University of New Mexico UNM Digital Repository Mathematics and Statistics Faculty and Staff Publications Scholarly Communication - Departments 2014 Collected papers, Vol. V Florentin Smarandache Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Mathematics Commons, Non-linear Dynamics Commons, Other Applied Mathematics Commons, and the Special Functions Commons Collected Papers, V Florentin Smarandache Papers of Mathematics or Applied mathematics Brussels, 2014 Florentin Smarandache Collected Papers Vol. V Papers of Mathematics or Applied mathematics EuropaNova Brussels, 2014 PEER REVIEWERS: Prof. Octavian Cira, Aurel Vlaicu University of Arad, Arad, Romania Dr. Stefan Vladutescu, University of Craiova, Craiova, Romania Mumtaz Ali, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Siad Broumi, Faculty of Arts and Humanities, Hay El Baraka Ben M'sik Casablanca, Morocco Cover: Conversion or transfiguration of a cylinder into a prism. EuropaNova asbl 3E, clos du Parnasse 1000, Brussels Belgium www.europanova.be ISBN 978-1-59973-317-3 TABLE OF CONTENTS MATHEMATICS .................................................................................... 13 Florentin Smarandache, Cătălin Barbu The Hyperbolic Menelaus Theorem in The Poincaré Disc Model Of Hyperbolic Geometry 14 Florentin Smarandache, Cătălin Barbu A new proof of Menelaus’s Theorem of Hyperbolic Quadrilaterals in the Poincaré Model of Hyperbolic Geometry 20 Ion Pătraşcu, Florentin Smarandache Some Properties of the Harmonic Quadrilateral 26 Ion Pătraşcu, Florentin Smarandache Non-Congruent Triangles with Equal Perimeters and Arias 32 Florentin Smarandache Another proof of the I. Patrascu’s theorem 35 Octavian Cira, Florentin Smarandache Luhn Prime Numbers 37 Mircea E. Şelariu, Florentin Smarandache, Marian Niţu Cardinal Functions And Integral Functions 45 Mihály Bencze, Florentin Smarandache About an Identity and its Applications 58 Florentin Smarandache On Crittenden and Vanden Eynden’s Conjecture 60 Marian Niţu, Florentin Smarandache, Mircea E. Şelariu Eccentricity, Space Bending, Dimension 61 Florentin Smarandache Professor Şelariu’s Supermathematics 71 Marian Niţu, Florentin Smarandache, Mircea E. Şelariu Excentricitatea, dimensiunea de deformare a spaţiului 81 Mircea E. Şelariu, Florentin Smarandache, Marian Niţu Funcţii cardinale şi funcţii integrale circulare excentrice 103 Florentin Smarandache SuperMatematica Profesorului Şelariu 121 EXTENICS .......................................................................................... 131 Xingsen Li, Yingjie Tian, Florentin Smarandache, Rajan Alex An Extension Collaborative Innovation Model in The Context of Big Data 132 Victor Vladareanu, Florentin Smarandache, Luige Vladareanu Extension Hybrid Force-Position Robot Control in Higher Dimensions 155 Florentin Smarandache, Ştefan Vlăduţescu Extension communication pentru rezolvarea contradicţiei ontologice dintre comunicare şi informaţie 165 Florentin Smarandache, Tudor Păroiu Extenica 177 MECHATRONICS................................................................................. 194 Luige Vlădăreanu, Gabriela Tonţ, Victor Vlădăreanu, Florentin Smarandache The navigation of mobile robots in non-stationary and non-structured environments 195 Luige Vlădăreanu, Gabriela Tonţ, Victor Vlădăreanu, Florentin Smarandache, Lucian Căpitanu The Navigation Mobile Robot Systems Using Bayesian Approach through the Virtual Projection Method 205 Kimihiro Okuyama, Mohd Anasri, Florentin Smarandache, Valeri Kroumov Mobile Robot Navigation Using Artificial Landmarks and GPS 211 STATISTICS........................................................................................ 217 Mukesh Kumar, Rajesh Singh, Ashish K. Singh, Florentin Smarandache Some Ratio Type Estimators 218 Manoj K. Chaudhary, Rajesh Singh, Rakesh K. Shukla, Mukesh Kumar, Florentin Smarandache A Family of Estimators for Estimating Population Mean in Stratified Sampling under Non-Response 223 Rajesh Singh, Sachin Malik, A. A. Adewara, Florentin Smarandache Multivariate Ratio Estimation With Known Population Proportion of Two Auxiliary Characters For Finite Population 231 V.V. Singh, Alka Mittal, Neetish Sharma, Florentin Smarandache Determinants of Population Growth in Rajasthan: An Analysis 239 Rajesh Singh, Mukesh Kumar, Florentin Smarandache Ratio Estimators in Simple Random Sampling when Study Variable is an Attribute 251 Jayant Singh, Hansraj Yadav, Florentin Smarandache Rural Migration A Significant Cause Of Urbanization: A District Level Review Of Census Data For Rajasthan 255 Jayant Singh, Hansraj Yadav, Florentin Smarandache Urbanization due to Migration: A District Level Analysis of Migrants from Different Distances for The Rajasthan State 262 MISCELLANEA.................................................................................... 