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This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems that arise in science and engineering and require an optimal mathematical representation of physical reality. The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of real functions of one real variable by real polynomials; shape-preserving approximation of real functions of several real variables by multivariate real polynomials; shape-preserving approximation of analytic functions of one complex variable by complex polynomials in the unit disk; and shape-preserving approximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendix treats related results of non-polynomial and non-spline approximations preserving shape including those by complexified operators with applications to complex partial differential equations. Shape-Preserving Approximation by Real and Complex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students and researchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, chemistry, fluid mechanics, and engineering.

Mathematics. --- Approximations and Expansions. --- Real Functions. --- Functions of a Complex Variable. --- Computational Mathematics and Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Math Applications in Computer Science. --- Computer science. --- Functions of complex variables. --- Computer science --- Engineering mathematics. --- Mathématiques --- Informatique --- Fonctions d'une variable complexe --- Mathématiques de l'ingénieur --- Approximation theory. --- Bernstein polynomials. --- Mathematical optimization. --- Multivariate analysis. --- Approximation theory --- Bernstein polynomials --- Multivariate analysis --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Algebra --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Polynomials, Bernstein --- Theory of approximation --- Algebra. --- Functions of real variables. --- Computer mathematics. --- Applied mathematics. --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Analysis of variance --- Mathematical statistics --- Matrices --- Convergence --- Integrals --- Probabilities --- Series --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Real variables --- Functions of complex variables

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This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions. The study is developed for the univariate and bivariate cases using well-known classical interpolation operators of Lagrange, Grünwald, Hermite-Fejér and Shepard type. One of the first books on the subject, it presents interesting new results alongwith an excellent survey of past research. Key features include: - potential applications to data fitting, fluid dynamics, curves and surfaces, engineering, and computer-aided geometric design - presents recent work featuring many new interesting results as well as an excellent survey of past research - many interesting open problems for future research presented throughout the text - includes 20 very suggestive figures of nine types of Shepard surfaces concerning their shape preservation property - generic techniques of the proofs allow for easy application to obtaining similar results for other interpolation operators This unique, well-written text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer-aided geometric design, fluid mechanics, and engineering researchers.

Operator theory --- Functional analysis --- Mathematical analysis --- Numerical analysis --- Engineering sciences. Technology --- Computer science --- analyse (wiskunde) --- functies (wiskunde) --- informatica --- ingenieurswetenschappen --- numerieke analyse

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It was in 1660s England, according to the received view, in the Royal Society of London, that science acquired the form of empirical enquiry we recognize as our own: an open, collaborative experimental practice, mediated by specially-designed instruments, supported by civil discourse, stressing accuracy and replicability. Guided by the philosophy of Francis Bacon, by Protestant ideas of thisworldly benevolence, by gentlemanly codes of decorum and by a dominant interest in mechanics and the mechanical structure of the universe, the members of the Royal Society created a novel experimental practice that superseded former modes of empirical inquiry, from Aristotelian observations to alchemical experimentation. This volume focuses on the development of empiricism as an interest in the body - as both the object of research and the subject of experience. Re-embodying empiricism shifts the focus of interest to the ˜life sciences'; medicine, physiology, natural history. In fact, many of the active members of the Royal Society were physicians, and a significant number of those, disciples of William Harvey and through him, inheritors of the empirical anatomy practices developed in Padua during the 16th century. Indeed, the primary research interests of the early Royal Society were concentrated on the body, human and animal, and its functions much more than on mechanics. Similarly, the Académie des Sciences directly contradicted its self-imposed mandate to investigate Nature in mechanistic fashion, devoting a significant portion of its Mémoires to questions concerning life, reproduction and monsters, consulting empirical botanists, apothecaries and chemists, and keeping closer to experience than to the Cartesian standards of well-founded knowledge. These highlighted empirical studies of the body, were central in a workshop in the beginning of 2009 organized by the unit for History and Philosophy of Science in Sydney. The papers that were presented by some of the leading figures in this area are presented in this volume.

Philosophy of science --- History of civilization --- History of the United Kingdom and Ireland --- anno 1600-1699 --- Empiricism. --- Science --- Human body. --- Philosophy. --- Royal Society (Great Britain).

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Strangeness nuclear physics bears a broad impact on contemporary physics since it lies at the intersection of nuclear and elementary particle physics, having, moreover, significant implications to the astrophysics of compact objects. This set of extensive lectures presents a balanced theoretical and experimental introduction to, and survey of, the field, addressing topics such as the production and spectroscopy of strange nuclear systems, modern approaches to the hyperon-nucleon interaction, and weak decays of hypernuclei. With new experiments underway, this burgeoning research field is well served by this tutorial primer and review for both newcomers and seasoned researchers alike

Astrophysics --- Experimental nuclear and elementary particle physics --- Elementary particles --- Nuclear physics --- elementaire deeltjes --- quarks --- astrofysica --- deeltjesfysica --- kwantumleer --- kernenergie