742330978907deda322c7c4fab97baf5 watenvres_a2026m6v98n6pe70452.pdf 5bf201485859ee7ecbea2c7810bceb7eaffd9ad8 watenvres_a2026m6v98n6pe70452.pdf 565a36860e2860a8ee5065aba344ffa19455cbc4e93bffac58392c5259bf1607 watenvres_a2026m6v98n6pe70452.pdf Title: Computational Fluid Dynamics Reveals Mass Transfer Limitations in a Pilot‐Scale Microbial Electrolysis Cell Subject: Water Environment Research 2026.98:e70452 Author: Oscar Guerrero-Sodric, Rholand Jordi Navarro-Quispe, Martí Cortada-García, Juan Antonio Baeza, Albert Guisasola Creator: Adobe InDesign 19.5 (Windows) Producer: Adobe PDF Library 17.0; modified using iText 4.2.0 by 1T3XT CreationDate: Fri Jun 19 04:06:16 2026 CEST ModDate: Tue Jul 7 16:47:27 2026 CEST Custom Metadata: yes Metadata Stream: yes Tagged: yes UserProperties: no Suspects: no Form: none JavaScript: no Pages: 10 Encrypted: no Page size: 595.276 x 782.362 pts Page rot: 0 File size: 1712961 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID 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application/pdf Profile: Tagged PDF PDFMetadata: Objects: 0 FreeObjects: 2 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: false CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Language: en-US Outlines: Item: Title: Computational Fluid Dynamics Reveals Mass Transfer Limitations in a Pilot-Scale Microbial Electrolysis Cell Children: Item: Title: ABSTRACT Item: Title: Summary Item: Title: 1   |   Introduction Item: Title: 2   |   Methodology Children: Item: Title: 2.1   |   Computational Domain Item: Title: 2.2   |   CFD Modeling Item: Title: 2.3   |   MEC Model Item: Title: 2.4   |   Mass Balance Equations Item: Title: 2.5   |   Evaluation of Simulation Results Item: Title: 2.6   |   Simulation Parameters Item: Title: 3   |   Results and Discussion Children: Item: Title: 3.1   |   Investigating Fluid Flow Behavior and Substrate Distribution in the MEC Item: Title: 3.2   |   Sensitivity Analysis of External Mass Transfer Limitations Item: Title: 3.3   |   Model Validation Using Experimental Data From Three Pilot-Scale MECs Item: Title: 3.4   |   Practical Implications and Future Directions Item: Title: 4   |   Conclusions Item: Title: Author Contributions Item: Title: Acknowledgments Item: Title: Conflicts of Interest Item: Title: Data Availability Statement Item: Title: References Filters: FilterPipeline: FlateDecode FilterPipeline: DCTDecode Images: Image: NisoImageMetadata: FormatName: image/png ImageWidth: 228 ImageHeight: 45 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Image: NisoImageMetadata: FormatName: image/png ImageWidth: 228 ImageHeight: 45 ColorSpace: black is zero BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Image: NisoImageMetadata: FormatName: image/png 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ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 45 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 8 ImageHeight: 21 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 43 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 12 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 71 ImageHeight: 41 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 197 ImageHeight: 128 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 298 ImageHeight: 121 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 53 ImageHeight: 29 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 10 ImageHeight: 13 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 108 ImageHeight: 724 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 12 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 12 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 43 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 47 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 45 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 46 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 10 ImageHeight: 15 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 14 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 14 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 46 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 134 ImageHeight: 14 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 90 ImageHeight: 128 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 134 ImageHeight: 279 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 129 ImageHeight: 90 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 14 ImageHeight: 159 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 153 ImageHeight: 128 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 81 ImageHeight: 128 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 153 ImageHeight: 129 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 46 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 30 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 35 ImageHeight: 41 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 39 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 43 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 37 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 21 ImageHeight: 11 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 35 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 25 ImageHeight: 202 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 202 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 134 ImageHeight: 14 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 9 ImageHeight: 276 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 41 ImageHeight: 202 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 134 ImageHeight: 279 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 21 ImageHeight: 55 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 27 ImageHeight: 11 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 28 ImageHeight: 69 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 14 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 8 ImageHeight: 249 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 9 ImageHeight: 61 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 11 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 47 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 45 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 47 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 108 ImageHeight: 720 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 1071 ImageHeight: 1027 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 21 ImageHeight: 11 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 108 ImageHeight: 725 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 91 ImageHeight: 15 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 27 ImageHeight: 11 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 55 ImageHeight: 15 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 11 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 148 ImageHeight: 11 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 3 ImageHeight: 42 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 91 ImageHeight: 121 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 19 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 24 ImageHeight: 36 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 38 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 75 ImageHeight: 45 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 196 ImageHeight: 128 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 298 ImageHeight: 121 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 61 ImageHeight: 33 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 39 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 109 ImageHeight: 719 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 10 ImageHeight: 45 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 109 ImageHeight: 725 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 36 ImageHeight: 40 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 134 ImageHeight: 279 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 11 ImageHeight: 276 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 135 ImageHeight: 16 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 135 ImageHeight: 279 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 41 ImageHeight: 202 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 28 ImageHeight: 69 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 23 ImageHeight: 55 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 25 ImageHeight: 201 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 11 ImageHeight: 163 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/png ImageWidth: 25 ImageHeight: 202 ColorSpace: palette color BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 1071 ImageHeight: 1250 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 1071 ImageHeight: 1107 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 1568 ImageHeight: 997 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Intent: RelativeColorimetric Name: X Fonts: Type1: Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 28 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EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic FontBBox: -68, -220, 914, 785 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Italic FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Italic Flags: Symbolic FontBBox: 0, -187, 544, 668 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 29 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 24 LastChar: 31 FontDescriptor: FontName: 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WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 28 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: PIDMLO+STIXMathExtensions-Regular FontSubset: true FirstChar: 28 LastChar: 31 FontDescriptor: FontName: PIDMLO+STIXMathExtensions-Regular Flags: Symbolic FontBBox: 0, -2394, 1032, 66 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: PIDMLO+STIXMathExtensions-Regular FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: PIDMLO+STIXMathExtensions-Regular Flags: Symbolic FontBBox: 0, -2394, 1032, 66 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 28 LastChar: 31 FontDescriptor: FontName: 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Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: PIDMLO+STIXMathExtensions-Regular FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: PIDMLO+STIXMathExtensions-Regular Flags: Symbolic FontBBox: 0, -2394, 1032, 66 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic 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EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: PIDMLO+STIXMathExtensions-Regular FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: PIDMLO+STIXMathExtensions-Regular Flags: Symbolic FontBBox: 0, -2394, 1032, 66 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 30 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: RTATNK+STIXTwoText-Italic FontSubset: true FirstChar: 28 LastChar: 31 FontDescriptor: 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EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 28 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 29 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic FontBBox: -68, -220, 914, 785 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 25 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 29 LastChar: 31 FontDescriptor: 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true Font: BaseFont: SPMEBI+STIXMath-Regular FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXMath-Regular Flags: Symbolic FontBBox: 0, -177, 637, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic FontBBox: -68, -220, 914, 785 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 27 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic FontBBox: -68, -220, 914, 785 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: SPMEBI+STIXTwoText-Italic FontSubset: true FirstChar: 31 LastChar: 31 FontDescriptor: FontName: SPMEBI+STIXTwoText-Italic Flags: Symbolic FontBBox: -68, -220, 914, 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