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Books on the topic 'IDF equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Succi, Sauro. Approach to Equilibrium, the H-Theorem and Irreversibility. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0003.

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Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underl

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Morawetz, Klaus. Nonequilibrium Quantum Hydrodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0015.

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The balance equations resulting from the nonlocal kinetic equation are derived. They show besides the Landau-like quasiparticle contributions explicit two-particle correlated parts which can be interpreted as molecular contributions. It looks like as if two particles form a short-living molecule. All observables like density, momentum and energy are found as a conserving system of balance equations where the correlated parts are in agreement with the forms obtained when calculating the reduced density matrix with the extended quasiparticle functional. Therefore the nonlocal kinetic equation fo

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3

Students Solutions Manual Fundamentals Of Differential Equations With Boundary Value Problems With Ide Cd. Addison Wesley Longman, 2008.

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4

Nagle, R. Kent. Fundamentals of Differential Equations with Boundary Value Problems with IDE CD (Saleable Package) (5th Edition). 5th ed. Addison Wesley, 2007.

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5

Nagle, R. Kent. Fundamentals of Differential Equations bound with IDE CD (Saleable Package) (7th Edition). 7th ed. Addison Wesley, 2007.

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6

Kohler, Werner E., and Lee W. Johnson. Elementary Differential Equations with Boundary Value Problems with IDE CD Package (2nd Edition). 2nd ed. Addison Wesley, 2005.

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7

Anjum, Rani Lill, and Stephen Mumford. Do We Need Causation in Science? Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198733669.003.0002.

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Some claim that there is no causation to be found in the mature sciences, as Russell did in a famous and often quoted paper. Physics deals with equations, for example, which are symmetric rather than directed. Causal talk gets dismissed as primitive ‘folk’ science. However, it cannot be concluded that there is no asymmetric causation simply because a science does not represent it. We often will read an equation directionally as we know we can intervene on one variable to change another. This shows that scientific notions of experiment, intervention, and even observation presuppose the reality

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8

Deruelle, Nathalie, and Jean-Philippe Uzan. The Einstein equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0044.

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This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if the gravitational field created by the matter can be neglected, the appropriate framework for describing the matter is that of special relativity. Einstein gravitational equations relate geometry and matter: specifically, they relate the Riemann tensor, or more precisely the Einstein tensor, to the geometrical object describing ‘inertia’, the energy content of the matter—that is, the energy–moment

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9

Rajeev, S. G. Ideal Fluid Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0004.

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Some solutions of Euler’s equations are found here. The simplest are the steady flows: water flowing out of a tank at a constant rate, the Venturi and Pitot tubes. Another is the static solution of a self-gravitating fluid of variable density (e.g., a star). If the total mass is too large, such a star can collapse (Chandrasekhar limit). If the flow is both irrotational and incompressible, it must satisfy Laplace’s equation. Complex analysismethods can be used to solve for the flow past a cylinder or inside a disk with a stirrer. Joukowski used conformal transformations on the cylinder to find

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10

Isett, Philip. The Main Iteration Lemma. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0010.

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This chapter properly formalizes the Main Lemma, first by discussing the frequency energy levels for the Euler-Reynolds equations. Here the bounds are all consistent with the symmetries of the Euler equations, and the scaling symmetry is reflected by dimensional analysis. The chapter proceeds by making assumptions that are consistent with the Galilean invariance of the Euler equations and the Euler-Reynolds equations. If (v, p, R) solve the Euler-Reynolds equations, then a new solution to Euler-Reynolds with the same frequency energy levels can be obtained. The chapter also states the Main Lem

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11

Isett, Philip. Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.001.0001.

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Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with

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12

Walsh, Bruce, and Michael Lynch. Selection Response in Natural Populations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0020.

