NONE 20260714094000102 wseas/wseas content-registration-form@crossref.org content-registration-form International Journal of Applied Mathematics Computational Science and Systems Engineering 2766-9823 Antoine Trad Business and Common Transformation Architecture and Projects IBISTM, Paris FRANCE Enterprise’s Performant Distributed Computing (EPM), needs well-defined structured Mathematical Methods (MM), and modelling technics. And the Applied Polymathical/Holistic Mathematical Model (AHMM) for EPM (APMM4EPM) supports Enterprise’s transformation projects (simply Project). The APMM4EPM is a set (and collections) of related Polymathical Mathematical Models (PMM), Enterprise’s legacy transformed resources (and artefacts), critical success factors (or Project’s tuning-factors), Enterprise performances patterns, Artificial Intelligence (AI) Subdomains (AIS) Models (AISM), complex Enterprise Architecture (EA) Models (EAM); and many other Project’s modules, fields and parts. The proposed AHMM and related PMMs were already presented and applied to various domains; and the author’s latest work, the AHMM for Enterprise’s Business Process Modelling (AHMM4EBPM) is this article’s main reference, stub, and logical continuation [1]. PMMs, transformed artefacts, AISMs, and Complex EAMs (CEAM), use standardized and convened sets of names, mapping-concepts, services-architectures, relations, used to model Projects’ and to ensure their Validity Checking Processes (VCP). The VCP is used to check and reorient EPM’s main areas like Information Communication System (ICS) components, Processing units’ concept, Various models’ performances, ICS availability, Enterprise security, and other. 07 14 2026 07 14 2026 44 4 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232026.2026.8.4 https://wseas.com/journals/amcse/2026/a08amcse-004(2026).pdf Trad, A. Enterprise Transformation ProjectsThe Applied Polymathical/Holistic Mathematical Model for Enterprise’s Business Process Modelling (AHMM4EBPM). Journal: International Journal of Computers. Volume 9. Publisher: International Association of Research and Science. 2024. iaras.org Project Polymath. The history of polymaths-A brief history of polymathy. Project Polymath. 2024. https://projectpolymath.unixploria.net/2024/ 06/28/the-history-of-polymaths/ IEEE. IEEE Standard for Digital Transformation Architecture and Framework. IEEE Std 2023-2025 , vol., no., pp.1-67, 23 Jan. 2026, doi: 10.1109/IEEESTD.2026.11361417. CONECT. Comprehensive Glossary of Digital Transformation Concepts-A Modernised Enterprise Architecture Framework. 2026. https://oconect.com/glossary-of-digitaltransformation-concepts/ Cuemath (2024). Math Symbols. https://www.cuemath.com/numbers/mathsymbols/ MathVault (2024). Mathematical Symbols. MathVault. https://mathvault.ca/hub/highermath/math-symbols/ Trad, A. The Business Transformation and Enterprise Architecture Framework-The Applied Holistic Mathematical Model’s Persistence Concept (AHMMPC). WSEAS. 2019. Perez-Castillo, R. Ruiz, F. Piattini, M. & Ebert, C. Enterprise Architecture. IEEE Software, vol. 36, no. 4, pp. 12-19, July-Aug. 2019, doi: 10.1109/MS.2019.2909329. Ambrose, G.. A MATHEMATICAL FRAMEWORK FOR ENTERPRISE ARCHITECTURE REPRESENTATION AND DESIGN. International Journal of Information Technology & Decision Making. 2011. 03. 10.1142/S0219622004000623. Trad, A. The Transformation and Enterprise Architecture Framework: The Applied Holistic Mathematical Model for Geopolitical Analysis (AHMM4GA). Book: Responsible AI and Ethical Issues for Businesses and Governments. Pages 80-127. IGI Global. USA. 2021. Trad, A. POLYMATHIC APPROACH FOR ENTERPRISE TRANSFORMATION PROJECTSIMPLEMENTING A BUSINESS METAMODEL THAT RESPECTS ENVIRONMENTAL SUSTAINABILITY (PETP-IBMMES). SCF. Journal Article. 