Relevant bibliographies by topics / Dimension theorem

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Dimension theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Dimension theorem"

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FENG, ZHIGANG, and GANG CHEN. "ON THE MINKOWSKI DIMENSION OF FUNCTIONAL DIGRAPH." Fractals 11, no. 01 (March 2003): 87–92. http://dx.doi.org/10.1142/s0218348x03001616.

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Functional digraphs are sometimes fractal sets. As a special kind of fractal sets, the dimension properties of the functional digraph are studied in this paper. Firstly, the proof of a Minkowski dimension theorem is discussed and a new proof is given. Secondly, according to this dimension theorem, the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions are discussed. And the relations between these Minkowski dimensions and the Minkowski dimensions of the digraphs of the two functions are established. In the conclusion, the maximum Minkowski dimension of the two functional digraphs plays a decisive part in the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions.
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LIMA, YURI, and CARLOS GUSTAVO MOREIRA. "A Marstrand Theorem for Subsets of Integers." Combinatorics, Probability and Computing 23, no. 1 (October 25, 2013): 116–34. http://dx.doi.org/10.1017/s0963548313000461.

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We propose a counting dimension for subsets of $\mathbb{Z}$ and prove that, under certain conditions on E,F ⊂ $\mathbb{Z}$, for Lebesgue almost every λ ∈ $\mathbb{R}$ the counting dimension of E + ⌊λF⌋ is at least the minimum between 1 and the sum of the counting dimensions of E and F. Furthermore, if the sum of the counting dimensions of E and F is larger than 1, then E + ⌊λF⌋ has positive upper Banach density for Lebesgue almost every λ ∈ $\mathbb{R}$. The result has direct consequences when E,F are arithmetic sets, e.g., the integer values of a polynomial with integer coefficients.
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Zhang, N. L., and T. Kocka. "Effective Dimensions of Hierarchical Latent Class Models." Journal of Artificial Intelligence Research 21 (January 1, 2004): 1–17. http://dx.doi.org/10.1613/jair.1311.

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Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and Bayesian networks with latent nodes in general. Nonetheless, empirical studies suggest that the BIC score is a reasonable criterion to use in practice for learning HLC models. Empirical studies also suggest that sometimes model selection can be improved if standard model dimension is replaced with effective model dimension in the penalty term of the BIC score. Effective dimensions are difficult to compute. In this paper, we prove a theorem that relates the effective dimension of an HLC model to the effective dimensions of a number of latent class models. The theorem makes it computationally feasible to compute the effective dimensions of large HLC models. The theorem can also be used to compute the effective dimensions of general tree models.
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GHOSHAL, DEBASHIS, and SUDIPTA MUKHERJI. "NO GHOST THEOREM AND COHOMOLOGY THEOREM FOR STRINGS IN ARBITRARY STATIC BACKGROUNDS." Modern Physics Letters A 06, no. 10 (March 28, 1991): 939–47. http://dx.doi.org/10.1142/s0217732391000981.

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We consider a string moving in an arbitrary time-independent background given by an arbitrary conformal field theory of appropriate central charge (e.g., c=25 for bosonic string) and one flat time-like dimension. We show that the physical subspace of the Hilbert space is positive semi-definite (no ghost theorem) and that the cohomology of the BRST operator is trivial except for the ghost number one (for open bosonic string) sector (cohomology theorem). Both the proofs are reductio ad absurdum proofs based on the corresponding theorems for the strings moving in flat background. In cases where there is an extra flat space-like dimension (besides the flat time-like one), the transverse subspace with positive-definite norm can be constructed.
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Temur, Faruk. "A quantitative Balian–Low theorem for higher dimensions." Georgian Mathematical Journal 27, no. 3 (September 1, 2020): 469–77. http://dx.doi.org/10.1515/gmj-2018-0046.

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AbstractWe extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is possible.
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PANTILIE, RADU. "Harmonic morphisms with one-dimensional fibres on conformally-flat Riemannian manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 1 (July 2008): 141–51. http://dx.doi.org/10.1017/s0305004108001060.