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The breeder's equation often fails when applied to natural populations. In large part, this likely occurs because the assumed trait is not the actual target of selection. A within-generation change in the mean of a suggested target trait can arise as a correlated response from selection acting elsewhere. This chapter examines sources of error in the breeder's equation and approaches that attempt to determine if an assumed trait is actually the true target of selection. It also reviews a number of long-term studies from natural populations and examines possible sources for the failure of most o

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13

Deruelle, Nathalie, and Jean-Philippe Uzan. Gravitational radiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0054.

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This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitat

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14

Rajeev, S. G. Instabilities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0008.

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The most well-known of the many instabilities of a fluid is the Rayleigh–Taylor instability. A denser fluid sitting on top of a lighter fluid is in unstable equilibrium, much like a pendulum standing on its head. Kapitza showed that rapidly oscillating the point of support of a pendulum can counteract this instability. The Rayleigh–Taylor instability can also be inhibited by shaking the two fluid layers rapidly. The Orr–Sommerfeld equations are a linear model of instabilities of a steady solution of Navier-Stokes. The Orr–Sommerfeld operator is not normal (does not commute with its adjoint). T

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15

Escudier, Marcel. Kinematic description of fluids in motion and approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0006.

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In this chapter some of the terminology and simplifications which enable us to begin to describe and analyse practical fluid-flow problems are introduced. The terms ‘fluid particle’ and ‘streamline’ are defined. The principle of conservation of mass applied to steady one-dimensional flow through a streamtube of varying cross-sectional area resulted in the continuity equation. This important equation relates mass flowrate ṁ, volumetric flowrate Q̇, average fluid velocity V̄, fluid density ρ‎, and cross-sectional area A: m = ρ‎ Q̇ = ρ‎AV̅ = constant. For a constant-density fluid this result sho

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16

Huffaker, Ray, Marco Bittelli, and Rodolfo Rosa. Entropy and Surrogate Testing. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782933.003.0005.

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Reconstructing real-world system dynamics from time series data on a single variable is challenging because real-world data often exhibit a highly volatile and irregular appearance potentially driven by several diverse factors. NLTS methods help eliminate less likely drivers of dynamic irregularity. We set a benchmark for regular behavior by investigating how linear systems of ODEs are restricted to exponential and periodic dynamics, and illustrating how irregular behavior can arise if regular linear dynamics are corrupted with noise or shift over time (i.e., nonstationarity). We investigate h

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17

Isett, Philip. Gluing Solutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0012.

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This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of refer

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18

Deruelle, Nathalie, and Jean-Philippe Uzan. Electromagnetism and differential geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0040.

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This chapter begins by examining p-forms and the exterior product, as well as the dual of a p-form. Meanwhile, the exterior derivative is an operator, denoted d, which acts on a p-form to give a (p + 1)-form. It possesses the following defining properties: if f is a 0-form, df(t) = t f (where t is a vector of Eₙ), which coincides with the definition of differential 1-forms. Moreover, d(α‎ + β‎) = dα‎ + dβ‎, where α‎ and β‎ are forms of the same degree. Moreover, the exterior calculus can be used to obtain a compact and elegant formulation of Maxwell’s equations.

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19

Deruelle, Nathalie, and Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0064.

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This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor. It states without proof the intrinsic versions of the properties of the Riemann–Christoffel tensor of a covariant derivative already given in Chapter 2. This chapter then performs the same derivation as in Chapter 4 by obtaining the Einstein equations of general relativity by varying the Hilbert action. However, this will be done in the intrinsic manner, using

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20

Kachelriess, Michael. Baryogenesis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0022.

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This chapter shows that a baryon asymmetry can be generated only if the Sakharov conditions are satisfied. The required departure from thermal equilibrium can be realised either in first-order phase transitions or in out-of-equilibrium decays. Sphaleron transitions as a possible way to transfer a lepton into a baryon asymmetry are covered and the Boltzmann equation governing the baryon asymmetry generated in particle decays is derived. A brief review of baryogenesis during the electroweak phase transition is presented.

