# Lloyd Dines
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{{short description|American-Canadian mathematician}}
'''Lloyd Lyne Dines''' (29 March 1885, in [Shelbyville, Missouri](/source/Shelbyville%2C_Missouri) – 17 January 1964, in [Quincy, Illinois](/source/Quincy%2C_Illinois)) was an American-Canadian mathematician, known for his pioneering work on linear inequalities.[[http://artsandscience.usask.ca/math/department/people.php Lloyd L. Dines (1885–1964), The Department of Mathematics and Statistics - College of Arts and Science, University of Saskatchewan] {{webarchive|url=https://web.archive.org/web/20121127140501/http://artsandscience.usask.ca/math/department/people.php |date=2012-11-27 }}]
==Education and career==
Dines received B.A. in 1906 and M.A. in 1907 from [Northwestern University](/source/Northwestern_University)[[https://books.google.com/books?id=SCoXAAAAYAAJ&pg=PA69 Lloyd Lyne Dines, p. 69 of ''Annual Register'', U. of Chicago, 1910]] and Ph.D. in 1911 from the [University of Chicago](/source/University_of_Chicago) under [Gilbert Bliss](/source/Gilbert_Bliss) with thesis ''The highest common factor of a system of polynomials in one variable, with an application to implicit functions''.[{{MathGenealogy|id=5897|title=Lloyd Lyne Dines}}] In 1911 he became an instructor of mathematics at [Columbia University](/source/Columbia_University) and then became an associate professor at the [University of Arizona](/source/University_of_Arizona). From 1915 to 1934 he was a professor at the [University of Saskatchewan](/source/University_of_Saskatchewan). In 1928 he was elected to the [Royal Society of Canada](/source/Royal_Society_of_Canada). In 1932 he was an [invited speaker at the International Congress of Mathematicians](/source/list_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers) in [Zürich](/source/Z%C3%BCrich). From 1934 to 1945 he was a professor at the [Carnegie Institute of Technology](/source/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](/source/Smith_College), and Northwestern University.[
==Selected publications==
*{{cite journal|title=Concerning two recent theorems on implicit functions|journal=Bull. Amer. Math. Soc.|year=1913|volume=19|pages=462–467|mr=1559394|doi=10.1090/s0002-9904-1913-02397-8|url=https://zenodo.org/record/1431545|doi-access=free|last1=Dines|first1=Lloyd L.|issue=9}}
*{{cite journal|title=Complete existential theory of Sheffer's postulates for Boolean algebras|journal=Bull. Amer. Math. Soc.|year=1915|volume=21|pages=183–188|mr=1559609|doi=10.1090/s0002-9904-1915-02595-4|doi-access=free|last1=Dines|first1=L. L.|issue=4}}
*{{cite journal|title=Projective transformations in function space|journal=Trans. Amer. Math. Soc.|year=1919|volume=20|pages=45–65|mr=1501115|doi=10.1090/s0002-9947-1919-1501115-2|doi-access=free|last1=Dines|first1=L. L.}}
*{{cite journal|title=Concerning a suggested and discarded generalization of the Weierstrass factorization theorem|journal=Bull. Amer. Math. Soc.|year=1924|volume=30|pages=233–236|mr=1560882|doi=10.1090/s0002-9904-1924-03889-0|doi-access=free|last1=Dines|first1=L. L.|issue=5–6}}
*{{cite journal|title=A theorem on the factorization of polynomials of a certain type|journal=Trans. Amer. Math. Soc.|year=1924|volume=26|pages=17–24|mr=1501262|doi=10.1090/s0002-9947-1924-1501262-7|doi-access=free|last1=Dines|first1=Lloyd L.}}
*{{cite journal|title=Linear inequalities in general analysis|journal=Bull. Amer. Math. Soc.|year=1927|volume=33|pages=695–700|mr=1561451|doi=10.1090/s0002-9904-1927-04461-5|doi-access=free|last1=Dines|first1=L. L.|issue=6}}
*{{cite journal|title=On sets of functions of a general variable|journal=Trans. Amer. Math. Soc.|year=1927|volume=29|pages=463–470|mr=1501398|doi=10.1090/s0002-9947-1927-1501398-3|doi-access=free|last1=Dines|first1=Lloyd L.|issue=2}}
*{{cite journal|title=A theorem on orthogonal sequences|journal=Trans. Amer. Math. Soc.|year=1928|volume=30|pages=439–446|mr=1501437|doi=10.1090/s0002-9947-1928-1501437-0|doi-access=free|last1=Dines|first1=L. L.|issue=2}}
*{{cite journal|title=A theorem on orthogonal functions with an application to integral inequalities|journal=Trans. Amer. Math. Soc.|year=1928|volume=30|pages=425–438|mr=1501436|doi=10.1090/s0002-9947-1928-1501436-9|doi-access=free|last1=Dines|first1=Lloyd L.|issue=2}}
*{{cite journal|title=Linear inequalities and some related properties of functions|journal=Bull. Amer. Math. Soc.|year=1930|volume=36|pages=393–405|mr=1561956|doi=10.1090/s0002-9904-1930-04956-3|doi-access=free|last1=Dines|first1=L. L.|issue=6}}
*{{cite journal|title=Convex extension and linear inequalities|journal=Bull. Amer. Math. Soc.|year=1936|volume=42|pages=353–365|mr=1563300|doi=10.1090/s0002-9904-1936-06299-3|last1=Dines|first1=L. L.|issue=6|s2cid=44594799 |url=http://projecteuclid.org/euclid.bams/1183498913|doi-access=free}}
*with David Moskovitz: {{cite journal|title=On the supporting-plane property of a convex body|journal=Bull. Amer. Math. Soc.|year=1940|volume=46|pages=482–489|mr=0002008|doi=10.1090/s0002-9904-1940-07242-8|doi-access=free|last1=Moskovitz|first1=David|last2=Dines|first2=L. L.|issue=6}}
*{{cite journal|title=On the mapping of quadratic forms|journal=Bull. Amer. Math. Soc.|year=1941|volume=47|pages=494–498|mr=0004216|doi=10.1090/s0002-9904-1941-07494-x|doi-access=free|last1=Dines|first1=Lloyd L.|issue=6}}
*{{cite journal|title=On the mapping of ''n'' quadratic forms|journal=Bull. Amer. Math. Soc.|year=1942|volume=48|pages=467–471|mr=0006141|doi=10.1090/s0002-9904-1942-07707-x|doi-access=free|last1=Dines|first1=Lloyd L.|issue=6}}
*{{cite journal|title=On linear combinations of quadratic forms|journal=Bull. Amer. Math. Soc.|year=1943|volume=49|pages=388–393|mr=0008068|doi=10.1090/s0002-9904-1943-07925-6|doi-access=free|last1=Dines|first1=Lloyd L.|issue=6}}
*{{cite journal|title=On a theorem of von Neumann|journal=Proc Natl Acad Sci U S A|date=November 1947|volume=33|issue=11|pages=329–31|pmc=1079066|pmid=16588759|doi=10.1073/pnas.33.11.329 | last1 = Dines | first1 = LL|bibcode=1947PNAS...33..329D|doi-access=free}}
==References==
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{{Authority control}}
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Category:1885 births
Category:1964 deaths
Category:20th-century American mathematicians
Category:Canadian mathematicians
Category:Northwestern University alumni
Category:University of Chicago alumni
Category:Academic staff of the University of Saskatchewan
Category:Carnegie Mellon University faculty
Category:People from Shelbyville, Missouri
Category:Fellows of the Royal Society of Canada
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