**Pavel Krejčí**studied at the Lyée Alphonse Daudet, Nîmes, France, from 1970 to 1973. This school had educated a number of leading mathematicians over the years including Gaston Darboux in the 19

^{th}century and Jean-Pierre Serre in the 20

^{th}century. He then entered the Faculty of Mathematics and Physics of the Charles University of Prague, where he studied until 1978. He was awarded his RNDr. in 1978. This degree, although having the same initials as doctorates awarded in many European countries, was a degree as Master's level in Czechoslovakia (and later in the Czech Republic).

After the award of his Master's degree, Krejčí became a computer programmer at the Poldi Steel Company, Kladno, Czechoslovakia. He held this position for less than a year, taking up the appointment in September 1978 and leaving in June 1979. In the following month he returned to the academic world when he was appointed as a Researcher at the Institute for Fluid Dynamics of the Czechoslovak Academy of Sciences. He worked there until December 1981 when he became a Researcher at the Institute for Mathematics of the Czechoslovak Academy of Sciences. In 1982 he published *Normalization of relational data model*. We give the following extract from Krejčí's own summary:-

His next papers wereWe discuss a new approach to normalization of a relational data model. In the first part we define the concepts of dependency and multidependency among domains of attributes. We explain the kinds of update anomalies that can occur if there are undesirable dependencies or multidependencies in relations. We review the definition of the third normal form, i.e. a relation which does not express undesirable dependencies, and define a new form of relation, third multinormal form, which does not express undesirable multidependencies. Advantages and disadvantages of these definitions are discussed. We distinguish the two aspects of normalization - normalization with regard to values of domains and normalization concerning dependencies - and define a new normal form which is based on new concepts. In the second part we describe some approaches to normalizing relations ...

*On solvability of equations of the 4*(1983),

^{th}order with jumping nonlinearities*Hard implicit function theorem and small periodic solutions to partial differential equations*(1984) and

*Periodic solutions of a class of abstract nonlinear equations of the second order*(1985). He was awarded a Candidate's degree, the CSc. (equivalent to a Ph.D.), in June 1984 for his thesis

*Periodic vibrations of the electromagnetic field in ferromagnetic media*(Czech). In this thesis he investigated the existence of periodic solutions of Maxwell's equations in nonlinear media in the Sobolev spaces of divergence-free vector functions in three dimensions.

Krejčí continued to work at the Institute of Mathematics in Prague until December 1996 but during these years spent part of his time visiting other institutions. He was a visiting professor at the University of Wisconsin at Milwaukee, USA, for the last four months of 1990. He held a highly prestigious Alexander von Humboldt fellowship, awarded by the German Humboldt Foundation, at the University of Kaiserslautern (October 1991 - April 1992), also at the Technische Hochschule Munich (May 1992-September 1992) and again at the University of Kaiserslautern (January 1993-June 1993). From March to June of 1995 he was a visiting professor at the Université de Technologie de Compiègne in France. His next visit was to the Weierstrass Institute for Applied Analysis and Stochastics in Berlin from April to June 1996. This was highly significant for in the following year he became a researcher at that Institute. He returned to Prague in January 2001 and spent three years there as leader of the 'Evolution equations' research group and Head of the Department of Evolution Differential Equations. He was back in the Weierstrass Institute for Applied Analysis and Stochastics in Berlin in January 2004 and, in the following year, he became the deputy leader of the 'Thermodynamic Modeling and Analysis of Phase Transitions' Research group. He returned to the Institute of Mathematics of the Czech Academy of Sciences, Prague, in 2009 where he became the director of the Institute. He continued in this role until 2014. Jürgen Sprekels writes [5]:-

In February 2015, MathSciNet lists 120 publications by Krejčí. Most of these papers discuss problems associated with hysteresis, for example early examples of such papers areLooking from the outside, and having for understandable reasons a certain tendency to appreciate the accomplishments of directors, the present author does not entertain any doubt that Pavel Krejci. must have done a wonderful job indeed: the positive development of this institute in the last years is a truly outstanding piece of achievement. Today, the Institute for Mathematics of the Czech Academy of Sciences is an internationally highly recognized institution that enjoys the reputation of being a worldwide leading center of excellence in mathematics.

