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1

Pang, Xiaoyan, Chen Feng, and Xinying Zhao. "Evolution of spin density vectors in a strongly focused composite field." Chinese Optics Letters 19, no. 2 (2021): 022601. http://dx.doi.org/10.3788/col202119.022601.

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2

Seppänen, Anne, and Kalle Parvinen. "Evolution of Density-Dependent Cooperation." Bulletin of Mathematical Biology 76, no. 12 (September 12, 2014): 3070–87. http://dx.doi.org/10.1007/s11538-014-9994-y.

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3

Heuser, P., and V. Lamzin. "Density modification by directed evolution of electron-density maps." Acta Crystallographica Section A Foundations of Crystallography 64, a1 (August 23, 2008): C220. http://dx.doi.org/10.1107/s0108767308092921.

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4

Wang, C. C., S. R. Kulkarni, and H. V. Poor. "Density Evolution for Asymmetric Memoryless Channels." IEEE Transactions on Information Theory 51, no. 12 (December 2005): 4216–36. http://dx.doi.org/10.1109/tit.2005.858931.

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5

Brüning, E., and F. Petruccione. "Density Matrices and Their Time Evolution." Open Systems & Information Dynamics 15, no. 02 (June 2008): 109–21. http://dx.doi.org/10.1142/s1230161208000109.

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Already in the case of finite dimensional Hilbert spaces [Formula: see text] the general form of density matrices ρ is not known. The main reason for this lack of knowledge is the nonlinear constraint for these matrices. We propose a representation of density matrices on finite dimensional Hilbert spaces in terms of finitely many independent parameters. For dimensions 2, 3, and 4 we write down this representation explicitly. As a further application of this representation we study the time dependence of density matrices ρ(t) which in our case is implemented through time dependence of the independent parameters. Under obvious differentiability assumptions the explicit form of [Formula: see text] is determined. As a special case we recover, for instance, the Lindblad form.
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6

Travis, Justin M. J., David J. Murrell, and Calvin Dytham. "The evolution of density–dependent dispersal." Proceedings of the Royal Society of London. Series B: Biological Sciences 266, no. 1431 (September 22, 1999): 1837–42. http://dx.doi.org/10.1098/rspb.1999.0854.

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7

Fisher, Karl B., Michael A. Strauss, Marc Davis, Amos Yahil, and John P. Huchra. "The density evolution of IRAS galaxies." Astrophysical Journal 389 (April 1992): 188. http://dx.doi.org/10.1086/171196.

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8

Balitsky, I. I., and A. V. Belitsky. "Nonlinear evolution in high-density QCD." Nuclear Physics B 629, no. 1-3 (May 2002): 290–322. http://dx.doi.org/10.1016/s0550-3213(02)00149-9.

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9

Braun, Mikhail, and Gian Paolo Vacca. "Evolution of the gluon density in." European Physical Journal C 4, no. 1 (1998): 85. http://dx.doi.org/10.1007/s100520050187.

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10

Morikawa, Masahiro. "Evolution of the cosmic density matrix." Physical Review D 40, no. 12 (December 15, 1989): 4023–27. http://dx.doi.org/10.1103/physrevd.40.4023.

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11

Geerlings, Paul. "From Density Functional Theory to Conceptual Density Functional Theory and Biosystems." Pharmaceuticals 15, no. 9 (September 6, 2022): 1112. http://dx.doi.org/10.3390/ph15091112.

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The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.
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12

Park, Min, Hong-Young Chang, Shin-Jae You, Jung-Hyung Kim, and Yong-Hyeon Shin. "Anomalous evolution of Ar metastable density with electron density in high density Ar discharge." Physics of Plasmas 18, no. 10 (October 2011): 103510. http://dx.doi.org/10.1063/1.3640518.

