Dr. Milan Merkle

- Updated October 18, 2011 -

1. Convexity, Gamma function, inequalities

• M. Merkle, M. M. R. Merkle, {\em Krull's theory for the double gamma function}, Appl. Math. Comput. 218 (2011), 935-943, doi: 10.1016-j.amc.2011.01.090.
• S. Jankovic, M. Merkle, A mean value theorem for systems of integrals, J. Math. Analysis Appl. 342 (2008), 334-339.
• M. Merkle, Convexity in the theory of the Gamma function, International Journal of Applied Mathematics and Statistics, 11, No V07, November 2007, 103-117, ISSN 0973-1377 (Print), ISSN 0973-7545 (Online)
• M. Merkle, Inequalities for the Gamma function via convexity, In: P.Cerone, S. S. Dragomir (Eds.), 'Advances in Inequalities for Special Functions', Nova Science Publishers, Hauppauge-NewYork, 2008, 81-100.
• M. Merkle, Gurland's ratio for the Gamma function, Computers and Math. with Applications, 49 (2005), 389-406.
• M. Merkle, Reciprocally convex functions, J. Math. Analysis Appl., 293 (2004), 210-218.
• M. Merkle, Conditions for convexity of aderivative and applications to the Gamma and Digamma function, Facta Universitatis (Niš), Ser. Math. Inform.16 (2001), 13-20.
• M. Merkle, Representation of the error termin Jensen's and some related inequalities with applications, J. Math. Analysis Appl., 231 (1999), 76-90.
• M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 10 (1999), 113-117.
• M. Merkle, Conditions for convexity of aderivative and some applications to the Gamma function, Aequ. Math., 55 (1998), 273-280.
• M. Merkle, Inequalities for residuals of power expansions for the expo-nentialfunction and completely monotone functions, J. Math. Analysis Appl. 212 (1997), 126-134.
• M. Merkle, Convexity, Schur-convexity and bounds for the Gamma function involving the Digamma function, Rocky Mountain J.Math., 28, No 3 (1998), 1053-1066.
• M. Merkle, Convolutions o logarithmically concave functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 9 (1998), 113-117.
• M. Merkle, On log convexity of a ratio of Gamma functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 8 (1997), 114-119.
• M. Merkle, Logarithmic convexity and inequalities for the Gamma function, J. Math. Analysis Appl. 203 (1996), 369-380.
• M. J. Merkle, P.M.Vasic, An inequality for residual of Maclaurin expansion, Arch. Math., 66 (1996), 194-196.
• M. Merkle, Logarithmic concavity of distribution functions, International memorial conference 'D.S.Mitrinovic', Niš, 1996, In: G. V. Milovanovic (ed.), 'Recent progress in Inequalities ', Kluwer Academic Publishers, Dordrecht, 1998, 481-484.
• M. Merkle, Inequalities for residuals of power series: A review, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 6 (1995), 79-85.
• M. Merkle, Lj.Petrovic, On Schur-convexity of some distribution functions, Publ. Inst. Math. 56 (70) (1994), 111-118.
• M. Merkle, Some Inequalities for the Chi Square distribution function and the exponential function, Arch. Math., 60 (1993), 451-458.
• I. Lazarevic, M. Merkle, An Inequality Involving ERF and hyperbolic functions, Bulletin Mathematique (Bucure, sti), 36 (84) (1992), 317-318.
• M. Merkle, Some inequalities for the Chi Squared Distribution Function, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 2 (1991), 89-94.
• M. Merkle, Mills Ratio for the Gamma Distribution, Publ. Elektrotehn. Fak. Univ. Beograd. Ser. Mat-Fiz No 692 (1980)
• M. Merkle, A Contribution to Young's inequality, Publ.Elektrotehn. Fak.Univ. Beograd. Ser. Mat-Fiz No 461-497 (1974)

2. Statistics

• M. Merkle, Jensen's inequality for multivariate medians, J. Math. Anal. Appl. 370 (2010), 258-269, doi:10.1016/j.jmaa.2010.04.033
• Ð. Baljozovic, M. Merkle, Spatial medians, depth functions and multivariate Jensen's inequality, 2007, http://arxiv.org/abs/math/0701922
• M. Merkle, Jensen's inequality for medians, Statistics & Probability Letters, 71 (2005), 277-281.
• B. Mendez, M. Merkle, Some remarks on Pitman's criterion, Publ. Elektrotehn. Fak. Ser. Mat16 (2005), 1-11.
• M. Merkle, Biased Estimation of a Variance, Journal of the Italian Statistical Society (now 'Statistical Methods and Applications') 5, No.3 (1996), 323-334.

3. Topological spaces and measures

• Z. Mitrović, M. Merkle, On Generalized Vector Equilibrium Problem with Bounds, Appl. Math. Lett. 23 (2010), 783-787, doi:10.1016/j.aml.2010.03.009
• M. Merkle, Topics in weak convergence of probability measures, Zb. radova Mat. Inst. Beograd, 9 (17) (2000), 235-274.
• M. Merkle, Completion of countably seminormed space, Acta Math. Hung. 80 (1-2) (1998), 1-7.
• M. Merkle, On Positive Definite Functions Defined on Vector Spaces, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 1 (1990), 35-40.
• M. Merkle, Multi-Hilbertian Spaces and Their Duals, Techn. Report No 291, Center for Stochastic Processes, Department of Statistics, University of North Carolina at Chapel Hill, 1990.
• M. Merkle, On Weak Convergence of Measures on Hilbert Spaces, J. Multivariate Analysis, 29 (1989), No 2, 252-259.

4. Probability theory and stochastic processes

• M. Merkle, Lj.Petrovic, Gaussian processes and linear interpolation, Sankhya, Ser.A., 58 (1996), 382-391.
• M. Merkle, Lj.Petrovic, Inequalities for sums of independent geometrical random variables, Aequ. Math.54 (1997), 173-180.

5. Applications

• Yuri F. Saporito, Rodrigo dos S. Targino, Milan Merkle, Bayesian selection for Heston models with volatilities determined by Fourier series method, Research in Options 2008, poster
• J. Raicevic, M. Merkle, J. Ehrhardt, M. Ninkovic, Loss of life time due to radiation exposure: averaging problems, Health Phys., 72, No 4 (1997), 550-557.
• D. Vukmirovic, M. Merkle, Statistical parameters of upper wind, Zbornik meteoroloških i hidroloških radova 15 (1996), 30-37. (In Serbian)
• R.Gajic, M. Merkle, Signal Averaging in Fourier Transform Spectroscopy (Two Sided Interferograms), Infrared Physics 28, No 5 (1988).

6. Miscelaneous

• M. Merkle, From PEF to AADM, via MAGT, Appl.Anal.DiscreteMath.1, No1 (2007), 1-2.
• M. Merkle, From PEF to AADM, Publ. Elektrotehn. Fak. Ser. Mat.18 (2007), 1-2.
• Zagorka Lozanov-Crvenkovic, Slobodanka Jankovic, Milan Merkle, Andrej Nikolajevic Kolmogorov, Statisticka revija, 1-4 (2006), 126-137.