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Séminaire de théorie des nombres Paris 1986–1987
286
Book Reviews
classical theory are shown to be valid for these systems. The author includes the classical results and a number of new ideas. Contents: 1. Equations with the Right-Hand Side Continuous in X and Discontinuous in t. 2. Existence and General Properties of Solutions of Discontinuous Systems. 3. Basic Methods of Qualitative Theory. 4. Local Singularities of Two-Dimensional Systems. 5. Local Singularities of Three-Dimensional and Multidimensional Systems. (WPA) C. Goldstein, Skminaire de lk!orie des Nombres Paris 1986-87 (Vol. 75 Progress in Mathematics), Birkhauser, Basel, Boston, 1988. 475 pp., $45, ISBN 3-7643-3414-2 (Basel), O-8176-3414-2 (Boston). This is the seventh annual volume of 19 papers based on lectures given at the titled seminar, including some additional papers of interest. These results presented by an international group of mathematicians reflect recent work in many areas of number theory. A good cross section of number theorists is represented. (WPA) P.Y. Papalambros and D.J. Wilde, Principles of Optimal Design-Modeling and Computation, Cambridge University Press, Cambridge, New York, 1988. 416 pp., $49.50, ISBN O-521-30674-4. This is a textbook for a one-semester course in optimal design. It is suitable for seniors or first year graduate students. It can also be used by researchers concerned with design, operations research and many other areas in which computers are heavily used for designs and planning. Classical optimization theory and numerical algorithms are integrated with the newer ideas of monotonicity analysis and model boundedness. While the book has a heavy engineering flavor this should not discourage others from its use. Contents: 1. Optimization Models. 2. Model Boundedness. 3. Interior Optima. 4. Boundary Optima. 5. Model Reduction. 6. Global Bound Construction. 7. Local Computation. 8. Principles and Practice. References and Index. (WPA) G.M. Henkin and J. Leiterer, Andreotti-Grauert Theory by Integral Formulas (Vol. 74 of Progress in Mathematics), Birkhauser, Boston, Basel, 1988. 270 pp., $44.90. ISBN 3-7643-3413-4 (Basel), O-8176-3413-4 (Boston). This monograph develops the theory of the Dolbeault cohomology of q-convex and q-concave manifolds from the integral representation standpoint. New proofs in which explicit integral formulas lead to improved versions of classical results such as uniform estimates for solutions of the Cauchy-Riemann equations, solution of the Levi problem for the Dolbeault cohomology with uniform estimates etc. The book is intended for serious workers in the theory of functions of several complex variables. (WPA)
Book Reviews
classical theory are shown to be valid for these systems. The author includes the classical results and a number of new ideas. Contents: 1. Equations with the Right-Hand Side Continuous in X and Discontinuous in t. 2. Existence and General Properties of Solutions of Discontinuous Systems. 3. Basic Methods of Qualitative Theory. 4. Local Singularities of Two-Dimensional Systems. 5. Local Singularities of Three-Dimensional and Multidimensional Systems. (WPA) C. Goldstein, Skminaire de lk!orie des Nombres Paris 1986-87 (Vol. 75 Progress in Mathematics), Birkhauser, Basel, Boston, 1988. 475 pp., $45, ISBN 3-7643-3414-2 (Basel), O-8176-3414-2 (Boston). This is the seventh annual volume of 19 papers based on lectures given at the titled seminar, including some additional papers of interest. These results presented by an international group of mathematicians reflect recent work in many areas of number theory. A good cross section of number theorists is represented. (WPA) P.Y. Papalambros and D.J. Wilde, Principles of Optimal Design-Modeling and Computation, Cambridge University Press, Cambridge, New York, 1988. 416 pp., $49.50, ISBN O-521-30674-4. This is a textbook for a one-semester course in optimal design. It is suitable for seniors or first year graduate students. It can also be used by researchers concerned with design, operations research and many other areas in which computers are heavily used for designs and planning. Classical optimization theory and numerical algorithms are integrated with the newer ideas of monotonicity analysis and model boundedness. While the book has a heavy engineering flavor this should not discourage others from its use. Contents: 1. Optimization Models. 2. Model Boundedness. 3. Interior Optima. 4. Boundary Optima. 5. Model Reduction. 6. Global Bound Construction. 7. Local Computation. 8. Principles and Practice. References and Index. (WPA) G.M. Henkin and J. Leiterer, Andreotti-Grauert Theory by Integral Formulas (Vol. 74 of Progress in Mathematics), Birkhauser, Boston, Basel, 1988. 270 pp., $44.90. ISBN 3-7643-3413-4 (Basel), O-8176-3413-4 (Boston). This monograph develops the theory of the Dolbeault cohomology of q-convex and q-concave manifolds from the integral representation standpoint. New proofs in which explicit integral formulas lead to improved versions of classical results such as uniform estimates for solutions of the Cauchy-Riemann equations, solution of the Levi problem for the Dolbeault cohomology with uniform estimates etc. The book is intended for serious workers in the theory of functions of several complex variables. (WPA)