Books: 'Equivalence theorem'

1

Rustichini, Aldo. Commodity pair desirability and the core equivalence theorem. Champaign: University of Illinois at Urbana-Champaign, 1991.

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2

Greenberg, Joseph. A simple proof of the equivalence theorem for oligopolistic mixed markets. Stanford, Calif: Institute for Mathematical Studies in the Social Sciences, Stanford University, 1986.

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3

Restricted orbit equivalence. Providence, R.I., USA: American Mathematical Society, 1985.

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4

Kechris, A. S. Topics in orbit equivalence. Berlin: Springer, 2004.

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5

Hjorth, Greg. Classification and orbit equivalence relations. Providence, RI: American Mathematical Society, 2000.

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6

Borel equivalence relations: Structure and classification. Providence, R.I: American Mathematical Society, 2008.

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7

Pemberton, James. Growth, inequality, fairness, and Ricardian equivalence. Reading, England: University of Reading, Dept. of Economics, 1992.

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8

Pemberton, James. Growth, inequality, fairness, and Ricardian Equivalence. Reading: University of Reading. Department of Economics, 1992.

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9

Shankar, Rashmi. Distinguishing between observationally equivalent theories of crises. Washington, D.C: Office of the Chief Economist, Latin America and the Caribbean Region, World Bank, 2002.

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10

Hjorth, Greg. Rigidity theorems for actions of product groups and countable Borel equivalence relations. Providence, RI: American Mathematical Society, 2005.

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11

Bozzolo, Guillermo. Equivalent Crystal Theory of alloys. Cleveland, Ohio: Lewis Research Center, 1991.

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12

1975-, Sigurdsson J., ed. Parametrized homotopy theory. Providence, R.I: American Mathematical Society, 2006.

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13

G, Sushkov B., ed. Preobrazovanie logicheskikh funkt͡siĭ na klasse ėkvivalentnykh dvoichnykh derevʹev. Moskva: Vychislitelʹnyĭ t͡sentr AN SSSR, 1986.

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14

The mapping class group from the viewpoint of measure equivalence theory. Providence, R.I: American Mathematical Society, 2008.

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15

Equivalences of classifying spaces completed at the prime two. Providence, R.I: American Mathematical Society, 2006.

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16

Schulz, E. Matthew. Grade equivalent and IRT representations of growth. Iowa City, Iowa: ACT, Inc., 1997.

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17

Fulman, Igor. Crossed products of von Neumann algebras by equivalence relations and their subalgebras. Providence, R.I: American Mathematical Society, 1997.

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18

Derigs, Ulrich. Programming in networks and graphs: On the combinatorial background and near-equivalence of network flow and matching algorithms. Berlin: Springer-Verlag, 1988.

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19

Dudek, Hanna. Skale ekwiwalentności-- estymacja na podstawie kompletnych modeli popytu: Equivalence scales--estimation on the base of complete demand systems. Warszawa: Wydawnictwo SGGW, 2011.

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20

Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines. Providence, R.I: American Mathematical Society, 2004.

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21

Hrushovski, Ehud, and François Loeser. An equivalence of categories. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0013.

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This chapter deduces from Theorem 11.1.1 an equivalence of categories between a certain homotopy category of definable subsets of quasi-projective varieties over a given valued field and a suitable homotopy category of definable spaces over the o-minimal Γ‎. The chapter introduces three categories that can be viewed as ind-pro definable and admit natural functors to the category TOP of topological spaces with continuous maps. The discussion is often limited to the subcategory consisting of A-definable objects and morphisms. The morphisms are factored out by (strong) homotopy equivalence. The chapter presents the proof of the equivalence of categories before concluding with remarks on homotopies over imaginary base sets.

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22

Caramello, Olivia. A duality theorem. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0005.

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This chapter presents a duality theorem providing, for each geometric theory, a natural bijection between its geometric theory extensions (also called ‘quotients’) and the subtoposes of its classifying topos. Two different proofs of this theorem are provided, one relying on the theory of classifying toposes and the other, of purely syntactic nature, based on a proof-theoretic interpretation of the notion of Grothendieck topology. Via this interpretation the theorem can be reformulated as a proof-theoretic equivalence between the classical system of geometric logic over a given geometric theory and a suitable proof system whose rules correspond to the axioms defining the notion of Grothendieck topology. The role of this duality as a means for shedding light on axiomatization problems for geometric theories is thoroughly discussed, and a deduction theorem for geometric logic is derived from it.

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23

Blaha, Stephen. The Equivalence of Elementary Particle Theories and Computer Languages: Quantum Computers, Turing Machines, Standard Model, Superstring Theory, and a Proof that Godel's Theorem Implies Nature Must Be Quantum. Pingree-Hill Publishing, 2005.

