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Books on the topic '2.5 geometry'

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Author: Grafiati

Published: 3 September 2022

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1

Shafarevich, Igor R. Basic Algebraic Geometry 2. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38010-5.

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2

Convegno, italiano di geometria integrale probabilità geometriche e. corpi convessi (4th 1994 Bari Italy). IV Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi: Bari, 2-5 maggio 1994. Palermo: Sede della società, 1995.

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3

1952-, Brooks Robert, Entov Michael 1969-, Pinchover Yehuda 1953-, Sageev Michah 1966-, and Workshop on Groups, Geometry, and Dynamics (2004 : Haifa, Israel), eds. Geometry, spectral theory, groups, and dynamics: Proceedings in memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel. Providence, R.I: American Mathematical Society, 2005.

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4

1959-, Blasco Oscar, and Universidad Politécnica de Valencia, eds. Topics in complex analysis and operator theory: Third Winter School Complex Analysis and Operator theory, February 2-5, 2010, Universidad Politécnica de Valencia, Valencia, Spain. Providence, R.I: American Mathematical Society, 2012.

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5

Nuffield Mathematics 5-11 (Nuffield Maths 5-11 Project). Longman, 1990.

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6

(Editor), Jan Denef, Leonard Lipshitz (Editor), Thanases Pheidas (Editor), and Jan Van Geel (Editor), eds. Hilbert's Tenth Problem: Relations With Arithmetic and Algebraic Geometry : Workshop on Hilbert's Tenth Problem : Relations With Arithemtic and Algebraic ... November 2-5 (Contemporary Mathematics). American Mathematical Society, 2001.

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7

1951-, Denef Jan, ed. Hilbert's tenth problem: Relations with arithmetic and algebraic geometry : workshop on Hilbert's tenth problem : relations with arithmetic and algebraic geometry, November 2-5, 1999, Ghent University, Belgium. Providence, R.I: American Mathematical Society, 2000.

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8

(Editor), Doug Clements, ed. Picturing Polygons: 2-D Geometry (Investigations in Number, Data, and Space, Grades 5-6) (MacIntosh Disk Included). Dale Seymour Publications, 1996.

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9

Laboratoire Gravitation et Cosmologie Re. Gravitation, Geometry and Relativistic Physics: Proceedings of the "Journees Relativistes" held at Aussois, France, May 2-5, 1984. Springer, 2014.

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10

Chruściel, Piotr T. Geometry of Black Holes. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855415.001.0001.

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There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

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11

Steane, Andrew M. Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.001.0001.

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This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.

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12

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 to treat the cases alike. These similarity relations can be analyzed and represented geometrically. In such a geometric representation, the distance in moral space between cases reflects their degree of similarity. The more similar a pair of cases are from a moral point of view, the shorter is the distance between them. To assess to what extent the geometric method is practically useful for analyzing real-world cases the author has conducted three experimental studies based on data gathered from academic philosophers in the United States and Europe and engineering students at Texas A&M University. The results indicate that experts (philosophers) and laypeople (engineering students) do in fact apply geometrically construed moral principles in roughly, but not exactly, the manner advocates of geometrically construed principles believe they ought to be applied.

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13

Research, Ctr for Occupational. Geometric Optics: Light Sources and Wave Optics (Laser-Electro-Optics Technology Series, Course 2-5). Center for Occupational, 1987.

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14

Schuberth, Ernst. Der Geometrieunterricht an Waldorfschulen, Bd.2, Vergleichende Geometrie und geometrische Grundkonstruktionen in den Klassen 4 und 5. Freies Geistesleben, 1998.

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15

Zoccali, Carmine, Davide Bolignano, and Francesca Mallamaci. Left ventricular hypertrophy in chronic kidney disease. Edited by David J. Goldsmith. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199592548.003.0107_update_001.

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Alterations in left ventricular (LV) mass and geometry and LV dysfunction increase in prevalence from stage 2 to stage 5 in CKD. Nuclear magnetic resonance is the most accurate and precise technique for measuring LV mass and function in patients with heart disease. Quantitative echocardiography is still the most frequently used means of evaluating abnormalities in LV mass and function in CKD. Anatomically, myocardial hypertrophy can be classified as concentric or eccentric. In concentric hypertrophy, the muscular component of the LV (LV wall) predominates over the cavity component (LV volume). Due to the higher thickness and myocardial fibrosis in patients with concentric LVH, ventricular compliance is reduced and the end-diastolic volume is small and insufficient to maintain cardiac output under varying physiological demands (diastolic dysfunction). In those with eccentric hypertrophy, tensile stress elongates myocardiocytes and increases LV end-diastolic volume. The LV walls are relatively thinner and with reduced ability to contract (systolic dysfunction). LVH prevalence increases stepwisely as renal function deteriorates and 70–80% of patients with kidney failure present with established LVH which is of the concentric type in the majority. Volume overload and severe anaemia are, on the other hand, the major drivers of eccentric LVH. Even though LVH may regress after renal transplantation, the prevalence of LVH after transplantation remains close to that found in dialysis patients and a functioning renal graft should not be seen as a guarantee of LVH regression. The vast majority of studies on cardiomyopathy in CKD are observational in nature and the number of controlled clinical trials in these patients is very small. Beta-blockers (carvedilol) and angiotensin receptors blockers improve LV performance and reduce mortality in kidney failure patients with LV dysfunction. Although current guidelines recommend implantable cardioverter-defibrillators in patients with ejection fraction less than 30%, mild to moderate symptoms of heart failure, and a life expectancy of more than 1 year, these devices are rarely offered to eligible CKD patients. Conversion to nocturnal dialysis and to frequent dialysis schedules produces a marked improvement in LVH in patients on dialysis. More frequent and/or longer dialysis are recommended in dialysis patients with asymptomatic or symptomatic LV disorders if the organizational and financial resources are available.

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16

Finn, R. Advances in Geometric Analysis and Continuum Mechanics: Proceedings of a Conference Held at Stanford University on August 2-5, 1993 in Honor of the Seventieth Birthday of Robert Finn. International Press of Boston, 1995.

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