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Control of Partial Differential Equations
The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.
The Leading Edge
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Jerome and the Monastic Clergy
In Jerome and the Monastic Clergy, Andrew Cain provides the first full-scale commentary on the famous Letter to Nepotian, in which Jerome articulates his radical plan for imposing a strict ascetic code of conduct on the contemporary clergy. Cain comprehensively addresses stylistic, literary, historical, text-critical and other issues of interpretive interest. Accompanying the commentary is an introduction which situates the Letter in the broader context of its author’s life and work and exposes its fundamental propagandistic dimensions. The revised critical Latin text and the new facing-page translation will make the Letter more accessible than ever before and will provide a reliable textual apparatus for future scholarship on this key writing by one of the most prolific authors in Latin antiquity.
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Appli...
Jerome's Commentaries on the Pauline Epistles and the Architecture of Exegetical Authority
In the late fourth and early fifth centuries, during a fifty-year stretch sometimes dubbed a Pauline renaissance of the western church, six different authors produced over four dozen commentaries in Latin on Paul's epistles. Among them was Jerome, who commented on four epistles (Galatians, Ephesians, Titus, Philemon) in 386 after recently having relocated to Bethlehem from Rome. His commentaries occupy a time-honored place in the centuries-long tradition of Latin-language commenting on Paul's writings. They also constitute his first foray into the systematic exposition of whole biblical books (and his only experiment with Pauline interpretation on this scale), and so they provide precious in...
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proof...
Jerome
As a scholar, writer and ascetic, Jerome was a major intellectual force in the early Church and influenced the ideals of Christian chastity and poverty for many generations after his death. This book assembles a representative selection of his voluminous output. It will help readers to a balanced portrait of a complex and brilliant, but not always likeable man.
Jerome's Epitaph on Paula
Composed in 404, Jerome's Epitaph on Saint Paula (Epitaphium Sanctae Paulae) is an elaborate eulogy commemorating the life of Paula (347-404), a wealthy Christian widow from Rome who renounced her senatorial status and embraced an ascetic lifestyle and in 386 co-founded with Jerome a monastic complex in Bethlehem.
Jewish, Christian, and Classical Exegetical Traditions in Jerome’s Translation of the Book of Exodus
In Jewish, Christian, and Classical Exegetical Traditions in Jerome’s Translation of the Book of Exodus: Translation Technique and the Vulgate, Matthew Kraus offers a layered understanding of Jerome’s translation of biblical narrative, poetry, and law from Hebrew to Latin. Usually seen as a tool for textual criticism, when read as a work of literature, the Vulgate reflects a Late Antique conception of Hebrew grammar, critical use of Greek biblical traditions, rabbinic influence, Christian interpretation, and Classical style and motifs. Instead of typically treating the text of the Vulgate and Jerome himself separately, Matthew Kraus uncovers Late Antiquity in the many facets of the translator at work—grammarian, biblical exegete, Septuagint scholar, Christian intellectual, rabbinic correspondent, and devotee of Classical literature.
