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Issue 4 | 1977 | pp. vi-790

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Select this Article		Errata: The Korteweg—de Vries Equations: A Survey of Results Robert M. Miura SIAM Rev. 19, pp. vi-vi ( pages) Full Text: \| Download PDF
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Select this Article		Errata: Fixed Point Theorems and Nonlinear Eigenvalue Problems in Ordered Banach Spaces Herbert Amann SIAM Rev. 19, pp. vii-vii ( pages) Full Text: \| Download PDF
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Select this Article		Formal Approximations and Singular Perturbations Wiktor Eckhaus SIAM Rev. 19, pp. 593-633 (41 pages) \| Cited 4 times Full Text: \| Download PDF
	+ -	Show Abstract The problem of proving the validity of a formal approximation as an asymptotic approximation in singular perturbation problems is studied in a general formulation. Various ramifications of the problem are investigated; pathologies and peculiarities of singular behavior are illustrated by simple examples. The analysis leads to a classification of singular perturbations. A survey of methods and results concerning estimates of solutions of singularly perturbed linear elliptic and parabolic problems is presented in the Appendix.

Select this Article		On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems G. W. Stewart SIAM Rev. 19, pp. 634-662 (29 pages) \| Cited 79 times Full Text: \| Download PDF
	+ -	Show Abstract This paper surveys perturbation theory for the pseudo–inverse (Moore–Penrose generalized inverse), for the orthogonal projection onto the column space of a matrix, and for the linear least squares problem.

Select this Article		Nonlinear Evolution Equations—Continuous and Discrete Mark J. Ablowitz SIAM Rev. 19, pp. 663-684 (22 pages) \| Cited 15 times Full Text: \| Download PDF
	+ -	Show Abstract An important recent advance in nonlinear wave motion has been the discovery of a method of solution to a class of nonlinear evolution equations. The technique relies on a relation between the evolution equation, and an associated linear eigenvalue (scattering) problem. The initial value solution is found by the method of inverse scattering. In this paper, procedures are outlined which systematically isolate certain nonlinear evolution equations which fit into the above methodology. As examples of the ideas, the partial differential nonlinear Schrodinger and a differential-difference nonlinear Schrodinger equation are considered in detail. Some of the other physically important evolution equations are enumerated and an analogy to Fourier analysis is brought out.

Select this Article		Dynamic Optimal Control Models in Advertising: a Survey Suresh P. Sethi SIAM Rev. 19, pp. 685-725 (41 pages) \| Cited 65 times Full Text: \| Download PDF
	+ -	Show Abstract The last ten years have seen a growing number of optimal control theory applications to the field of advertising. This paper presents an up-to-date survey of dynamic optimal control models in advertising that have appeared in the literature. The basic problem underlying these models is an optimal control problem to determine the optimal rate of advertising expenditures over time in a way that maximizes the present value of a firm’s net profit streams over a finite or infinite horizon. The profit depends on sales (or an appropriate surrogate), the state variable and the rate of advertising expenditures, the control variable. Sales, in turn, is related to advertising expenditures via a differential or difference equation termed a state equation. The models covered in this survey are organized under four headings: advertising capital models, sales-advertising response models, micromodels, and control-theoretic empirical studies. The discussion involves specifications, methods used, results and the economic significance of various models.The survey concludes with suggestions for extensions and future direction of research.

Select this Article		Announcement SIAM Rev. 19, pp. 726-726 (1 page) Full Text: \| Download PDF
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Select this Article		The Pig House Problem or the Detection and Measurement of Pairwise Associations R. C. Grimson SIAM Rev. 19, pp. 727-731 (5 pages) Full Text: \| Download PDF
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Select this Article		A Model for Drug Concentration L. E. Thomas SIAM Rev. 19, pp. 732-735 (4 pages) Full Text: \| Download PDF
	+ -	Show Abstract A model, suitable for classroom use, is developed to describe the concentration of a drug in the body when the drug is administered repeatedly. The model shows that under certain conditions there are limiting values for the maximum and minimum concentrations of the drug in the system. Cases of random detoxification and enzymatic detoxification are discussed.