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AbstractWe classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four (Theorem 3.1), and (2) between conformally-flat Riemannian manifolds of dimensions at least three (Corollaries 3.4 and 3.6).Also, we prove (Proposition 2.5) an integrability result for any real-analytic submersion, from a constant curvature Riemannian manifold of dimensionn+2 to a Riemannian manifold of dimension 2, which can be factorised as ann-harmonic morphism with two-dimensional fibres, to a conformally-flat Riemannian manifold, followed by a horizontally conformal submersion, (n≥4).
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Duggan, John. "May’s theorem in one dimension." Journal of Theoretical Politics 29, no. 1 (July 9, 2016): 3–21. http://dx.doi.org/10.1177/0951629815603694.

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This paper provides three versions of May’s theorem on majority rule, adapted to the one-dimensional model common in formal political modeling applications. The key contribution is that single peakedness of voter preferences allows us to drop May’s restrictive positive responsiveness axiom. The simplest statement of the result holds when voter preferences are single peaked and linear (no indifferences), in which case a voting rule satisfies anonymity, neutrality, Pareto, and transitivity of weak social preference if and only if the number of individuals is odd and the rule is majority rule.
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Brodsky, N., and A. Chigogidze. "Hurewicz theorem for extension dimension." Topology and its Applications 129, no. 2 (March 2003): 145–51. http://dx.doi.org/10.1016/s0166-8641(02)00144-x.

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BONNIN, MICHELE, FERNANDO CORINTO, and MARCO GILLI. "DILIBERTO'S THEOREM IN HIGHER DIMENSION." International Journal of Bifurcation and Chaos 19, no. 02 (February 2009): 629–37. http://dx.doi.org/10.1142/s0218127409023251.

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The study of the local behavior of nonlinear systems in the neighborhood of a periodic orbit is a classical problem in nonlinear dynamics. Most of our knowledge stems from simulations or the numerical integration of the variational equation. Only in the case of planar oscillators, the solution of the variational equation can be found analytically, provided that an explicit expression for the periodic trajectory is available. The aim of this paper is to extend a classical theorem due to S. P. Diliberto to higher dimensional systems. In doing so, we show how the fundamental matrix solution to the variational equation of higher order differential equations can be obtained in a closed analytical form. To obtain this result, the knowledge of the periodic trajectory is not sufficient anymore, and a specific set of orthogonal vectors has to be determined. The analysis of some examples reveals that finding these vectors may be easier than solving the variational equations.
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Cliff, G., and B. Hartley. "Sjogren's theorem on dimension subgroups." Journal of Pure and Applied Algebra 47, no. 3 (1987): 231–42. http://dx.doi.org/10.1016/0022-4049(87)90048-x.

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Dissertations / Theses on the topic "Dimension theorem"

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Montgomery, Martin. "Dimension of certain cleft binomial rings /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874501&sid=7&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.
Typescript. Includes vita and abstract. Includes bibliographical references (leaf 77). Also available for download via the World Wide Web; free to University of Oregon users.
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Shi, Ronggang. "Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439.

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Min, Aleksey. "Limit theorems for statistical functionals with applications to dimension estimation." Doctoral thesis, [S.l.] : [s.n.], 2004. http://webdoc.sub.gwdg.de/diss/2004/min/min.pdf.

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Kalajdzievski, Damjan. "Measurability Aspects of the Compactness Theorem for Sample Compression Schemes." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23133.

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In 1998, it was proved by Ben-David and Litman that a concept space has a sample compression scheme of size $d$ if and only if every finite subspace has a sample compression scheme of size $d$. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same time measurability of the hypotheses is a necessary condition for learnability. In this thesis we discuss when a sample compression scheme, created from compression schemes on finite subspaces via the compactness theorem, have measurable hypotheses. We show that if $X$ is a standard Borel space with a $d$-maximum and universally separable concept class $\m{C}$, then $(X,\CC)$ has a sample compression scheme of size $d$ with universally Borel measurable hypotheses. Additionally we introduce a new variant of compression scheme called a copy sample compression scheme.
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Farkas, Ábel. "Dimension and measure theory of self-similar structures with no separation condition." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/7854.