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24

Voisin, Claire. Decomposition of the Diagonal. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160504.003.0003.

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This chapter explains the method initiated by Bloch and Srinivas, which leads to statements of the following: if a smooth projective variety has trivial Chow groups of k-cycles homologous to 0 for k ≤ c − 1, then its transcendental cohomology has geometric coniveau ≤ c. This result is a vast generalization of Mumford's theorem. A major open problem is the converse of this result. It turns out that statements of this kind are a consequence of a general spreading principle for rational equivalence. Consider a smooth projective family X → B and a cycle Z → B, everything defined over C; then, if at the very general point b ∈ B, the restricted cycle Z𝒳b ⊂ X𝒳b is rationally equivalent to 0, there exist a dense Zariski open set U ⊂ B and an integer N such that NZsubscript U is rationally equivalent to 0 on Xsubscript U.

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25

Baker, David John. The Philosophy of Quantum Field Theory. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199935314.013.33.

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This is an opinionated survey of some interpretive puzzles in quantum field theory. The problem of inequivalent representations is sketched, including its connections with competing accounts of physical equivalence. The controversy between variant formulations of the theory, algebraic versus Lagrangian, is given a conciliatory resolution. Arguments against particles are addressed, demarcating clearly between different forms of particle interpretation. Field interpretations are then considered, including wavefunctional, spacetime state realist and Heisenberg operator realist interpretations. Ruetsche’s coalesced structure interpretation is presented and juxtaposed with an alternative, more traditional view of the theory’s laws and state space. Finally, the CPT theorem is discussed, together with its implications about the nature of spacetime.

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26

Hrushovski, Ehud, and François Loeser. Definable compactness. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0004.

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This chapter describes the notion of definable compactness for subsets of unit vector V. One of the main results is Theorem 4.2.20, which establishes the equivalence between being definably compact and being closed and bounded. The chapter gives a general definition of definable compactness that may be useful when the definable topology has enough definable types. The o-minimal formulation regarding limits of curves is replaced by limits of definable types. The chapter relates definable compactness to being closed and bounded and shows that the expected properties hold. In particular, the image of a definably compact set under a continuous definable map is definably compact.

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27

Deruelle, Nathalie, and Jean-Philippe Uzan. The equivalence principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0041.

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This chapter recalls several relevant aspects of Newton’s theory of gravity, as well as Maxwell’s theory of electromagnetism, to describe the conceptual path that Albert Einstein followed in going from the theory of special relativity to general relativity. Looking at 1907 and beyond, the chapter shows that the ambition of Einstein was to construct a theory in which all reference frames (and therefore none) were privileged. Moreover, there were no longer any inertial forces, no ordering of Newton’s absolute space. Therefore, Einstein’s theory was one in which the laws of physics had the same form in all frames, inertial or not, so that no frame could be regarded as being privileged. In brief, he sought a theory of general relativity.

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28

Abbes, Ahmed, and Michel Gros. Representations of the fundamental group and the torsor of deformations. Local study. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.003.0002.

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This chapter focuses on representations of the fundamental group and the torsor of deformations. It considers the case of an affine scheme of a particular type, qualified also as small by Faltings. It introduces the notion of Dolbeault generalized representation and the companion notion of solvable Higgs module, and then constructs a natural equivalence between these two categories. It proves that this approach generalizes simultaneously Faltings' construction for small generalized representations and Hyodo's theory of p-adic variations of Hodge–Tate structures. The discussion covers the relevant notation and conventions, results on continuous cohomology of profinite groups, objects with group actions, logarithmic geometry lexicon, Faltings' almost purity theorem, Faltings extension, Galois cohomology, Fontaine p-adic infinitesimal thickenings, Higgs–Tate torsors and algebras, Dolbeault representations, and small representations. The chapter also describes the descent of small representations and applications and concludes with an analysis of Hodge–Tate representations.

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29

Weatherall, James Owen. Category Theory and the Foundations of Classical Space–Time Theories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0013.

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I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang–Mills theories. In particular, the chapter explains how the Baez–Bartel–Dolan framework for classifying forgetful functors provides a precise way of saying when one formulation of a physical theory posits more or less structure than another, and also when two theories posit equivalent amounts of structure.

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30

Back, Kerry E. Information, Strategic Trading, and Liquidity. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0024.

