# Elena Moldovan Popoviciu

### Born: 26 August 1924 in Cluj, Romania

Died: 24 June 2009 in Cluj, Romania

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**Elena Moldovan**, the daughter of Ioan Moldovan and of his wife Rozalia, was born in August 1924 in Cluj. She married the mathematician Tiberiu Popoviciu in 1964 and, from that time on, was known as

**Elena Popoviciu**. She wrote papers both under the name of Elena Moldovan and the name Elena Popoviciu. We will use both the names Elena Moldovan and Elena Popoviciu throughout this biography, trying our best to use the correct name for the time to which we refer. She attended primary and secondary school in Cluj where, in addition to showing an outstanding talent for mathematics, she also showed great talents in painting, music and literature.

After graduating from high school, Elena began her studies at the University of Cluj. In August 1940, after the start of World War II, the north-west part of Romania (including Cluj) was surrendered to Hungary in the Vienna Dictate. This was a decision taken in Vienna under severe pressure from the German Third Reich. The Romanian university in Cluj moved to Alba-Iulia, Turda, Sibiu and Timișoara. In 1945, following the end of World War II, the Romanian University returned to Cluj and was named Babeș University (after the Romanian natural scientist Victor Babeș). It was the Babeș University of Cluj that Elena Moldovan entered and she was awarded a bachelor's degree in mathematics in the summer of 1947. After graduating, she was appointed as an instructor in a high school in Cluj.

Elena Moldovan studied for a Ph.D. in Mathematics. She began research advised by the academician Grigore Calugăreănu but, after a while, fascinated by the remarkable personality of Tiberiu Popoviciu, her research topic moved to convex function theory and interpolation function theory. From that time on her research was supervised by the academician Tiberiu Popoviciu. She began publishing papers in Romanian, the first being

*Observations on certain generalised processes of interpolation*(1954) in which, for Fejér's interpolation polynomials, which converge for every continuous function, she found a formula for the order of the approximation. Her next papers were, in Romanian,

*On a generalisation of the notion of convexity*(1955),

*On certain theorems about means*(1956), and

*Properties of generalised convex functions*(1957). In a long series of articles she studied approximation by interpolatory sets, convexity with respect to them, etc. She was awarded a Ph.D. in 1960 after submitting her thesis entitled

*Sets of Interpolating Functions And The Notion of Convex Function*.

Her work on generalising the concept of convexity formed the basis of her research over the whole of her career. She introduced the 'allure' or 'behaviour' of a function. As an example of this concept we give one of her own examples. The allure of a function

*f*is whether the Lagrange interpolating polynomial of degree

*n*has leading coefficient greater than zero, or less than zero, or equal to zero. The authors of [1] discuss this work in detail. We give here their introduction to the Chapter of their book entitled 'Behaviours. Convexity with respect to a behaviour':-

The entire didactical activity of Elena Popoviciu took place at the Faculty of Mathematics of the University of Cluj. The authors of [5] write about her marriage in 1964:-The concept of behaviour of an object is largely used in order to make the difference between things. As a mathematical concept, Elena Popoviciu used the term 'behaviour' for the first time in1965, on the occasion of a conference held at the Babeș-Bolyai University of Cluj, without publishing it. The discussions on this theme have been reconsidered during the meetings of the Interdisciplinary Researches Laboratory of the Babeș-Bolyai University of Cluj between1980-83. In this period, she wrote especially about the particular case of behaviours that are shapes of functions, in order to generalise the property of convexity of a function. The main results in this direction are written down in the papers of E Moldovan(1955,1958,1959)and[under her married name]E Popoviciu(1969,1972,1983).

From 1969, Elena Popoviciu was appointed a full professor in the Mathematical Analysis Chair of the Babeș-Bolyai University of Cluj. She taught several courses such as: Mathematical Analysis, Abstract Algebra, Functional Analysis, Linear Programming, Distribution Theory, Approximation Theory, and Operational Calculus.She married the academician Tiberiu Popoviciu in1964, who she helped to build the prestige of the Cluj mathematical school, at the same time offering the academician a pleasant family environment, so much needed for a person involved in the academic creation.

Starting with 1974, Elena Popoviciu became a Ph.D. supervisor and, in total throughout her career, she supervised 23 doctoral students. Elena Popoviciu founded, in 1960, the research Seminar on Best Approximation and Mathematical Programming and, in 1974, the Interdisciplinary Research Laboratory. These achievements were highlighted in the announcement of her death put out by the Babeș-Bolyai University Cluj:-

Elena Popoviciu was also very much involved in the editorial work of the following journals:The Faculty of Mathematics and Computer Science from the University "Babeș-Bolyai" Cluj-Napoca announces, with deep sorrow, the passing of prof. Dr. doc. Elena Popoviciu, a mathematician with broad national and international recognition. Prof. Doc. Elena Popoviciu was one of the main contributors to the school of Mathematical Analysis in Cluj, mentor to many generations of students and PhD coordinator. For many years she directed the Seminar "Tiberiu Popoviciu" on Functional Equations, Approximation and Convexity. She founded the Interdisciplinary Research Laboratory. The Romanian School of Mathematics loses today one of its highly valued people.

*Revue d'Analyse Numérique et de Théorie de l'Approximation*and

*Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity*. A conference was held in her honour at Cluj-Napoca on 15-16 October 1999 on the occasion of her 75

^{th}birthday. The topics of the conference were analysis, functional equations, approximation and convexity. Wolfgang Breckner contributed the biographical article [3] while Elena Popoviciu contributed the article

*Les mathématiques sont les plus belles parmi les disciplines scientifiques*which she summarised as follows:-

The proceedings of the conference also contains her biographical articleThe purpose of the paper is to present some results concerning my theory of allure. This presents a new point of view in the analysis of various convexity properties and their applications.

*Life is beautiful if you understand it, if you live it with dignity, if you don't betray it*(Romanian). Five years later, on 30 September 2004, a Scientific Session was organised at the Babeș-Bolyai University of Cluj-Napoca to celebrate Elena Popoviciu's eightieth birthday. The scientific sessions took place in the Tiberiu Popoviciu Amphitheatre, named after her late husband, and a celebratory dinner was held in the evening in University House.

Elena Popoviciu wrote several articles which give great insight into the research group that she and her husband ran in Cluj. In 1992 she wrote

*Hommage à l'occasion d'un important anniversaire*Ⓣ in which she discussed some results about convexity obtained by Tiberiu Popoviciu and his students. Five years later she wrote

*Sur certaines allures remarquables*Ⓣ (1997). We quote from her introduction:-

In 2002 she wroteI would like to present some ideas of Tiberiu Popoviciu which strongly influenced certain branches of mathematics. It is going mainly into his research on convexity, on approximation theory, and on extensions of these two domains towards functional analysis and other branches of modern mathematics, including e.g., theoretic and practical computing.

*Un important anniversaire pour la science roumaine*Ⓣ which she summarised as follows:-

Elena Popoviciu died in June 2009 at Cluj-Napoca.We commemorate the foundation, in1957, of the Institute of Numerical Analysis in Cluj-Napoca, by Tiberiu Popoviciu. We underline the research programme of the Institute and the main results obtained here.

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

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