272 Florentin Smarandache Administration, Teaching and Research Philosophies 273 Florentin Smarandache, Ştefan Vlăduţescu An Application of The Systemic Theory in The Field of Industrial Companies 281 V. Christianto, Florentin Smarandache On Gödel's incompleteness theorem(s), Artificial Intelligence/Life, and Human Mind 285 Priti Singh, Florentin Smarandache, Dipti Chauhan, Amit Bhaghel A Unit Based Crashing Pert Network for Optimization of Software Project Cost 293 Florentin Smarandache Çok Kriterli Karar Verme için Alfa İndirgeme Yöntemi (α-İ ÇKKV) 303 Florentin Smarandache Recreational Mathematics: Puzzle Me! 325 Florentin Smarandache A Scientist and Haiku Poet 327 Florentin Smarandache Review of the journal „Us and the Sky” 329 Dmitri Rabounski Florentin Smarandache: polymath, professor of mathematics 330 AUTHORS Mathematics Cătălin Barbu, 14-19, 20-25 Mihály Bencze, 58-59 Octavian Cira, 37-44 Marian Niţu, 45-57, 61-70, 81-102, 103-120 Ion Pătraşcu, 26-31, 32-34 Florentin Smarandache, 14-19, 20-25, 26-31, 32-34, 35-36, 37-44, 45-57, 58-59, 60, 61-70, 71-80, 81-102, 103-120, 121-130 Mircea E. Şelariu, 45-57, 61-70, 81-102, 103-120 Extenics Rajan Alex, 132-154 Xingsen Li, 132-154 Tudor Păroiu, 177-193 Florentin Smarandache, 132-154, 155-164, 165-176, 177-193 Luige Vlădăreanu, 155-164 Victor Vlădăreanu, 155-164 Ştefan Vlăduţescu, 165-176 Yingjie Tian, 132-154 Mechatronics Mohd Anasri, 211-216 Lucian Căpitanu, 205-210 Valeri Kroumov, 211-216 Kimihiro Okuyama, 211-216 Florentin Smarandache, 195-204, 205-210, 211-216 Luige Vlădăreanu, 195-204, 205-210 Victor Vlădăreanu, 195-204, 205-210 Gabriela Tonţ, 195-204, 205-210 Statistics A. A. Adewara, 231-238 Manoj K. Chaudhary, 223-230 Mukesh Kumar, 218-222, 223-230, 251-254 Sachin Malik, 231-238 Alka Mittal, 239-250 Neetish Sharma, 239-250 Rakesh K. Shukla, 223-230 Ashish K. Singh, 218-222 Jayant Singh, 255-261, 262-271 Rajesh Singh, 218-222, 223-230, 231-238, 251-254 V.V. Singh, 239-250 Florentin Smarandache, 218-222, 223-230, 231-238, 239-250, 251-254, 255-261, 262-271 Hansraj Yadav, 255-261, 262-271 Miscellanea Amit Bhaghel, 293-302 Dipti Chauhan, 293-302 V. Christianto, 285-292 Dmitri Rabounski, 330-334 Priti Singh, 293-302 Florentin Smarandache, 273-280, 281-284, 285-292, 293-302, 303-324, 325-326, 327-328, 329 Ştefan Vlăduţescu, 281-284 Florentin Smarandache Collected Papers, V Introductory Note This volum includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration with the following co-authors: Cătălin Barbu, Mihály Bencze, Octavian Cira, Marian Niţu, Ion Pătraşcu, Mircea E. Şelariu, Rajan Alex, Xingsen Li, Tudor Păroiu, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Yingjie Tian, Mohd Anasri, Lucian Căpitanu, Valeri Kroumov, Kimihiro Okuyama, Gabriela Tonţ, A. A. Adewara, Manoj K. Chaudhary, Mukesh Kumar, Sachin Malik, Alka Mittal, Neetish Sharma, Rakesh K. Shukla, Ashish K. Singh, Jayant Singh, Rajesh Singh,V.V. Singh, Hansraj Yadav, Amit Bhaghel, Dipti Chauhan, V. Christianto, Priti Singh, and Dmitri Rabounski. They were written during the years 2010-2014, about the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry, and the Menelaus theorem for quadrilaterals in hyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, about Luhn prime numbers, and also about the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics; there are some notes on Crittenden and Vanden Eynden's conjecture, or on new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM), but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM); also, about extenics, in general, and extension innovation model and knowledge management, in particular, about advanced methods for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set, or about the notion of point-set position indicator and that of point-two sets position indicator, and the navigation of mobile robots in non-stationary and nonstructured environments; about applications in statistics, such as estimators based on geometric and harmonic mean for estimating population mean using information; about Godel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind, and many more. References: Florentin Smarandache: Collected Papers, Vol. I (first edition 1996, second edition 2007) http://fs.gallup.unm.edu/CP1.pdf