ISSN 2086-0382 E-ISSN 2477-3344 CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 CAUCHY Vol. 6 No. 1 Pages: 1 – 48 Malang November 2019 ISSN 2086-0382 E-ISSN 2477-3344 𝜒 CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 ISSN : 2086-0382 E-ISSN : 2477-3344 CAUCHY is a mathematical journal published twice a year on May and November by the Mathematics Department, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic University of Malang. This journal includes research papers, literature studies, analysis, and problem solving in Mathematics (Algebra, Analysis, Statistics, Computing and Applied Mathematics). EDITORIAL BOARD Editor in Chief : Dr. Sri Harini, M.Si, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia. Managing Editor : Mohammad Jamhuri, M.Si, Universitas Islam Negeri Maulana Malik Ibrahim Malang. Juhari, M.Si, Universitas Islam Negeri Maulana Malik Ibrahim Malang. Editorial Board : Mario Rosario Guarracino, Computational and Data Science Laboratory High Performance Computing and Networking Institute National Research Council of Italy, Italy Kartick Chandra Mondal, Jadavpur University, Salt Lake Campus, India Rowena Alma L. Betty, University of the Philippines Diliman, Philippines Subanar Seno, Gadjah Mada University, Indonesia Toto Nusantara, State University Of Malang, Indonesia Edy Tri Baskoro, Institut Teknologi Bandung, Indonesia Eridani Eridani, Airlangga University, Indonesia Abdul Halim Abdullah, University of Technology Malaysia, Malaysia Kusno, University of Jember, Indonesia Slamin, University of Jember, Indonesia Riswan Efendi, UIN Sultan Syarif Kasim Riau, Indonesia Arief Fatchul Huda, UIN Sunan Gunung Djati Bandung, Indonesia Usman Pagalay, Maulana Malik Ibrahim State Islamic University of Malang, Indonesia Abdussakir, Maulana Malik Ibrahim State Islamic University of Malang, Indonesia Ari Kusumastuti, Maulana Malik Ibrahim State Islamic University of Malang, Indonesia Fachrur Rozi, Maulana Malik Ibrahim State Islamic University of Malang, Indonesia Elly Susanti, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 ISSN : 2086-0382 E-ISSN : 2477-3344 EDITORIAL BOARD Assistant Editor : Mohammad Nafie Jauhari, M.Si, Universitas Islam Negeri Maulana Malik Ibrahim Malang. Editorial Office Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang Gajayana st. 50 Malang, East Java, Indonesia 65144 Phone (+62) 81336397956, Faximile (+62) 341 558933 e-mail: cauchy@uin-malang.ac.id CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 ISSN : 2086-0382 E-ISSN : 2477-3344 FOCUS AND SCOPE CAUCHY-Jurnal Matematika Murni dan Aplikasi is a mathematical journal published twice a year in May and November by the Mathematics Department, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic University of Malang. We we lc om e a u t h or s for original articles (research), review articles, interesting case reports, special articles illustrations that focus on the Mathematics Pure and Applied. Subjects suitable for publication include, but are not limited to the following fields of: 1. Actuaria 2. Algebra 3. Analysis 4. Applied 5. Computing 6. Econometry 7. Statistics CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 ISSN : 2086-0382 E-ISSN : 2477-3344 INDEXING AND ABSTRACTING CAUCHY-Jurnal Matematika Murni dan Aplikasi has been covered (indexed and abstracted) by following services: 1. DOAJ - (2016-,)(https://doaj.org/toc/2477-3344) 2. Sherpa/Romeo - (2016-,)-(http://www.sherpa.ac.uk/romeo/search.php) 3. Infobase Index - (2016-,)-(http://infobaseindex.com/journal-accepted.php) 4. Index Copernicus - (2015-,)-(http://journals.indexcopernicus.com/form/login.php) 5. Moraref - (2015-,)-(http://moraref.or.id/index.php/browse/index/36) 6. OneSearch Indonesia - (2015-,)-(http://onesearch.id/Search/Results?filter[]=repoId:IOS2732) 7. ROAD - (2015-,)-(http://road.issn.org/issn/2477-3344-cauchy#.V6AkW2deBT-) 8. Advanced Sciences Index - (2015-,)-(http://journal-index.org/index.php/asi/issue/view/17) 9. DAIJ - (2015-,)-(http://www.daij.org/journal-detail.php?jid=1147) 10. ISSUU - (2015-,)-(https://issuu.com/journalcauchy) 11. JournalTOCs-(2015-,) (http://www.journaltocs.ac.uk/index.php?action=search&subAction=hits&journalID=26700&userQueryI D=25934&high=1&ps=30&page=1&items=0&journal_filter=&journalby=) 12. I2OR - (2015-,)-(http://www.i2or.com/7.html) 13. AcademicKeys - (2015-,)-(http://socialsciences.academickeys.com/jour_main.php) 