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Books on the topic 'Non linear geometric'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Gaven, Martin, ed. Geometric function theory and non-linear analysis. Clarendon, 2001.

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2

Ivanova, Jordanka. Geometric method for stability of non-linear elastic thin shells. Kluwer Academic Publishers, 2002.

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3

Ivanova, Jordanka, and Franco Pastrone. Geometric Method for Stability of Non-Linear Elastic Thin Shells. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-1511-1.

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4

Franco, Pastrone, ed. Geometric method for stability of non-linear elastic thin shells. Kluwer Academic Publishers, 2002.

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5

Górski, Jarosław. Non-linear models of structures with random geometric and material imperfactions [sic] simulation-based approach. Wydawn. Politechniki Gdańskiej, 2006.

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6

Artin, Emil. Algèbre géométrique. Editions Jacques Gabay, 1996.

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7

Holden, Helge. Soliton Equations and Their Algebro-Geometric Solutions: Volume I: (1+1)-Dimensional Continuous Models. Cambridge University Press, 2003.

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8

Liana, Lupșa, ed. Non-connected convexities and applications. Kluwer Academic Publishers, 2002.

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9

Geometric, control, and numerical aspects of nonholonomic systems. Springer, 2002.

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10

1942-, Corneil D. G., and Mathon R. A, eds. Geometry and combinatorics: Selected works of J.J. Seidel. Academic Press, 1991.

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11

1962-, Sturmfels Bernd, ed. Introduction to tropical geometry. American Mathematical Society, 2015.

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12

The role of nonassociative algebra in projective geometry. American Mathematical Society, 2014.

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13

Marrakesh Workshop on Geometric Analysis of Several Complex Variables and Related Topics (2010 Marrakech, Morocco). Geometric analysis of several complex variables and related topics: Marrakesh Workshop on Geometric Analysis of Several Complex Variables and Related Topics, May 10-14, 2010, Marrakesh, Morocco. Edited by Barkatou Y. 1967-. American Mathematical Society, 2011.

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14

Spaces of constant curvature. 6th ed. AMS Chelsea Pub., 2011.

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15

Topology and geometry in dimension three: Triangulations, invariants, and geometric structures : conference in honor of William Jaco's 70th birthday, June 4-6, 2010, Oklahoma State University, Stillwater, OK. American Mathematical Society, 2011.

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16

Concentration, functional inequalities, and isoperimetry: International workshop, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida. American Mathematical Society, 2011.

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17

Bard, Gregory V. Sage for undergraduates. American Mathematical Society, 2015.

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18

1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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19

Iwaniec, Tadeusz, and Gaven Martin. Geometric Function Theory and Non-linear Analysis. Oxford University Press, USA, 2002.

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20

Ivanova, Jordanka, and Franco Pastrone. Geometric Method for Stability of Non-Linear Elastic Thin Shells. Springer, 2014.

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21

Artin, Emil. Geometric Algebra. Wiley-Interscience, 1988.

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22

Invariant geometric structures: A non-linear extension of the Borel density theorem. 1989.

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23

Holden, Helge, and Fritz Gesztesy. Soliton Equations and their Algebro-Geometric Solutions (Cambridge Studies in Advanced Mathematics). Cambridge University Press, 2003.

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24

Edmunds, D. E., and W. D. Evans. Entropy Numbers, s-Numbers, and Eigenvalues. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0002.

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The geometric quantities entropy numbers, approximation numbers and n-widths are defined for compact linear maps, and connections with the analytic entities eigenvalues and essential spectra discussed. The celebrated inequality of Weyl between the approximation numbers and eigenvalues is established in the general context of Lorentz sequence spaces. Also included are an axiomatic approach to s-numbers, a discussion of non-compact maps, and the Schmidt decomposition theory for compact linear operators in Hilbert spaces.

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25

Pomeau, Yves, and Basile Audoly. Elasticity and Geometry: From Hair Curls to the Non-Linear Response of Shells. Oxford University Press, 2018.

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26

Elasticity anf geometry: From hair curls to the non-linear response of shells. Oxford University Press, 2010.

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27

Hellman, Geoffrey, and Stewart Shapiro. Non-Euclidean Extensions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198712749.003.0006.

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This chapter adapts the foregoing results to present two non-Euclidean theories, both in line with the (semi-)Aristotelian theme of rejecting points, as parts of regions (but working with actual infinity). The first theory is a two-dimensional hyperbolic space, that is, one that has a negative constant curvature. The second theory captures a space of constant positive curvature, a two-dimensional spherical geometry. The task here is to formulate axioms on regions which allow us to prove that (i) there are no infinitesimal regions and (ii) that there are no parallels to any given “line” through

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28

Cristescu, G., and L. Lupsa. Non-Connected Convexities and Applications. Springer, 2014.

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29

Cristescu, G., and L. Lupsa. Non-Connected Convexities and Applications (Applied Optimization). Springer, 2002.

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30

Dietrich, Franz, and Christian List. Probabilistic Opinion Pooling. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.37.

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Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This chapter is a review of several proposed solutions to this problem, focusing on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). Axiomatic characterizations of e

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31

Epstein, Charles L., and Rafe Mazzeo. Wright-Fisher Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0002.

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This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural domains of definition for generalized Kimura diffusions: polyhedra in Euclidean space or, more generally, abstract manifolds with corners. Amongst the convex polyhedra, the chapter distinguishes the subclass of regular convex polyhedra P. P is a regular convex polyhedron if it is convex and if near any corner, P is the intersection of no more than N half-spaces with corresponding normal vectors that a

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32

Peterson, Martin. The Ethics of Technology. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190652265.001.0001.

