# Alexandru Ioan Lupas

### Biography

**Alexandru Lupas**was brought up in Arad, Romania. Arad is in western Romania, the city belonging to Hungary until the end of World War I. He attended the Moise Nicoara high-school in Arad, an excellent school which had been taken over by the Romanian State in 1934. After graduating from the high school he entered Babeș-Bolyai University in Cluj. The University was an excellent one at which to study mathematics and there he was taught by some outstanding mathematicians including Gheorghe Calugăreănu, Dumitru V Ionescu, Tiberiu Mihailescu, Petru T Mocanu, Gheorghe Pic, Tiberiu Popoviciu, Ferenc Rado, and Dimitrie D Stancu.

Lupas graduated in 1964 and was then appointed as a researcher at the Institute of Numerical Computation of the Romanian Academy in Cluj-Napoca. The Romanian Academy had set up the Mathematical Institute at Cluj-Napoca in 1948 and it had become the Institute of Numerical Computation of the Romanian Academy in 1957. At this time it consisted of two departments, the Department of Approximation and Calculus, and the Computer Department. Lupas held this appointment until 1975 when the Institute of Numerical Computation was transferred from the Romanian Academy to the National Education Minister and the number of researchers reduced from 48 to 6. While working at the Institute of Numerical Computation, Lupas published a number of excellent papers. For example

*On Bernstein power series*(1966) was reviewed by D E Wulbert who wrote:-

The author first develops a method for constructing sequences of positive linear operators on a subspace of bounded functions on the real line. As special cases of his general method, the author constructs the Szász-Mirakjan and Baskakov operators. These latter operators are studied in the second part of the paper, where they are shown to exhibit some properties similar to those of the Bernstein operator.In 1967 he published

*Some properties of the linear positive operators. I*,

*Approximationseigenschaften der Gammaoperatoren*,

*Some properties of the linear positive operators. II*, and (with Gheorghe Cimoca)

*Two generalizations of the Meyer-König and Zeller operator*.

His outstanding work led to him winning a Humboldt scholarship to enable him to undertake research at the Universities of Stuttgart and Tübingen. He worked for his doctorate with Werner Meyer-König as his thesis advisor and was awarded the degree of Doktor der Naturwissenschaften from Universität Stuttgart in 1972 for his thesis

*Die Folge der Betaoperatoren*Ⓣ. He graduated with distinction on 28 April 1972 and then returned to Cluj where he undertook research for a second doctorate. His advisor Tiberiu Popoviciu sadly died in 1975 so Lupas was advised by Dimitrie D Stancu for the final months of his work. He submitted this second thesis

*Contributions to the Theory of Approximation by Linear Operators*to Babeș-Bolyai University in 1976. In the same year he was appointed as a lecturer at the University of Sibiu, the year in which the university became an independent institution. Before this higher education in Sibiu had been part of the University of Cluj.

In 1969 he attended, by invitation, the conference 'Iterationsverfahren, Numerische Mathematik, Approximationstheorie' at the Oberwolfach research centre in the Black Forest in Germany. There he presented a paper

*On the approximation by linear positive operators*which was summarised by Sheldon Eisenberg:-

In the first part of this paper, the author discusses the graphic behaviour of the Szász-Mirak'jan operator. Specifically, he gives conditions under which the operator preserves convexity, concavity, and polynomiality. The second part of the paper continues his work on the Baskakov operator. Here he gives conditions under which the Baskakov operator is variation-diminishing.In 1971 he published

*On the approximation by linear operators of the class*$S_{m}$, and in the following year

*An integral inequality for convex functions*. In all he published over 100 research papers, 6 research level monographs and 10 textbooks.

We noted above that Lupas was appointed to the University of Sibiu in 1976. The university did not find favour with the government and gradually through the 1980s they closed down the schools until only the School of Mechanical Engineering remained. At this point it became part of the Polytechnic School of Cluj-Napoca. After the Revolution of December 1989 moves were rapidly put in place to refound the University of Sibiu and it was formally reconstituted on 5 March 1990. On 12 May 1995, the University of Sibiu was granted the name of the distinguished Romanian writer and philosopher, Lucian Blaga.

Lupas was a major figure in the affairs of the university through this difficult period. In 1980 he was promoted to associate professor, then to full professor in 1990 when the University was formally founded again. He held this professorship until his death. He also held a number of important positions such as the Chair of Applied Mechanics from 1982 to 1985. After the University of Sibiu properly existed again as an institution in its own right in 1990 he became Rector of the University for the year and Dean of the Faculty of Sciences from 1990 until 1992. He was also appointed vice-rector of the Romanian-German University of Sibiu (1998-1999) and, after the University was renamed, Head of the Department of Mathematics of Lucian Blaga University from 1999 to 2000.

Lupas was married to Luciana who was herself an eminent mathematician on the staff of the university. Alexandru and Luciana Lupas, together with Heiner, were editors of the Proceedings of the conference

*Mathematical analysis and approximation theory*which consisted of papers presented to the 5th Romanian-German Seminar on Approximation Theory held in Sibiu from 12 to 15 June 2002. He published two papers in these proceedings,

*The positivity of a certain quadrature*and

*q-analogues of Stancu operators*. In 2002 he published a joint paper with his wife in

*Properties of Stancu operators*. Alexandru and Luciana Lupas write:-

The paper is concerned with the Stancu operators ... After the pioneering work of D D. Stancu (1968), these operators have been successfully used by other mathematicians to study properties of linear positive methods of approximation. A substantial part of contributions in this field can be found in the survey [B Della Vecchia (1992)]. In this paper we present some properties related to the operators ... . For instance, we prove a representation of the remainder term and also some mean value theorems. At the end we discuss a quadrature formula for Stancu operators.The authors of [2] pay this tribute to Lupas:-

This year, on August 14, the mathematical community suffered a big loss: the decease of Professor Alexandru Lupas, a distinguished Romanian mathematician, one of the most important of his generation. Professor at the Department of Mathematics of the University "Lucian Blaga" in Sibiu, Romania, he was a specialist in Approximation Theory, Classical Analysis, Inequalities, Convexity, Numerical Analysis, Special Functions, Finite Operatorial Calculus (Umbral Calculus) and q-Calculus. His unexpected death, occurring only one year after the death of his wife Luciana Lupas, also a distinguished mathematician at the University "Lucian Blaga" in Sibiu, shocked not only his family, but also his friends, disciples, PhD students and students. He was an extraordinarily kind man, with a pleasant personality and an optimistic view of the world, life and work. For many, he was a master, an advisor and a friend.

### References (show)

- E Draghici, Professor Ph.D. Alexandru Lupas at his 65-th anniversary,
*Gen. Math.***15**(1) (2007), 3-20. - S Gal and A Vernescu, Obituary: Professor Alexandru Lupas (1942--2007),
*J. Inequal. Pure Appl. Math.***8**(3) (2007).

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update December 2008

Last Update December 2008