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13

FINKELSHTEIN, DMITRI, YURI KONDRATIEV, and OLEKSANDR KUTOVIY. "VLASOV SCALING FOR THE GLAUBER DYNAMICS IN CONTINUUM." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 04 (December 2011): 537–69. http://dx.doi.org/10.1142/s021902571100450x.

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We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive density system in infinite volume is shown. Chaos preservation property of this evolution gives a possibility to derive a nonlinear Vlasov-type equation for the particle density of the limiting system.
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14

Travis, Joseph, Jeff Leips, and F. Helen Rodd. "Evolution in Population Parameters: Density-Dependent Selection or Density-Dependent Fitness?" American Naturalist 181, S1 (May 2013): S9—S20. http://dx.doi.org/10.1086/669970.

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15

kiran, P. Ravi, and Mehul C. Patel. "Density Evolution of Low Density Parity Check codes over different channels." International Journal of VLSI & Signal Processing 4, no. 4 (August 25, 2017): 1–6. http://dx.doi.org/10.14445/23942584/ijvsp-v4i4p101.

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16

JIE, LI, and CHEN JIANBING. "PROBABILITY DENSITY EVOLUTION EQUATIONS — A HISTORICAL INVESTIGATION." Journal of Earthquake and Tsunami 03, no. 03 (September 2009): 209–26. http://dx.doi.org/10.1142/s1793431109000536.

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The paper aims at clarifying the essential relationship between traditional probability density evolution equations and the generalized probability density evolution equation which is developed by the authors in recent years. Using the principle of preservation of probability as a uniform fundamental, the probability density evolution equations, including the Liouville equation, Fokker–Planck equation and the Dostupov–Pugachev equation, are derived from the physical point of view. It is pointed out that combining with Eulerian or Lagrangian description of the associated dynamical system will lead to different probability density evolution equations. Particularly, when both the principle and dynamical systems are viewed from Lagrangian description, we are led to the generalized probability density evolution equation.
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17

Blanc, G., and L. Greggio. "Supernova progenitors and iron density evolution from SN rate evolution measurements." New Astronomy 13, no. 8 (November 2008): 606–18. http://dx.doi.org/10.1016/j.newast.2008.03.010.

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18

Tao, Weifeng, and Jie Li. "An ensemble evolution numerical method for solving generalized density evolution equation." Probabilistic Engineering Mechanics 48 (April 2017): 1–11. http://dx.doi.org/10.1016/j.probengmech.2017.03.001.

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19

LIU Qing-juan, 刘庆娟, 张英杰 ZHANG Ying-jie, and 夏云杰 XIA Yun-jie. "Evolution of Entanglement Density in Band Gap." Acta Sinica Quantum Optica 19, no. 3 (2013): 249–55. http://dx.doi.org/10.3788/asqo20131903.0249.

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20

Zhang, Xingwen, Zhengyang Zhou, Hongping Wu, Shilie Pan, Chen Lei, Lu Liu, and Zhihua Yang. "An unusual density evolution between SrCdB2O5 polymorphs." Dalton Transactions 44, no. 36 (2015): 15823–28. http://dx.doi.org/10.1039/c5dt00915d.

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A new SrCdB2O5 phase (β-SrCdB2O5) has been discovered and an unusual density phenomenon between SrCdB2O5 polymorphs has been investigated in detail. Furthermore, the Pb2+-doped compounds, PbxSr1−xCdB2O5 (x = 0.125, 0.25, 0.375, 0.5), have also been investigated by powder refinement.
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21

Taylor, A. N., and P. I. R. Watts. "Evolution of the cosmological density distribution function." Monthly Notices of the Royal Astronomical Society 314, no. 1 (May 1, 2000): 92–98. http://dx.doi.org/10.1046/j.1365-8711.2000.03339.x.

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22

Bing-Ren, Shi. "Semi-analytical modeling of tokamak density evolution." Chinese Physics B 19, no. 6 (June 2010): 065202. http://dx.doi.org/10.1088/1674-1056/19/6/065202.

