Shingo NAKANISHI (Osaka Institute of Technology), "
Geometric Characterizations of Spirals or Isometric Projection about Pythagorean Theorem and Standard Normal Distribution
 Modeling with Triangles, Squares, and Similar Metallic Ratios  (in Japanese)", Memoirs of Osaka Institute of Technology, Vol. 65, No. 2, (2020), pp. 103~127.
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University) , "Rotationally Symmetric Relations of Standard Normal Distribution Using Right Triangles, Circles, and Squares
 Ordinary Differential Equations, Pythagorean Theorem, Equilateral Triangles, and Golden Ratio  ", Theory and Its Application of Mathematical Decision Making under Uncertainty and Ambiguity, RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, No.205820,pp.????(Total 13 pages),(2020.7.1)
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Symmetric Relations and Geometric Characterizations about Standard Normal Distribution by Circle and Square", The 15th International Symposium on Econometric Theory and Applications (SETA2019, 2019.6.12), Osaka University, Toyonaka, Osaka Prefecture, Japan, (2019.6.2)
 Presentaion PDF (Symmetric Relations and Geometric Characterizations about Standard Normal Distribution by Circle and Square(SETA2019))
 Presentaion PPT (Symmetric Relations and Geometric Characterizations about Standard Normal Distribution by Circle and Square(SETA2019))
 Presentaion MP4 (Symmetric Relations and Geometric Characterizations about Standard Normal Distribution by Circle and Square(SETA2019))
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Geometric Characterizations of Standard Normal Distribution  Two Types of Differential Equations, Relationships with Square and Circle, and Their Similar Characterizations  ", Decision making theories under uncertainty and its applications: the extensions of mathematics for programming, RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, No. 2078, pp. 5864,(2018.9)
Fast announcement of some misspelled equations and mistakes of my thinking on November 14,2018.
Modified Version on November 22,2018 (on March 7, 2019 at our website).
Shingo NAKANISHI (Osaka Institute of Technology), "Uncertainties of economic evaluation on the largescale repair planning of condominiums", Theory and application of mathematical models under uncertainty, RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, No. 2044, pp. 101111 (2017.9) in Japanese
Shingo NAKANISHI (Osaka Institute of Technology), "Characteristics and Uncertainties of MeanVariance Model  Mathematical Modeling and Data Analysis Using Microsoft Excel ", Memoirs of Osaka Institute of Technology, Vol. 59, No. 2, pp. 1746 (2015.1) in Japanese
Shingo NAKANISHI (Osaka Institute of Technology), "Maximization For Sum Total Expected Gains By Winners of repetition game of coin toss considering the Charge Based On Its Number Of Trial", Transactions of the Operations Research Society of Japan, Vol. 55, pp. 126 (2012.12) in Japanse
Shingo NAKANISHI (Osaka Institute of Technology), "Product Mix based on Uncertainties of Standard Operations Time Considered Correlations of Each Division by Using ChanceConstrained Model", Shokeigakuso, Journal of Business Studies, Vol.58, No.3, pp.173195 (2012.3) in Japanese
Shingo NAKANISHI (Osaka Institute of Technology), "Product Mix based on Uncertainties of Standard Operation Time", Memoirs of the Osaka Institute of Technology, Series A, Vol. 55, No. 2, pp.19 (2011.2) in Japanese
Shingo NAKANISHI (Osaka Institute of Technology), "Development of Local Database for Obtainable Data of Stock Prices from Website and Its Applications of Mean Variance Model and Capital Asset Pricing Model", Memoirs of the Osaka Institute of Technology, Series A, Vol. 55, No. 1, pp.1124 (2010.10) in Japanese
Shingo NAKANISHI (Osaka Institute of Technology), "Study on sales mix based on uncertain times of standard operations", Proceedings of the 38th International Conference on Computers and Industrial Engineering, pp. 6772, (2008.10)