2024. Trad, A. Enterprise Transformation Projects-A Mathematical Models’ based Enterprise Refinement Concept (ETP-ERC). Journal: International Journal of Applied Mathematics, Computational Science and Systems Engineering. Volume 5. Pages 30- 51. 2023. Bashynska, I., Mukhamejanuly, S., Malynovska, Y., Bortnikova, M., Saiensus, M., & Malynovskyy, Y. Assessing the Outcomes of Digital Transformation Smartization Projects in Industrial Enterprises: A Model for Enabling Sustainability. Sustainability, 15(19), 14075. (2023). https://doi.org/10.3390/su151914075 Mahboub, H., Sadok, H., Chehri, A., & Saadane, R. Measuring the Digital Transformation: A Key Performance Indicators Literature Review. Procedia Computer Science, Volume 225, 2023, Pages 4570-4579, ISSN 1877-0509. https://doi.org/10.1016/j.procs.2023.10.455. https://www.sciencedirect.com/science/articl e/pii/S1877050923016137. Pavlova, O., Zabarna, E., Pierkova, M., Kuzmin, A., & Kostiuk, A. (2024). Mathematical model for digital transformation of business processes in the coordinates of digital marketing CEUR-WS. https://ceur-ws.org/Vol-3899/paper7.pdf Holistics. Dataset's Best Practices. Holistics. 2024. https://docs.holistics.io/docs/datasets/bestpractices Myers, B., Pane, J., & Ko, A. Natural programming languages and environments. ACM New York, NY, USA. 2004. Lankhorst, M. Enterprise Architecture at Work Modelling, Communication and Analysis. Springer, Berlin, Heidelberg. Germany. 2009. Peterson, S. Why it Worked: Critical Success Factors of a Financial Reform Project in Africa. Faculty Research Working Paper Series. Harvard Kennedy School. 2011. Putri, N., & Yusof, S.M. Critical success factors for implementing quality engineering tools and techniques in malaysian’s and indonesian’s automotive industries: An Exploratory Study. Journal Proceedings of the International MultiConference of Engineers and Computer Scientists. Volume 2. Pages 18-20. 2009. Sheldon, R. What is a data set? 2024. https://www.techtarget.com/whatis/definition /data-set Siman, E. What Is a Dataset? Definitive Guide. BrightData. 2024. https://brightdata.com/blog/web-data/whatis-a-dataset My Atlas. XML Data Access Architecture. My Atlas / Charts & Illustrations. 2020. https://www.directionsonmicrosoft.com/char ts-illustrations/xml-data-access-architecture/ SAP. PowerDesigner-ObjectOriented Modeling. SAP. 2016. Bird, L., Goodchild, A., & Halpin, T. Object Role Modelling and XML-Schema. Distributed System Technology Center (DSTC), University of Queensland, AUSTRALIA. DOI: 10.1007/3-540-45393- 8_23. 2000. https://www.researchgate.net/publication/22 1269041_Object_Role_Modelling_and_XM L-Schema Burke, P. THE POLYMATH A CULTURAL HISTORY FROM LEONARDO DA VINCI TO SUSAN SONTAG. YALE UNIVERSITY PRESS. NEW HAVEN AND LONDON. 2020. Clark, M., Fletcher, P., Hanson, J., Irani, R., Waterhouse, M., & Thelin, J. Web Services Business Strategies and Architectures. Apress. USA. 2013. Gibson, D., Kovanovic, V., Ifenthaler, D., Dexter, S., & Feng, Sh. Learning theories for artificial intelligence promoting learning processes. 2023. https://doi.org/10.1111/bjet.13341. https://berajournals.onlinelibrary.wiley.com/doi/10.1111 /bjet.13341 . Danenas, P. & Skersys, T. Exploring Natural Language Processing in Model-To-Model Transformations. IEEE Access, vol. 10, pp. 116942-116958, 2022. doi: 10.1109/ACCESS.2022.3219455. Hine, G. S. C. The importance of action research in teacher education programs. In Design, develop, evaluate: The core of the learning. environment. Proceedings of the 22nd Annual Teaching Learning Forum, 7-8 February 2013. Perth: Murdoch University. 