The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Computational modelling of impact damage in brittle materials

A fast incremental/iterative solution procedure that handles "snap-through"

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Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators

Fortran-77 simulation of word-addressable files

This is the fourth of a set of five volumes which describe the software architecture for the Computational Structural Mechanics Testbed. Derived from NICE, an integrated software system developed at Lockheed Palo Alto Research Laboratory, the architecture is composed of the command language CLAMP, the command language interpreter CLIP, and the data manager GAL. Volumes 1, 2, and 3 (NASA CR's 178384, 178385, and 178386, respectively) describe CLAMP and CLIP and the CLIP-processor interface. Volumes 4 and 5 (NASA CR's 178387 and 178388, respectively) describe GAL and its low-level I/O. CLAMP, an acronym for Command Language for Applied Mechanics Processors, is designed to control the flow of execution of processors written for NICE. Volume 4 describes the nominal-record data management component of the NICE software. It is intended for all users.

The computational structural mechanics testbed architecture. Volume 4: The global-database manager GAL-DBM

This paper deals with modelling the effect of low-velocity impact damage upon the vibration response of CFRP laminates through a micro-mechanical description of the induced internal damage The serial-parallel (SP) continuum approach is used to estimate the map of induced internal damage by considering the micro-structural interaction between the composite constituents and modifying their constitutive performance through a continuum damage formulation An eigenvalue analysis is then done to determine the modal response of impacted laminates The validity of the modelling approach to successfully reproduce the vibration response of impacted coupons is assessed through a comparison with an experimental test series conducted on a set of 48 CFRP laminated coupons The results confirm the ability of the described approach in comparison to competing ones used to reproduce the experimentally observed behaviour

/pdf/micro-mechanical-approach-for-the-vibration-analysis-of-cfrp-o4yikilhql.pdf

Micro-mechanical approach for the vibration analysis of CFRP laminates under impact-induced damage

A variational justification of the assumed natural strain formulation of finite elements. I - Variational principles. II - The C(0) four-node plate element

I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.

Carlos A. Felippa

Papers

Fortran-77 simulation of word-addressable files

The computational structural mechanics testbed architecture. Volume 4: The global-database manager GAL-DBM

Micro-mechanical approach for the vibration analysis of CFRP laminates under impact-induced damage

A variational justification of the assumed natural strain formulation of finite elements. I - Variational principles. II - The C(0) four-node plate element

Towards parallel I/O in finite element simulations