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21

Deruelle, Nathalie, and Jean-Philippe Uzan. Dynamics of massive systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0006.

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This chapter presents the laws of motion of an ensemble of point masses forming a solid body whose shape is invariant, or a fluid whose shape can vary with time. It argues that an ensemble of point masses constitutes a solid if the distances between the points can be assumed constant. The chapter then provides examples of the motions of a solid. Finally, it demonstrates the Euler equations of fluid motion. Here, it states that a perfect fluid is characterized by its (inertial) mass density ρ‎(t, xⁱ), its pressure p(t, xⁱ) which phenomenologically describes its internal collisions, and a veloci

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22

Basu, Sanjay. Waiting Lines and Waiting Times. Edited by Sanjay Basu. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190667924.003.0004.

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This chapter seeks to determine if can we reduce the time it takes to deliver a public health or healthcare service, such as the long waiting times in emergency departments, long waiting lists for under-supported services such as drug rehabilitation, and vast periods of uncertainty for scarce commodities such as organ transplants. How can we minimize the time it takes to provide people with the services they need? Embedded in this question is the problem of making strategic decisions about distributing our resources. Should we invest in that new resource, or is our money better spent on someth

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23

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Network growth algorithms. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0008.

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Growth processes are a fundamentally different approach compared to probability-driven exponential models covered in earlier chapters. This chapter studies how growth rules can be designed to mimic processes observed in the real world, and how the process can be mathematically analyzed in order to obtain information about the likely topological properties of the resulting networks. The configuration (stub joining) model is described, including a careful discussion of how bias can be introduced if backtracking is used instead of restarting if stubs join to form a self or double link. The second

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24

Birch, Jonathan. Hamilton’s Rule as an Organizing Framework. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198733058.003.0002.

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Queller’s version of Hamilton’s rule (HRG), derived from the Price equation, states that the mean breeding value for a social character increases if and only if rb > c, where r is the coefficient of relatedness between social partners, b is the benefit conferred on recipients, and c is the cost incurred by actors. The value of HRG lies in its ability to provide an organizing framework for social evolution theory, helping us to interpret, classify, and compare more detailed models of particular scenarios. HRG does this by allowing us to classify causal explanations of positive change by thei

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25

Deruelle, Nathalie, and Jean-Philippe Uzan. Newtonian cosmology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0016.

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This chapter discusses the construction of models of the universe, which is ambiguous in Newtonian theory. It presents some results recovered within the framework of general relativity, which in addition makes it possible to lay the foundation of the theory of the formation of large-scale structures in the universe such as galaxies and galactic clusters. The chapter first constructs models of an expanding sphere. If galaxies are treated as the particles of a uniform cloud which is spherically symmetric about the origin of an inertial frame, then these models describe a universe which expands a

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26

Williamson, Timothy. Suppose and Tell. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198860662.001.0001.

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The book argues that our use of conditionals is governed by imperfectly reliable heuristics, in the psychological sense of fast and frugal (or quick and dirty) ways of assessing them. The primary heuristic is this: to assess ‘If A, C’, suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’. This heuristic yields both the equation of the probability of ‘If A, C’ with the conditional probability of C on A and standard natural deduction rules for the conditional. However, t

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27

Walsh, Bruce, and Michael Lynch. Associative Effects: Competition, Social Interactions, Group and Kin Selection. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0022.

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The phenotypes of those individuals with which an focal individual interacts often influences the trait value in the focal individual. Maternal effects is a classic example of this phenomena, as is fitness. If these traits are heritable, then the selection response depends on both the change in the direct effects influencing a target trait and the associative effects contributed by interacting individuals. In such a setting, the breeder's equation no longer holds, as the problem is now a multiple trait one. This chapter examines the theory of response under models with both direct and associat

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28

Glazov, M. M. Dynamical Nuclear Polarization. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198807308.003.0005.