Select this Article		A First Order Nonlinear Differential Equation I. Rubinstein SIAM Rev. 19, pp. 736-736 (1 page) Full Text: \| Download PDF
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Select this Article		A System of Second Order Differential Equations L. Carlitz SIAM Rev. 19, pp. 736-736 (1 page) Full Text: \| Download PDF
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Select this Article		An Infinite Summation A. M. Liebetrau SIAM Rev. 19, pp. 736-737 (2 pages) Full Text: \| Download PDF
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Select this Article		Two Inequalities P. Barrucand SIAM Rev. 19, pp. 737-737 (1 page) Full Text: \| Download PDF
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Select this Article		When is the Modified Bessel Function Equal to Its Derivative? I. Nåsell SIAM Rev. 19, pp. 737-737 (1 page) Full Text: \| Download PDF
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Select this Article		A Polynomial Inequality (K. B. Stolarsky and L. J. Yang) L. J. Yang SIAM Rev. 19, pp. 737-739 (3 pages) Full Text: \| Download PDF
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Select this Article		A Reverse Card Shuffle (David Berman and M. S. Klamkin) D. E. Knuth SIAM Rev. 19, pp. 739-740 (2 pages) Full Text: \| Download PDF
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Select this Article		A Monotonicity Property for Moments (A. A. Jagers) I. Olkin SIAM Rev. 19, pp. 741-742 (2 pages) Full Text: \| Download PDF
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Select this Article		On the Extreme Eigenvalues of an $n \times n$ Matrix (L. B. Bushard) Dennis C. Jespersen SIAM Rev. 19, pp. 742-743 (2 pages) Full Text: \| Download PDF
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Select this Article		A Zero Of Maximum Multiplicity (N. Liron and L. A. Rubenfeld) w. B. Jordan SIAM Rev. 19, pp. 743-744 (2 pages) Full Text: \| Download PDF
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Select this Article		Fourier Analysis of Time Series: An Introduction (Peter Bloomfield) Ralph A. Willoughby SIAM Rev. 19, pp. 745-746 (2 pages) Full Text: \| Download PDF
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Select this Article		Syntactic Methods in Pattern Recognition (K. S. Fu) Patrick Suppes SIAM Rev. 19, pp. 746-746 (1 page) Full Text: \| Download PDF
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Select this Article		Theoretical Statistics (D. R. Cox and D. V. Hinkley) Howard Reinhardt SIAM Rev. 19, pp. 746-747 (2 pages) Full Text: \| Download PDF
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Select this Article		Continuum Mechanics of Viscoelastic Liquids (R. R. Huilgol) F. Oberhettinger SIAM Rev. 19, pp. 747-749 (3 pages) Full Text: \| Download PDF
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Select this Article		Ordinary Differential Equations in the Complex Domain (Einar Hills) Wilfred Kaplan SIAM Rev. 19, pp. 749-749 (1 page) Full Text: \| Download PDF
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Select this Article		Treatise on Analysis, Vol. IV (J. Dieudonné) Robert Hermann SIAM Rev. 19, pp. 750-750 (1 page) Full Text: \| Download PDF
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Select this Article		Optimization Theory; The Finite Dimensional Case (Magnus R. Hestenes) Jane Cullum SIAM Rev. 19, pp. 750-752 (3 pages) Full Text: \| Download PDF
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Select this Article		Statistical Techniques in Simulation, Part II (Jack P. C. Kleijnen) Nils Blomqvist SIAM Rev. 19, pp. 752-753 (2 pages) Full Text: \| Download PDF
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Select this Article		Applications of Fuzzy Sets to Systems Analysis (C. V. Negoita and R. A. Ralescu) Michael A. Arbib SIAM Rev. 19, pp. 753-753 (1 page) Full Text: \| Download PDF
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Select this Article		Other Books Received SIAM Rev. 19, pp. 754-758 (5 pages) Full Text: \| Download PDF
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Select this Article		SIAM 1976 Fall Meeting SIAM Rev. 19, pp. 759-783 (25 pages) Full Text: \| Download PDF
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Select this Article		New mwmbers SIAM Rev. 19, pp. 784-785 (2 pages) Full Text: \| Download PDF
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Select this Article		Society for Industrial and Applied Mathematics SIAM Rev. 19, pp. 786-789 (4 pages) Full Text: \| Download PDF
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Select this Article		Treasurer’s Report SIAM Rev. 19, pp. 790-790 (1 page) Full Text: \| Download PDF
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