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We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on non-overlapping self-similar sets to overlapping self-similar sets. We investigate how the Hausdorff dimension and measure of a self-similar set K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0. We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a self-similar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj - ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets. We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any self-similar or graph directed self-similar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `self-similar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δ-approximate packing pre-measure coincide for sufficiently small δ > 0.
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Fontes, Nuno Ricardo Moura. "Sistemas dinâmicos, análise numérica de séries temporais e aplicações às finanças." Master's thesis, Instituto Superior de Economia e Gestão, 2013. http://hdl.handle.net/10400.5/6454.

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Mestrado em Matemática Financeira
Taken's theorem (1981) shows how the series of measurements from a given system can be used to reconstruct the original system's underlying dynamic process. In this work we start from this point and build a bridge between theoretical results and its practical application. Several algorithms are presented and then rebuilt in an effort to reach a middle ground between computer resources optimization and output accuracy. Among these algorithms, the biggest emphasis is put on the correlation dimension algorithm by Grassberger and Procaccia which allows for the deduction of the system's embedding dimension. The results derived are then used to build a forecast approach inspired by the analogues method. The purpose of this work is to show there is potential for dynamical systems' modelling tools to be used in financial markets, especially for intra-day purposes where decision and computational times need to be very small.
O teorema de Takens (1981) mostra como uma série de medições obtidas de um dado sistema podem ser usadas para reconstruir o sistema dinâmico original. Neste trabalho, parte-se deste teorema e constrói-se a ponte entre conceitos teóricos e a sua aplicação numérica. Vários algoritmos são apresentados e depois reconstruídos com o objetivo de se atingir um compromisso entre otimização de recursos computacionais e rigor nos resultados. Entre esses algoritmos, a maior ênfase é colocada no do cálculo do integral de correlação de Grassberger-Procaccia que permite a dedução da dimensão de imersão de um dado sistema. Os resultados obtidos são usados na construção de um modelo de previsão inspirado pela abordagem dos pontos análogos, ou método dos análogos. O objetivo deste trabalho é mostrar que existe potencial na aplicação de ferramentas de modelação de sistemas dinâmicos caóticos no mercado financeiro, em especial em transações intra-diárias onde tempos de decisão e computação têm de ser muito reduzidos.
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Joanpere, Salvadó Meritxell. "Fractals and Computer Graphics." Thesis, Linköpings universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-68876.

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Fractal geometry is a new branch of mathematics. This report presents the tools, methods and theory required to describe this geometry. The power of Iterated Function Systems (IFS) is introduced and applied to produce fractal images or approximate complex estructures found in nature. The focus of this thesis is on how fractal geometry can be used in applications to computer graphics or to model natural objects.
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Pötzelberger, Klaus. "The General Quantization Problem for Distributions with Regular Support." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1508/1/document.pdf.

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We study the asymptotic behavior of the quantization error for general information functions and prove results for distributions P with regular support. We characterize the information functions for which the uniform distribution on the set of prototypes converges weakly to P. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
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Freire, Ageu Barbosa. "Cúbicas Reversas e Redes de Quádricas." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9275.

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In this work, we present an explicit geometric characterization for the space of quadratcs form vanishing precisely on a twisted cubic. We show that the set of degenerate quadrics lying on a net of quadrics containing a twisted cubic is described by a curve whose equation is given by the square of an irreducible conic. Conversely, if is a net of quadrics whosw intersection with the set of degenerate quadrics is a curve given by the square of an irreducible conic, we furnish conditions under which the cammon zero locus of turns out to be a twisted cubic. It is enough to require that does not contain a pair of planes.
Neste trabalho, apresentamos uma caracteriza c~ao geom etrica expl cita para o espa co das formas quadr aticas que se anulam precisamente sobre uma c ubica reversa. Mostramos que o conjunto das qu adricas degeneradas pertencentes a uma rede de qu adricas que cont em a c ubica reversa e descrita por uma curva cuja equa c~ao e dada pelo quadrado de uma c^onica irredut vel. Rec procamente, se e uma rede de qu adricas cuja interse c~ao com o conjunto das qu adricas n~ao degeneradas e uma curva dada pelo quadrado de uma c^onica irredut vel, fornecemos condi c~oes sob as quais o lugar dos zeros comuns de seja uma c ubica reversa. E su ciente que n~ao contenha um par de plano.
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Debin, Clément. "Géométrie des surfaces singulières." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM078/document.