2013. http://ctl.curtin.edu.au/professional_develop ment/conferences/tlf/tlf2013/refereed/hine.ht ml Morawski, R. An application-oriented mathematical meta-model of measurement. Elsevier. Journal Measurement: Volume 46, Issue 9, November 2013, Pages 3753-3765. https://doi.org/10.1016/j.measurement.2013. 04.004. 2013. Easterbrook, S., Singer, J., Storey, M., & Damian, D. Guide to Advanced Empirical Software Engineering-Selecting Empirical Methods for Software Engineering Research. F. Shull et al. (eds.). Springer. 2008. Rice, D. AN ANALYTICAL MODEL FOR COMPUTER SYSTEM PERFORMANCE EVALUATION. Honeywell. Arizona. USA. 1973. Airbyte. Types of AI Models: Your Ultimate Guide. 2024. https://airbyte.com/dataengineering-resources/types-of-ai-models McCaffrey, J. How to Create a Machine Learning Decision Tree Classifier Using C#. Microsoft. (2020). https://visualstudiomagazine.com/Articles/20 20/01/21/decision-tree-classifier.aspx Ranjan, R. Computer Organization and Architecture-Boolean Algebra. BCA. 2011. Van Meter, R. Quantum Computer Architecture. Keio University. 2011. The Open Group. Introduction to the Architecture Development Method (ADM). The Open Group. USA. 2011. Klarlund, N., Schwentick, Th., & Suciu, D. (2004). XML: Model, Schemas, Types, Logics, and Queries. Logics for Emerging Applications of Databases. Chapter, pp 1–41. Springer. https://link.springer.com/chapter/10.1007/97 8-3-642-18690-5_1. Wada, H., Suzuki, J., & Oba, K. Leveraging Early Aspects in End-to-End Model Driven Development for Non-Functional Properties in Service Oriented Architecture. Journal of Database Management 22(2):93-123. DOI: 10.4018/jdm.2011040104. 2011. Jonkers, H., Band, I., Quartel, D. & Lankhorst, M. ArchiSurance Case Study. The Open Group. 2016. Sparx. Exchanging BPMN Models. Sparx Systems Pty Ltd. 2024. https://sparxsystems.com/enterprise_architec t_user_guide/17.0/modeling_languages/bpm n_20_xml.html Macek, O., & Richta, K. The BPM to UML activity diagram transformation using XSLT. Conference: Proceedings of the Dateso 2009 Annual International Workshop on DAtabases, TExts, Specifications and Objects, Spindleruv Mlyn, Czech Republic, April 15-17, 2009. Cobb, M. Security log management and logging best practices. Techtarget. 2023. https://www.techtarget.com/searchsecurity/ti p/Security-log-management-and-loggingbest-practices Raza, M. Log Monitoring with AI: What Makes Monitoring Intelligent? Splunk. 2024. https://www.splunk.com/en_us/blog/learn/lo g-monitoring.html Guangcheng, Z., Lei, W., & Long, L. (1996). Abstract mathematical model of general management information systems. Information technology, database. Computers & Industrial Engineering, Volume 31, Issues 3–4, December , Pages 893-895. https://www.sciencedirect.com/science/articl e/abs/pii/S0360835296002720 Doncean, G., Doncean, M., & Sulenco, M. (2021). Abstract mathematical models used in colour management. Journal of Public Administration, Finance and Law. 2021. https://doi.org/10.47743/jopafl-2021-22-13 Diskin, Z. (2003). Mathematics of UML. In: Kilov, H., Baclawski, K. (eds) Practical Foundations of Business System Specifications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2740- 2_8 Wilson, P., & Mantooth, A. Model-Based Engineering for Complex Electronic Systems. Chapter 5 - Graphical Modeling. Pages 127- 167. 2013. https://doi.org/10.1016/B978-0- 12-385085-0.00005-1. https://www.sciencedirect.com/topics/engine ering/model-abstraction