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Books on the topic 'N) equation'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

1949-, Dervieux A., and Langley Research Center, eds. Looking for O(N) Navier-Stokes solutions on non-structured meshes. National Aeronautics and Space Administration, Langley Research Center, 1993.

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2

1949-, Dervieux A., and Langley Research Center, eds. Looking for O(N) Navier-Stokes solutions on non-structured meshes. National Aeronautics and Space Administration, Langley Research Center, 1993.

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3

Morano, Eric. Looking for O(N) Navier-Stokes solutions on non-structured meshes. Institute for Computer Applications in Science and Engineering, 1993.

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4

1949-, Dervieux A., and Langley Research Center, eds. Looking for O(N) Navier-Stokes solutions on non-structured meshes. National Aeronautics and Space Administration, Langley Research Center, 1993.

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5

Jorgenson, Jay. Heat Eisenstein series on SL[subscript n](C). American Mathematical Society, 2009.

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6

Jorgenson, Jay. Heat Eisenstein series on SL[subscript n](C). American Mathematical Society, 2009.

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7

Serge, Lang, ed. Heat Eisenstein series on SL[subscript n](C). American Mathematical Society, 2009.

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8

Zhukova, Galina. Differential equations: examples and tasks. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072182.

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To master the skills of solving examples and problems of the course "Ordinary differential equations" proposed a cycle of workshops covering the topics: differential equations of first, second, n-th orders; systems of linear differential equations; integration of initial and boundary value problems; stability theory. Given the large number of examples and tasks for independent operation with answers. This sample tests with solutions and analysis. It is recommended that teachers, postgraduates and students of higher educational institutions studying differential equations.

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9

Ambrosio, Vincenzo. Nonlinear Fractional Schrödinger Equations in R^N. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60220-8.

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10

Arkhipova, Arina A., and Alexander I. Nazarov. Nonlinear partial differential equations and related topics: Dedicated to Nina N. Uraltseva. American Mathematical Society, 2010.

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11

Andrea, Malchiodi, ed. Perturbation methods and semilinear elliptic problems on R[superscript n]. Birkhäuser Verlag, 2006.

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12

Hillel, Tal-Ezer, and Langley Research Center, eds. Modified Chebyshev pseudospectral method with O (N) time step restriction. National Aeronautics and Space Administration, Langley Research Center, 1990.

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13

Vekua, Ilʹi͡a Nestorovich. Academician N. Muskhelishvili: Short biography and survey of scientific works. Edited by Mandzhavidze G. F. "Metsniereba" Pub. House, 1991.

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14

Banks, Stephen P. Existence of periodic solutions in n-dimensional retarded functional differential equations. University of Sheffield, Dept. of Control Engineering, 1987.

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15

Uralʹt︠s︡eva, N. N. (Nina Nikolaevna), ed. Nonlinear partial differential equations and related topics: Dedicated to Nina N. Uraltseva. American Mathematical Society, 2010.

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16

Ecole d'été de probabilités de Saint-Flour (18th 1988). Ecole d'été de probabilités de Saint-Flour XVIII, 1988: A. Ancona, D. Geman, N. Ikeda ; editor, P.L. Hennequin. Springer-Verlag, 1990.

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17

Imbens, Huib-Jan. Finite dimensional solutions of hierarchies of soliton equations =: Eindig dimensionale oplossingen van hie rarchiee n van soliton vergelijkingen. [s.n.], 1989.

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18

Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. American Mathematical Society, 2014.

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19

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. American Mathematical Society, 2013.

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20

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.

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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

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21

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

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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

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22

Derivation of q-analogs for the radial Schrödinger equation in N space-dimensions. Nova Science Publishers, 1997.

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23

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.

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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

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24

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.

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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

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25

Sherwood, Dennis, and Paul Dalby. Thermodynamics and mathematics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0004.

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Most school mathematics is about how one variable, y, varies with respect to one other variable, x, according to an equation such as y = 3x2. Equations like this underpin the student’s knowledge of algebra, and differential and integral calculus. Thermodynamics, however, is necessarily about how a variable, such as the pressure P, varies with respect not to one but to three variables simultaneously – for example, the mole number n, the volume V, and the temperature T. This makes the algebra of thermodynamics more complex, and also implies that mutual changes between pairs of variables is descr

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26

Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and dis

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27

A presentation of the theory of Hermite's form of Lamé's equation: With a determination of the explicit forms in terms of the p function for the case n equal to three... Druck von B. G. Teubner, 1990.

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28

Solymar, L., D. Walsh, and R. R. A. Syms. Principles of semiconductor devices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0009.

