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1

Sapaty, P. S. "Mosaic Warfare: from philosophy to model to solutions." Mathematical machines and systems 3 (2019): 17–34. http://dx.doi.org/10.34121/1028-9763-2019-3-17-34.

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2

Hillert, Mats. "A modified regular-solution model for terminal solutions." Metallurgical Transactions A 17, no. 10 (October 1986): 1878–79. http://dx.doi.org/10.1007/bf02817285.

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3

Zemlyanukhin, A. I., and A. V. Bochkarev. "Analytical Properties and Solutions of the FitzHugh – Rinzel Model." Nelineinaya Dinamika 15, no. 1 (2019): 3–12. http://dx.doi.org/10.20537/nd190101.

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4

Valentová, H., S. Škrovánková, Z. Panovská, and J. Pokorný. "Determination of astringent taste in model solutions and in beverages." Czech Journal of Food Sciences 19, No. 5 (February 10, 2013): 196–200. http://dx.doi.org/10.17221/6607-cjfs.

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The astringent taste is important for the sensory quality of beverages. Perception thresholds of two important astringent compounds – tannic acid and (+)-catechin were determined using two procedures. The concentration-intensity dependence was linear at low concentrations and up to medium intensities of the astringent taste if unstructured graphical scales were used, but the saturation threshold was soon attained in the case of tannic acid. Recording the results on printed forms gave similar results as using a touch-sensitive monitor. The optimum tasting was achieved at swallowing after degustation of 5 s. The duration of degustation increased the intensity. The astringent flavour was suppressed by sugar, but was not significantly influenced by ethanol, citric acid or quinine hydrochloride. Astringent substances were accurately perceived and rated in wine, tea infusion and orange drink, but the increase of astringency was smaller than in model solutions. The astringent taste was easily distinguished from the bitter taste.
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5

Cieplińska, Jagienka, and Agnieszka Szmelter-Jarosz. "Toward Most Valuable City Logistics Initiatives: Crowd Logistics Solutions’ Assessment Model." Central European Management Journal 28, no. 2 (June 15, 2020): 38–56. http://dx.doi.org/10.7206/cemj.2658-0845.21.

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Introduction: Crowd logistics is a widely accepted concept in times of the growing popularity of sharing economy solutions. The popularity of e-commerce and a tendency to provide same-day delivery are the main reasons for their development. Developing those trends requires new products and services, now available on the market, known in the transport area as crowd logistics solutions. Purpose: The purpose of the paper is to provide a tool for assessing crowd-logistics solutions, taking into consideration customers’ requirements. The text includes groups of environmental, economic, and social criteria to facilitate the choice of the best crowd logistics solution for freight transport. Methodology: The research is based on the critical analysis of different sources (literature, European Commission reports, other reports and analyses) and practical solutions in the field of crowd logistics. The main data analysis method is the Analytic Hierarchy Process, usually used to evaluate variants in decision-making processes. This method was chosen because of the variety of data types (quantitative and qualitative) and formats, its popularity, universality, and replicability. Results: This paper contains ready-to-use weights for the assessment of crowd logistics solutions. The proposed set of criteria and weights can be a useful tool for customers to evaluate the sharing- -economy services landscape in the areas they manage.
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6

Alisherovich, Alisherov Akramboy. "MATHEMATICAL MODEL AND NUMERICAL METHODS OF FILTRATION PROCESSES OF LIQUID SOLUTIONS." American Journal of Applied Science and Technology 4, no. 10 (October 1, 2024): 43–47. http://dx.doi.org/10.37547/ajast/volume04issue10-07.

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Filtration processes of liquid solutions are fundamental in many natural and industrial applications, such as environmental protection, chemical engineering, water purification, and petroleum extraction. This article develops a mathematical model for describing filtration processes and explores various numerical methods for solving the governing equations. The model is based on Darcy’s law, continuity equation, and constitutive relations of liquid solutions in porous media. Numerical methods, including finite difference, finite element, and finite volume approaches, are discussed with applications to various filtration scenarios. We also provide analysis of the stability, convergence, and efficiency of these methods.
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7

McNaughton, Alastair. "Model Solutions to Quadratic Equations." Mathematics Teacher 79, no. 5 (May 1986): 332–36. http://dx.doi.org/10.5951/mt.79.5.0332.

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Here is a method of representing quadratic functions by three-dimensional wire models. It enables one to form a simple geometric concept of the location of the imaginary zeros. I have been using this material with my students and have been delighted with the ease with which they respond to it. As a result, their confidence in dealing with complex numbers has increased, their concept of functions has shown much improvement, and they are attacking problems with real insight.
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8

Zhang, Ruifeng, Nan Liu, and Man An. "Analytical solutions of Skyrme model." Discrete and Continuous Dynamical Systems - Series S 9, no. 6 (November 2016): 2201–11. http://dx.doi.org/10.3934/dcdss.2016092.

