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Books on the topic 'Surface ball'

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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Holzapfel, Rolf-Peter. Ball and surface arithmetics. Braunschweig: Vieweg, 1998.

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2

Holzapfel, Rolf-Peter. Ball and Surface Arithmetics. Wiesbaden: Vieweg+Teubner Verlag, 1998. http://dx.doi.org/10.1007/978-3-322-90169-9.

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3

Schon̈beck, J. Evaluation of a process for the repair of area array and other surface mounted packages. Noordwijk, the Netherlands: ESA Publications Division, 2004.

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4

Allcock, Daniel. The moduli space of cubic threefolds as a ball quotient. Providence, R.I: American Mathematical Society, 2011.

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5

1946-, Carlson James A., and Toledo Domingo, eds. The moduli space of cubic threefolds as a ball quotient. Providence, R.I: American Mathematical Society, 2011.

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6

Holzapfel, Rolf-Peter. Ball and Surface Arithmetics. Springer, 2012.

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7

Holzapfel, Rolf-Peter. Ball and Surface Arithmetics (Aspects of Mathematics). American Mathematical Society, 1996.

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8

The impact dynamics of a tennis ball striking a hard surface. 1990.

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9

The impact dynamics of a tennis ball striking a hard surface. 1989.

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10

Tretkoff, Paula. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0001.

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This chapter explains that the book deals with quotients of the complex 2-ball yielding finite coverings of the projective plane branched along certain line arrangements. It gives a complete list of the known weighted line arrangements that can produce such ball quotients, and then provides a justification for the existence of the quotients. The Miyaoka-Yau inequality for surfaces of general type, and its analogue for surfaces with an orbifold structure, plays a central role. The book also examines the explicit computation of the proportionality deviation of a complex surface for finite covers of the complex projective plane ramified along certain line arrangements. Candidates for ball quotients among these finite covers arise by choosing weights on the line arrangements such that the proportionality deviation vanishes.

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11

Institute, British Standards. British Standard 7044/2.1 1989: Artificial Sports Surfaces. Methods of Test. Methods for Determination of Ball/Surface Interaction. BSI Standards, 1989.

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12

Tretkoff, Paula. Algebraic Surfaces and the Miyaoka-Yau Inequality. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0005.

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This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.

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13

Tretkoff, Paula. Line Arrangements in P2(C) and Their Finite Covers. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0006.

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This chapter discusses the free 2-ball quotients arising as finite covers of the projective plane branched along line arrangements. It first considers a surface X obtained by blowing up the singular intersection points of a linear arrangement in the complex projective plane, as well as a smooth compact complex surface Y that is a finite covering of X. If Y is of general type with vanishing proportionality deviation, then it is a free 2-ball quotient. The chapter then looks at line arrangements that have equal ramification indices along each of the proper transforms of the original lines, along with cases of blowing down rational curves and removing elliptic curves. It also enumerates all possibilities for the assigned weights of the arrangements, under the assumption that divisors of negative or infinite weight on the blown-up line arrangements do not intersect.

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14

Farb, Beₙsoₙ, and Dan Margalit. Overview. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0001.

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This book deals with two fundamental objects attached to a surface S and how they relate to each other: a group and a space. The group is the mapping class group of S, denoted by Mod(S). It is defined as the group of isotopy classes of orientation-preserving diffeomorphisms of S. The space is the Teichmüller space of S, a metric space homeomorphic to an open ball. The book considers the relations between the algebraic structure of Mod(S), the geometry of Teich(S), and the topology of M(S). Underlying these connections is the combinatorial topology of the surface S. The Nielsen–Thurston classification theorem, which gives a particularly nice representative for each element of Mod(S), is also discussed.

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15

Sugihara, Kokichi. Antigravity Slopes. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0033.

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A new type of illusion, called the antigravity slope illusion, is presented in this chapter. In this illusion a slope orientation is perceived opposite to the true orientation and hence a ball put on it appears to be rolling uphill, defying the law of gravity. This illusion is based on the ambiguity in the distance from a viewpoint to the surface of a three-dimensional solid represented in a single-view image. This illusion also arises in human real life, for example, when a car driver misunderstands the orientation of a road along which he or she is driving. Two assumptions are explored: (a) the human brain prefers to interpret vertical columns in a two-dimensional image as being vertical in three-dimensional space to being slanted and (b) the human brain prefers the most symmetric shape as the interpretation of a two-dimensional image.

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16

Livermore, Roy. All at Sea. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198717867.003.0009.

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According to first-generation plate tectonics, sea-floor spreading was nice and simple. Plates were pulled apart at mid-ocean ridges, and weak mantle rocks rose to fill the gap and began to melt. The resulting basaltic magma ascended into the crust, where it ponded to form linear ‘infinite onion’ magma chambers beneath the mid-ocean tennis-ball seam. At frequent intervals, vertical sheets of magma rose from these chambers to the surface, where they erupted to form new ocean floor or solidified to form dykes, in the process acquiring a magnetization corresponding to the geomagnetic field at the time. Mid-ocean ridge axes were defined by rifted valleys and divided into segments by transform faults with offsets of tens to hundreds of kilometres, resulting in the staircase pattern seen on maps of the ocean floor. All mid-ocean ridges were thus essentially identical. Such a neat and elegant theory was bound to be undermined as new data were acquired in the oceans.

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17

Tretkoff, Paula, and Hans-Christoph Im Hof. Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51). Princeton University Press, 2016.

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18

Complex Ball Quotients and Line Arrangements in the Projective Plane. Princeton University Press, 2016.

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19

Damman, P. Instability of thin films. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198789352.003.0008.

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We will first discuss the stability of liquid films deposited on solid surfaces with an emphasis on the nature of intermolecular forces and thermal fluctuations that conspire to generate complex morphologies. We will see how the global dewetting dynamics is driven by the solid–fluid interface and that dewetting can be a powerful tool to study the nanorheology of complex fluids, such as polymer melts in ultra thin films. In the second part, we will consider thin elastic sheets constrained by mechanical forces. The canonical example of such a system is given by a simple paper ball. We will see how the global geometry of these constraints drastically affects the final shape adopted by the sheet.

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20

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 of years. In this book, the author has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers. Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.

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