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Volume 33

Issue 4 | 1991 | pp. 519-694

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1991

Volume 33, Issue 4, pp. 519-694

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Select this Article		Frequency Content of Randomly Scattered Signals M. Asch, W. Kohler, G. Papanicolaou, M. Postel, and B. White SIAM Rev. 33, pp. 519-625 (107 pages) \| Cited 67 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract The statistical properties of acoustic signals reflected by a randomly layered medium are analyzed when a pulsed spherical wave issuing from a point source is incident upon it. The asymptotic analysis of stochastic equations and geometrical acoustics is used to arrive at a set of transport equations that characterize multiply scattered signals observed at the surface of the layered medium. The results of extensive numerical simulations are presented, illustrating the scope of the theory. A number of inverse problems for randomly layered media are also formulated where we recover large-scale properties of the sound speed profile from the statistics of reflected signals.

Select this Article		Nonlinear and Stochastic Phenomena: The Grand Challenge for Partial Differential Equations James Glimm SIAM Rev. 33, pp. 626-643 (18 pages) \| Cited 8 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract The major problems for partial differential equations are either nonlinear or stochastic or both. Considerable progress has occurred recently in these areas, much of which has resulted from a striking interplay among theory, computation, and applications. The nonlinear structures emphasized here are the nonlinear hyperbolic waves, which occur in the solutions of nonlinear hyperbolic conservation laws and associated dissipative equations. These equations are those most commonly used to model physical and chemical processes in continuum systems. In one space dimension these nonlinear waves form traveling waves, for which the methods of dynamical systems and bifurcation theory are very useful. Established points of view toward mathematical theories have been challenged by recent work (e.g., uniqueness of solutions, entropy conditions, and elliptic regions in hyperbolic equations). A type of geometry is defined in the state space of the conservation law by the nonlinear waves. This geometry is generically singular in the case of nonlinear resonance. A regularizing space, called the Fundamental Wave Manifold, has been constructed which removes nonessential singularities in this geometry; the remaining, essential, sin-gularities serve as organizing centers for the bifurcation of the nonlinear hyperbolic waves. Stochastic solutions of partial differential equations may result from stochastic data, for example, in the form of random initial conditions or equation coefficients. This phenomenon can be called forced, driven, or external chaos. Stochastic solutions can also result from internal considerations, i.e., from instabilities inherent in the equation itself, if the equation is nonlinear. The instabilities which give rise to chaotic solutions are generally unstable on a very large range of length scales, or in some approximation, on all length scales. Fractal geometries provide one model for the typically intermittent, or blotchy, chaos which can occur, and the renormalization group is an analytic tool which in some cases has given a quantitatively correct theory of chaotic solutions of partial differential equations.

Select this Article		The Electric Bell as a Nonlinear Oscillator W. O. Criminale and T. F. Mar SIAM Rev. 33, pp. 644-649 (6 pages) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract A nonlinear autonomous model is constructed to explain the fundamental motion of the electric doorbell. Operation is graphically depicted under a variety of physical conditions by numerical integration of the governing equations.

Select this Article		Measuring the Speed and Altitude of an Aircraft Using Similar Triangles Hassan Sedaghat SIAM Rev. 33, pp. 650-654 (5 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract In this note a simple and sometimes practical method is devised with which the average speed and the cruising altitude of an aircraft in flight can be computed from a window seat inside the aircraft. No knowledge of the mechanical structure of the vehicle is assumed. Rather, either two separate time measurements or a time and a length measurement are used allowing one to construct sets of similar triangles. These triangles can then be used to derive the formulas for speed and altitude. This method can also be used to determine the average speed of moving ground vehicles such as trains and buses.