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La recherche d'une compactification de l'ensemble des métriques Riemanniennes à singularités coniques sur une surface amène naturellement à l'étude des "surfaces à Courbure Intégrale Bornée au sens d'Alexandrov". Il s'agit d'une géométrie singulière, développée par A. Alexandrov et l'école de Leningrad dans les années 1970, et dont la caractéristique principale est de posséder une notion naturelle de courbure, qui est une mesure. Cette large classe géométrique contient toutes les surfaces "raisonnables" que l'on peut imaginer.Le résultat principal de cette thèse est un théorème de compacité pour des métriques d'Alexandrov sur une surface ; un corollaire immédiat concerne les métriques Riemanniennes à singularités coniques. On décrit dans ce manuscrit trois hypothèses adaptées aux surfaces d'Alexandrov, à la manière du théorème de compacité de Cheeger-Gromov qui concerne les variétés Riemanniennes à courbure bornée, rayon d'injectivité minoré et volume majoré. On introduit notamment la notion de rayon de contractibilité, qui joue le rôle du rayon d'injectivité dans ce cadre singulier.On s'est également attachés à étudier l'espace (de module) des métriques d'Alexandrov sur la sphère, à courbure positive le long d'une courbe fermée. Un sous-ensemble intéressant est constitué des convexes compacts du plan, recollés le long de leurs bords. A la manière de W. Thurston, C. Bavard et E. Ghys, qui ont considéré l'espace de module des polyèdres et polygones (convexes) à angles fixés, on montre que l'identification d'un convexe à sa fonction de support fait naturellement apparaître une géométrie hyperbolique de dimension infinie, dont on étudie les premières propriétés
If we look for a compactification of the space of Riemannian metrics with conical singularities on a surface, we are naturally led to study the "surfaces with Bounded Integral Curvature in the Alexandrov sense". It is a singular geometry, developed by A. Alexandrov and the Leningrad's school in the 70's, and whose main feature is to have a natural notion of curvature, which is a measure. This large geometric class contains any "reasonable" surface we may imagine.The main result of this thesis is a compactness theorem for Alexandrov metrics on a surface ; a straightforward corollary concerns Riemannian metrics with conical singularities. We describe here three hypothesis which pair with the Alexandrov surfaces, following Cheeger-Gromov's compactness theorem, which deals with Riemannian manifolds with bounded curvature, injectivity radius bounded by below and volume bounded by above. Among other things, we introduce the new notion of contractibility radius, which plays the role of the injectivity radius in this singular setting.We also study the (moduli) space of Alexandrov metrics on the sphere, with non-negative curvature along a closed curve. An interesting subset is the set of compact convex sets, glued along their boundaries. Following W. Thurston, C. Bavard and E. Ghys, who considered the moduli space of (convex) polyhedra and polygons with fixed angles, we show that the identification between a convex set and its support function give rise to an infinite dimensional hyperbolic geometry, for which we study the first properties
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Books on the topic "Dimension theorem"

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

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

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

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

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

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

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

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

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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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Book chapters on the topic "Dimension theorem"

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Charalambous, Michael G. "The Countable Sum Theorem for Covering Dimension." In Dimension Theory, 15–22. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_3.

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Charalambous, Michael G. "Failure of the Subset Theorem for Hereditarily Normal Spaces." In Dimension Theory, 155–64. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_21.

