By Karmeshu (auth.), Professor Karmeshu (eds.)
This ebook is devoted to Prof. J. Kapur and his contributions to the sector of entropy measures and greatest entropy functions. Eminent students in a variety of fields of utilized info thought were invited to give a contribution to this Festschrift, accrued at the get together of his 75th birthday. The articles conceal themes within the components of actual, organic, engineering and social sciences akin to info know-how, delicate computing, nonlinear platforms or molecular biology with a thematic coherence. the quantity can be worthy to researchers operating in those various fields allowing them to determine the underlying solidarity and gear of entropy optimization frameworks.
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Extra info for Entropy Measures, Maximum Entropy Principle and Emerging Applications
He has shown that entropy function appears in the observed stimulus - response relationship describing car following platoon. Consider a platoon of N cars moving along a single-lane highway with no overtaking allowed. u - AO Xj ( t ) - Xj+1(t ) ' j = 1,2,··· ,N. 5 sec. 1 Uncertainty, Entropy and MEP 41 In terms of traffic density Pn at location of the nth car and bumper-tobumper close density Pc (at which Vn = 0), Montroll  gives the following expression for the mean flow rate : q = >"0 Pc (-~ t Pn log pn) .
Pb'" ,Pi-b O,PHb'" ,Pn; a) = HOI. (P1 , ... ,Pi-1,PHb ... ,Pn; a) for every i = 1,2, ... (Pb ... (p b .. ·,Pi-1,Pi,PHb .. (~ ~ ) Pi'Pi;a, for every ril + ri2 = Pi > 0, i = 1,2, ... ,n. Havrda - Charvat proved that axioms (a) - (d) determine structural a-entropy unambiguously and it equals HOI. (PbP2, ... 42) 1 Uncertainty, Entropy and MEP and 29 n H 1 (pl,P2, ... ,Pn; 1) = - LPi logpi. , when a ~ 1, and it can be viewed as a generalization of Shannon's entropy. 44) which shows that Ha(p) == Ha(Pl, ...
This entropy measure however does not have additivity, recursivity and sum representation properties and is related to Renyi, and also to Havrda - Charvat entropies. Taneja  has given a list of generalized entropies which reduce to Shannon entropy either in the limiting or in particular cases. One may refer to Taneja  for mathematical expressions of entropies due to Aczel and Dar6czy (1963), Varma (1966), Kapur (1967), Sharma and Mittal (1975), Sharma and Taneja (1975,1977), Picard (1979), Ferreri (1980), Santanna and Taneja (1983).