Albert Turner Bharucha-Reid
Born: February 22, 1930 Birthplace: Hampton, Virginia
Died: _ 1985
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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×men. (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.
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