14. Universal Impact Factor - (2015-,)-(http://www.uifactor.org/JournalDetails.aspx?jid=4353) 15. WorlCat-OCLC - (2015-,)-(https://www.worldcat.org/title/cauchy-jurnal-matematika-murni-dan- aplikasi/oclc/950752934&referer=brief_results) 16. CiteFactor - (2015-,)-(http://www.citefactor.org/journal/index/13830/cauchy#.V6Aw42deBT-) 17. ESJI - (2015-,)-(http://esjindex.org/search.php?id=1042) 18. ScholarSteer - (2015-,)- (http://www.scholarsteer.com/?s=cauchy&post_type=custom_journal&submit=Submit) 19. iiiFactor - (2015-,)- (http://iiifactor.org/index.php?option=com_jvld&Itemid=479&view=links&cid=124&limitstart=-1) 20. International Innovative Journal Impact Factor - (2015-,)- (http://iijif.com/Indexed%20Journals.php?page=1) 21. Academia.edu - (2014-,)-(https://uin-malang.academia.edu/Cauchy) 22. ResearchBib - (2014-,)-(http://journalseeker.researchbib.com/view/issn/2086-0382) 23. BASE - (2014-,)-(https://www.base- search.net/Search/Results?lookfor=dccoll%3Aftuniinmalangojs+url%3Amath&refid=dclink) 24. Tei - (2014-,)-(http://turkegitimindeksi.com/Journals.aspx?ID=412) 25. Cosmos Impact Factor - (2014-,)- (http://www.cosmosimpactfactor.com/page/journals_details/943.html) 26. GIF - (2014-,)-(http://globalimpactfactor.com/cauchy/) 27. Scientific Indexing Service - (2014-,)-(http://www.sindexs.org/JournalList.aspx?ID=2193) 28. Mendeley - (2013-,)-(https://www.mendeley.com/groups/5034091/cauchy/papers/) 29. Indonesian Scientific Journal Database (ISJD) - (2013-,)-(http://isjd.pdii.lipi.go.id/index.php/Direktori- Jurnal.html) 30. Google Scholar - (2009-,)-(https://scholar.google.co.id/citations?hl=en&view_op=list_works&gmla=AJsN- F6OmoFBk7Q0o2Q-9- XUIMca1zI8OZ9Lp2EhCtubhL9dCisxNYH9sAiEAU0g0UDT8tyM6Jk3Z666Zu46VRsBYZ6Vjc2a_w&user=dr K-5HkAAAAJ) 31. IPI - (2009-,)-(http://id.portalgaruda.org/?ref=browse&mod=viewjournal&journal=5272) http://www.sherpa.ac.uk/romeo/search.php http://infobaseindex.com/journal-accepted.php http://journals.indexcopernicus.com/form/login.php http://moraref.or.id/index.php/ http://onesearch.id/Search/Results http://road.issn.org/issn/2477-3344-cauchy#.V6AkW2deBT- http://journal-index.org/index.php/ http://www.daij.org/journal-detail.php http://www.journaltocs.ac.uk/index.php http://www.i2or.com/7.html http://socialsciences.academickeys.com/jour_main.php http://www.uifactor.org/JournalDetails.aspx http://www.worldcat.org/title/cauchy-jurnal-matematika-murni-dan- http://www.citefactor.org/journal/index/13830/cauchy#.V6Aw42deBT- http://esjindex.org/search.php http://www.scholarsteer.com/ http://www.scholarsteer.com/ http://iiifactor.org/index.php http://iiifactor.org/index.php http://iijif.com/Indexed%20Journals.php http://iijif.com/Indexed%20Journals.php http://journalseeker.researchbib.com/view/issn/2086-0382 http://www.base-/ http://turkegitimindeksi.com/Journals.aspx http://www.cosmosimpactfactor.com/page/journals_details/943.html http://www.cosmosimpactfactor.com/page/journals_details/943.html http://globalimpactfactor.com/cauchy/ http://www.sindexs.org/JournalList.aspx http://www.mendeley.com/groups/5034091/cauchy/papers/ http://isjd.pdii.lipi.go.id/index.php/ http://id.portalgaruda.org/ CAUCHY Jurnal Matematika Murni dan Aplikasi Volume 6, Issue 1, November 2019 ISSN : 2086-0382 E-ISSN : 2477-3344 TABLE OF CONTENTS A Discrete Numerical Solution of The SIR Model with Horizontal and Vertical Transmission ............................................................................................................................... 1 – 9 On the Local Adjacency Metric Dimension of Generalized Petersen Graphs .......... 10 – 17 A Finitely Generated Module over a Valuation Domain .................................................. 18 – 26 Modification of Chaos Game with Rotation Variation on a Square .............................. 27 – 33 The Study Geometry Fractals Designed on Batik Motives .............................................. 34 – 39 On The Local Edge Antimagic Coloring of Corona Product of Path and Cycle ........ 40 – 48 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6413 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6413 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6487 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6798 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6936 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/8081 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/8054