Albert Turner Bharucha-Reid

Born: February 22, 1930 Birthplace: Hampton, Virginia

Died: _ 1985

thesis:

Last position: Clarke-Atlanta University

Research Interests: Mathematical Biology, Probability and Statistics

Bharucha-Reis was advisor to at least 13 Ph.D. students.

Albert Turner Reid (he later exchanged names with is wife, Bharucha) was born to the familty of Hampton Institute faculty members (his father and Great Uncle).

Albert Turner Reid wrote his first paper, in mathematical biology, when he was 18. His interest in the subject is perhaps explained as his uncle was the great African American Biologist Charles Henry Turner. At 19, in 1949, he earned a B.S. in Mathematics and in Biology from the University of Iowa. Between 1950 and 1958, he held a variety of positions from research assistant to instructor at such places as The Univeristy of Chicago, Columbia University, University of California at Berkeley, and The Polish Academy of Sciences. While studying in graduate school at the University of Chicago, 1950-53, he produced mathematics for eight published papers, but did not produce a Ph.D. thesis (he said in 1953 it was a waste of his time). In 1959, he became Assistant Professor of Mathematics at the University of Oregon. In 1961 he became an Associate Professor of Mathematics at Wayne State University in Detroit, Full Professor in 1965, and in 1970, Dean of the School of Arts and Sciences at Wayne State Univeristy. Professor Bharucha-Reid has also held positions at Clark-Atlanta Univeristy.

RESEARCH

Between 1951 and 1996, Albert T. Bharucha-Reid published more than 70 papers and 6 books in algebra, analysis, mathematical biology, statistics, and topology. His first book was published in 1960.

PUBLICATIONS

books by Albert T. Bharucha-Reid

Bharucha-Reid, A. T. Probabilistic analysis and related topics, Vol. 3. Academic Press, New York-London, 1983.

Bharucha-Reid, A. T.; M. Sambandham. Random polynomials, Probability and Mathematical Statistics, Academic Press, Inc., Orlando, Fla., (1986). xvi+206 pp. ISBN: 0-12-095710-8 60G99 (30C15 60F05 60H25)

Bharucha-Reid, A. T. Random integral equations, Mathematics in Science and Engineering, 96, Academic Press, New York-London, (1972).

Bharucha-Reid, A. T. Probabilistic methods in applied mathematics , Vol. 1, Academic Press, New York-London (1968 ).

Bharucha-Reid, A. T. Elements of the theory of Markov processes and their applications , Reprint of the 1960 original. Dover Publications, Inc., Mineola, NY, 1997. xii+468 pp. ISBN: 0-486-69539-5 60-01 (60Jxx). Original: Elements of the theory of Markov processes and their applications, McGraw-Hill Series in Probability and Statistics McGraw-Hill Book Co., Inc., New York-Toronto-London (1960).

Probabilistic analysis and related topics , Vol. 3. Edited by A. T. Bharucha-Reid. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1983. x+260 pp. ISBN: 0-12-095603-9 60-06

papers by Albert T. Bharucha-Reid

Kannan, D.; Bharucha-Reid, Albert T. On a stochastic integro-differential evolution equation of Volterra type, Integro-differential evolution equations and applications (Trento, 1984). J. Integral Equations 10 (1985), no. 1-3, suppl., 351--379. 45K05 (60H99)

Sambandham, M.; Christensen, M. J.; Bharucha-Reid, A. T. Numerical solutions of random integral equation. III. Random Chebyshev polynomials and Fredholm equations of the second kind. Stochastic Anal. Appl. 3 (1985), no. 4, 467--484. 65R20

Bharucha-Reid, A. T.; Rsmisch, W. Projective schemes for random operator equations. I. Weak compactness of approximate solution measures. J. Integral Equations 8 (1985), no. 2, 95--11. 60H20 (45N05 47H17 60H25)

Sambandham, M.; Srivatsan, T. S.; Bharucha-Reid, A. T. Numerical solution of random singular integral equation appearing in crack problems. Integral methods in science and engineering (Arlington, Tex., 1985), 130--148, Hemisphere, Washington, DC, 1986.

