# Dimitrie D Stancu

### Born: 11 February 1927 in Calacea, Timis county, Romania

Died: 17 April 2014 in Cluj, Romania

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**Dimitrei D Stancu**was born at the village of Calacea, Timis county in February 1927. Calacea is around 25 km north of Timișoara, the capital of Timis county. It became part of Romania following World War I so was Romanian at the time that Dimitrie (known as Didi to his friends and colleagues) was born there. His family were farmers but his early years were ones of great difficulty. His father died when he was a baby and his mother had to earn a living so she worked as a shepherd. The family were unable to care for Dimitrie, so his oldest brother, who worked as a painter in the city of Arad, took him to the Regina Maria orphanage in Arad where he was brought up. The first two years of his primary school studies, 1937-39, were in the Regina Maria orphanage and his next two years were spent at the Sânnicolaul Mic. After completing his primary education, in 1941 he went to the Gymnasium in "New Arad" where he spent two years before completing his schooling at the Moise Nicoara in the years 1943-47. This school was founded in 1873 when Arad was part of Austria-Hungary and only received the name "Moise Nicoara" in 1919 when Transylvania became part of Romania. His time at school was, however, difficult as the authors of [3] point out:-

Stancu entered the Faculty of Mathematics of the Babeș University of Cluj in 1947. At the time Stancu began his university studies, there were two universities in Cluj. The Romanian University of Cluj which had been the King Ferdinand I University, had been renamed Babeș University (after the Romanian natural scientist Victor Babeș) while the Hungarian University of Cluj was named the Bolyai University (after the mathematician János Bolyai). The two universities combined to become the Babeș-Bolyai University in 1959. Stancu had a very successful undergraduate career in Cluj, where he was taught by Tiberiu Popoviciu. Because of Stancu's obvious abilities, Tiberiu Popoviciu encouraged him to undertake research in mathematics. He graduated with his first degree in 1951. Because of his remarkable achievements during his undergraduate studies, in 1951 Stancu was appointed as assistant to the Chair of Mathematical Analysis, held at that time by the academician Tiberiu Popoviciu. At the same time, Stancu began undertaking research for his Ph.D. thesis advised by Tiberiu Popoviciu. He was awarded his doctorate in Mathematics in 1956 with a thesis entitledIn his schooling he had many difficulties being an orphan and very poor, but with the help of his mathematics teachers he succeeded in making progress in his studies at the prestigious Lyceum "Moise Nicoara" from the large city of Arad.

*A study of the polynomial interpolation of functions of several variables, with application to the numerical differentiation and integration; methods for evaluating the remainders*(Romanian).

Stancu published a series of papers related to the work of his doctoral thesis in 1956-57. The first of these was

*Contribution to the partial numerical differentiation of functions of two and several variables*(Romanian) (1956). Emil Grosswald writes in a review:-

Some other papers in this series wereWhile there is a large literature on the numerical differentiation of functions of a single variable, the corresponding problem for several variables has received less attention. The author establishes such formulae, giving approximate values of the partial derivatives, by linear combinations of values of the function and its successive, lower order, partial derivatives at a finite set of points. ... The author gives the degrees of exactness for his formulae of numerical partial differentiation. Newton's, alternatively also Lagrange's, interpolation polynomials are taken as starting points in the proofs. These are elementary in character, but rather complicated. In some of them, only the cases of2or3variables are worked out, in order to keep notations reasonably simple. In the case of lattice points with unequal distances, use is made of divided differences. Somewhat simpler results are found in the case of equidistant lattice points ...

*On polynomial interpolation formulas for functions of several variables*(Romanian) (1957),

*Generalisation of some interpolation formulas for functions of several variables and certain thoughts on the numerical integration formula of Gauss*(Romanian) (1957),

*A generalisation of the Gauss-Christoffel quadrature formula*(Romanian) (1957),

*Generalisation of certain interpolation formulas for functions of several variables*(Romanian) (1957),

*Sur une classe de polinômes orthogonaux et sur des formules générales de quadrature à nombre minimum de termes*Ⓣ (1957),

*Contributions to the numerical integration of functions of several variables*(Romanian) (1957), and

*On the Hermite interpolation formula and on some of its applications*(Romanian) (1957).

During the academic year 1961-1962 Stancu was awarded a fellowship from the Romanian Ministry of Education to undertake research in the Department of Numerical Analysis of the University of Wisconsin at Madison in the United States. This department was led by Preston C Hammer (1913-1986) and the year he spent there proved important for the future development of Stancu's career. After his return to Romania, he was named as a full professor in 1968 in the Numerical and Statistical Calculus Chair from the Faculty of Mathematics at the Babeș-Bolyai University of Cluj.

Dimitrie D Stancu taught high level courses on Mathematical Analysis, Numerical Analysis, Approximation Theory, Probability Theory, etc. He was Vice-Dean of the Faculty of Mathematics and, for many years, Head of the Numerical and Statistical Calculus Chair.