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23

Che, H., Y. Yang, and R. J. Nemiroff. "Source Density Evolution of Gamma‐Ray Bursts." Astrophysical Journal 516, no. 2 (May 10, 1999): 559–62. http://dx.doi.org/10.1086/307154.

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24

Grzybowski, H. Tomasz. "Total linearization of probability density evolution equations." International Journal of Theoretical Physics 28, no. 3 (March 1989): 377–80. http://dx.doi.org/10.1007/bf00670209.

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25

Richardson, Tom, and Rudiger Urbanke. "Fixed Points and Stability of Density Evolution." Communications in Information and Systems 4, no. 1 (2004): 103–16. http://dx.doi.org/10.4310/cis.2004.v4.n1.a6.

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26

Singhal, Harsh, Anand Agarwal, V. M. Gadre, and Nalin Pithwa. "Density Evolution for Multiple-Channel Communication Scenarios." IETE Journal of Research 51, no. 2 (March 2005): 163–69. http://dx.doi.org/10.1080/03772063.2005.11416391.

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27

Wanzenried, Gabrielle, and Sandra Nocera. "The Evolution of Physician Density in Switzerland." Swiss Journal of Economics and Statistics 144, no. 2 (January 2, 2008): 247–82. http://dx.doi.org/10.1007/bf03399254.

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28

Braasch, H., Y. Estrin, and Y. Bréchet. "A stochastic model for dislocation density evolution." Scripta Materialia 35, no. 2 (July 1996): 279–84. http://dx.doi.org/10.1016/1359-6462(96)00131-5.

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29

Seo, B. H., J. H. Kim, and S. J. You. "Normal and abnormal evolution of argon metastable density in high-density plasmas." Physics of Plasmas 22, no. 5 (May 2015): 053510. http://dx.doi.org/10.1063/1.4921213.

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30

Pishdast, M., J. Yazdanpanah, and S. A. Ghasemi. "Electron acceleration by an intense laser pulse inside a density profile induced by non-linear pulse evolution." Laser and Particle Beams 36, no. 1 (January 25, 2018): 41–48. http://dx.doi.org/10.1017/s0263034617000970.

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AbstractBy sophisticated application of particle-in-cell simulations, we demonstrate the ultimate role of non-linear pulse evolutions in accelerating electrons during the entrance of an intense laser pulse into a preformed density profile. As a key point in our discussions, the non-linear pulse evolutions are found to be very fast even at very low plasma densities, provided that the pulse length exceeds the local plasma wavelength. Therefore, these evolutions are sufficiently developed during the propagation of typical short density scale lengths occurred at high contrast ratios of the pulse, and lead to plasma heating via stochastic acceleration in multi-waves. Further analysis of simulation data at different physical parameters indicates that the rate of evolutions increases with the plasma density leading to higher plasma heating and overgrown energetic electrons. In the same way, shortening the density scale length results into increase in the evolution rate and, simultaneously, decrease in the interaction time. This behavior can describe the observed optimum value of pre-plasma scale length for the maximum electron heating.
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31

Oda, Takeshi, Tomonori Totani, Naoki Yasuda, Takahiro Sumi, Tomoki Morokuma, Mamoru Doi, and George Kosugi. "Implications for Galaxy Evolution from Cosmic Evolution of the Supernova Rate Density." Publications of the Astronomical Society of Japan 60, no. 2 (April 25, 2008): 169–82. http://dx.doi.org/10.1093/pasj/60.2.169.

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32

Wei, X., and A. N. Akansu. "Density evolution for low-density parity-check codes under Max-Log-MAP decoding." Electronics Letters 37, no. 18 (2001): 1125. http://dx.doi.org/10.1049/el:20010755.

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33

SILVA E COSTA, SANDRO. "DENSITY PERTURBATIONS AND THE CHAPLYGIN GAS." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1674–77. http://dx.doi.org/10.1142/s0217751x09045212.