Chandrasekharan, P. S.; Bharucha-Reid, A. T. Measures of noncompactness and fixed points of random operators. Stochastic Anal. Appl. 2 (1984), no. 4, 423--430. 47H09 (54H25 60H25)

Bharucha-Reid, A. T.; Christensen, M. J. Approximate solution of random integral equations: general methods, Math. Comput. Simulation 26 (1984), no. 4, 321--328. 60H20 (65R20 93E03)

Sambandham, M.; Thangaraj, V.; Bharucha-Reid, A. T. On the variance of the number of real roots of random algebraic polynomials, Stochastic Anal. Appl. 1 (1983), no. 2, 215--238. 60G99

[10] [PDF] 83g:60073 Bharucha-Reid, A. T. Weak compactness of solution

measures associated with random equations. Probability in Banach spaces, III

(Medford, Mass., 1980), pp. 25--34, Lecture Notes in Math., 860, Springer,

Berlin-New York, 1981. (Reviewer: H. Salehi) 60H25

[11] [PDF] 82j:65094b Christensen, M. J.; Bharucha-Reid, A. T. Numerical

solution of random integral equations. II. Fredholm equations with

degenerate kernels. J. Integral Equations 3 (1981), no. 4, 333--344. 65R20

(45B05 60H20)

[12] [PDF] 82j:65094a Christensen, M. J.; Bharucha-Reid, A. T. Numerical

solution of random integral equations. I. Fredholm equations of the second

kind. J. Integral Equations 3 (1981), no. 3, 217--229. 65R20 (45B05 60H20)

[13] [PDF] 82b:60075 Chandrasekharan, P. S.; Bharucha-Reid, A. T.

Approximate solution of fixed point equations for random operators.

Approximate solution of random equations, pp. 27--35, North-Holland, New

York-Amsterdam, 1979. (Reviewer: B. L. S. Prakasa Rao) 60H25 (47H10)

[14] [PDF] 81m:60121 Bharucha-Reid, A. T.; Kannan, R. Newton's method for

random operator equations. Nonlinear Anal. 4 (1980), no. 2, 231--240.

(Reviewer: M. Z. Nashed) 60H25 (60B12 65U05)

[15] [PDF] 81k:60065 Christensen, Mark J.; Bharucha-Reid, A. T. Companion

matrices associated with random algebraic polynomials. Multivariate

analysis, V (Proc. Fifth Internat. Sympos., Univ. Pittsburgh, Pittsburgh,

Pa., 1978), pp. 265--272, North-Holland, Amsterdam-New York, 1980.

(Reviewer: V. L. Girko) 60H99

[16] [PDF] 81k:60064 Christensen, Mark J.; Bharucha-Reid, A. T. Stability

of the roots of random algebraic polynomials. Comm. Statist. B---Simulation

Comput. 9 (1980), no. 2, 179--192. (Reviewer: V. L. Girko) 60H99 (65U05)

[17] [PDF] 81j:60002 Approximate solution of random equations. Edited by

A. T. Bharucha-Reid. North Holland Series in Probability and Applied

Mathematics. North-Holland Publishing Co., New York-Amsterdam, 1979. ix+242

pp. ISBN: 0-444-00344-4 60-06 (47Hxx)

[18] [PDF] 80j:60001 Probabilistic analysis and related topics. Vol. 2.

Edited by Albert T. Bharucha-Reid. Academic Press [Harcourt Brace

Jovanovich, Publishers], New York-London, 1979. ix+207 pp. ISBN:

0-12-095602-0 60-06 (82A05 93E20)

[19] [PDF] 57 #4269 Probabilistic analysis and related topics. Vol. 1.

Edited by A. T. Bharucha-Reid. Academic Press [Harcourt Brace Jovanovich,

Publishers], New York-London, 1978. ix+239 pp. ISBN: 0-12-095601-2 60-06

(93E10)

[20] [PDF] 56 #13300 Chi, C.-P. G.; Bharucha-Reid, A. T. Probability

measures on tensor products of Banach spaces. I. J. Multivariate Anal. 7

(1977), no. 3, 440--453. (Reviewer: Walter Schachermayer) 60B05 (28A40)

[21] [PDF] 56 #6869 Bharucha-Reid, A. T.; Mukherjea, A.; Tserpes, N. A. On

the existence of random solutions of some random integral equations. Rev.

Roumaine Math. Pures Appl. 22 (1977), no. 6, 737--745. (Reviewer: J. S.

Milton) 60H20 (45F05)

[22] [PDF] 56 #1459 Bharucha-Reid, A. T. Random integral equations.

Mathematics in Science and Engineering, Vol. 96. Academic Press, New

York-London, 1972. xiii+267 pp. (Reviewer: J. S. Milton) 60H20 (45F05)

[23] [PDF] 56 #566 Christensen, Mark J.; Bharucha-Reid, A. T. Algebraic

models for probability measures associated with solutions of random

equations. I. J. Math. Anal. Appl. 58 (1977), no. 2, 397--404. (Reviewer: M.

P. Ersov) 28A10 (26A60)

[24] [PDF] 55 #13515 Christensen, Mark J.; Bharucha-Reid, A. T. Algebraic

models for Gaussian measures on Banach spaces. Probability in Banach spaces

(Proc. First Internat. Conf., Oberwolfach, 1975), pp. 53--65. Lecture Notes

in Math., Vol. 526, Springer, Berlin, 1976. (Reviewer: Albert Tortrat) 60B05

[25] [PDF] 54 #1390 Bharucha-Reid, A. T. Fixed point theorems in

probabilistic analysis. Bull. Amer. Math. Soc. 82 (1976), no. 5, 641--657.