Dimitrie D Stancu's research activity was decisively influenced by his scientific cooperation with academician Tiberiu Popoviciu. Stancu's main research topics were: interpolation theory, derivative and numerical integration, orthogonal polynomials, spline functions, approximation of the functions by linear and positive operators, probabilistic and combinatorial methods in approximation theory. Stancu devoted part of his research work to Numerical Analysis in connection with the new subject of Computer Science. Stancu was the thesis advisor of 41 Ph.D. students in the field of Numerical Analysis and Approximation Theory. He published more than 120 research papers which have had a strong international impact.

More than 200 papers have the name of Dimitrie D Stancu in their title and the concept of a Stancu operator is nowadays a very well-known notion in the mathematics literature. What are today called the 'Bernstein-Stancu operators' were introduced by Stancu in 1968 in his paper

*Approximation of functions by a new class of linear polynomial operators*and also studied in his paper

*Approximation of functions by means of a new generalized Bernstein operator*(1983). What are today called 'Stancu beta operators' were introduced by Stancu in his paper

*On the Beta approximation operators of second kind*(1995). Along with co-authors Petru Blaga and Gheorghe Coman, Stancu wrote the two-volume 850-page treatise

*Numerical analysis and approximation theory*(Romanian) (2001, 2002).

Stancu was an invited lecturer at the 'SIAM Symposium on Approximation' at Gatlinburg, Tennessee in October 1963 and at meetings of the American Mathematical Society in Milwaukee, Chicago and New York. In 2000 Stancu presented an invited paper to the conference 'Trends in Approximation Theory' in Nashville, Tennessee. While in the United States he was invited to lecture at several American Universities: Ohio State University at Columbus, Ohio, the University of South Carolina at Columbia, South Carolina, Vanderbilt University at Nashville, Tennessee, and PACE University at Pleasantville, New York. He attended a large number of conferences, giving lectures at many of them. These include meetings in Germany at Stuttgart, Hannover, Hamburg, Göttingen, Dortmund, Münster, Siegen, Würzburg, Berlin and Oberwolfach, in Italy at Rome, Naples, Potenza and L'Aquila, in England at Lancaster (where he gave the lecture 'Probabilistic methods in the theory of approximation of functions of several variables by linear positive operators') and Durham (where he gave the lecture 'Approximation of bivariate functions by means of some Bernstein-type operators'), in Hungary at Budapest, in France at Paris, in Bulgaria at Sofia and Varna, in Poland at Warsaw and in the Czech Republic at Brno.

In 1995 the "Lucian Blaga" University of Sibiu awarded Stancu an honorary doctorate. He was also awarded an honorary doctorate by the "North University" of Baia Mare. He was elected an honorary member of the Romanian Academy of Sciences in 1999. He also was an active collaborator of the Tiberiu Popoviciu Institute on Computing of the Romanian Academy of Sciences. He was an editor of

*Studia. Universitatis Babeș-Bolyai Mathematica*, the Italian journal

*Calcolo. A Quarterly on Numerical Analysis and Theory of Computation*, and editor-in-chief of the Romanian journal

*Revue d'Analyse Numérique et de Théorie de l'Approximation*. In May 2002 the 'International Symposium on Numerical Analysis and Approximation Theory' was organised at the Babeș-Bolyai University of Cluj to honour Stancu's 75

^{th}birthday. The 'International Seminar on Approximation Theory and its Applications' was held at the Lucian Blaga University of Sibiu, 29 May-1 June 2014 "in honour of the memory of Academician Professor Dimitrie D Stancu and his lifetime contributions to the Approximation Theory". At this meeting, lectures included: Heiner Gonska, 'Academician Prof. Dr. D. D. Stancu (1927 - 2014): his influence on my mathematical work'; Voichita Adriana Radu, 'Academician Professor D. D. Stancu : a life time dedicated to the numerical analysis and theory of approximation'; and Andrei Vernescu, 'Acad. Prof. D. D. Stancu, a respectful remember and a deep homage'.

Dimitrie D Stancu was married to Felicia, who was also a mathematician teaching at the Babeș-Bolyai University of Cluj. They had two daughters, Angela Stancu (born 1957) and Mirela (born 1958), who both became secondary school teachers of mathematics. The authors of [2] write (we have changed their words to the past tense):-

Stancu died at Cluj-Napoca in April 2014.He had the extraordinary ability to touch deeply the lives of all whom he associated, whatever their background and experience. He had a warm and sensitive personality. One of the really remarkable things about Dimitrie D Stancu's commitment to mathematics was that he knew how to hand it on others. In this way he inspired many students and colleagues to do some of their best work. His door was always open to them. Professor D D Stancu was an important - a very influential - mathematician. He was a mathematician whose work possessed power, grace and beauty. He was a wonderful human being and a brilliant and profound mathematician.

**Article by:** *J J O'Connor* and *E F Robertson*

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