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The chapter describes some asymmetric information models of liquidity. In these models, trades move prices because of the possibility that the trades are based on information not known to the market. A strategic trader is one who takes into consideration that her trades move prices. The chapter describes the Glosten‐Milgrom model of the bidask spread, the Kyle model of market depth, the Glosten model of limit‐order markets, and models of auctions. Except for the auction models, prices are set in these models by uninformed market makers who face adverse selection from informed traders. In the auction models, prices are set by informed individuals bidding against one another. The winner’s curse, the revenue equivalence theorem, and related aspects of auctions are explained.

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31

Hrushovski, Ehud, and François Loeser. Applications to the topology of Berkovich spaces. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0014.

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This chapter presents various applications to the topology of classical Berkovich spaces. It deduces from the main theorem several new results on the topology of V(superscript an) which were not known previously in such a level of generality. In particular, it shows that V(superscript an) admits a strong deformation retraction to a subspace homeomorphic to a finite simplicial complex and that V(superscript an) is locally contractible. The chapter also proves the existence of strong retractions to skeleta for analytifications of definable subsets of quasi-projective varieties and goes on to prove finiteness of homotopy types in families in a strong sense and a result on homotopy equivalence of upper level sets of definable functions. Finally, it describes an injection in the opposite direction (over an algebraically closed field) which in general provides an identification between points of Berkovich analytifications and Galois orbits of stably dominated points.

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32

Restricted Orbit Equivalence of Discrete Amenable Groups. Cambridge University Press, 2002.

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33

Shankar, Rashmi. Distinguishing between Observationally Equivalent Theories of Crises. The World Bank, 2002. http://dx.doi.org/10.1596/1813-9450-2926.

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34

Mashhoon, Bahram. Introduction. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0001.

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This introductory chapter is mainly about the locality postulate of the standard relativity theory. The fundamental laws of microphysics have been formulated with respect to inertial observers. However, inertial observers do not in fact exist, since actual observers are accelerated. What do accelerated observers measure? Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. That is, an accelerated observer at each instant is equivalent to an otherwise identical momentarily comoving inertial observer. This hypothesis of locality, which underlies the special and general theories of relativity, is described in detail. The locality postulate fits perfectly together with Einstein’s local principle of equivalence to ensure that every observer in a gravitational field is pointwise inertial. When coupled with the hypothesis of locality, Einstein’s principle of equivalence provides a physical basis for a field theory of gravitation that is consistent with local Lorentz invariance.

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35

Koff, Caroline Nan. A specialized ATMS for equivalence relations. 1988.

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36

Huybrechts, D. Abelian Varieties. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0009.

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Historically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this chapter functions as a reminder of the basic facts from the rich theory of abelian varieties, and the case of principally polarized abelian varieties is studied. A general investigation of derived equivalences between abelian varieties and derived autoequivalences of a single abelian variety is included.

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37

Automorphisms and Equivalence Relations in Topological Dynamics. Cambridge University Press, 2014.

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38

Nancy, Jean-Luc. After Fukushima: The Equivalence of Catastrophes. Fordham University Press, 2014.

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39

Mandell, Charlotte, and Jean-Luc Nancy. After Fukushima: The Equivalence of Catastrophes. Fordham University Press, 2014.

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40

Mandell, Charlotte, and Jean-Luc Nancy. After Fukushima: The Equivalence of Catastrophes. Fordham University Press, 2014.

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41

Young, Michael, and Tim Blackwell. Live Algorithms for Music. Edited by Benjamin Piekut and George E. Lewis. Oxford University Press, 2013. http://dx.doi.org/10.1093/oxfordhb/9780199892921.013.002.

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Live algorithms are an ideal concept: computational systems able to collaborate proactively with humans in the creation of group-based improvised music. The challenge is to achieve equivalence between human and computer collaborators, both in formal terms and in practice (evident to both performers and audience alike). The fundamental question is the capacity for computational processes to exhibit “creativity.” The problems inherent in computer music performance are considered, in which computers are quasi-instruments or act in proxy for another musician. Theories from social psychology and pragmatics are explored to help understand live music-making as a special case of social organization; namely, Kelley’s covariation model of Attribution Theory and Grice’s Maxims of Cooperation. This chapter outlines a description of how human beings and computers might engage on an equivalent basis and proposes how social psychology theories, rendered in formal language, can point to new horizons in human-computer performance practice.

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42

Gilbert, Margaret. Contemporary Rights Theories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198813767.003.0006.

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The most influential theories of claims within contemporary rights theory are considered in relation to the demand-right problem. Starting with Hohfeld’s equivalence, contemporary theorists generally aim for an account of claims such that the members of a certain canonical set of claim-ascriptions are true. In pursuit of this aim they tend to focus on directed duties and to assume that these are in part constituted by plain duties. Reviewing the results obtained by adopting this aim and method, this chapter argues that in order to solve the demand-right problem we need to go beyond the resources of Thomson’s constraint theory, Joseph Raz’s “interest” theory, and similar views. The same goes for Hart’s “choice” theory and related positions, and several other approaches more briefly considered.