(Reviewer: H. Salehi) 60H99 (47H10)

[26] [PDF] 52 #15582 Probabilistic methods in applied mathematics. Vol. 3.

Edited by A. T. Bharucha-Reid. Academic Press [Harcourt Brace Jovanovich,

Publishers], New York-London, 1973. xi+346 pp. 60-06

[27] [PDF] 51 #6988 Gopalsamy, K.; Bharucha-Reid, A. T. On a class of

parabolic differential equations driven by stochastic point processes. J.

Appl. Probability 12 (1975), 98--106. (Reviewer: G. Niculescu) 60H15 (35K99)

[28] [PDF] 51 #4344 Gauglhofer, Margrit; Bharucha-Reid, A. T. $\varepsilon$-entropy of sets of probability distribution functions and their

Fourier-Stieltjes transforms. Ann. Inst. H. Poincar* Sect. B (N.S.) 9

(1973), 113--114. (Reviewer: I. Csiszar) 60E05 (94A15)

[29] [PDF] 50 #14931 Kannan, D.; Bharucha-Reid, A. T. Random integral

equation formulation of a generalized Langevin equation. J. Statist. Phys. 5

(1972), 209--233. (Reviewer: G. Papanicolaou) 60H20 (82.45)

[30] [PDF] 47 #4333 Pun, Ping Sham; Bharucha-Reid, Albert T. Mesures

associ*es la solution de quelques *quations int*grales de Fredholm

al*atoires. (French) C. R. Acad. Sci. Paris S*r. A-B 276 (1973), A699--A701.

(Reviewer: H. P. McKean, Jr.) 60H20 (60G30)

[31] [PDF] 46 #9956 Sehgal, V. M.; Bharucha-Reid, A. T. Fixed points of

contraction mappings on probabilistic metric spaces. Math. Systems Theory 6

(1972), 97--102. (Reviewer: B. Schweizer) 54H25 (60B99)

[32] [PDF] 46 #4576 Kannan, D.; Bharucha-Reid, A. T. Probability measures

on $H\sb{p}$ spaces. Ann. Inst. H. Poincar* Sect. B (N.S.) 7 (1971),

205--217. (Reviewer: R. Jajte) 60B05 (28A40)

[33] [PDF] 46 #2741 Kannan, D.; Bharucha-Reid, A. T. An operator-valued

stochastic integral. Proc. Japan Acad. 47 (1971), 472--476. (Reviewer: J. J.

Uhl, Jr.) 60H05

[34] [PDF] 44 #1068 Kannan, D.; Bharucha-Reid, A. T. Note on covariance

operators of probability measures on a Hilbert space. Proc. Japan Acad. 46

1970 124--129. (Reviewer: J. J. Uhl, Jr.) 60.08

[35] [PDF] 43 #6771 Buche, A. B.; Bharucha-Reid, A. T. On the generalized

semigroup relation in the strong operator topology. Nederl. Akad. Wetensch.

Proc. Ser. A 74=Indag. Math. 33 1971 26--31. (Reviewer: J. A. Goldstein)

47.50

[36] [PDF] 43 #5565 Schreiber, B. M.; Sun, T.-C.; Bharucha-Reid, A. T.

Algebraic models for probability measures associated with stochastic

processes. Trans. Amer. Math. Soc. 158 1971 93--105. (Reviewer: Y.-K. Chan)

60.05

[37] [PDF] 41 #6263 Umegaki, Hisaharu; Bharucha-Reid, A. T. Banach

space-valued random variables and tensor products of Banach spaces. J. Math.

Anal. Appl. 31 1970 49--67. (Reviewer: A. de Korvin) 60.08

[38] [PDF] 41 #6260 Bharucha-Reid, A. T. Random algebraic equations. 1970

Probabilistic Methods in Applied Mathematics, Vol. 2 pp. 1--52 Academic

Press, New York (Reviewer: L. A. Shepp) 60.99

[39] [PDF] 41 #4701b Probabilistic methods in applied mathematics, Vol. 2.

Edited by A. T. Bharucha-Reid Academic Press, New York-London 1970 x+220 pp.

60.90 (69.00)

[40] [PDF] 41 #4701a Probabilistic methods in applied mathematics, Vol. 1.

Edited by A. T. Bharucha-Reid Academic Press, New York-London 1968 x+291 pp.

