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    • Contributions to Nonlinear Functional Analysis

      Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, April 12-14, 1971
      • 1st Edition
      • Eduardo H. Zarantonello
      • English
      Contributions to Nonlinear Functional Analysis contains the proceedings of a Symposium on Nonlinear Functional Analysis, held in Madison, Wisconsin, on April 12-14, 1971, under the sponsorship of the University of Wisconsin's Mathematics Research Center. The symposium provided a forum for discussing various topics related to nonlinear functional analysis, from transversality in nonlinear eigenvalue problems to monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Comprised of 15 chapters, this book begins by presenting an extension of Leray-Schauder degree and an application to a nonlinear elliptic boundary value problem. The discussion then turns to the use of degree theory to prove the existence of global continua of solutions of nonlinear eigenvalue problems; transversality in nonlinear eigenvalue problems; and how variational structure can be used to study some local questions in bifurcation theory. Subsequent chapters deal with the notion of monotone operators and monotonicity theory; a nonlinear version of the Hille-Yosida theorem; a version of the penalty method for the Navier-Stokes equations; and various types of weak solutions for minimizing problems in the spirit of duality theory for convex functionals. This monograph will be of interest to students and practitioners in the field of mathematics who want to learn more about nonlinear functional analysis.

    • Computer Aided Geometric Design

      • 1st Edition
      • Robert E. Barnhill + 1 more
      • English
      Computer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers.

    • Applications of Number Theory to Numerical Analysis

      • 1st Edition
      • S. K. Zaremba
      • English
      Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.

    • Optimal Control of Differential and Functional Equations

      • 1st Edition
      • J. Warga
      • English
      Optimal Control of Differential and Functional Equations presents a mathematical theory of deterministic optimal control, with emphasis on problems involving functional-integral equations and functional restrictions. The book reviews analytical foundations, and discusses deterministic optimal control problems requiring original, approximate, or relaxed solutions. Original solutions involve mathematicians, and approximate solutions concern engineers. Relaxed solutions yield a complete theory that encompasses both existence theorems and necessary conditions. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original minimum. The text illustrates a class of ordinary differential problems with examples, and explains some conflicting control problems with relaxed adverse controls, as well as conflicting control problems with hyper-relaxed adverse controls. The book is intended for mature mathematicians, graduate students in analysis, and practitioners of optimal control whose primary interests and training are in science or engineering.

    • Multivariable Calculus with Linear Algebra and Series

      • 1st Edition
      • William F. Trench + 1 more
      • English
      Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also considered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

    • Topics in Multivariate Approximation

      • 1st Edition
      • C. K. Chui + 2 more
      • English
      Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

    • Photosynthesis

      The Biochemistry of Plants
      • 1st Edition
      • M. D. Hatch + 1 more
      • English
      The Biochemistry of Plants: A Comprehensive Treatise, Volume 10: Photosynthesis provides information pertinent to the biochemistry of photosynthesis. This book discusses the advances in the field of photosynthesis and emphasizes that not only certain synthetic bacteria and microalgae but also other aquatic phototrophs possess mechanisms for concentrating CO2 or bicarbonate in their cells. Organized into six chapters, this volume begins with an overview of the ways of minimizing the wasteful oxygenase reaction catalyzed by the enzyme. This text then examines the molecular basis underlying the structure of the chloroplast thylakoid membrane and its biogenesis during the maturation of the chloroplast. Other chapters consider the dynamics of the thylakoid membrane, including the role of protein phosphorylation and the lateral distribution of electrical charge and protein components. This book discusses as well the molecular processes governing the development of the organelle. This book is a valuable resource for plant biochemists, neurobiochemists, molecular biologists, senior graduate students, and research workers.

    • Archaeological Hammers and Theories

      • 1st Edition
      • James A. Moore + 1 more
      • English
      Studies in Archaeology: Archaeological Hammers and Theories provides information pertinent to the archeological method, with emphasis on the interaction of data and technique with theory and problems. This book describes the nature of archeological data, the range of archeological theories, and the scope of archeological problems. Organized into three parts encompassing 13 chapters, this book begins with an overview of the products of the archeological record. This text then examines survey sampling, site formation studies, and lithic and ceramic analysis. Other chapters consider the behavioral concepts that are implicit in the notions of special behavior, optimization, decision making, and population dynamics. This book discusses as well the analysis of pottery, which plays a leading part in the reconstruction of culture histories in archeology. The final chapter suggests an alternative set of philosophical issues that might serve to focus a philosophy or archeology. This book is a valuable resource for archeologists.

    • Applied Fuzzy Systems

      • 1st Edition
      • Toshiro Terano + 2 more
      • English
      Applied Fuzzy Systems provides information pertinent to the fundamental aspects of fuzzy systems theory and its application. This book discusses the development of high-level artificial intelligence and information processing systems, as well as the realization of fuzzy computers. Organized into six chapters, this book begins with an overview of the fundamental problems addressed by fuzzy systems. This text then reviews standard computer logic or two-valued Boolean algebra. Other chapters consider bus scheduling, evaluation of structural reliability, applications of schema systems for decision-making, and processing of natural-language information and systems for medical diagnosis as examples of fuzzy expert systems. This book discusses as well a practical fuzzy expert system for durability evaluations of reinforced concrete slabs for bridges, along with an example of application. The final chapter deals with the important parts of the construction of fuzzy computers, their architecture, and the outlook for the future. This book is a valuable resource for engineers, mathematicians, technicians, and research workers.

    • Stochastic Economics

      Stochastic Processes, Control, and Programming
      • 1st Edition
      • Gerhard Tintner + 1 more
      • English
      Stochastic Economics: Stochastic Processes, Control, and Programming presents some aspects of economics from a stochastic or probabilistic point of view. The application of stochastic processes to the theory of economic development, stochastic control theory, and various aspects of stochastic programming is discussed. Comprised of four chapters, this book begins with a short survey of the stochastic view in economics, followed by a discussion on discrete and continuous stochastic models of economic development. The next chapter focuses on methods of stochastic control and their application to dynamic economic models, with emphasis on those aspects connected especially with the theory of quantitative economic policy. Some basic operational problems of applying stochastic control, particularly in economic systems and organizations for problems such as dynamic resource allocation, growth planning, and economic coordination are considered. The last chapter is devoted to stochastic programming, paying particular attention to the decision rule theory of operations research under the chance-constrained model and a method of incorporating reliability measures into a systems reliability model. This book will be of interest to economists, statisticians, applied mathematicians, operations researchers, and systems engineers.

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