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Harvey Thomas Banks

Bio: Harvey Thomas Banks is an academic researcher from North Carolina State University. The author has contributed to research in topics: Nonlinear system & Inverse problem. The author has an hindex of 57, co-authored 499 publications receiving 11994 citations. Previous affiliations of Harvey Thomas Banks include Technion – Israel Institute of Technology & University of Southern California.


Papers
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Book
01 Jan 1989
TL;DR: Inverse problems in the study of flexible structures as discussed by the authors have been identified in many applications, e.g., in ecology and lake and sea sedimentation analysis, as well as in the analysis of linear parabolic systems.
Abstract: I Examples of Inverse Problems Arising in Applications.- I.1. Inverse Problems in Ecology.- I.2. Inverse Problems in Lake and Sea Sedimentation Analysis.- I.3. Inverse Problems in the Study of Flexible Structures.- I.4. Inverse Problems in Physiology.- II Operator Theory Preliminaries.- II.1. Linear Semigroups.- II.2. Galerkin Schemes.- III Parameter Estimation: Basic Concepts and Examples.- III.1. The Parameter Estimation Problem.- III.2. Application of the Theory to Special Schemes for Linear Parabolic Systems.- III.2.1. Modal Approximations.- III.2.2. Cubic Spline Approximations.- III.3. Parameter Dependent Approximation and the Nonlinear Variation of Constants Formula.- IV Identifiability and Stability.- IV.1. Generalities.- IV.2. Examples.- IV.3. Identifiability and Stability Concepts.- IV.4. A Sufficient Condition for Identifiability.- IV.5. Output Least Squares Identifiability.- IV.5.1. Theory.- IV.5.2. Applications.- IV.6. Output Least Squares Stability.- IV.6.1. Theory.- IV.6.2. An Example.- IV.7. Regularization.- IV.7.1. Tikhonov's Lemma and Its Application.- IV.7.2. Regularization Revisited.- IV.8. Concluding Remarks on Stability.- IV.8.1. A Summary of Possible Approaches.- IV.8.2. Remarks on Implementation.- V Parabolic Equations.- V.1. Modal Approximations: Discrete Fit-to-Data Criteria.- V.2. Quasimodal Approximations.- V.3. Operator Factorization: A = -C*C.- V.4. Operator Factorization: A = A1/2A1/2.- V.5. Numerical Considerations.- V.6. Numerical Test Examples.- V.7. Examples with Experimental Data.- VI Approximation of Unknown Coefficients in Linear Elliptic Equations.- VI.1. Parameter Estimation Convergence.- VI.2. Function Space Parameter Estimation Convergence.- VI.3. Rate of Convergence for a Special Case.- VI.4. Methods Other Than Output-Least-Squares.- VI.4.1. Method of Characteristics.- VI.4.2. Equation Error Method.- VI.4.3. A Variational Technique.- VI.4.4. Singular Perturbation Techniques.- VI.4.5. Adaptive Control Methods.- VI.4.6. An Augmented Lagrangian Technique.- VI.5. Numerical Test Examples.- VII An Annotated Bibliography.- Al) Preliminaries.- A2) Linear Splines.- A3) Cubic Hermite Splines.- A5) Polynomial Splines, Quasi- Interpolation.

606 citations

Book
01 Jan 1996
TL;DR: In this article, the authors present a survey of the well-posedness of Abstract Structural Models, including Shells, Plates and Beams, and their application in smart materials technology and control applications.
Abstract: Smart Materials Technology and Control Applications. Modeling Aspects of Shells, Plates and Beams. Patch Contributions to Structural Equations. Well-Posedness of Abstract Structural Models. Estimation of Parameters and Inverse Problems. Damage Detection in Smart Material Structures. Infinite Dimensional Control and Galerkin Approximation. Implementation of Finite-Dimensional Compensators. Modeling and Control in Coupled Systems. Bibliography. Notation. Index.

391 citations

Journal ArticleDOI
TL;DR: In this paper, an approximation scheme involving approximation of linear functional differential equations by systems of high order ordinary differential equations is formulated and convergence is established in the context of known results from linear semigroup theory.
Abstract: An approximation scheme involving approximation of linear functional differential equations by systems of high order ordinary differential equations is formulated and convergence is established in the context of known results from linear semigroup theory. Applications to optimal control problems are discussed and a summary of numerical results is given. The paper is concluded with a brief survey of previous literature on this class of approximations for systems with delays.

304 citations

Journal ArticleDOI
TL;DR: In this article, a partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite four separate damping mechanisms consisting of air damping, strain rate damping and spatial hysteresis.
Abstract: A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally Dynamic tests were performed to produce time histories The time history data is then used along with an approximate model to form a sequence of least squares problems The solution of the least squares problem yields the estimated damping coefficients The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis

260 citations

Journal ArticleDOI
TL;DR: A dynamic mathematical model is formulated that describes the interaction of the immune system with the human immunodeficiency virus and that permits drug "cocktail" therapies and supports a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
Abstract: We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.

230 citations


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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Book ChapterDOI
01 Jan 2011
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

3,554 citations

Journal ArticleDOI
TL;DR: Some open problems are discussed: the constructive use of the delayed inputs, the digital implementation of distributed delays, the control via the delay, and the handling of information related to the delay value.

3,206 citations

Journal ArticleDOI

3,152 citations