From Wikipedia, the free encyclopedia
American-Canadian mathematician
Lloyd Lyne Dines (29 March 1885, in
Shelbyville, Missouri – 17 January 1964, in
Quincy, Illinois ) was an American-Canadian mathematician, known for his pioneering work on linear inequalities.
[1]
Education and career
Dines received B.A. in 1906 and M.A. in 1907 from
Northwestern University
[2] and Ph.D. in 1911 from the
University of Chicago under
Gilbert Bliss with thesis The highest common factor of a system of polynomials in one variable, with an application to implicit functions .
[3] In 1911 he became an instructor of mathematics at
Columbia University and then became an associate professor at the
University of Arizona . From 1915 to 1934 he was a professor at the
University of Saskatchewan . In 1928 he was elected to the
Royal Society of Canada . In 1932 he was an
invited speaker at the International Congress of Mathematicians in
Zürich . From 1934 to 1945 he was a professor at the
Carnegie Institute of Technology and chair of the mathematics department. After his retirement in 1945, Dines held visiting professorships at the University of Saskatchewan,
Smith College , and Northwestern University.
[1]
Selected publications
Dines, Lloyd L. (1913).
"Concerning two recent theorems on implicit functions" . Bull. Amer. Math. Soc . 19 (9): 462–467.
doi :
10.1090/s0002-9904-1913-02397-8 .
MR
1559394 .
Dines, L. L. (1915).
"Complete existential theory of Sheffer's postulates for Boolean algebras" . Bull. Amer. Math. Soc . 21 (4): 183–188.
doi :
10.1090/s0002-9904-1915-02595-4 .
MR
1559609 .
Dines, L. L. (1919).
"Projective transformations in function space" . Trans. Amer. Math. Soc . 20 : 45–65.
doi :
10.1090/s0002-9947-1919-1501115-2 .
MR
1501115 .
Dines, L. L. (1924).
"Concerning a suggested and discarded generalization of the Weierstrass factorization theorem" . Bull. Amer. Math. Soc . 30 (5–6): 233–236.
doi :
10.1090/s0002-9904-1924-03889-0 .
MR
1560882 .
Dines, Lloyd L. (1924).
"A theorem on the factorization of polynomials of a certain type" . Trans. Amer. Math. Soc . 26 : 17–24.
doi :
10.1090/s0002-9947-1924-1501262-7 .
MR
1501262 .
Dines, L. L. (1927).
"Linear inequalities in general analysis" . Bull. Amer. Math. Soc . 33 (6): 695–700.
doi :
10.1090/s0002-9904-1927-04461-5 .
MR
1561451 .
Dines, Lloyd L. (1927).
"On sets of functions of a general variable" . Trans. Amer. Math. Soc . 29 (2): 463–470.
doi :
10.1090/s0002-9947-1927-1501398-3 .
MR
1501398 .
Dines, L. L. (1928).
"A theorem on orthogonal sequences" . Trans. Amer. Math. Soc . 30 (2): 439–446.
doi :
10.1090/s0002-9947-1928-1501437-0 .
MR
1501437 .
Dines, Lloyd L. (1928).
"A theorem on orthogonal functions with an application to integral inequalities" . Trans. Amer. Math. Soc . 30 (2): 425–438.
doi :
10.1090/s0002-9947-1928-1501436-9 .
MR
1501436 .
Dines, L. L. (1930).
"Linear inequalites and some related properties of functions" . Bull. Amer. Math. Soc . 36 (6): 393–405.
doi :
10.1090/s0002-9904-1930-04956-3 .
MR
1561956 .
Dines, L. L. (1936).
"Convex extension and linear inequalities" . Bull. Amer. Math. Soc . 42 (6): 353–365.
doi :
10.1090/s0002-9904-1936-06299-3 .
MR
1563300 .
S2CID
44594799 .
with David Moskovitz: Moskovitz, David; Dines, L. L. (1940).
"On the supporting-plane property of a convex body" . Bull. Amer. Math. Soc . 46 (6): 482–489.
doi :
10.1090/s0002-9904-1940-07242-8 .
MR
0002008 .
Dines, Lloyd L. (1941).
"On the mapping of quadratic forms" . Bull. Amer. Math. Soc . 47 (6): 494–498.
doi :
10.1090/s0002-9904-1941-07494-x .
MR
0004216 .
Dines, Lloyd L. (1942).
"On the mapping of n quadratic forms" . Bull. Amer. Math. Soc . 48 (6): 467–471.
doi :
10.1090/s0002-9904-1942-07707-x .
MR
0006141 .
Dines, Lloyd L. (1943).
"On linear combinations of quadratic forms" . Bull. Amer. Math. Soc . 49 (6): 388–393.
doi :
10.1090/s0002-9904-1943-07925-6 .
MR
0008068 .
Dines, LL (November 1947).
"On a theorem of von Neumann" . Proc Natl Acad Sci U S A . 33 (11): 329–31.
Bibcode :
1947PNAS...33..329D .
doi :
10.1073/pnas.33.11.329 .
PMC
1079066 .
PMID
16588759 .
References