Papers: Preprints
Preprints of papers published in the online repository "arXiv"
“Manifold Structures in Regular Irreducible Algebraic Monoids”, a study of regular irreducible algebraic monoids over the field of complex numbers equipped with the euclidean topology (12 pages). Available HERE or in arXiv.org. (14 August 2011)
“On Normed Semigroups”, a paper which presents a new definition of a normed semigroup (10 pages). Available HERE or in arXiv.org. (16 August 2015)
“Geometry of the Set of Real Square Roots of the Matrices ± I_2”, a paper which shows that the set of real square roots of I_2 is a hyperboloid of one sheet and obtains several other similar results (32 pages). Available HERE or in arXiv.org.
“Mystery of the 18th Elephant Solved,” a popular article that attempts to explain the mystery behind an 18th elephant that appears in many popular legends involving the division of a herd of 17 elephants into groups in the ratio 1/2:1/3:1/9 (4 pages). Available HERE or in arXiv.org.
"Where Do the Terms of the Power Series Expansions of Sine and Cosine Functions Come from? Involutes!", an expository paper (13 pages, 7 figures). Available HERE or in arXiv.org.
"Differential Equations: A Historical Refresher", a talk delivered in an ISTE sponsored Faculty Development Programme on Applications of Advanced Mathematics in Engineering held in Vidya Academy of Science & Technology during 27.11.2017 - 01.12.2017 (24 pages). Available HERE or in arXiv.org.
"Quadrics via Semigroups", National Seminar on Recent Trends in Analysis, held in Govt. Victoria College, Palakkad, during March 2007.Available HERE or in arXiv.org.
"Ramanujan in Computing Technology", a paper presented in the National Conference on Advances in Computing Technology 2020 (NC-ACT 2020) organised by Department of Computer Applications, Vidya Academy of Science and Technology, Thrissur - 680501, Kerala, India during 4 - 5 December 2020 (32 pages). Available HERE or in arXiv.org.
Preprints of other papers
“An Overview of Optimisation Techniques”, an expository paper on some of the well known problems in optimization theory presented as a talk at Rajiv Gandhi Institute of Technology, Kottayam, on 03 March 2005, as part of a short-term course on “Decision Support Systems – Tools and Techniques” (25 pages). Available HERE.
“Nambooripad's Theory of Cross-connections”, an outline of the theory of cross-connections developed by K. S. S. Nambooripad as a generalisation to arbitrary regular semigroups of Grillet's theory of cross-connections (16 pages). Available HERE.
“Homotopy Properties of the Space of Idempotent Endomorphisms”, a paper which studies the homotopy properties of the space of idempotent endomorphisms of a finite dimensional real or complex vector space (18 pages). Available HERE.
“Yet Another Simple proof of FLT?”, a note exposing the error in a paper (T. Unnikrishnan, “Finding Numbers Satisfying The Condition A^n + B^n = C^n", IOSR Journal of Mathematics, Jul-Aug 2013) purportedly carrying a proof of the well known Fermat’s Last Theorem (FLT) and also the dubiousness of the journal in which the paper was published (5 pages). Available HERE.
“Basic Linux Commands”, lecture notes for giving a first introduction to the Linux operating system (17 pages). Available HERE.
“Google sites: Hands on!”, notes used for a presentation on Google Sites in a Two-day workshop (christened Chip-to-Net) organised by the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur – 680501, for the students of neighbouring arts and science colleges on 8 - 9 January 2015 (22 pages). Available HERE.
“A Catalogue of Elementary Statistical Tests”, a categorized catalogue of elementary statistical tests and relevant tables based on Probability and Statistics for Engineers (Third Edition) by Irwin Miller and John E Freund, Prentice Hall of India intended for the use of undergraduate engineering students and teachers, prepared in October 1992 (10 pages). Available HERE.
“A Ladder Problem”, a note giving a detailed analysis of the problem of determining the height to which a person can climb a ladder (7pages). Available HERE.
"Excelling in Errors", a compilation of some of the computational errors that lie hidden in the much popular Excel software (4 pages). Available HERE.
"Of a system in which doubling the cause doubles the effect!", a paper discussing the solutions of the functional equation f(2x) = 2f(x). (4 pages). Available HERE.
"Plausible Reasoning" (8 pages), a very concise summary of a two-volume book titled "Mathematics and Plausible Reasoning" authored by George Polya which presents plausible reasoning as a way of generating new mathematical conjectures. Available HERE.
"SVM computation: Pedagogical examples", a paper which illustrates the support vector machine (SVM) computations with actual numerical values using small data sets and hand computations (13 pages). Available HERE.
"GeoGebra commands for 2D geometrical constructions", a paper containing brief descriptions of GeoGebra commands for 2D geometrical constructions and illustrations of the applications of these commands in producing beautiful diagrams in triangle geometry (35 pages). Available HERE.
"Free software: An introduction" (10 pages). Available HERE.
"Determining Whether Meat Samples Come from Dead or Slaughtered Animals Using Machine Learning" (jointly with Dr V N Vasudevan, College of Veterinary and Animal Sciences, Mannuthy, Thrissur - 680651) (10 pages). Available HERE.
"An algorithm to find the largest rectangle in a union of rectangles" (7 pages). Available HERE.