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Books on the topic 'Dimension theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Mill, J. van. Infinite-dimensional topology: Prerequisites and introduction. Amsterdam: North-Holland, 1989.

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2

Zohuri, Bahman. Dimensional Analysis Beyond the Pi Theorem. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-45726-0.

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3

Zeeman, Christopher. Three-dimensional theorems for schools. Leicester: Mathematical Association, 2005.

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4

B, Pesin Ya. Dimension theory in dynamical systems: Contemporary views and applications. Chicago: University of Chicago Press, 1997.

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5

Polanyi, Michael. The tacit dimension. Chicago: The University of Chicago Press, 2009.

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6

Munier, Roger. La dimension d'inconnu. Paris: José Corti, 1998.

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7

Mill, J. van. The infinite-dimensional topology of function spaces. Amsterdam: Elsevier, 2001.

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8

Farias, Domenico. Dimensioni dell'uomo. 2nd ed. Soveria Mannelli (Catanzaro): Rubbettino, 1996.

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9

1931-, Nishiura Togo, ed. Dimension and extensions. Amsterdam: North Holland, 1993.

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10

Jacob, Sonnenschein, ed. Non-perturbative field theory: From two dimensional conformal field theory to QCD in four dimensions. New York: Cambridge University Press, 2009.

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11

Buhren, Frank. Dimensionen einer kritischen Theorie des Subjekts. Berlin: WVB, Wissenschaftlicher Verlag Berlin, 2012.

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12

New dimension of human knowledge. Kolkata: Raktakarabee, 2012.

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13

The hyperbolization theorem for fibered 3-manifolds. Providence, R.I: American Mathematical Society, 2001.

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14

Coloring theories. Providence, R.I: American Mathematical Society, 1989.

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15

Rucker, Rudy v. B. ha- Memad ha-reviʻi: Siyur mudrakh ba-yeḳumim ha-gevohim. Yerushalayim: Hotsaʾat sefarim ʻa. sh. Y.L. Magnes, ha-Universiṭah ha-ʻIvrit, 1999.

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16

Rucker, Rudy v. B. The fourth dimension: [and how to get there]. Harmondsworth: Penguin, 1986.

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17

Braid and knot theory in dimension four. Providence, RI: American Mathematical Society, 2002.

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18

Conformally invariant quantum field theories in two dimensions. Singapore: World Scientific, 1995.

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19

Quantum physics in one dimension. Oxford: Clarendon, 2004.

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20

Epistemic dimensions of personhood. New York: Oxford University Press Inc., 2008.

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21

Breidbach, Olaf. Deutungen: Zur philosophischen Dimension der internen Repräsentation. Weilerswist: Velbrück Wissenschaft, 2001.

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22

Breidbach, Olaf. Deutungen: Zur philosophischen Dimension der internen Repräsentation. Weilerswist: Velbrück Wissenschaft, 2001.

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23

1947-, Schechtman Gideon, ed. Asymptotic theory of finite dimensional normed spaces. Berlin: Springer-Verlag, 1986.

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24

Milman, Vitali D. Asymptotic theory of finite dimensional normed spaces. 2nd ed. Berlin: Springer, 2001.

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25

Prondczynsky, Andreas von. Pädagogik und Poiesis: Eine verdrängte Dimension des Theorie-Praxis-Verhältnisses. Opladen: Leske + Budrich, 1993.

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26

Yoccoz, Jean-Christophe. Petits diviseurs en dimension 1. Paris: Société mathématique de France, 1995.

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27

Lipscomb, Stephen. Fractals and universal spaces in dimension theory. New York, NY: Springer, 2009.

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28

Wege zur Globalisierung: Theorien-Chancen-Aporien-praktische Dimensionen. Nordhausen: Bautz, 2010.

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29

Morandi, Giuseppe, Pasquale Sodano, Arturo Tagliacozzo, and Valerio Tognetti, eds. Field Theories for Low-Dimensional Condensed Matter Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04273-1.

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30

1947-, Oystaeyen F. van, ed. Dimensions of ring theory. Dordrecht, Holland: D. Reidel Pub. Co., 1987.

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31

Kapit︠s︡a, S. P. (Sergeĭ Petrovich), 1928-2012, ed. Fraktalʹnai︠a︡ logika. Moskva: "Progress-tradit︠s︡ii︠a︡", 2002.

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32

O, Gustavo N. Rubiano. Fractales para profanos. Bogotá, D.C: Universidad Nacional de Colombia, 2000.

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33

Eberlein, Ernst. High Dimensional Probability. Basel: Birkhäuser Basel, 1998.

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34

Fractals and universal spaces in dimension theory. New York, NY: Springer, 2009.

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35

Systemic yoyos: Some impacts of the second dimension. Boca Raton: Auerbach Publications, 2008.

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36

Dimension and recurrence in hyperbolic dynamics. Basel: Birkhäuser, 2008.

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37

Harold, Simmons, ed. Derivatives, nuclei, and dimensions on the frame of torsion theories. Harlow, Essex, England: Longman Scientific & Technical, 1988.

