Dr Milan Merkle

e-mail: emerkle@etf.rs

           merkle@eunet.yu

zvanje: redovni profesor

kabinet: 107

tel: 3218308

• Doktorat iz Verovatnoce i Statistike (1984), Michigan State University (SAD), Department of Statistics and Probability. Mentor: Prof. V. Mandrekar.
• Magistratura iz primenjene matematike (1981), Elektrotehnicki fakultet, Beograd.
• Diploma Prirodno-matematickog fakultet u Beogradu, grupa za matematiku (1979).
• Diploma Elektrotehnickog fakulteta u Beogradu, odsek za tehnicku fiziku (1977).

Zaposlenja

• Septembar 1980-: Katedra za Primenjenu matematiku Elektrotehnickog fakulteta u Beogradu. Sadasnje zvanje: redovni profesor (od jula 1997). Sef katedre od oktobra 2000.
• 1982-1984: Department of Statistics and Probability, Michigan State University, asistent (graduate teaching assistant).
• 1978-1979: Vojno-tehnicki institut u Beogradu, istrazivac pripravnik.

Profesionalne aktivnosti:

 

• Predavanja: Matematicki predmeti, Teorija Verovatnoce, Matematicka statistika, na redovnim i postdiplomskim studijama.
• Oblasti istrazivanja: Matematicka analiza (konveksnost, specijalne funkcije, beskonacno dimenzionalni prostori), Teorija verovatnoce (slucajni procesi, raspodele), Statistika, primene u raznim oblastima.
• Udzbenici: Autor ili koautor pet univerzitetskih udzbenika.
• Ucestvovao u projektima vezanim za razne primene matematike, verovatnoce i statistike u elektrotehnici, akustici, fizici, meteorologiji i medicini.
• Korisnik T_EX sistema, matematickog softvera, iskustvo u programiranj u u Fortranu i Visual Basic-u.
• Urednik casopisa Publications of the Faculty of Electrical Engineering, University of Belgrade - Series Mathematics i urednik Problemske sekcije u istom casopisu.
• Sluzio kao recenzent za: Journal of Mathematical Analysis and Applications, The Rocky Mountain Journal of Mathematics, Aequationes Mathematicae, Facta Universitatis, International Journal for Mathematics and Mathematical Sciences, Publications Inst. Math. Beograd, Zentralblatt für Mathematik.
• Posete stranim univerzitetima: Department of Mathematical Sciences, Johns Hopkins University (leto 1987), Department of Statistics and Probability, Michigan State University (leto 1987), Center for Stochastic Processes, University of North Carolina at Chapel Hill (jesen 1988 i prolece 1990).

Licni podaci

Rodj en 21. februara 1954. Govori engleski jezik, sluzi se ruskim i francuskim. Cerka Ana, rodjena 1995. Biografski podaci mogu se naci i u knj izi Marquis Who's Who In the World, izdanj e 2000 i 2001.

[1]

M. Merkle, Representation of the error term in Jensen's and some related inequalities with applications, J. Math. Analysis Appl., 231 (1999), 76-90.

[2]

M. Merkle, Biased Estimation of a Variance , Journal of the Italian Statistical Society, 5, No. 3 (1996), 323-334.

[3]

M. Merkle, Completion of a countably seminormed space, Acta Math. Hung. 80 (1-2) (1998), 1-7.

[4]

M. Merkle, Conditions for convexity of a derivative and some applications to the Gamma function, Aequ. Math., 55 (1998), 273-280.

[5]

M. Merkle, Inequalities for residuals of power expansions for the exponential function and completely monotone functions, J. Math. Analysis Appl. 212 (1997), 126-134.

[6]

J. Raicevic, M. Merkle, J. Ehrhardt, M. Ninkovic, Loss of lifetime due to radiation exposure: averaging problems, Health Phys., 72, No 4 (1997), 550-557.

[7]

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.

[8]

M. Merkle, Lj. Petrovic, Gaussian processes and linear interpolation, Sankhya, Ser. A., 58(1996), 382-391.

[9]

M. Merkle, Lj. Petrovic, Inequalities for sums of independent geometrical random variables, Aequ. Math. 54(1997), 173-180.

[10]

M. Merkle, Logarithmic convexity and inequalities for the Gamma function, J. Math. Analysis Appl. 203 (1996), 369-380.

[11]

M.J. Merkle, P.M. Vasic, An inequality for residual of Maclaurin expansion, Arch. Math., 66 (1996), 194-196.

[12]

M.Merkle, Some Inequalities for the Chi Square distribution function and the exponential function, Arch. Math., 60 (1993), 451-458.