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One approach in modern cosmology consists in supposing that dark matter and dark energy are different manifestations of a single 'quartessential' fluid. Following such idea, this work presents a summary of some studies of the evolution of density perturbations in a flat cosmological model with a modified Chaplygin gas acting as a single component. Our goal is to obtain properties of the model which can be used to distinguish it from another cosmological models which have the same solutions for the general evolution of the scale factor of the universe, even without the construction of the power spectrum. Both our analytical and numerical results clearly indicate as one interesting feature of the model the presence of peaks in the evolution of the density constrast.
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34

Rodrigues, António M. M., and Rufus A. Johnstone. "Evolution of positive and negative density-dependent dispersal." Proceedings of the Royal Society B: Biological Sciences 281, no. 1791 (September 22, 2014): 20141226. http://dx.doi.org/10.1098/rspb.2014.1226.

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Understanding the evolution of density-dependent dispersal strategies has been a major challenge for evolutionary ecologists. Some existing models suggest that selection should favour positive and others negative density-dependence in dispersal. Here, we develop a general model that shows how and why selection may shift from positive to negative density-dependence in response to key ecological factors, in particular the temporal stability of the environment. We find that in temporally stable environments, particularly with low dispersal costs and large group sizes, habitat heterogeneity selects for negative density-dependent dispersal, whereas in temporally variable environments, particularly with high dispersal costs and small group sizes, habitat heterogeneity selects for positive density-dependent dispersal. This shift reflects the changing balance between the greater competition for breeding opportunities in more productive patches, versus the greater long-term value of offspring that establish themselves there, the latter being very sensitive to the temporal stability of the environment. In general, dispersal of individuals out of low-density patches is much more sensitive to habitat heterogeneity than is dispersal out of high-density patches.
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35

Alfaro, Matthieu, and Mario Veruete. "Density dependent replicator-mutator models in directed evolution." Discrete & Continuous Dynamical Systems - B 25, no. 6 (2020): 2203–21. http://dx.doi.org/10.3934/dcdsb.2019224.

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36

Dunnavan, Edwin L., Zhiyuan Jiang, Jerry Y. Harrington, Johannes Verlinde, Kyle Fitch, and Timothy J. Garrett. "The Shape and Density Evolution of Snow Aggregates." Journal of the Atmospheric Sciences 76, no. 12 (November 27, 2019): 3919–40. http://dx.doi.org/10.1175/jas-d-19-0066.1.

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Abstract Snow aggregates evolve into a variety of observed shapes and densities. Despite this diversity, models and observational studies employ fractal or Euclidean geometric measures that are assumed universal for all aggregates. This work therefore seeks to improve understanding and representation of snow aggregate geometry and its evolution by characterizing distributions of both observed and Monte Carlo–generated aggregates. Two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations suggest the use of a bivariate beta distribution model for capturing aggregate shapes. Product moments of this model capture shape effects to within 4% of observations. This mathematical model is used along with Monte Carlo simulated aggregates to study how combinations of monomer properties affect aggregate shape evolution. Plate aggregates of any aspect ratio produce a consistent ellipsoid shape evolution whereas thin column aggregates evolve to become more spherical. Thin column aggregates yield fractal dimensions much less than the often-assumed value of 2.0. Ellipsoid densities and fractal analogs of density (lacunarity) are much more variable depending on combinations of monomer size and shape. Simple mathematical scaling relationships can explain the persistent triaxial ellipsoid shapes that appear in both observed and modeled aggregates. Overall, both simulations and observations prove aggregates are rarely oblate. Therefore, the use of the proposed bivariate ellipsoid distribution in models will allow for similar-sized aggregates to exhibit a realistic dispersion of masses and fall speeds.
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37

Knell, R. J. "Population density and the evolution of male aggression." Journal of Zoology 278, no. 2 (June 2009): 83–90. http://dx.doi.org/10.1111/j.1469-7998.2009.00566.x.

