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1

Burris, Stanley. Number theoretic density and logical limit laws. Providence, RI: American Mathematical Society, 2001.

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2

Danos, Michael. Irreducible density matrices. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards, 1985.

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3

Danos, Michael. Irreducible density matrices. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards, 1985.

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4

A. J. H. van Es. Aspects of nonparametric density estimation. Amsterdam, The Netherlands: Centrum voor Wiskunde en Informatica, 1991.

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5

A course in density estimation. Boston: Birkhäuser, 1987.

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6

Paštéka, Milan. On four approaches to density. Frankfurt am Main: Peter Lang, 2013.

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7

Sahni, Viraht. Quantal Density Functional Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004.

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8

Devroye, Luc. Nonparametric density estimation: The L₁ view. New York: Wiley, 1985.

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9

Devroye, Luc. Nonparametric density estimation: The L1 view. New York: Wiley, 1985.

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10

W, Scott David. Multivariate density estimation: Theory, practice, and visualization. New York: Wiley, 1992.

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11

Gidopoulos, N. I. The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State. Dordrecht: Springer Netherlands, 2003.

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12

Rovini, Massimo. Low-density parity-check codes: A tutorial. Noordwijk: ESA Publications Division, 2004.

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13

Gallagher, Robert G. Low-density parity-check codes. Cambridge, Mass: MIT-Press, 2003.

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14

Gallager, Robert G. Low-density parity-check codes. Cambridge: M.I.T. Press, 2005.

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15

Petkov, I. Zh. Nuclear density functional theory. Oxford: Clarendon Press, 1991.

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16

Silverman, B. W. Density estimation for statistics and data analysis. London: Chapman and Hall, 1986.

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17

Density estimation for statistics and data analysis. Boca Raton: Chapman & Hall/CRC, 1998.

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18

Putz, Mihai V. Quantum theory: Density, condensation, and bonding. Toronto: Apple Academic Press, 2013.

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19

Density waves in solids. Reading, Mass: Addison-Wesley Pub. Co., Advanced Book Program, 1994.

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20

1981-, Suzuki Taiji, and Kanamori Takafumi 1971-, eds. Density ratio estimation in machine learning. Cambridge: Cambridge University Press, 2012.

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21

1916-, Lin C. C., ed. Spiral structure in galaxies: A density wave theory. Cambridge, Mass: MIT Press, 1996.

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22

Lubow, Stephen H. Shapes of star-gas waves in spiral galaxies. Baltimore, MD: Space Telescope Science Institute, 1990.

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23

Lubow, Stephen H. Shapes of star-gas waves in spiral galaxies. Baltimore, MD: Space Telescope Science Institute, 1990.

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24

Ballot, Christian. Density of prime divisors of linear recurrences. Providence, R.I: American Mathematical Society, 1995.

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25

Visscher, Mark Ivar. Transport in mesoscopic charge density wawe systems. Delft: Delft Univ. Press, 1998.

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26

Weitao, Yang, ed. Density-functional theory of atoms and molecules. New York: Oxford University Press, 1989.

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27

Moon, Jaekyun. Sequence detection for high-density storage channels. Boston: Kluwer Academic, 1992.

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28

Raynal, Ph. Unambiguous state discrimination of two density matrices in quantum information theory. Erlangen: Lehrstuhl für Mikrocharakterisierung, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2008.

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29

service), SpringerLink (Online, ed. Density Matrix Theory and Applications. 3rd ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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30

Inc, ebrary, ed. Functional estimation for density, regression models and processes. Singapore: World Scientific, 2011.

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31

Klemelä, Jussi. Smoothing of multivariate data: Density estimation and visualization. Hoboken, N.J: Wiley, 2008.

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32

Brunner, Lawrence J. Bayesian nonparametric methods for data from a unimodal density. Toronto: Dept. of Statistics, University of Toronto, 1991.

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33

Koch, Wolfram. A chemist's guide to density functional theory. 2nd ed. Weinheim: Wiley-VCH, 2001.

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34

C, Holthausen Max, ed. A chemist's guide to density functional theory. Weinheim: Wiley-VCH, 2000.

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35

Zadachi teorii potent͡siala i obobshchennai͡a Zemli͡a. Moskva: "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1991.

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36

D, Mateescu Gh. 2D NMR: Density matrix and product operator treatment. Englewood Cliffs, N.J: PTR Prentice Hall, 1993.

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37

Jeffrey, George A. The Application of Charge Density Research to Chemistry and Drug Design. Boston, MA: Springer US, 1991.

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38

Filippi, Claudia. Generalized gradient approximations to density functional theory: Comparison with exact results. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.

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39

NATO Advanced Study Institute on the Application of Charge Density Research to Chemistry and Drug Design (1990 San Felíu de Guixols, Spain). The application of charge density research to chemistry and drug design. New York: Plenum Press, 1991.

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40

Tanabe, Kunio. BNDE, FORTRAN subroutines for computing Bayesian nonparametric univariate and bivariate density estimator. Tokyo: Institute of Statistical Mathematics, 1988.

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41

Cannizzaro, Stanislao. Sunto di un corso di filosofia chimica. Palermo: Sellerio, 1991.

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42

Johnson, Sarah J. Iterative error correction: Turbo, low-density parity-check and repeat-accumulate codes. New York: Cambridge University Press, 2009.

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43

Invariant geometric structures: A non-linear extension of the Borel density theorem. 1989.

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44

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 discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.
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45

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

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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 for the quasiparticle distribution forms a consistent theory. The entropy is shown to consist also of a quasiparticle part and a correlated part. The explicit entropy gain is proved to complete the H-theorem even for nonlocal collision events. The limit of Landau theory is explored when neglecting the delay time. The rearrangement energy is found to mediate between the spectral quasiparticle energy and the Landau variational quasiparticle energy.
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46

United States. National Aeronautics and Space Administration., ed. Magnetospheric-ionospheric poynting flux: Final report. Menlo Park, CA: SRI International, 1994.

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47

Magnetospheric-ionospheric poynting flux: Final report. Menlo Park, CA: SRI International, 1994.

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48

United States. National Aeronautics and Space Administration., ed. Magnetospheric-ionospheric poynting flux: Final report. Menlo Park, CA: SRI International, 1994.

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49

Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. Density Functional Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.003.0001.

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Density functional theory (DFT) has established itself as a very capable platform for modelling from first principles electronic, optical, mechanical and structural properties of materials. Starting out from the Dirac equation for the many-body system of electrons and nuclei, an effective theory has been developed allowing for materials specific and parameter free simulations of non-magnetic and magnetic solid matter. In this Chapter an introduction will be given to DFT, the Hohenberg-Kohn theorems, the Kohn-Sham equation, and the formalism for how to deal with non-collinear magnetism.
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50

Bondarev, Boris V., ed. Density Matrix Theories in Quantum Physics. BENTHAM SCIENCE PUBLISHERS, 2020. http://dx.doi.org/10.2174/97898114754121200101.

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