Dimitrie Pompeiu
Encyclopedia
Dimitrie Pompeiu was a well-known Romanian mathematician
.
and Bucharest, he went to France
, where he studied mathematics at the University of Paris
(the Sorbonne
). He obtained a Ph.D.
degree in mathematics in 1905 with a thesis, On the continuity of complex variable functions, written under the direction of Henri Poincaré
. After returning to Romania, he was named Professor of Mechanics
at the University of Iaşi. In 1912, he assumed a chair at the University of Bucharest
. In 1934, he was elected member of the Romanian Academy
.
His contributions were mainly in the field of mathematical analysis
, complex functions theory, and rational mechanics. In an article published in 1929, he posed a challenging conjecture
in integral geometry
, now widely known as the Pompeiu problem
. Among his contributions to real analysis
there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set. Such derivatives are now called Pompeiu derivative
s.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Biography
After studying in DorohoiDorohoi
Dorohoi is a city in the Botoşani County, Romania, on the right bank of the Jijia River, which broadens into a lake on the north.Dorohoi used to be a market for the timber and farm produce of the north Moldavian highlands; merchants from the neighboring states flocked to its great fair, held on...
and Bucharest, he went to France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, where he studied mathematics at the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
(the Sorbonne
Sorbonne
The Sorbonne is an edifice of the Latin Quarter, in Paris, France, which has been the historical house of the former University of Paris...
). He obtained a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
degree in mathematics in 1905 with a thesis, On the continuity of complex variable functions, written under the direction of Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
. After returning to Romania, he was named Professor of Mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
at the University of Iaşi. In 1912, he assumed a chair at the University of Bucharest
University of Bucharest
The University of Bucharest , in Romania, is a university founded in 1864 by decree of Prince Alexander John Cuza to convert the former Saint Sava Academy into the current University of Bucharest.-Presentation:...
. In 1934, he was elected member of the Romanian Academy
Romanian Academy
The Romanian Academy is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 acting members who are elected for life....
.
His contributions were mainly in the field of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, complex functions theory, and rational mechanics. In an article published in 1929, he posed a challenging conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
in integral geometry
Integral geometry
In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant transformations from the space of functions on one geometrical space to the...
, now widely known as the Pompeiu problem
Pompeiu problem
In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929,as follows. Suppose f is a nonzero continuous function defined on a Euclidean space, and K is a simply connected Lipschitz domain, so that the integral of f vanishes...
. Among his contributions to real analysis
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set. Such derivatives are now called Pompeiu derivative
Pompeiu derivative
In mathematical analysis, a Pompeiu derivative is a real-valued function of one real variable that is the derivative of an everywhere differentiable function and that vanishes in a dense set. Note in particular that a Pompeiu derivative is discontinuous at any point where it is not 0...
s.
Sources
- National Institute for R&D in Informatics ,Short biography of Dimitrie Pompeiu
- http://www.imar.ro/events/pompifip.pdf, One hundred years since the introduction of the set distance by Dimitrie Pompeiu, by T. Bârsan and D. Tiba, Institute of Mathematics of the Romanian AcademyInstitute of Mathematics of the Romanian AcademyThe Institute of Mathematics "Simion Stoilow" of the Romanian Academy is a research institute in Bucharest, specialized in Mathematics. It was named after Simion Stoilow, who was its first Director, in 1949. In 1974 Nicolae Ceauşescu's daughter Zoia was permitted into the institute because of her...
- http://www.cs.ubbcluj.ro/www/index.php?module=pagemaster&PAGE_user_op=view_page&PAGE_id=126, Short biography of Dimitrie Pompeiu, by Petre Mocanu, Babeş-Bolyai UniversityBabes-Bolyai UniversityThe Babeș-Bolyai University in Cluj-Napoca is an university in Romania. With almost 50,000 students, the university offers 105 specialisations, of which there are 105 in Romanian, 67 in Hungarian, 17 in German, and 5 in English...
External links
- http://www.gap-system.org/~history/Biographies/Pompeiu.html