Nicholas D. Kazarinoff Explained

Nicholas Donat Kazarinoff (August 12, 1929, Ann Arbor, Michigan – November 21, 1991, Albuquerque, New Mexico) was an American mathematician, specializing in differential equations.[1] In 1988 he was elected a Fellow of the American Association for the Advancement of Science (AAAS).[2]

Education and career

Kazarinoff grew up in Ann Arbor, Michigan, and went to college in his hometown at the University of Michigan. There he graduated with a B.S. in 1950 and an M.S. in 1951. He graduated in 1954 with a Ph.D. in mathematics from the University of Wisconsin–Madison. His Ph.D. thesis Asymptotic Forms for the Whitaker Functions of Large Complex Order m was supervised by Rudolf Ernest Langer. In the mathematics department of Purdue University, Kazarinoff was from 1953 to 1955 an instructor and from 1955 to 1956 an assistant professor. At the University of Michigan, he was from 1956 to 1960 an assistant professor, from 1960 to 1964 an associate professor, and from 1964 to 1971 a full professor. In 1971 he resigned from the University of Michigan to become the chair of the mathematics department at the University of Buffalo (also known as SUNY Buffalo or the State University of New York, Buffalo). There he was the Martin Professor of Mathematics from 1972 until his death in 1991. He died in Albuquerque when he was a visiting professor at the University of New Mexico,[1] where he was also a visiting professor in 1985. He also held visiting appointments at the University of Wisconsin–Madison's Army Mathematics Research Center (AMRC) (1958–1960), at Rome's Consiglio Nazionale delle Ricerche, CNR (1978 and 1980), and at Beijing University of Technology (1987). At Moscow's Steklov Institute of Mathematics, he was an exchange professor for the academic year 1960–1961 and again in the spring semester of 1965.[3]

Kazarinoff's research focused mainly on differential equations.[3] His speciality was partial differential equations applied to reaction-diffusion systems.[4] His research on differential equations included fluid dynamics and dynamical systems. He also did research on the geometry of convex sets, the geometry of theta series, and iteration of real-valued and complex-valued maps.[5] He was the author or co-author of more than 80 research articles and monographs.[1] After his death, the University of Michigan established the Nicholas D. Kazarinoff Collegiate Professorship of Complex Systems, Mathematics, and Physics.[4]

D. K. Kazarinoff's inequality for tetrahedra

Kazarinoff dedicated his book Geometric Analysis to his father, Donat Konstantinovich Kazarinoff (1892–1957), who taught mathematics and engineering at the University of Michigan for 35 years (with 37 years of affiliation and 2 years of academic leave).[6] [7]

Theorem: Let Ⲧ be a tetrahedron and let P be a point belonging to T. Let the distances from P to the vertices and to the faces of Ⲧ be denoted by Ri and ri, respectively, for i = 1,2,3,4. Then:
For any tetrahedron Ⲧ whose circumcenter is not an exterior point,
ΣRi/Σri > 2 and 2 is the greatest lower bound.

According to László Fejes Tóth,[8] D. K. Kazarinoff stated the inequality but never published his proof, perhaps because he thought that his proof was not simple enough. However, shortly before his death, D. K. Kazarinoff provided a simple proof of the Erdős-Mordell inequality for triangles and gave a generalization to three dimensions. Nicholas D. Kazarinoff used the work of his father as a basis for a proof of D. K. Kazarinoff's inequality for tetrahedra.[9]

Personal life

In July 1948, Kazarinoff married Margaret Louise Koning. They had five sons and a daughter. Upon his death in 1991 at age 62, he was survived by his widow, their six children, and eight grandchildren. He was an active member of the Unitarian Universalist Church of Buffalo and served on the church's finance committee.[1]

Selected publications

Articles

Books

References

  1. News: Obituary. Nicholas D. Kazarinoff, UB Math Professor. Buffalo News. November 23, 1991.
  2. Web site: Historic Fellows. American Association for the Advancement of Science (aaas.org). (Search on last_name="Kazarinoff".)
  3. 10.1080/00029890.1973.11993397 . Squaring Rectangles and Squares . 1973 . Kazarinoff . N. D. . Weitzenkamp . Roger . The American Mathematical Monthly . 80 . 8 . 877–888 . (See Notes on contributors which accompanies the article.)
  4. Web site: Continuum, UM Department of Mathematics, Newsletter 2015. University of Michigan. 2.
  5. 10.1080/00029890.1988.11972073 . Special Functions and the Bieberbach Conjecture . 1988 . Kazarinoff . Nicholas D. . The American Mathematical Monthly . 95 . 8 . 689–696 . (See Notes on contributors which accompanies the article.)
  6. Web site: end matter for Geometric Inequalities by Nicholas D. Kazarinoff. American Mathematical Society (ams.org).
  7. Book: February Meeting, 1957. Report of the Board of Regents. 1954 . University of Michigan. https://books.google.com/books?id=sDYXAQAAMAAJ&pg=PA1429. 1429–1430.
  8. p. 120 of 2013 pbk reprint
  9. D. K. Kazarinoff's inequality for tetrahedra. 1957. Michigan Math. J.. 4. 2. 99–104. Kazarinoff, Nicholas D.. 10.1307/mmj/1028988999.
  10. Web site: Stenger, Allen. review of Analytic Inequalities by Nicholas D. Kazarinoff. March 12, 2011. MAA Reviews, Mathematical Association of America.
  11. Web site: Stenger, Allen. March 10, 2011. review of Geometric Inequalities by Nicholas D. Kazarinoff. MAA Reviews, Mathematical Association of America.

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