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38

Chen, Guoxong, and Tsu‐Jye A. Nee. "A local measurement of Ba+density temporal evolution." Journal of Applied Physics 61, no. 9 (May 1987): 4707–10. http://dx.doi.org/10.1063/1.338047.

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39

Krishnanan, M. S., and B. C. Sanctuary. "Evolution of Spin Density Matrix in Pure NQR." Zeitschrift für Naturforschung A 42, no. 8 (August 1, 1987): 907–8. http://dx.doi.org/10.1515/zna-1987-0825.

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40

Lugaz, N., W. B. Manchester IV, and T. I. Gombosi. "The Evolution of Coronal Mass Ejection Density Structures." Astrophysical Journal 627, no. 2 (July 10, 2005): 1019–30. http://dx.doi.org/10.1086/430465.

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41

Winter, Thomas G., Chizuko M. Dutta, and Neal F. Lane. "Evolution of electronic probability density inα-H collisions." Physical Review A 31, no. 4 (April 1, 1985): 2702–5. http://dx.doi.org/10.1103/physreva.31.2702.

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42

Tomasel, F. G., J. J. Rocca, O. D. Cortázar, B. T. Szapiro, and R. W. Lee. "Plasma-density evolution in compact polyacetal capillary discharges." Physical Review E 47, no. 5 (May 1, 1993): 3590–97. http://dx.doi.org/10.1103/physreve.47.3590.

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43

Santambrogio, Filippo. "Crowd motion and evolution PDEs under density constraints." ESAIM: Proceedings and Surveys 64 (2018): 137–57. http://dx.doi.org/10.1051/proc/201864137.

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This is a survey about the theory of density-constrained evolutions in theWasserstein space developed by B. Maury, the author, and their collaborators as a model for crowd motion. Connections with microscopic models and other PDEs are presented, as well as several time-discretization schemes based on variational techniques, together with the main theorems guaranteeing their convergence as a tool to prove existence results. Then, a section is devoted to the uniqueness question, and a last one to different numerical methods inspired by optimal transport.
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44

Doran, Michael, Khamphee Karwan, and Christof Wetterich. "Observational constraints on the dark energy density evolution." Journal of Cosmology and Astroparticle Physics 2005, no. 11 (November 22, 2005): 007. http://dx.doi.org/10.1088/1475-7516/2005/11/007.

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45

Salvador-Solé, E., A. Manrique, and G. González-Casado. "Evolution and Origin of Dark Halo Density Profiles." EAS Publications Series 20 (2006): 55–58. http://dx.doi.org/10.1051/eas:2006047.

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46

Guo, P. Z., L. D. Mueller, and F. J. Ayala. "Evolution of behavior by density-dependent natural selection." Proceedings of the National Academy of Sciences 88, no. 23 (December 1, 1991): 10905–6. http://dx.doi.org/10.1073/pnas.88.23.10905.

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47

Stutz, A. M., and J. Kainulainen. "Evolution of column density distributions within Orion A." Astronomy & Astrophysics 577 (May 2015): L6. http://dx.doi.org/10.1051/0004-6361/201526243.

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48

Galli, M., F. Marabelli, and E. Bauer. "Evolution of carrier density in the seriesYCu5−xInx." Physical Review B 53, no. 15 (April 15, 1996): 9517–20. http://dx.doi.org/10.1103/physrevb.53.9517.

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49

Calura, Francesco, and Francesca Matteucci. "The Cosmic Evolution of the Galaxy Luminosity Density." Astrophysical Journal 596, no. 2 (October 20, 2003): 734–47. http://dx.doi.org/10.1086/378195.

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50

Strobl, Karl, and Thomas J. Weiler. "Anharmonic evolution of the cosmic axion density spectrum." Physical Review D 50, no. 12 (December 15, 1994): 7690–702. http://dx.doi.org/10.1103/physrevd.50.7690.

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