Geodesic
Properties of sums of some elementary functions and their application to computational and modeling problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 748-761 
Yu. K. Shestopaloff. Properties of sums of some elementary functions and their application to computational and modeling problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 748-761. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a1/
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     title = {Properties of sums of some elementary functions and their application to computational and modeling problems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article proposes methods for creating corresponding sums of functions and sums of corresponding series, whose appropriate equations have equal number of solutions. We consider equations composed of power functions (generalized polynomials) and sums of exponential functions. Using the concept of corresponding functions, we prove the relationships between the properties of polynomial, power and sums of exponential functions. One of the results is generalization of Descartes Rule of Signs for sums of other than polynomial functions and sums of their series. Obtained results are applied to two practical problems. One is the finding of an adequate description of transition electrical signals. Secondly, the proved theorems are applied to the problem of finding the initial value for iterative algorithms used to solve one particular case of IRR (internal rate of return) equation for mortgage calculations. Overall, the results are proved to be beneficial for theoretical and practical applications in industry and in different areas of science and technology.

[1] Shestopaloff Yu. K., Science of inexact mathematics. Investment performance measurement. Mortgages and annuities. Computing algorithms. Attribution. Risk valuation, AKVY Press, Toronto, 2009

[2] Hull J. C., Fundamentals of futures and options Markets, 7-th edition, Prentice Hall, 2009

[3] Shestopaloff Yu. K., Investment valuation. Mathematical challenges and solutions, Report at meeting of European Bond Commission, Paris, October 2009 http://www.effas-ebc.org/

[4] Shestopalov Yu. K., Mortgages and annuities. Mathematical foundations and computational algorithms, AKVY Press, Toronto, 2010

[5] Shestopaloff Yu. K., Properties and interrelationships of polynomial, exponential, logarithmic and power functions with applications to modeling natural phenomena, AKVY Press, Coral Springs, FL, USA, 2010

[6] Shestopaloff Yu. K., “The role of conceptual context in the problem of finding rate of return”, J. Performance Measurement., 13 (2008), 37–50

[7] Bertrand B., Bihan F., Sottile F., “Polynomial systems with few real zeroes”, Math. Z, 253:2 (2006), 361–385

[8] Shestopaloff Yu. K., Physics of growth and replication. Physical and geometrical perspectives on living organisms' development, AKVY Press, Toronto, 2010