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  • College Physics

    College Physics is an OpenStax College resource... encouraging learners towards higher levels of learning. A strong foundation in introductory physics (covering a very wide range of topics), with algebra as a prerequisite. Topics are introduced conceptually with a steady progression to precise definition and analytical applications. The analytical aspect (problem solving) is tied back to the conceptual before moving on to another subject. The OpenStax project encourages community curation, and welcomes feedback, suggestions and examples to make it even more relevant for today's students. Flooved will assist with this by submitting all of the annotations made which include examples and suggestions to OpenStax every once in a while, in their authors' names.

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  • Combinatorial Data Analysis: Optimization by Dynamic Programming

    Chapter 1 is a short preview that introduces the general topic by noting areas in combinatorial data analysis that can be approached by the optimization strategy of dynamic programming, and that presents a number of data sets to be used throughout the remaining chapters. The second chapter introduces the general dynamic programming paradigm (the GDPP, for short) and gives an introductory example of its usage in the well-known linear assignment task. The next two chapters focus the GDPP on topics within Cluster Analysis (Chapter 3) and Object Sequencing and Seriation (Chapter 4). Chapter 3 is further subdivided by several dichotomies: whether the clustering involves a single object partition (partitioning) or a hierarchy of nested partitions (and the associated representing ultrametric); the presence or absence of constraints on the type of partitions sought (typically through subsets contiguous with respect to some object order); the form of the available data with the usual distinction of having proximities between objects from a single set (one-mode) or between objects from two sets (two-mode). Chapter 4 can also be characterized by several dichotomies: whether the one-mode proximities are symmetric or skew-symmetric, with the latter representing dominance information among the objects, or whether the proximities are initially one- or two-mode. In addition, several related topics are introduced: sequencing through the construction of optimal paths (linear and circular); the incorporation of precedence constraints in the construction of an optimal order; and unifying the general areas of clustering and sequencing by identifying optimal partitions of an object set in which the classes are themselves ordered. Chapter 5 extends the GDPP heuristically for use with large(r) object sets in both the clustering and sequencing context, while (unfortunately) removing the absolute guarantee of optimality for the identified object arrangements. Finally, Chapter 6 provides preliminary discussion of a number of areas of extension and generalization that are now being pursued by the current authors and others.

    • 172 Pages
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  • Research Directions in Distributed Parameter Systems

    In Chapter 1, Albanese, Medina and Penn deal with electromagnetic effects in dielectric materials, in particular in living plants and animals. They deal with physics and biology and address unresolved questions of concern (thermal dissipation, storage, etc.) that play a major role in biomedical considerations. In Chapter 2, Burns raises fundamental issues on approximation in DPS and the role of science and engineering applications in framing the research questions we pursue. He illustrates ideas in the context of flow problems, cogently arguing that approximations perfectly suitable for simulation may not be appropriate for control design. Homogenization techniques that can be used to model modern composite material structures (where multiscale issues play significant roles) are discussed in Chapter 3 by Cioranescu. Chapters 4 and 6 by Curtain and by Byrnes, Gilliam and Shubov treat feedback control design for DPS - in one case in the context of a system theoretic framework and in the other in a geometric framework. In Chapter 5, Fleming presents a survey chapter on control problems using max-plus stochastic calculus techniques. Applications of the techniques include the celebrated Hamilton-Jacobi-Bellman equation and nonlinear filtering. Both Chapter 7 by Inman and Carneiro and Chapter 9 by Kojima focus on inverse problems. Inman and Carneiro treat vibration-based damage detection and health monitoring in structures using "smart systems" techniques. Kojima considers NonDestructive Evaluation (NDE) methods based on Eddy Current Techniques (ECT), a specific electromagnetic-based interrogation technique that can be used in conductive structures. The discussions are motivated by applications in the nuclear power industry; i.e., computational algorithms for the noninvasive inspection of pressure vessels. In Chapter 8, Kappel and Batzel discuss modeling of control systems embodied in the human respiratory and cardiovascular systems. Their survey includes models based on our current but ever-evolving understanding of the underlying physiology. Finally, Chapters 10 and 11 return to topics in mainsteam control theory. Lions discusses several conjectures in the context of approximate controllability of the Navier-Stokes equations for flow of a perfect incompressible viscous fluid. The survey by Kunisch on computational methods for optimality systems and suboptimal controls covers contributions made over the last decade. Techniques for efficient computations, including those based on the Karhunen-Loeve or Proper Orthogonal Decomposition (POD) approach, are presented. These reduced-order modeling techniques (also discussed by Curtain in Chapter 4) are of growing interest and importance in the inverse-problem and control communities and are most certainly at the frontier of current computational ideas being explored.

    • 283 Pages
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  • Singular Perturbations and Hysteresis

    The first chapter presents an introduction to a relationship between singularly perturbed differential equations and equations with hysteresis. The second chapter is entirely devoted to applications of models of hysteresis in economics. In the third chapter a discontinuous hysteresis law is rigorously derived as a singular limit in differential equations with non-monotone nonlinearities, which arises, for example, in a model for instabilities of a fluid flow in a tube with a pump and a valve with uncertain parameters. A structured and synthetic presentation of Vasilieva's combined expansions is given in the fourth chapter. In the fifth and sixth chapters singularly perturbed partial differential equations are considered and typical problems of the asymptotic theory of contrast structures are discussed. The last four chapters are concerned with the geometrical approach to an investigation of models with singular perturbations and hysteresis. The integral manifold method is elaborated in Chapter 7, which is devoted to the study of different critical cases in the theory of singular perturbations. A further development of this method, with applications to lasers, control and problems of chemical kinetics and combustion, is contained in the eighth chapter. In the ninth chapter the integral manifold method is used to investigate the problem of pressure driven flames in inert porous media. The last chapter is devoted to an extension of the geometric approach to systems with small hysteresis. The chaotic behavior of laser models is examined to demonstrate the validity of this approach.

    • 356 Pages
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  • The Structural Representation of Proximity Matrices with MATLAB

    Part I develops linear and circular uni- and multidimensional scaling using the city-block metric as the major representational device; Part II is concerned with characterizations based on various graph-theoretic tree structures, specifically with those usually referred to as ultrametrics and additive trees; Part III uses representations defined solely by order properties, particularly to what are called (strongly) anti-Robinson forms

    • 220 Pages
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