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9

Shi, Chang-Guang, and Minoru Hirayama. "Solitonic solutions of Faddeev model." Journal of Mathematical Physics 53, no. 2 (February 2012): 022301. http://dx.doi.org/10.1063/1.3682246.

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10

Bhadeshia, H. K. D. H. "Quasichemical model for interstitial solutions." Materials Science and Technology 14, no. 4 (April 1998): 273–76. http://dx.doi.org/10.1179/mst.1998.14.4.273.

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11

Kosmidis, Leonidas. "METASAT's Model Based Design Solutions." ACM SIGAda Ada Letters 44, no. 1 (December 2, 2024): 51–52. https://doi.org/10.1145/3706601.3706608.

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METASAT is a recently started project (January 2023) in the Horizon Europe programme, in the SPACE call, coordinated by the Barcelona Supercomputing Center (BSC). METASAT will develop model-based design (MBD) solutions for high performance on-board processors such as multicores, Graphics Processing Units (GPUs) and Artificial Intelligence (AI) Accelerators. While the developed tools and methodologies are particularly focusing on the space domain, reusability to other safety critical domains is also a project goal. This talk will provide an overview of the solutions which will be developed during the project, which will be centered around the open source TASTE framework used at the European Space Agency (ESA), which leverages AADL.
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12

Kasperchik, V. P., and A. V. Bil'dyukevich. "Ultrafiltration of model heparin solutions." Pharmaceutical Chemistry Journal 29, no. 4 (April 1995): 294–96. http://dx.doi.org/10.1007/bf02219558.

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13

Han, I. S., and M. Cheryan. "Nanofiltration of model acetate solutions." Journal of Membrane Science 107, no. 1-2 (November 1995): 107–13. http://dx.doi.org/10.1016/0376-7388(95)00107-n.

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14

Bijalwan, Naveen. "Exact solutions: classical electron model." Astrophysics and Space Science 336, no. 2 (September 6, 2011): 485–89. http://dx.doi.org/10.1007/s10509-011-0796-5.

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15

Zarea, Sana’a A. "NEW SOLUTIONS FOR BIOLOGICAL MODEL." Advances in Differential Equations and Control Processes 17, no. 3 (September 30, 2016): 213–29. http://dx.doi.org/10.17654/de017030213.

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16

Storbacka, Kaj. "A solution business model: Capabilities and management practices for integrated solutions." Industrial Marketing Management 40, no. 5 (July 2011): 699–711. http://dx.doi.org/10.1016/j.indmarman.2011.05.003.

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17

Li, Jiequan, and Gerald Warnecke. "On measure solutions to the Zero-pressure gas model and their uniqueness." Mathematica Bohemica 127, no. 2 (2002): 265–73. http://dx.doi.org/10.21136/mb.2002.134173.

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18

Kislenko, Volodymyr, Liliya Oliynyk, and Svyatoslav Ivanyshyn. "The Model of Metal Oxide Particle Formation from Water Solutions of Salts." Chemistry and Chemical Technology 4, no. 2 (June 15, 2010): 95–100. http://dx.doi.org/10.23939/chcht04.02.095.

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The model describing the formation of metal oxide particles from water solutions of salts was suggested. Dependence of instability constants of metal complexes and ionization constants of oxygen containing inorganic acids on the electron density upon the central ion or atom allows to calculate these values for metal hydroxides. Equations describing the number of metal ions in polyion, the concentration of polyions in solution, the number of metal ions in primary metal oxide particles and their concentration in the system were suggested.
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19

Bogdanov, Andrey. "A DISTRIBUTION SYSTEM DESIGN MODEL." Journal Scientific and Applied Research 25, no. 1 (November 29, 2023): 59–69. http://dx.doi.org/10.46687/jsar.v25i1.381.

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20

Perry, R. L., J. D. Massie, and P. T. Cummings. "An analytic model for aqueous electrolyte solutions based on fluctuation solution theory." Fluid Phase Equilibria 39, no. 3 (January 1988): 227–66. http://dx.doi.org/10.1016/0378-3812(88)85007-6.

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21

Cranston, Michael. "Properties of the Parabolic Anderson Model and the Anderson Polymer Model." ISRN Probability and Statistics 2013 (March 19, 2013): 1–21. http://dx.doi.org/10.1155/2013/857984.

