the classical ensembles for finite N or the universal eigenvalue distribution functions in the large N limit. This article examines the latter. It first considers the main features of the Riemann–Hilbert method in the theory of Painlevé equations using the second Painlevé equation as a case study before analysing the two most celebrated universal dist

APA, Harvard, Vancouver, ISO, and other styles

47

Deruelle, Nathalie, and Jean-Philippe Uzan. The Cartan structure equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0065.

Full text

Abstract:

This chapter focuses on Cartan structure equations. It first introduces a 1-form and its exterior derivative, before turning to a study of the connection and torsion forms, thereby expressing the torsion as a function of the connection forms and establishing the torsion differential 2-forms. It then turns to the curvature forms drawn from Chapter 23 and Cartan’s second structure equation, along with the curvature 2-forms. It also studies the Levi-Civita connection. The components of the Riemann tensor are then studied, with a Riemannian manifold, or a metric manifold with a torsion-less connec

APA, Harvard, Vancouver, ISO, and other styles

48

translator, Curtis Howard 1949, ed. The African equation. 2015.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

49

Succi, Sauro. Lattice Boltzmann Models for Microflows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0029.

Full text

Abstract:

The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fa

APA, Harvard, Vancouver, ISO, and other styles

50

Kleyn, Aleks. Introduction into Differential Equations: Banach Algebra. Independently Published, 2021.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!