Shingo NAKANISHI (Osaka Institute of Technology), "Study on Reliability Evaluation for Gaming Simulation", Proceedings of the 37th International Conference on Computers and Industrial Engineering, pp. 23592366, (2007.10)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Konan University), "Principal component analysis for limit state functions of structural system", Structural Safety and Reliability (ICOSSAR'01) Corotis et. al. (eds), Swets and Zeitlinger, ISBN 90 5809 197 X, p.208, FCO256.pdf, (2003.1)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Konan University), "Reliability design of structural system with cost effectiveness during life cycle", Computers and Industrial Engineering, Vol. 42, pp. 447456, (2002.9)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Konan University), "Basic risk assessment model for reliabilitybased design of structural system", Proceedings of the 5th International Conference of Probabilistic Safety Assessment and Management (PSAM5) , Vol. 2, pp. 701707, (2000)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Konan University), "Reliability design of structural system with cost effectiveness during life cycle", Proceedings of the 26th International Conference of Computers and Industrial Engineering, Vol. 1, pp. 606610, (1999)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Konan University), "Practical effective bound for system reliability using conditional reliability indices", Proceedings of the 7th International Conference on Structural Safety and Reliability (ICOSSAR'97), Vol.1, pp.681684, (1998)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Osaka Institute of Technology), "Review of standardized transformation methods for structural reliability", Proceedings of the 15th International Conference on Offshore Mechanics and Arctic Engineering, OMAE1996, ASME, Vol. 2, pp. 95102, (1996)
Shingo NAKANISHI (Osaka Institute of Technology) and Hidetoshi NAKAYASU (Osaka Institute of Technology), "Uncertainties of safety index on structural safety", IFIP Transactions (International Federation for Information Processing), No. B12, pp. 189196, (1993)

Shingo NAKANISHI (Osaka Institute of Technology),
"Visualizations of Sinusoidal Spirals, Limacons of Pascal, and Conic Curves using Equiangular Spirals of Secondary Metallic Ratios
[Theoretical Graphics and Geometry]", The Poster of The 21st International Conference on Geometry and Graphics, Kitakyushu International Conference Center, Fukuoka, Japan, (2024.8.6)
Shingo NAKANISHI (Osaka Institute of Technology), "Visualizations of discrete equiangular spirals based on similar metallic ratios using Pythagorean theorem and weighted Fibonacci sequences", 31th European Conference on Operational Research (the EURO2021 ) (2021.7.12), Athens, Greece.
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Geometric Characterizations and Symmetric Relations between Standard Normal Distribution and Inverse Mills Ratio based on Pythagorean Theorem", Royal Statistical Society International Conference 2019 (RSS2019), (2019.9.34), ICC Belfast, Belfast, UK.
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Symmetric Relations and Geometric Characterizations about Standard Normal Distribution by Circle and Square", The 15th International Symposium on Econometric Theory and Applications (SETA2019), (2019.6.2), Osaka University, Toyonaka, Osaka Prefecture, Japan.
Shingo NAKANISHI (Osaka Institute of Technology), "Equilibrium point on standard normal distribution between expected growth return and its risk", 28th European Conference on Operational Research (the EURO XXVIII ) (2016.7), Poznan, Poland.
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Equilibrium Relationship between the Performance and the Information Ratio with Transaction Costs", the 20th Conference of the International Federation of Operational Research Societies (IFORS2014) (2014.7), Barcelona, Spain.
Shingo NAKANISHI (Osaka Institute of Technology) and Masamitsu OHNISHI (Osaka University), "Equilibrium relationship between the profit of the market and its transaction cost by financial institution", 26th European Conference on Operational Research (the EURO XXVI ) (2013.7), Rome, Italy.
Shingo NAKANISHI (Osaka Institute of Technology), "Study on sales mix based on uncertain times of standard operations", Proceedings of the 38th International Conference on Computers and Industrial Engineering (2008.10), Beijing, China.
Shingo NAKANISHI (Osaka Institute of Technology), "Study on Reliability Evaluation for Gaming Simulation", Proceedings of the 37th International Conference on Computers and Industrial Engineering (2007.10), Alexandria, Egypt