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38

Beyond "justification": Dimensions of epistemic evaluation. Ithaca, NY: Cornell University Press, 2004.

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39

Dimensions, embeddings, and attractors. Cambridge: Cambridge University Press, 2011.

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40

One-dimensional stable distributions. Provindence, R.I: American Mathematical Society, 1986.

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41

Escudier, Marcel. Units of measurement, dimensions, and dimensional analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0003.

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In this chapter the crucial role of units and dimensions in the analysis of any problem involving physical quantities is explained. The International System of Units (SI) is introduced. The major advantage of collecting the physical quantities, which are included in either a theoretical analysis or an experiment, into non-dimensional groups is shown to be a reduction in the number of quantities which need to be considered separately. This process, known as dimensional analysis, is based upon the principle of dimensional homogeneity. Buckingham’s Π‎ theorem is introduced as a method for determining the number of non-dimensional groups (the Π‎’s) corresponding with a set of dimensional quantities and their dimensions. A systematic and simple procedure for identifying these groups is the sequential elimination of dimensions. The scale-up from a model to a geometrically similar full-size version is shown to require dynamic similarity. The definitions and names of the non-dimensional groups most frequently encountered in fluid mechanics have been introduced and their physical significance explained.

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42

Witten, Edward. Two Lectures on the Jones Polynomial and Khovanov Homology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198784913.003.0001.

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In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable q is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.

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43

Zohuri, Bahman. Dimensional Analysis Beyond the Pi Theorem. Springer, 2018.

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44

Cataldo, Mark Andrea de, Luca Migliorini Lectures 4–5, and Mark Andrea de Cataldo. The Hodge Theory of Maps. 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/9780691161341.003.0006.

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This chapter showcases two further lectures on the Hodge theory of maps, and they are mostly composed of exercises. The first lecture details a minimalist approach to sheaf cohomology, and then turns to the intersection cohomology complex, which is limited to the definition and calculation of the intersection complex Isubscript X of a variety of dimension d with one isolated singularity. Finally, this lecture discusses the Verdier duality. The second lecture sets out the Decomposition theorem, which is the deepest known fact concerning the homology of algebraic varieties. It then considers the relative hard Lefschetz and the hard Lefschetz for intersection cohomology groups.

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45

Neta, Ram. Causal Theories of Knowledge and Perception. Edited by Helen Beebee, Christopher Hitchcock, and Peter Menzies. Oxford University Press, 2010. http://dx.doi.org/10.1093/oxfordhb/9780199279739.003.0028.

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This article first surveys those ‘causal theories of perception’ that attempt to explain what it is for someone to perceive an external thing. Then it surveys the other ‘causal theories of perception’ (or alternatively, ‘causal theories of knowledge’) that attempt to explain what it is for someone to know about external things by means of perception. Within each of these two topics, we can locate all the various causal theories on a two-dimensional map: along one dimension are the various things that have been taken to do the causing, and along the other dimension are the various things that have been taken to be thus caused.

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46

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Quadratic Forms over a ∈ Local Field. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0007.

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This chapter presents various results about quadratic forms over a field complete with respect to a discrete valuation. The discussion is based on the assumption that K is a field of arbitrary characteristic which is complete with respect to a discrete valuation ν‎ and uses the usual convention that ν‎(0) = infinity. The chapter starts with a notation regarding the ring of integers of K and the natural map from it to the residue field, followed by a number of propositions regarding an anisotropic quadratic space. These include an anisotropic quadratic space with residual quadratic spaces, an unramified quadratic space of finite dimension, unramified finite-dimensional anisotropic quadratic forms over K, unramified anisotropic quadratic forms and a bilinear form, and a round quadratic space over K. The chapter concludes with a theorem that there exists an anisotropic quadratic form over K, unique up to isometry, and is non-singular.

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47

Charalambous, Michael G. Dimension Theory: A Selection of Theorems and Counterexamples. Springer, 2019.

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48

Altruismus: Dimensionen – Theorien – Formen. J.B. Metzler, 2020.

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49

Carlson, James. Period Domains and Period Mappings. 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/9780691161341.003.0004.

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This chapter seeks to develop a working understanding of the notions of period domain and period mapping, as well as familiarity with basic examples thereof. It first reviews the notion of a polarized Hodge structure H of weight n over the integers, for which the motivating example is the primitive cohomology in dimension n of a projective algebraic manifold of the same dimension. Next, the chapter presents lectures on period domains and monodromy, as well as elliptic curves. Hereafter, the chapter provides an example of period mappings, before considering Hodge structures of weight. After expounding on Poincaré residues, this chapter establishes some properties of the period mapping for hypersurfaces and the Jacobian ideal and the local Torelli theorem. Finally, the chapter studies the distance-decreasing properties and integral manifolds of the horizontal distribution.

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50

Andersen, Robert N. Homotopy construction techniques applied to the cell like dimension raising problem and to higher dimensional dunce hats. 1990.

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