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In this article we examine some properties of the solutions of the parabolic Anderson model. In particular we discuss intermittency of the field of solutions of this random partial differential equation, when it occurs and what the field looks like when intermittency doesn't hold. We also explore the behavior of a polymer model created by a Gibbs measure based on solutions to the parabolic Anderson equation.
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22

Abbott, Steve, and Teunis C. Dorlas. "Statistical Mechanics: Fundamentals and Model Solutions." Mathematical Gazette 84, no. 500 (July 2000): 375. http://dx.doi.org/10.2307/3621734.

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23

Berdnikov, V. I., and Yu A. Gudim. "THREE-PARAMETER MODEL OF SUBREGULAR SOLUTIONS." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 58, no. 4 (June 10, 2015): 226. http://dx.doi.org/10.17073/0368-0797-2015-4-226-229.

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24

Strosnider, J. K., P. Nandi, S. Kumaran, S. Ghosh, and A. Arsnajani. "Model-driven synthesis of SOA solutions." IBM Systems Journal 47, no. 3 (2008): 415–32. http://dx.doi.org/10.1147/sj.473.0415.

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25

Kuznetsov, V. D., and N. S. Dzhalilov. "Anisotropic MHD model and some solutions." Plasma Physics Reports 36, no. 9 (September 2010): 788–93. http://dx.doi.org/10.1134/s1063780x10090059.

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26

Brihaye, Y., and T. N. Tomaras. "The Goldstone model static solutions onS1." Nonlinearity 12, no. 4 (January 1, 1999): 867–76. http://dx.doi.org/10.1088/0951-7715/12/4/307.

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27

Barbato, David, Francesco Morandin, and Marco Romito. "Smooth solutions for the dyadic model." Nonlinearity 24, no. 11 (September 30, 2011): 3083–97. http://dx.doi.org/10.1088/0951-7715/24/11/004.

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28

Amari, Yuki, Paweł Klimas, Nobuyuki Sawado, and Yuta Tamaki. "Solutions in the CPNSkyrme type model." Journal of Physics: Conference Series 670 (January 25, 2016): 012002. http://dx.doi.org/10.1088/1742-6596/670/1/012002.

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29

Leung, Kevin, and Félix S. Csajka. "Lattice Model for Metal Ammonia Solutions." Physical Review Letters 78, no. 19 (May 12, 1997): 3721–24. http://dx.doi.org/10.1103/physrevlett.78.3721.

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30

Chen, Ching L. "Analytic Solutions for Tidal Model Testing." Journal of Hydraulic Engineering 115, no. 12 (December 1989): 1707–14. http://dx.doi.org/10.1061/(asce)0733-9429(1989)115:12(1707).

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31

Xiong, Weiwen. "Solutions: A Mixed-Error Component Model." Econometric Theory 12, no. 2 (June 1996): 401–2. http://dx.doi.org/10.1017/s0266466600006721.

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32

Pan, Feng, and J. P. Draayer. "Analytical solutions for the LMG model." Physics Letters B 451, no. 1-2 (April 1999): 1–10. http://dx.doi.org/10.1016/s0370-2693(99)00191-4.

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33

Kučera, V., J. C. Martínez García, and M. Malabre. "Partial Model Matching: Parametrization of Solutions." IFAC Proceedings Volumes 29, no. 1 (June 1996): 1199–204. http://dx.doi.org/10.1016/s1474-6670(17)57828-3.

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34

Kučera, V., J. C. Martínez García, and M. Malabre. "Partial model matching: Parametrization of solutions." Automatica 33, no. 5 (May 1997): 975–77. http://dx.doi.org/10.1016/s0005-1098(96)00252-x.

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35

Ying, Lung-An. "Entropy solutions of a combustion model." Communications in Mathematical Sciences 1, no. 3 (2003): 393–407. http://dx.doi.org/10.4310/cms.2003.v1.n3.a1.

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36

Ingram, A., and S. Motta. "Solutions to the relativistic precession model." Monthly Notices of the Royal Astronomical Society 444, no. 3 (September 8, 2014): 2065–70. http://dx.doi.org/10.1093/mnras/stu1585.

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37

CHUAN, LE HUY, TOHRU TSUJIKAWA, and ATSUSHI YAGI. "STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL." Glasgow Mathematical Journal 51, no. 1 (January 2009): 1–17. http://dx.doi.org/10.1017/s0017089508004485.

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AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.
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38

Ranganathan, S. "The entity model of metallic solutions." Calphad 15, no. 2 (April 1991): 121–30. http://dx.doi.org/10.1016/0364-5916(91)90011-8.

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39

Yen, Yue-Horng, and Munir Cheryan. "Electrodialysis of model lactic acid solutions." Journal of Food Engineering 20, no. 3 (January 1993): 267–82. http://dx.doi.org/10.1016/0260-8774(93)90068-u.