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This book develops an analytic ethics of technology based on a geometric account of moral principles. The author argues that geometric concepts such as points, lines, and planes are useful for clarifying the structure and scope of five moral principles: (1) the cost-benefit principle, (2) the precautionary principle, (3) the sustainability principle, (4) the fairness principle, and (5) the autonomy principle. The geometric approach derives its normative force from the Aristotelian dictum that we should “treat like cases alike.” The more similar a pair of cases are, the more reason do we have t

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33

Abbott, Edwin A. Flatland. Edited by Rosemary Jann. Oxford University Press, 2008. http://dx.doi.org/10.1093/owc/9780199537501.001.0001.

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Upward, yet not Northward.’ How would a creature limited to two dimensions be able to grasp the possibility of a third? Edwin A. Abbott's droll and delightful ‘romance of many dimensions’ explores this conundrum in the experiences of his protagonist, A Square, whose linear world is invaded by an emissary Sphere bringing the gospel of the third dimension on the eve of the new millennium. Part geometry lesson, part social satire, this classic work of science fiction brilliantly succeeds in enlarging all readers‘ imaginations beyond the limits of our ‘respective dimensional prejudices’. In a worl

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34

Gillam, Barbara. An Analysis of Theoretical Approaches to Geometrical-Optical Illusions. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0004.

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The geometrical optical illusions, such as the Müller-Lyer and the Poggendorff, are simple line drawings, which demonstrate errors as large as 25% when people are asked to match their properties such as size, angles, and line collinearity. They have been tantalizing people for at least 150 years and are still not really understood. Illusion figures have been used to probe the consistency of different perceptual properties and also of perception and action with implications for the theory of two visual systems. Explanations of geometrical illusions tend to invoke either physiological processes

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35

Peterson, Martin. Introduction. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190652265.003.0001.

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The aim of this chapter is to introduce five moral principles that are necessary and jointly sufficient for analyzing ethical issues related to new and existing technologies. The five principles are not entirely new; it is primarily the method for articulating the principles that is novel. It is argued that geometric concepts such as points, distances, and lines can be used for construing moral principles as abstract regions in a multidimensional space, as well as for balancing conflicting principles against each other. The point of departure for the geometric approach is the following general

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36

Wackermann, Jiří. The Oppel–Kundt Illusion. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0035.

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A line segment, subdivided into smaller parts, appears longer than an undivided line segment of the same length. This phenomenon is known as “Oppel–Kundt illusion,” also named “illusion of interrupted extent” or “filled space illusion,” is a classic example of so-called “geometric-optical illusions.” It was described about 150 years ago but it is still insufficiently explored and not well understood. This chapter provides an overview of the research into the Oppel–Kundt illusion, summarizes the most important empirical findings and explanatory approaches, and points out relations to other illu

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37

Georgeson, Mark. The Graph-Paper Effect. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0107.

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Most visual illusions involve distorted or altered perception of objects or events or misinterpretation of image information. The discrepancy between what we experience and what is physically present in the world or in the retinal image can be large, surprising, and dramatic. It is much rarer to see things that simply are not there at all. Repetitive stimuli, such as grating patterns or flickering lights, can induce perception of a range of illusory geometric patterns, forms, and movements—during or after exposure to the inducing stimulus. This chapter describes one such illusory phenomenon—th

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38

1944-, Morozov Albert D., ed. Invariant sets for Windows. World Scientific, 1999.

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39

Dragunov, Timothy N., Svetlana A. Boykova, and Olga V. Malysheva. Invariant Sets for Windows: Resonance Structures, Attractors, Fractals, and Patterns (World Scientific Series on Nonlinear Science. Series a, Monographs and Treatises, V. 37.). World Scientific Publishing Company, 1999.

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40

Payne, Andrew. The Form of the Good II. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198799023.003.0009.

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This chapter is concerned with the image of the Divided Line, in which dianoia illustrates the use of the image-original relation. Dianoia employs visible objects such as the diagrams used in geometry as images for the purpose of gaining insight into intelligible objects. In the process of making its inquiries, dianoia employs hypotheses as starting points. These hypotheses include but are not limited to the definitions that mathematicians set forth as they make their demonstrations. Philosophers are expected to make a further transition from dianoia to dialectic and thus to move to the highes

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41

Blacklock, Mark. The Emergence of the Fourth Dimension. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198755487.001.0001.

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The idea of the fourth dimension of space has been of sustained interest to nineteenth-century and Modernist studies since the publication of Linda Dalrymple Henderson’s The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983). An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and grew to become an informing idea for a number of important Modernist writers and artists. Describing the post-Euclidean intellectual landscape of the late nineteenth century, The Emergence of the Fourth Dimension works with th

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42

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator

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43

Tretkoff, Paula, and Hans-Christoph Im Hof. Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.001.0001.

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This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that are free quotients of the complex 2-ball. The book also includes a background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The book began as a set of lecture notes, taken by the author, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded over a number

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44

McDuff, Dusa, and Dietmar Salamon. Introduction to Symplectic Topology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.001.0001.

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Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In 1998, a significantly revised second edition contained new sections and updates. This third edition includes both further updates and new material on this fast-developing area. All chapters have been revised to

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45

Henderson, Andrea. Algebraic Art. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809982.001.0001.

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Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian ma

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