[13]

I. Lazarevic, M. Merkle, An Inequality Involving ERF and hyperbolic functions, Bulletin Mathematique (Bucure sti), 36(84)(1992), 317-318.

[14]

M. Merkle, On Weak Convergence of Measures on Hilbert Spaces, J. Multivariate Analysis, 29 (1989), No 2, 252-259.

[15]

R. Gajic, M. Merkle, Signal Averaging in Fourier Transform Spectroscopy (Two Sided Interferograms), Infrared Physics 28, No 5 (1988).

2. Radovi objavljeni u domacim casopisima

[1]

M. Merkle, Topics in weak convergence of probability measures, Zb. radova Mat. Inst. Beograd, 9(17), 235-274.

[2]

M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 10 (1999).

[3]

M. Merkle, Convolutions of logarithmically concave functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 9 (1998), 113-117.

[4]

M. Merkle, On log convexity of a ratio of Gamma functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 8 (1997), 114-119.

[5]

D. Vukmirovic, M. Merkle, Statistical parameters of upper wind, Zbornik meteoroloskih i hidroloskih radova 15 (1996), 30-37. (In Serbian)

[6]

M. Merkle, Inequalities for residuals of power series: A review, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 6 (1995), 79-85.

[7]

M. Merkle, Lj. Petrovic, On Schur-convexity of some distribution functions, Publ. Inst. Math. 56 (70) (1994), 111-118.

[8]

M. Merkle, Some Inequalities for the Chi Squared Distribution Function, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 2 (1991), 89-94.

[9]

M. Merkle, On Positive Definite Functions Defined on Vector Spaces, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 1 (1990), 35-40.

[10]

M. Merkle, Mills Ratio for the Gamma Distribution, Publ. Elektrotehn. Fak. Univ. Beograd. Ser. Mat-Fiz No 692 (1980)

[11]

M. Merkle, A Contribution to Young's inequality, Publ. Elektrotehn. Fak. Univ. Beograd. Ser. Mat-Fiz No 461-497 (1974)

3. Interne publikacije inostranih univerziteta

[1]

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.

4. Udzbenici

[1]

M. Merkle: Matematicka analiza - teorija, Beograd 1996; drugo neizmenjeno stampanje, Beograd, 1997, x+276.

[2]

M. J. Merkle, P.M. Vasic: Verovatnoca i statistika - sa primenama i primerima, Elektrotehnicki fakultet, Beograd, 1995, II izdanje 1997. xii+307.

[3]

M. Merkle: Matematicka analiza - pregled teorije i zadaci, Grosknjiga, Beograd 1994; drugo izmenj eno i prosireno izdanj e - autorsko izdanj e, Beograd, 1997, xiv+686.

[4]

D- . Vukomanovic, D.Georgijevic, A. Zolic, D- . Jovanov, M. Lazic, M. Merkle, M. Milicic, R. Radovanovic, Z. Radosavljevic, Z. Sami: Zbirka zadataka i testova iz matematike za pripremanje prijemnog ispita za upis na tehnicke i prirodno-matematicke fakultete, Zavod za udzbenike i nastavna sredstva, Beograd 1994.

[5]

D. Cvetkovic, V. Kocic, I. Lackovic, M. Merkle, Z. Radosavljevic, S. Simic, P. Vasic: Matematika 1-Algebra, I izdanje Naucna Knjiga, Beograd 1989, peto izdanje Elektrotehnicki fakultet, Beograd 1997. x+285.

5. Prilozi u knjigama drugih autora

[1]

M. Merkle, Matricne reprezentacije grupa i neke njihove primene, (Matrix Representations of Groups and some Applications ), u knjizi: Dragos Cvetkovic, Kombinatorna teorija matrica, Naucna Knjiga, Beograd 1980.

[2]

M. Merkle, Neke primene sredina u teoriji verovatnoce, (Some Applications of Means in Probability Theory ), dodatak u knjizi: D.S. Mitrinovic, J.E. Pecaric, Srednje vrednosti u matematici, Naucna Knjiga, Beograd 1989.

6. Nepublikovani radovi i radovi spremni za publikovanje

[1]

M. Merkle, Weak star convergence and additive probability measures, 5th World Congress of the Bernoulli Society for Porbability and Mathematical Statistics, Guanajuato, Mexico, 2000, abstract No 208.

[2]

M. Merkle, Finitely additive measures and Banach's linear limes, 1999.

[3]

J. Raicevic, M. Merkle, J. Ehrhardt, M. Ninkovic, Years of life lost due to external radiation exposure, 1998, submitted.