60.90 (69.00)

[41] [PDF] 41 #2732 Mukherjea, A.; Bharucha-Reid, A. T. Separable random

operators. I. Rev. Roumaine Math. Pures Appl. 14 1969 1553--1561. (Reviewer:

I. J. Good) 60.08

[42] [PDF] 40 #2156 Baru\v ca-Rid, A. T. {\cyr élementy teorii markovskikh

protsessov i ikh prilozheniya}. (Russian) [Elements of the theory of Markov

processes and their applications] Translated from the English by V. V.

Kala\v snikov, Ju. V. Krutovski\u\i and M. S. épel\cprime man. Edited by A.

N. \v Sirjaev Izdat. Nauka'', Moscow 1969 511 pp. 60.60

[43] [PDF] 39 #6029 Bharucha-Reid, A. T.; Arnold, L. On Fredholm integral

equations with random degenerate kernels. Zastos. Mat. 10 1969 85--90.

(Reviewer: J. A. Goldstein) 45.11 (60.00)

[44] [PDF] 37 #5724 Buche, A. B.; Bharucha-Reid, A. T. On some functional

equations associated with semi-groups of operators. Proc. Nat. Acad. Sci.

U.S.A. 60 1968 1170--1174. (Reviewer: S. Kantorovitz) 47.50

[45] [PDF] 35 #7403 Seidman, T. I.; Bharucha-Reid, A. T. On processes

equivalent to Feller processes. 1967 Trans. Fourth Prague Conf. on

Information Theory, Statistical Decision Functions, Random Processes

(Prague, 1965) pp. 543--546 Academia, Prague (Reviewer: J. R. Kinney) 60.60

(47.00)

[46] [PDF] 32 #8402 Bharucha-Reid, A. T. Markov branching processes and

semigroups of operators. J. Math. Anal. Appl. 12 1965 513--536. (Reviewer:

G. E. H. Reuter) 60.67

[47] [PDF] 32 #6498 Bharucha-Reid, A. T. On the theory of random

equations. 1964 Proc. Sympos. Appl. Math., Vol. XVI pp. 40--69 Amer. Math.

Soc., Providence, R.I. 60.75

[48] [PDF] 30 #1375 Bharucha-Reid, A. T. On random solutions of non-linear

integral equations. 1964 Nonlinear Problems of Engineering pp. 23--28

Academic Press, New York (Reviewer: H. P. Thielman) 60.75 (45.30)

11. Bharucha-Reid, Albert T. Processus de Markov *quivalents et semi-groupes d'op*rateurs. (French) C. R. Acad. Sci. Paris 257 1963 1668--1670.

10. Bharucha-Reid, Albert Turner On random solutions of integral equations in Banach spaces. 1961 Trans. 2nd Prague Conf. Information Theory pp. 27--48 Publ. House Czehoslovak Acad. Sci., Prague Academic Press, New York

9. Bharucha-Reid, A. T. Über die Konvergenz der Folgen von verallgemeinerten zuf Slligen Grsssen in Orlicz'schen Ra&#215men. (German) Bull. Acad. Polon. Sci. S*r. Sci. Math. Astr. Phys. 7 1959 425--427. (unbound insert).

8. Bharucha-Reid, Albert T. Sur les *quations int*grales al*atoires de Fredholm noyaux s*parables, (French) C. R. Acad. Sci. Paris 250 1960 454--456.

7. Bharucha-Reid, Albert T. Sur les *quations int*grales al*atoires de Fredholm noyaux s*parables, (French) C. R. Acad. Sci. Paris 250 1960 657--658.

6. Bharucha-Reid, A. T. On random operator equations in Banach spaces, Bull. Acad. Polon. Sci. S*r. Sci. Math. Astr. Phys. 7 1959 561--564 (unbound insert).

5. Bharucha-Reid, A. T. On random solutions of Fredholm integral equations, Bull. Amer. Math. Soc. 66 1960 104--109.

4. Bharucha-Reid, A. T. Ergodic projections for semigroups of periodic operators, Studia Math. 17 1958 189--197.

3. Bharucha-Reid, A. T.; Rubin, Herman Generating functions and the semigroup theory of branching Markov processes, Proc. Nat. Acad. Sci. U.S.A. 44 1958 1057--1060.

2. Bharucha-Reid, A. T. On the stochastic theory of epidemics, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954--1955, vol. IV, pp. 111--119. University of California Press, Berkeley and Los Angeles, 1956.

1. Bharucha-Reid On random elements in Orlicz spaces, Bull. Acad. Polon. Sci. Cl. III. 4 (1956), 655--657.

BACK TO CONTENTS

The web pages
MATHEMATICIANS OF THE AFRICAN DIASPORA
are brought to you by

The Mathematics Department of
The State University of New York at Buffalo.

They are created and maintained by
Scott W. Williams
Professor of Mathematics