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Charalambous, Michael G. "The Mardešić Factorization Theorem and the Dimension of Metrizable Spaces." In Dimension Theory, 139–46. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_18.

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Kamada, Seiichi. "Alexander’s theorem in dimension four." In Mathematical Surveys and Monographs, 179–82. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/surv/095/24.

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Kamada, Seiichi. "Markov’s theorem in dimension four." In Mathematical Surveys and Monographs, 187–90. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/surv/095/26.

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Charalambous, Michael G. "No Finite Sum Theorem for the Small Inductive Dimension of Metrizable Spaces." In Dimension Theory, 153–54. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_20.

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Charalambous, Michael G. "No Compactification Theorem for the Small Inductive Dimension of Perfectly Normal Spaces." In Dimension Theory, 201–4. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_26.

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Talagrand, Michel. "The Ultimate Matching Theorem in Dimension ≥3." In Upper and Lower Bounds for Stochastic Processes, 475–513. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54075-2_15.

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Bădescu, Lucian. "The Classification Theorem According to Canonical Dimension." In Algebraic Surfaces, 123–35. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3512-3_9.

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Kamada, Seiichi. "Proof of Markov’s theorem in dimension four." In Mathematical Surveys and Monographs, 191–222. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/surv/095/27.

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Conference papers on the topic "Dimension theorem"

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Gao, Jie, Michael Langberg, and Leonard J. Schulman. "Analysis of incomplete data and an intrinsic-dimension Helly theorem." In the seventeenth annual ACM-SIAM symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1109557.1109609.

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Rodriguez-Quintero, Josè. "The dimension-two gluon condensate, the ghost-gluon vertex and the Taylor theorem." In International Workshop on QCD Green's Functions, Confinement and Phenomenology. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.136.0040.

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Tagade, Piyush M., and Han-Lim Choi. "An Efficient Bayesian Calibration Approach Using Dynamically Biorthogonal Field Equations." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70584.

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Present paper proposes new dynamic-biorthogonality based Bayesian formulation for calibration of computer simulators with parametric uncertainty. The formulation uses decomposition of solution field into mean and random field. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spacial dimensions. Both the dimensions are spectrally represented using respective orthogonal bases. In particular, present paper investigates polynomial chaos basis for stochastic dimension and eigenfunction basis for spacial dimension. Dynamic evolution equations are derived such that basis in stochastic dimension is retained while basis in spacial dimension is changed such that dynamic orthogonality is maintained. Resultant evolution equations are used to propagate prior uncertainty in input parameters to the solution output. Whenever new information is available through experimental observations or expert opinion, Bayes theorem is used to update the basis in stochastic dimension. Efficacy of the proposed methodology is demonstrated for calibration of 2D transient diffusion equation with uncertainty in source location. Computational efficiency of the method is demonstrated against Generalized Polynomial Chaos and Monte Carlo method.
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Ge, Zhihua, Yuguang Niu, Zhiping Song, and Zhongguang Fu. "Study on Self-Learning for Vibration Fault Diagnosis System of Rotating Machinery." In ASME 2005 Power Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pwr2005-50123.

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For an established fault diagnosis system which is based on it own expert system, it is usually incapable to diagnosis the new operating conditions, of which the knowledge has not been explored by the system. It is the purpose of the paper to develop the approach of identifying new fault and self-learning for diagnosis based on non-linear fractal theorem. It has been generally accepted that the vibration series has obvious fractal feature, which can reflect the essential characteristics of new fault. When the novel fault is taken place in the system, a related sub-net is increased to the system and trained with this sample. We have verified experimentally that the fractal dimensions of the same class faults are distributed approximately around a definite value that can represents the dimension of the standard sample for the novel fault. Based on non-linear theorem, the approach of identifying new fault and self-learning for diagnosing is put forward.
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Wang, Pingfeng, Byeng D. Youn, and Lee J. Wells. "Bayesian Reliability Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35524.