[4]

M. Merkle, Conditions for convexity of a derivative and applications to the Gamma and Digamma function, submitted.

[5]

M. Merkle, Krull's theory of a functional equation, 1997.

[6]

M. Merkle, Logarithmic convexity, Schur convexity, total positivity and complete monotonicity: An Interplay, 1996.

7. Projekti

[1]

Metodi i modeli u teorijskoj, industrijskoj i primenjenoj matematici, Matematicki institut SANU - Elektrotehnicki fakultet, 1996-2000.

[2]

Savremena matematika, Matematicki institut SANU - Elektrotehnicki fakultet, 1991-1995.

[3]

Matematika sa primenama, Matematicki institut SANU - Elektrotehnicki fakultet, 1986-1990.

[4]

Prostiranje lakih cestica difuzijom kroz atmosferu, Energoprojekt-Elektrotehnicki fakultet, 1989-1990.

[5]

Lokalno optimalna detekcija slabih signala u uslovima negausovog suma, Elektrotehnicki fakultet, 1989.

[6]

EUREKA-EUMAC, medjunarodni projekt 1987-1991.

• Ph.D. in Statistics (1984), Michigan State University, Department of Statistics and Probability. Thesis advisor: Prof. V. Mandrekar.
• M.Sc. in Applied Mathematics (1981), University of Belgrade, Yugoslavia.
• B.Sc. in Mathematics (1979), University of Belgrade, Faculty of Natural Sciences and Mathematics.
• B.Sc. in Electrical Engineering (1977), University of Belgrade, Faculty of Electrical Engineering.

Professional career

• September 1980-present: Department of Applied Mathematics, Faculty of Electrical Engineering, University of Belgrade. Present position: Full Professor (from July 1997). Chairman of the Department from October 2000.
• 1982-1984: Department of Statistics and Probability, Michigan State University, graduate teaching assistant.
• 1978-1979: Institute VTI, Belgrade, researcher.

Professional activities

• Teaching: Courses in Mathematics and Probability theory at various levels (undergraduate and graduate). Experience in teaching in English (two years).
• Research interests: Author of research papers in Mathematical Analysis (convexity, special functions, infinitely dimensional spaces), Probability theory (stochastic processes, distributions, weak convergence of probability measures), Statistics and applications.
• Textbooks: Author of five textbooks in Mathematics and Probability and Statistics.
• Has been participating in realization of computer software for various applications in electrical engineering, acoustics, physics and meteorology.
• Served as a consultant in various applications of probability and statistics.
• User of T_EX typesetting system, Mathematica and other standard mathematical software, programming experience in Fortran and Visual Basic.
• Co-editor of the journal Publications of the Faculty of Electrical Engineering, University of Belgrade - Series Mathematics and the editor of Problem Section of this journal.
• Has been a referee for: Journal of Mathematical Analysis and Applications, The Rocky Mountain Journal of Mathematics, Aequationes Mathematicae, Facta Universitatis, International Journal for Mathematics and Mathematical Sciences, Publications Inst. Math. Beograd a reviewer for Zentralblatt für Mathematik.
• Visits to other universities: Department of Mathematical Sciences, Johns Hopkins University (summer 1987), Department of Statistics and Probability, Michigan State University (summer 1987), Center for Stochastic Processes, University of North Carolina at Chapel Hill (fall 1988 and spring 1990).

Personal data

Born February 21, 1954. Speaks fluent English, working knowledge of French and Russian. Daughter Ana (born 1995). Likes swimming and mountain climbing. Selected biographical and professional data included in Marquis Who's Who in the World, 2000 and 2001.

[1]

M. Merkle, Topics in weak convergence of probability measures, Zb. radova Mat. Inst. Beograd, 9(17) (2000), 235-274.

[2]

M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 10 (1999), 113-117.

[3]

M. Merkle, Representation of the error term in Jensen's and some related inequalities with applications, J. Math. Analysis Appl., 231 (1999), 76-90.

[4]

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.

[5]

M. Merkle, Convolutions of logarithmically concave functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 9 (1998), 113-117.

[6]

M. Merkle, Logarithmic concavity of distribution functions, International memorial conference "D.S. Mitrinovic", Nis, 1996, Collection: G.V. Milovanovic (ed.), "Recent progress in Inequalities", Kluwer Academic Publishers, Dordrecht, 1998, 481-484.