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p–n junctions are examined initially and the potential distribution in the junction region is derived based on Poisson’s equation. Next the operation of the transistor is discussed, both in terms of the physics and of equivalent circuits. Potential distributions in metal–semiconductor junctions are derived and the concept of surface states is introduced. The physics of tunnel junctions is discussed in terms of their band structure. The properties of varactor diodes are described and the possibility of parametric amplification is touched upon. Further devices discussed are field effect transist

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29

Deruelle, Nathalie, and Jean-Philippe Uzan. Hamiltonian mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0009.

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This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension o

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30

Ambrosio, Vincenzo. Nonlinear Fractional Schr�dinger Equations in R^N. Springer International Publishing AG, 2021.

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31

Eynard, Bertrand. Random matrices and loop equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0007.

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This chapter is an introduction to algebraic methods in random matrix theory (RMT). In the first section, the random matrix ensembles are introduced and it is shown that going beyond the usual Wigner ensembles can be very useful, in particular by allowing eigenvalues to lie on some paths in the complex plane rather than on the real axis. As a detailed example, the Plancherel model is considered from the point of RMT. The second section is devoted to the saddle-point approximation, also called the Coulomb gas method. This leads to a system of algebraic equations, the solution of which leads to

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32

Deruelle, Nathalie, and Jean-Philippe Uzan. The N-body problem. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0013.

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This chapter discusses the N-body problem. In 1886, Karl Weierstrass submitted the following question to the scientific community on the occasion of a mathematical competition to mark the 60th birthday of King Oscar II of Sweden. Weierstrass asked that, ‘given a system of arbitrarily many mass points that attract each other according to Newton’s laws, try to find, under the assumption that no two points ever collide, a representation of the coordinates of each point as a series in a variable which is some known function of time and for all of whose values the series converges uniformly’. Henri

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33

Perturbation Methods and Semilinear Elliptic Problems on R[superscript N]. Birkhauser, 2006.

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34

Vyas, Nuka. GCE O / N Level Principles of Accounts - Formats and Equations. Pearson Education, Limited, 2007.

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35

Its, Alexander R. Random matrix theory and integrable systems. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.10.

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This article discusses the interaction between random matrix theory (RMT) and integrable theory, leading to ordinary and partial differential equations (PDEs) for the eigenvalue distribution of random matrix models of size n and the transition probabilities of non-intersecting Brownian motion models, for finite n and for n → ∞. It first provides an overview of the connection between the theory of orthogonal polynomials and the KP-hierarchy in integrable systems before examining matrix models and the Virasoro constraints. It then considers multiple orthogonal polynomials, taking into account no

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36

Ambrosetti, Antonio, and Andrea Malchiodi. Perturbation Methods and Semilinear Elliptic Problems on R^n (Progress in Mathematics Book 240). Birkhäuser, 2006.

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37

Khovanskii, Askold, Sergey Chulkov, and Sergey Chulkov. Geometry of the Semigroup Z_^n and its Applications to Combinatorics, Algebra and Differential Equations. Springer, 2021.

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38

Agmon, Shmuel. Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. Princeton University Press, 2014.

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39

Agmon, Shmuel. Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. Princeton University Press, 2014.

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40

Agmon, Shmuel. Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. Princeton University Press, 2016.

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41

Agmon, Shmuel. Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. Princeton University Press, 2014.

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42

Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identifie

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43

Raphael's Tables of Houses for Northern Latitudes from the Equator to 50 Degrees N. O', Also for Leningrad 59 Degrees N. 56'. Wehman Brothers, 1986.

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44

Series, Michigan Historical Reprint. Mathematical recreations, containing solutions of many very difficult and important equations, and of several useful problems in geometry, surveying and ... equations by projection. By H. N. Robinson. Scholarly Publishing Office, University of Michigan Library, 2005.

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45

Bartusek, M. Asymptotic properties of oscillatory solutions of differential equations of the n-TH order (Folia facultatis scientiarium naturalium Universitatis Masarykiana Brunensis/Mathematica). Masarykova Univerzita, 1992.

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46

Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.

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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η

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47

Polyglotta Africana Orientalis, a Collection of Words and Sentences in Languages Spoken South of the Equator [ed. by R. N. Cust]. Creative Media Partners, LLC, 2022.

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48

Polyglotta Africana Orientalis, a Collection of Words and Sentences in Languages Spoken South of the Equator [ed. by R. N. Cust]. Creative Media Partners, LLC, 2022.

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49

Back-of-the-Envelope Quantum Mechanics: With Extensions to Many-Body Systems and Integrable Pdes. World Scientific Publishing Co Pte Ltd, 2013.

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50

Back-Of-the-Envelope Quantum Mechanics: With Extensions to Many-Body Systems and Integrable Pdes. World Scientific Publishing Co Pte Ltd, 2013.

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