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In the last decade, considerable advances have been made in Reliability-Based Design Optimization (RBDO). It is assumed in RBDO that statistical information of input uncertainties is completely known (aleatory uncertainty), such as a distribution type and its parameters (e.g., mean, deviation). However, this assumption is not valid in practical engineering applications, since the amount of uncertainty data is restricted mainly due to limited resources (e.g., man-power, expense, time). In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, this paper proposes an integration of RBDO with Bayes Theorem, referred to as Bayesian Reliability-Based Design Optimization (Bayesian RBDO). However, when a design problem involves a large number of epistemic variables, Bayesian RBDO becomes extremely expensive. Thus, this paper presents a more efficient and accurate numerical method for reliability method demanded in the process of Bayesian RBDO. It is found that the Eigenvector Dimension Reduction (EDR) Method is a very efficient and accurate method for reliability analysis, since the method takes a sensitivity-free approach with only 2n+1 analyses, where n is the number of aleatory random parameters. One mathematical example and an engineering design example (vehicle suspension system) are used to demonstrate the feasibility of Bayesian RBDO. In Bayesian RBDO using the EDR method, random parameters associated with manufacturing variability are considered as the aleatory random parameters, whereas random parameters associated with the load variability are regarded as the epistemic random parameters. Moreover, a distributed computing system is used for this study.
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Liu, Chao, Liming Wan, Xinming Zhang, and Danling Zeng. "Investigation of Fractional Characteristic of Molecular Motion by Molecular Dynamics Simulation." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-62334.

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Molecular dynamics simulation (MDS) is adopted to investigate the characteristic of fractional motion of molecules in liquid phase, vapor phase and liquid-vapor interface in the paper. Based on the theory of mean free path and Shannon sampling theorem, the way to determine a universal criterion of time step of simulation is presented. It is shown that there exists difference in the regular pattern of molecular motion in the state of liquid and vapor phase. The fractional features are different for different matter states. Under the condition of same temperature, the characteristic fractional number of molecular motion in liquid state is greater than one in vapor state. It is shown that the fractional dimension numbers in the X, Y and Z direction of the liquid-vapor interface are different. This proves that the liquid-vapor interface has anisotropic character.
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Rana, Rohit, Karl Q. Schwarz, and Jason R. Kolodziej. "Non-Invasive Fault Detection in an Axial Flow Blood Pump Used as a Ventricle Assistive Device." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6084.

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A Ventricular Assistive Device (VAD) is a mechanical pump used to assist the functioning of a weak heart. A catastrophic obstruction in the VAD system could cost the patient their life. This paper discusses a fault detection approach using the commercially available Jarvik 2000 Flowmaker® VAD in a closed loop circuit that incorporates the ability to alter common causes of VAD congestion. Principal Component Analysis, a data compression technique used to discover patterns in data of high dimension, is implemented using frequency analysis of the VAD’s acoustic signature. This is followed by a health classification based on Bayes theorem. The classification results indicate that this technique is accurate to a high degree in detecting three levels of obstruction in the VAD system.
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Li, Pu, Jingxia Yue, Xiaobin Li, and Wenchao Wan. "Axial Compression and Collapse Properties of 3D Re-Entrant Hexagonal Auxetic Structures." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18418.

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Abstract A three-dimension (3D) re-entrant honeycomb structure which exhibits negative Poisson’s ratio in all three principal directions is modeled from a classical two-dimension (2D) auxetic material. In this work, on the basis of the Castigliano’s second theorem and Timoshenko beam model, the shear deformation and axial deformation of this structure are investigated. And the analytical formulas of the effective modulus and Poisson’s ratio in each principal direction of the honeycomb structure are derived. By comparing the analytical results with the finite element analysis results, the rationality of the formula is verified. Then, the collapse characteristics of honeycomb structures with different mechanical properties under variation impact velocities are studied. The results show that, the deformation of honeycomb structure can be divided into three patterns, “quasi-static” deformation, “transitional” deformation and “local” deformation varied with impact velocities. And due to inertial effect, with the increase of impact velocity, the load-bearing capacity and energy absorption of the structure also increased. In addition to the impact velocity, the cells’ configuration is also a non-negligible factor, and its turns out that the decrease of angle accelerates the deformation state of the honeycomb structure and strengthen the energy-absorption capability after being subjected to impact load.
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Freed, Daniel S. "On Wigner's theorem." In Low-dimensional manifolds and high-dimensional categories -- A conference in honor of Michael Hartley Freedman. Mathematical Sciences Publishers, 2012. http://dx.doi.org/10.2140/gtm.2012.18.83.