[7]

M. Merkle, Biased Estimation of a Variance , Journal of the Italian Statistical Society, 5, No. 3 (1996), 323-334.

[8]

M. Merkle, Completion of a countably seminormed space, Acta Math. Hung. 80 (1-2) (1998), 1-7.

[9]

M. Merkle, Conditions for convexity of a derivative and some applications to the Gamma function, Aequ. Math., 55 (1998), 273-280.

[10]

M. Merkle, Inequalities for residuals of power expansions for the exponential function and completely monotone functions, J. Math. Analysis Appl. 212 (1997), 126-134.

[11]

J. Raicevic, M. Merkle, J. Ehrhardt, M. Ninkovic, Loss of lifetime due to radiation exposure: averaging problems, Health Phys., 72, No 4 (1997), 550-557.

[12]

M. Merkle, On log convexity of a ratio of Gamma functions, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 8 (1997), 114-119.

[13]

M. Merkle, Lj. Petrovic, Gaussian processes and linear interpolation, Sankhya, Ser. A., 58(1996), 382-391.

[14]

M. Merkle, Lj. Petrovic, Inequalities for sums of independent geometrical random variables, Aequ. Math. 54(1997), 173-180.

[15]

M. Merkle, Logarithmic convexity and inequalities for the Gamma function, J. Math. Analysis Appl. 203 (1996), 369-380.

[16]

M.J. Merkle, P.M. Vasic, An inequality for residual of Maclaurin expansion, Arch. Math., 66 (1996), 194-196.

[17]

M. Merkle, Inequalities for residuals of power series: A review, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 6 (1995), 79-85.

[18]

M. Merkle, Lj. Petrovic, On Schur-convexity of some distribution functions, Publ. Inst. Math. 56 (70) (1994), 111-118.

[19]

M.Merkle, Some Inequalities for the Chi Square distribution function and the exponential function, Arch. Math., 60 (1993), 451-458.

[20]

I. Lazarevic, M. Merkle, An Inequality Involving ERF and hyperbolic functions, Bulletin Mathematique (Bucure sti), 36(84)(1992), 317-318.

[21]

M. Merkle, Some Inequalities for the Chi Squared Distribution Function, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 2 (1991), 89-94.

[22]

M. Merkle, On Positive Definite Functions Defined on Vector Spaces, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat 1 (1990), 35-40.

[23]

M. Merkle, On Weak Convergence of Measures on Hilbert Spaces, J. Multivariate Analysis, 29 (1989), No 2, 252-259.

[24]

R. Gajic, M. Merkle, Signal Averaging in Fourier Transform Spectroscopy (Two Sided Interferograms), Infrared Physics 28, No 5 (1988).

[25]

M. Merkle, Mills Ratio for the Gamma Distribution, Publ. Elektrotehn. Fak. Univ. Beograd. Ser. Mat-Fiz No 692 (1980)

[26]

M. Merkle, A Contribution to Young's inequality, Publ. Elektrotehn. Fak. Univ. Beograd. Ser. Mat-Fiz No 461-497 (1974)

2. Unpublished papers and technical reports

[1]

M. Merkle, Weak star convergence and additive probability measures, 5th World Congress of the Bernoulli Society for Porbability and Mathematical Statistics, Guanajuato, Mexico, 2000, abstract No 208.

[2]

M. Merkle, Finitely additive measures in the closure of the set of probability measures and Banach's linear limes, 1999.

[3]

M. Merkle, Conditions for convexity of a derivative and applications to the Gamma and Digamma function, 1998, submitted.

[4]

J. Raicevic, M. Merkle, J. Ehrhardt, M. Ninkovic, Years of life lost due to external radiation exposure, 1998, submitted.

[5]

M. Merkle, Krull's theory of a functional equation, 1997.

[6]

M. Merkle, Logarithmic convexity, Schur convexity, total positivity and complete monotonicity: An Interplay, 1996.

[7]

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.

3. Books (in Serbian)

[1]

M. J. Merkle, P.M. Vasic: Probability and Statistics - with applications and examples, second edition, Belgrade 1998, xii+307 pp.

[2]

M. Merkle: Matemathical Analysis -theory, second edition, Belgrade 1997, x+276 pp.

[3]

M. Merkle: Mathematical Analysis - problems with an outline of theory, second revised and enlarged edition, Belgrade 1997, xiv +686 pp.

[4]

D. Cvetkovic, V. Kocic, I. Lackovic, M. Merkle, Z. Radosavljevic, S. Simic, P. Vasic: Mathematics 1-Algebra, fifth edition 1997, x+285 pp.

Matematika Članovi Predmeti Ispiti SI Obaveštenja Istorijat Publikacije MAGT2006