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40

Blond, Geneviève. "Mechanical properties of frozen model solutions." Journal of Food Engineering 22, no. 1-4 (January 1994): 253–69. http://dx.doi.org/10.1016/0260-8774(94)90034-5.

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41

Haghtalab, A., and J. H. Vera. "Nonrandom factor model for electrolyte solutions." AIChE Journal 37, no. 1 (January 1991): 147–49. http://dx.doi.org/10.1002/aic.690370114.

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42

Abascal, J. L. F., and P. Turq. "Cluster structure in model electrolyte solutions." Chemical Physics 153, no. 1-2 (May 1991): 79–89. http://dx.doi.org/10.1016/0301-0104(91)90008-h.

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43

Williams, A. G., L. R. Dodd, and A. W. Thomas. "The colour-dielectric model: Numerical solutions." Physics Letters B 176, no. 1-2 (August 1986): 158–62. http://dx.doi.org/10.1016/0370-2693(86)90943-3.

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44

Hernández, Jairo Ernesto Castillo, Alvaro H. Salas, and José Gonzalo Escobar Lugo. "Exact solutions for a nonlinear model." Applied Mathematics and Computation 217, no. 4 (October 2010): 1646–51. http://dx.doi.org/10.1016/j.amc.2009.09.011.

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45

Aguirre-Ode, Fernando. "Unified model of associated solutions (UMAS)." Fluid Phase Equilibria 30 (January 1986): 315–26. http://dx.doi.org/10.1016/0378-3812(86)80065-6.

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46

Obukhov, Yuri N., and Eugen J. Vlachynsky. "Einstein-Proca model: spherically symmetric solutions." Annalen der Physik 8, no. 6 (September 1999): 497–509. http://dx.doi.org/10.1002/(sici)1521-3889(199909)8:6<497::aid-andp497>3.0.co;2-5.

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47

Tulebaev, Salavat, and Muhammed Harrasov. "Periodic solutions of Gurel - Rossler model." Izvestiya VUZ. Applied Nonlinear Dynamics 3, no. 1 (September 15, 1995): 3–10. https://doi.org/10.18500/0869-6632-1995-3-1-3-10.

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On the basis of the Bogoljubov’s asymptotic methods the existence of selfoscillating modes and a sequence of the period doubling bifurcation in dynamical Gurel - Rossler model are demonstrated. Qualitative results are confirmed by numerical calculations.
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48

Kalorkoti, K. "Model checking in the modal μ-calculus and generic solutions". Journal of Symbolic Computation 46, № 5 (травень 2011): 584–94. http://dx.doi.org/10.1016/j.jsc.2010.10.008.

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49

Mishra, Aamlan Saswat. "Social Acceptance Prediction Model for Generative Architectural Spaces in India." Journal of Advanced Research in Construction and Urban Architecture 6, no. 3 (July 23, 2021): 50–57. http://dx.doi.org/10.24321/2456.9925.202109.

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Generative Architectural design is an emerging design process that is evolving due to evolution of computational power of computers and its ability to provide multiple choices of design solutions in architecture. This process, however, has a few drawbacks, some of which are, a high number of solutions which take less time for computers to produce than for their human counterpart to interpret and choose from and the less social acceptance of generative architectural design solutions. Due to the algorithms being unaware of what humans deem as acceptable solutions, these problems persist. A way to bridge such gap is through a survey simulation model, which the computer can apply to simulate acceptance of the created solution if it were put through a survey. A mathematical model has been developed though analysis of a survey such that a computer can predict how acceptable a particular iteration of a Generative Architectural design process is if it were put through a similar survey. Scores obtained in the survey simulation can be used to predict how acceptable a particular design iteration is there by culling less acceptable solutions and reducing the number of iterations provided to humans for review after running Generative Architectural algorithms.
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50

Tahir, Jawad Kadhim. "ApproximatingAnalysisoftheDzektserMathematical Model." International Journal of Advances in Scientific Research and Engineering 10, no. 07 (2024): 81–85. http://dx.doi.org/10.31695/ijasre.2024.7.8.

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The article studies the solvability of the Dzektser mathematical model according to the theoretical consequences in the quasi-Sobolev. It employs the results to improve an algorithm form of the approximate approach to find approximate solutions of the Dzektser model. The work investigates the analog of the Dirichlet problem in a bounded domain with boundary conditions for the Dzektser model. A suggested numerical method allows us to find approximate solutions of the Dzektser mathematical model under consideration in quasi-Sobolev space. The convergence of the approximate solution to the analytical solution is fulfilled.
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