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43

Caramello, Olivia. Some Applications. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0012.

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This chapter describes some applications of the theory developed in the previous chapters in a variety of different mathematical contexts. The main methodology used to generate such applications is the ‘bridge technique’ presented in Chapter 2. The discussed topics include restrictions of Morita equivalences to quotients of the two theories involved, give a solution to a prozblem of Lawvere concerning the boundary operator on subtoposes, establish syntax-semantics ‘bridges’ for quotients of theories of presheaf type, present topos-theoretic interpretations and generalizations of Fraïssé’s theorem in model theory on countably categorical theories and of topological Galois theory, develop a notion of maximal spectrum of a commutative ring with unit and investigate compactness conditions for geometric theories allowing one to identify theories lying in smaller fragments of geometric logic.

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44

Argunov, B. I., V. G. Shervatov, L. A. Skornyakov, and V. G. Boltyanskii. Hyperbolic Functions: With Configuration Theorems and Equivalent and Equidecomposable Figures (Dover Science Books). Dover Publications, 2007.

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45

Zein, Fouad El, and Loring W. Tu. From Sheaf Cohomology to the Algebraic de Rham Theorem. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0002.

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This chapter proves Grothendieck's algebraic de Rham theorem. It first proves Grothendieck's algebraic de Rham theorem more or less from scratch for a smooth complex projective variety X, namely, that there is an isomorphism H*(Xₐₙ,ℂ) ≃ H*X,Ω‎subscript alg superscript bullet) between the complex singular cohomology of Xan and the hypercohomology of the complex Ω‎subscript alg superscript bullet of sheaves of algebraic differential forms on X. The proof necessitates a discussion of sheaf cohomology, coherent sheaves, and hypercohomology. The chapter then develops more machinery, mainly the Čech cohomology of a sheaf and the Čech cohomology of a complex of sheaves, as tools for computing hypercohomology. The chapter thus proves that the general case of Grothendieck's theorem is equivalent to the affine case.

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46

Caramello, Olivia. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0002.

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This book is devoted to a general study of geometric theories through the associated classifying toposes.A central theme of the book is a duality, established in Chapter 3, between the subtoposes of the classifying topos of a geometric theory T over a signature ∑ and the (syntactic-equivalence classes of) ‘quotients’ of the theory ...

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47

Caramello, Olivia. Classifying toposes and the ‘bridge’ technique. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0004.

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This chapter consists of two parts. The first part reviews the fundamental notion of classifying topos of a geometric theory and discusses the appropriate kinds of interpretations between theories which induce morphisms between the associated classifying toposes; the theoretical presentation is accompanied by a few concrete examples of classifying toposes of theories naturally arising in mathematics. A characterization theorem for universal models of geometric theories inside classifying toposes is also established. The second part presents the general unifying technique ‘toposes as bridges’. This technique, which allows one to extract ‘concrete’ information from the existence of different representations for the classifying topos of a geometric theory, is systematically exploited in the course of the book to establish theoretical results as well as applications. The ‘decks’ of topos-theoretic ‘bridges’ are normally given by Morita equivalences, while the ‘arches’ are given by site characterizations of topos-theoretic invariants.

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48

Weekly Reader Early Learning Library (Firm), ed. I know same and different. Milwaukee: Weekly Reader Early Learning Library, 2006.

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49

I Know Same And Different (I'm Ready for Math). Gareth Stevens Publishing, 2005.

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50

Saussy, Haun. Death and Translation. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198812531.003.0003.

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The first translation of a Baudelaire poem into Chinese, a 1924 version of “A Carcass” by Xu Zhimo, offers an example of creative adaptation in translation: in his version and preface Xu assimilates Baudelaire to the early Daoist philosopher Zhuangzi. This is a strange choice on general grounds, but reflects the translator’s strategy of creating a recognizable identity for the Flowers of Evil, and for modernist poetics generally, within the world of Chinese thought. Furthermore, the content of Baudelaire’s poem, the changes made to it in Xu’s translation, and the relationship Xu devises with the works of Zhuangzi together outline a different theory of translation: not the creation of equivalents, but the chewing, digestion, and assimilation of a previous text, whether native or foreign, as part of the life-process of a literary tradition. Xu’s version of “A Carcass” enacts what Baudelaire’s poem describes, thereby displacing the ground of translational equivalence.

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Books on the topic 'Equivalence theorem'

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