*Hysteresis and periodic solutions of semilinear and quasilinear wave equations*(1986) and

*Periodic solutions of partial differential equations with hysteresis*(1986). Let us quote an explanation of hysteresis from [1]:-

Rather surprisingly, in addition to this impressive collection of publications, Krejčí has been awarded (jointly with two colleagues) the patent 'Verfahren und Vorrichtung zur Online-Kompensation von Nicht-linearitäten im Übertragungsverhalten von Stellgliedern' by the German Patent Office [5]:-Hysteresis is an exciting and mathematically challenging phenomenon that occurs in rather different situations: it, can be a byproduct of fundamental physical mechanisms(such as phase transitions)or the consequence of a degradation or imperfection(like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hysteresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually non-smooth and thus not easy to treat mathematically. Hence it was only in the early seventies that the group of Russian scientists around M A Krasnoselskii initiated a systematic mathematical investigation of the phenomenon of hysteresis

He has also published an important book,This patent witnesses his special ability and steady readiness to cooperate successfully with engineers and researchers from other fields of science.

*Hysteresis, convexity and dissipation in hyperbolic equations*(1996). We give Krejčí's Preface and a list of contents of this book at THIS LINK.

He was the Principal Investigator for the project 'Mathematical modelling of processes in hysteresis materials' which ran for five years beginning in January 2010. Here is Krejčí's description of this project (see [3]):-

Krejčí has received prestigious awards such as the Research Award of the Minister of Education of the Czech Republic (2001), the John von Neumann Guest professorship at Munich (2010), and the Bernard Bolzano Honorary Medal for Merit in Mathematical Sciences from the Czech Academy of Sciences (2014). The Laudatio for the Bernard Bolzano Honorary Medal states [4]:-Hysteresis, i.e., nonlinear relations exhibiting a complicated input-output behavior in form of nested loops that cannot be described by functions or graphs, occurs in many fields of science, e.g., in ferromagnetism, micromagnetics, solid-solid phase transitions, and elastoplasticity. Hysteretic systems carry a memory of their former states, which renders their input-output mapping both nondifferentiable and nonlocal in time, so that conventional weak convergence techniques for solving evolution systems fail. Therefore, dynamical elastoplastic processes with hysteresis are found in the mathematical literature much less frequently than quasistatic ones, and a substantial progress in this direction is necessary. In a recent breakthrough, it was shown that the three-dimensional single-yield von Mises constitutive law leads, after a dimensional reduction to beams or plates, to a multi-yield Prandtl-Ishlinskii hysteresis operator. It is in fact quite natural that the lower dimensional observer does not see any sharp transition from the purely elastic to the purely plastic regime as in the von Mises model: if a plate is bent then small plasticized zones start forming first near the boundary and then propagate to the interior, which still preserves a partial elasticity. This gradual plasticizing is reflected by the Prandtl-Ishlinskii superposition of single-yield elements that are successively activated. This new groundbreaking theory will be expanded to more complex structures like Mindlin-Reissner plates, and curved rods and shells. Temperature and material fatigue effects will be included. A thermodynamically consistent theory of temperature and fatigue dependent Prandtl-Ishlinskii operators will be developed, along with efficient and reliable numerical methods. Questions of theoretical and numerical stability, and the long time behavior of the system of energy and momentum balance laws are central objectives.

Let us end with this assessment of his character by Jürgen Sprekels [5]:-Pavel Krejčí made important contributions to variational inequalities, to phase transition models, and to rate-independent problems in general. But from the very beginning of his career, he established himself as one of the world leaders in the development and the application of the theory of hysteresis operators in science. Many fundamental concepts in hysteresis theory go back to him. ... beyond any doubt, Pavel Krejcci is worthy of this honour, and the Czech Academy of Sciences can only be congratulated for the wise decision to bestow on him the Bernard Bolzano Honorary Medal for Merit in Mathematical Sciences.

Let us add a few words on his personality, since it is an important part of his success and definitely worth stressing: sincerity, truthfulness, integrity, fairness, reliability, sense of responsibility, tolerance, courage and steadfastness, and, last but not least, his wonderful sense of humor and self-mockery are parts of his character. No wonder that he is respected and liked everywhere.

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