José Luis Massera
Encyclopedia
José Luis Massera was an Uruguay
Uruguay
Uruguay ,officially the Oriental Republic of Uruguay,sometimes the Eastern Republic of Uruguay; ) is a country in the southeastern part of South America. It is home to some 3.5 million people, of whom 1.8 million live in the capital Montevideo and its metropolitan area...

an mathematician
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....

 who researched the stability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...

 of differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s.

Massera's lemma
Massera's lemma
In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2...

 is named after him. He published over 40 papers during 1940–1970. A militant Communist, he was a political prisoner during 1975–1984. In the 1930s, Rey Pastor gave regular weekend lectures on topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

 in Montevideo
Montevideo
Montevideo is the largest city, the capital, and the chief port of Uruguay. The settlement was established in 1726 by Bruno Mauricio de Zabala, as a strategic move amidst a Spanish-Portuguese dispute over the platine region, and as a counter to the Portuguese colony at Colonia del Sacramento...

 to a group that included Massera. Stimulated by contact with Argentine mathematics, the 1950s saw Uruguay develop a fine school in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, of which Massera was very much a part of.

Massera developed new notions of stability, and published several foundational papers and an influential textbook. His results in on periodic differential equations have been heavily cited and are referred to as Massera's theorem. His work in and on the converse to Lyapunov
Lyapunov stability
Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov...

's criterion is also influential, and contain the well known Massera's lemma
Massera's lemma
In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2...

. His textbook is also heavily cited.

In 1971, at age 62, Massera was elected to the senate as an alternate senator. After military intervention in Uruguay in 1973, Massera was arrested on October 22, 1975 in Montevideo and was held in solitary confinement
Solitary confinement
Solitary confinement is a special form of imprisonment in which a prisoner is isolated from any human contact, though often with the exception of members of prison staff. It is sometimes employed as a form of punishment beyond incarceration for a prisoner, and has been cited as an additional...

 for nearly a year. During this time he was subjected to repeated torture
Torture
Torture is the act of inflicting severe pain as a means of punishment, revenge, forcing information or a confession, or simply as an act of cruelty. Throughout history, torture has often been used as a method of political re-education, interrogation, punishment, and coercion...

 resulting in injuries including a fractured pelvis. In October 1976 he was taken from solitary confinement, tried and convicted for "subversive association", and given a 24-year prison sentence. He was released in 1984.
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