AUTHORS: Yingxu Wang, Audrey Ma, Siyuan Wang
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ABSTRACT: It is recognized that chemical reaction balancing problems are a mathematical problem in general. A set of mathematical models is created for formalizing the problems of chemical function calibrations. The complexity of the algorithm is O(n2) that indicates the nature of the problem where n is the number of types of atoms taking part in reactions. The problem is often manually insolvable because the complexity and interlocked relations among the coefficients of elements in reaction functions. Although empirical trial-and-error and heuristic methods were proposed, they would fail when n is considerably large, i.e., n > 6. Therefore, a general mathematical model and a rigorous methodology for solving chemical reaction balancing problems are yet to be formally studied. This paper presents a theory of chemical function calibration, which enables automatic balancing of complex reaction functions by numerical algorithms based on extended systems of linear equations.
KEYWORDS: Mathematical theory, mathematical models, algorithm, chemical reaction functions, balancing, calibration, denotational mathematics, numerical methods, applications
REFERENCES:
[1] Blakley, G.R. (1982), Chemical Equation Balancing, J. Chem. Educ. 59, 728–734.
[2] Gilat, A. and V. Subramaniam (2010), Numerical Methods for Engineers and Scientists, 2nd ed., John Wiley.
[3] Gowers, T. ed. (2008), The Princeton Companion to Mathematics, Princeton University Press, NJ.
[4] Kolb, D. (1979), More on Balancing Redox Reactions, Journal of Chemical Education, 56(3), 181–184.
[5] Krishnamurthy, E.V. (1978), Generalized Matrix Inverse Approach to Automatic Balancing of Chemical Equations, Int. J. Math. Educ. Sci. 6Technol, 9, 323–328.
[6] Masterton, W.L. and C.N. Hurley (1993), Chemistry: Principles and Reactions, 2d ed., Saunders College Publishing (1993).
[7] Porges, A. (1945), A Question of Balancing, Journal of Chemical Education, 22, 266–267.
[8] Sena,_S.K., H. Agarwalb, and S. Senc (2006), Chemical Equation Balancing: An Integer Programming Approach, Mathematical and Computer Modeling, 44, 678–691.
[9] Sienko, M.J. and R.A. Plane, (1965), Chemistry, McGraw-Hill Inc., NY.
[10] Standin, A. (1945), Some Simple Balancing, Journal of Chemical Education, 22, 461-462.
[11] Wang, Y. (2002), The Real-Time Process Algebra (RTPA), Annals of Software Engineering, (14), 235-274.
[12] Wang, Y. (2007), Software Engineering Foundations: A Software Science Perspective, CRC Series in Software Engineering, Vol. II, Auerbach Publications, NY, USA.
[13] Wang, Y. (2008), On Contemporary Denotational Mathematics for Computational Intelligence, Transactions of Computational Science, 2, 6-29.
[14] Wang, Y. (2012), In Search of Denotational Mathematics: Novel Mathematical Means for Contemporary Intelligence, Brain, and Knowledge Sciences, Journal of Advanced Mathematics and Applications, 1(1), 4-25.
[15] Wang, Y. (2015), Towards the Abstract System Theory of System Science for Cognitive and Intelligent Systems, Springer Journal of Complex and Intelligent Systems, 1(1), 1-22.
[16] Wang, Y. (2016), A Set of Improved Algorithms for Typical Numerical Methods, Journal of Advanced Mathematics and Applications, 5(2), in press.
[17] Zumdahl, S.S. and P.B. Kelter (1997), Chemistry, 4th ed., Houghton Mifflin Co., NY.