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Nguyen, Tu Dinh, Trung Le, Hung Bui, and Dinh Phung. "Large-scale Online Kernel Learning with Random Feature Reparameterization." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/354.

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A typical online kernel learning method faces two fundamental issues: the complexity in dealing with a huge number of observed data points (a.k.a the curse of kernelization) and the difficulty in learning kernel parameters, which often assumed to be fixed. Random Fourier feature is a recent and effective approach to address the former by approximating the shift-invariant kernel function via Bocher's theorem, and allows the model to be maintained directly in the random feature space with a fixed dimension, hence the model size remains constant w.r.t. data size. We further introduce in this paper the reparameterized random feature (RRF), a random feature framework for large-scale online kernel learning to address both aforementioned challenges. Our initial intuition comes from the so-called "reparameterization trick" [Kingma et al., 2014] to lift the source of randomness of Fourier components to another space which can be independently sampled, so that stochastic gradient of the kernel parameters can be analytically derived. We develop a well-founded underlying theory for our method, including a general way to reparameterize the kernel, and a new tighter error bound on the approximation quality. This view further inspires a direct application of stochastic gradient descent for updating our model under an online learning setting. We then conducted extensive experiments on several large-scale datasets where we demonstrate that our work achieves state-of-the-art performance in both learning efficacy and efficiency.
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Reports on the topic "Dimension theorem"

1

Hellerman, S. Dynamical Dimension Change in Supercritical String Theory. Office of Scientific and Technical Information (OSTI), October 2004. http://dx.doi.org/10.2172/839961.

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Kolb, E. W. Cosmology in theories with extra dimensions. Office of Scientific and Technical Information (OSTI), January 1985. http://dx.doi.org/10.2172/5851907.

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Chetverikov, Denis, Victor Chernozhukov, and Kengo Kato. Central limit theorems and bootstrap in high dimensions. IFS, December 2014. http://dx.doi.org/10.1920/wp.cem.2014.4914.

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Kato, Kengo, Victor Chernozhukov, and Denis Chetverikov. Central limit theorems and bootstrap in high dimensions. The IFS, August 2016. http://dx.doi.org/10.1920/wp.cem.2016.3916.

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Aharony, O., M. Berkooz, S. Kachru, and E. Silverstein. Matrix description of (1,0) theories in six dimensions. Office of Scientific and Technical Information (OSTI), September 1997. http://dx.doi.org/10.2172/666066.

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Crescimanno, M. J. Topics in low-dimensional field theory. Office of Scientific and Technical Information (OSTI), April 1991. http://dx.doi.org/10.2172/5730644.

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Rao, S., and R. Yahalom. Parity anomalies in gauge theories in 2 + 1 dimensions. Office of Scientific and Technical Information (OSTI), January 1986. http://dx.doi.org/10.2172/6006134.

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Bergman, O., and C. B. Thorn. Super-Galilei invariant field theories in 2+1 dimensions. Office of Scientific and Technical Information (OSTI), December 1995. http://dx.doi.org/10.2172/179291.

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Mirabelli, E. Realistic Field Theories on Submanifolds of Compact Extra Dimensions. Office of Scientific and Technical Information (OSTI), April 2005. http://dx.doi.org/10.2172/839828.

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Arkani-Hamed, Nima. Early Inflation and Cosmology in Theories with Sub-Millimeter Dimensions. Office of Scientific and Technical Information (OSTI), March 1999. http://dx.doi.org/10.2172/10022.

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