Select this Article		An Affirmative Action Graph D. J. Newman SIAM Rev. 33, pp. 655-655 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Inequality of the AGM and the Logarithmic Mean B. C. Carlson and M. Vuorinen SIAM Rev. 33, pp. 655-655 (1 page) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Linear Integro-Differential Equation John Melville SIAM Rev. 33, pp. 655-656 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Finite Part Integral B. Bertram and O. G. Ruehr SIAM Rev. 33, pp. 656-656 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Approximation for the Location of the Center of a Disk M. L. Glasser and J. Koplowitz SIAM Rev. 33, pp. 657-657 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Simultaneous Functional Equations (Paul Schweitzer) Wolfgang Berndt SIAM Rev. 33, pp. 657-658 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Exponentially Windowed Estimates of a Periodically Sampled Time-Series, and Its First and Second Derivatives Using Quadratic Regression Ken Lever SIAM Rev. 33, pp. 658-661 (4 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Orthogonal Matrices and the Matrix Exponential (Dennis S. Bernstein) William C. Waterhouse SIAM Rev. 33, pp. 661-662 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		The Mathematics of Great Amateurs (Julian Lowell Coolidge) Peter Braunfeld SIAM Rev. 33, pp. 663-664 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Introduction to Dynamical Systems (D. K. Arrowsmith and C. M. Place) Kenneth R. Meyer SIAM Rev. 33, pp. 664-664 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Pearls in Graph Theory: A Comprehensive Introduction (N. Hartsfield and G. Ringel) John S. Maybee SIAM Rev. 33, pp. 664-665 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Chaos in Systems with Noise (Tomasz Kapitaniak) R. S. MacKay SIAM Rev. 33, pp. 666-666 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Chaotic Dynamics: An Introduction (Gregory Baker and Jerry Gollub) Peter J. Bryant SIAM Rev. 33, pp. 666-668 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Measure, Topology, and Fractal Geometry (Gerald A. Edgar) Robert L. Devaney SIAM Rev. 33, pp. 668-669 (2 pages) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Ordinary Differential Equations: An Introduction to Nonlinear Analysis (Herbert Amann) Robert W. Easton SIAM Rev. 33, pp. 669-670 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Course in Mathematics for Students of Physics. Volume 2 (Paul Bamberg and Shlomo Sternberg) Roger Waxler SIAM Rev. 33, pp. 670-671 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Optimization of Stochastic Systems: Topics in Discrete-Time Dynamics (Masanao Aoki) Tze Leung Lai SIAM Rev. 33, pp. 671-672 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Asymptotic Modeling of Atmospheric Flows (R. Zeytounian) Huijun Yang SIAM Rev. 33, pp. 672-673 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		The Physics of Fluid Turbulence (W. D. McComb) James Glimm SIAM Rev. 33, pp. 673-674 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		General Relativity. An Introduction to the Theory of the Gravitational Field (Hans Stephani) Jorge Pullin SIAM Rev. 33, pp. 674-675 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Numerical Continuation Methods, An Introduction (Eugene Allgower and Kurt Georg) Romesh Saigal SIAM Rev. 33, pp. 675-675 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Semiconductor Equations (P. A. Markowich, C. A. Ringhofer, and C. Schmeiser) Carl L. Gardner SIAM Rev. 33, pp. 675-677 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Statistical Spectral Analysis: A Nonprobabilistic Theory (William A. Gardner) Melvin J. Hinich SIAM Rev. 33, pp. 677-678 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Kinematic Geometry of Mechanisms (K. H. Hunt) Joseph Duffy SIAM Rev. 33, pp. 678-679 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Introduction to the History of Structural Mechanics, Part I: Statics and Resistance of Solids, Part II: Vaulted Structures and Elastic Systems (Edoardo Benvenuto) W. R. Spillers SIAM Rev. 33, pp. 679-680 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Multilevel Adaptive Methods for Partial Differential Equations (Stephen F. McCormick) Alan Weiser SIAM Rev. 33, pp. 680-681 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Mathematical Modelling. A Tool for Problem Solving in Engineering, Physical, Biological and Social Sciences (D. N. P. Murthy, N. W. Page, and E. Y. Rodin) Arthur Sherman SIAM Rev. 33, pp. 681-682 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Electro-Diffusion of Ions (Isaak Rubinstein) Joseph W. Jerome SIAM Rev. 33, pp. 682-684 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		New Computer Methods for Global Optimization (H. Ratschek and J. Rokne) Faiz Al-Khayyal and Panos Pardalos SIAM Rev. 33, pp. 684-686 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Adaptive Markov Control Processes (D. Hernandez-Lerma) Gerhard Hübner SIAM Rev. 33, pp. 686-687 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Parameter Estimation in Ecology: The Link between Data and Models (O. Richter and D. Söndgerath) Philip M. Dixon SIAM Rev. 33, pp. 687-688 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Aspects of Risk Theory (Jan Grandell) Matti Ruohonen SIAM Rev. 33, pp. 688-689 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		New Members SIAM Rev. 33, pp. 690-692 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Report of the Treasurer for the Year Ended December 31, 1990 SIAM Rev. 33, pp. 693-694 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

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