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The transfer of nonequilibrium spin polarization between the electron and nuclear subsystems is studied in detail. Usually, a thermal orientation of nuclei in magnetic field is negligible due to their small magnetic moments, but if electron spins are optically oriented, efficient nuclear spin polarization can occur. The microscopic approach to the dynamical nuclear polarization effect based on the kinetic equation method, along with a phenomenological but very powerful description of dynamical nuclear polarization in terms of the nuclear spin temperature concept is given. In this way, one can

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29

Aspell, Luke. Shivers. Liverpool University Press, 2019. http://dx.doi.org/10.3828/liverpool/9781911325970.001.0001.

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Shivers (1975) was David Cronenberg's first commercial feature and his first horror film. In a modern apartment block, a scientific project to unleash the id results in the equation of passion with contagion and predation. Because the writer-director's imaginative landscape arrived in the genre fully formed, the unique forms of this début have often been overlooked or mistaken for shortcomings. Cronenberg's most comedic film until Map to the Stars, Shivers is also his most spectacularly unnerving, throwing more images of extreme behavior at us than any of his subsequent films; it remains, with

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30

Githire, Njeri. Cannibal Love. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038785.003.0002.

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This chapter examines the juxtaposition of cannibalism and sexual appetites in Maryse Condé's Histoire de la femme cannibale (hereinafter referred to as Story, reflecting the 2007 English translation) and Andrea Levy's Small Island (2004). It argues that while the ideologically fraught figure of the cannibal has long offered a fertile ground on which to construct a counter-hegemonic aesthetic of Caribbean discourses, few if any writers explore the equation between two major constructs—the sexual and alimentary transgressions—that define the cannibal. Story and Small Island evidence that (post)

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31

Boucher, David. Hobbes among the Classic Jurists. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198817215.003.0005.

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The classic foundational status that Hobbes has been afforded by contemporary international relations theorists is largely the work of Hans Morgenthau, Martin Wight, and Hedley Bull. They were not unaware that they were to some extent creating a convenient fiction, an emblematic realist, a shorthand for all of the features encapsulated in the term. The detachment of international law from the law of nature by nineteenth-century positivists opened Hobbes up, even among international jurists, to be portrayed as almost exclusively a mechanistic theorist of absolute state sovereignty. If we are to

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32

Kirchman, David L. Microbial growth, biomass production, and controls. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789406.003.0008.

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Soon after the discovery that bacteria are abundant in natural environments, the question arose as to whether or not they were active. Although the plate count method suggested that they were dormant if not dead, other methods indicated that a large fraction of bacteria and fungi are active, as discussed in this chapter. It goes on to discuss fundamental equations for exponential growth and logistic growth, and it describes phases of growth in batch cultures, continuous cultures, and chemostats. In contrast with measuring growth in laboratory cultures, it is difficult to measure in natural env

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33

Çidam, Çiğdem. In the Street. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780190071684.001.0001.

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The 2010s were a decade of protests, and if the initial few months of 2020 are any indication, various forms of street politics, including spontaneous protests, demonstrations, acts of civil disobedience, and occupations are here to stay. Yet, contemporary discussions on the democratic significance of such events remain limited to questions of success and failure and the relative virtues of spontaneity and organization. In the Street: Democratic Action, Theatricality, and Political Friendship moves beyond these limited and limiting debates by breaking the hold of a deeply engrained way of thin

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34

Pool, Robert. Beyond Engineering. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195107722.001.0001.

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We have long recognized technology as a driving force behind much historical and cultural change. The invention of the printing press initiated the Reformation. The development of the compass ushered in the Age of Exploration and the discovery of the New World. The cotton gin created the conditions that led to the Civil War. Now, in Beyond Engineering, science writer Robert Pool turns the question around to examine how society shapes technology. Drawing on such disparate fields as history, economics, risk analysis, management science, sociology, and psychology, Pool illuminates the complex, of

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