Thematische Bibliographien / Non-Euclidean spaces / Zeitschriftenartikel
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Zeitschriftenartikel zum Thema „Non-Euclidean spaces“

Autor: Grafiati
Veröffentlicht am 28. Juni 2021
Zuletzt aktualisiert am 1. Februar 2022

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1

Lally, Nick, and Luke Bergmann. "Mapping dynamic, non-Euclidean spaces." Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-204-2019.

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<p><strong>Abstract.</strong> Space is often described as a dynamic entity in human geographic theory, one that resists being pinned down to static representations. Co-produced in and through relations between various things and phenomena, space in these accounts is variously described as being contingent, processual, plastic, relational, situated, topological, and uneven. In contrast, most cartographic methods and tools are based on static, Euclidean understandings of space that can be reduced to a simple, mathematical description. In this work, I explore how cartography can deal with space as a dynamic and fluid concept that is entangled with the phenomena and objects being mapped. To those ends, I describe a method for creating animated maps based on relational understandings of space that are always in flux.</p><p>This work builds on research in collaboration with Luke Bergmann, where we suggest a move from Geographic Information Systems (GIS) as we commonly know them to the broader realm of <i>geographical imagination systems (gis)</i> that are informed by spatial theory in human geography. The animated maps here are produced using our prototype <i>gis</i> software Enfolding, which use multidimensional scaling (MDS) to visualize relational spaces, in combination with Blender, an open-source 3D rendering program. Written in JavaScript and available as open source software, Enfolding is our first attempt to make gis an accessible set of tools that expand the possibilities for mapping by providing new grammars for creative cartographic practices.</p><p>In the cartographic workflow presented here, I use Enfolding to produce manifolds from a set of points and user-defined distances between points. Changing those measures of distance – which might represent travel times, affective connections, communicative links, or any other relationship as defined by a user – produces shifting manifolds. Using the .obj export option in Enfolding, I then import the manifolds into Blender, using them as animation keyframes. In Figure 1, I have added a digital elevation model (DEM) to the 3D figure, producing an animated visualization of a dynamic and relational space that includes a hillshade.</p><p>This workflow represents only one of many creative possibilities for innovative cartographic practices that engage with space as a matter of concern. With growing interest in 3D cartographic methods comes expanded possibilities for visualizing dynamic and relational spaces. Combining conceptual antecedents in both human and quantitative geography with current cartographic methods allows for new approaches to both mapping and space. The workflow and tools that have emerged from this research are presented here with the hope of spurring creative and exploratory cartographic work that draws from but also contributes to vibrant discussions in spatial theory and creative cartography.</p>
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2

Courrieu, Pierre. "Function approximation on non-Euclidean spaces." Neural Networks 18, no. 1 (2005): 91–102. http://dx.doi.org/10.1016/j.neunet.2004.09.003.

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3

Novello, Tiago, Vincius da Silva, and Luiz Velho. "Global illumination of non-Euclidean spaces." Computers & Graphics 93 (December 2020): 61–70. http://dx.doi.org/10.1016/j.cag.2020.09.014.

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4

Urban, Philipp, Mitchell R. Rosen, Roy S. Berns, and Dierk Schleicher. "Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement." Journal of the Optical Society of America A 24, no. 6 (2007): 1516. http://dx.doi.org/10.1364/josaa.24.001516.

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5

BORELL, STEFAN, and FRANK KUTZSCHEBAUCH. "NON-EQUIVALENT EMBEDDINGS INTO COMPLEX EUCLIDEAN SPACES." International Journal of Mathematics 17, no. 09 (2006): 1033–46. http://dx.doi.org/10.1142/s0129167x06003795.

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We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ↪ ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.
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6

Borisov, A. V., and I. S. Mamaev. "Rigid body dynamics in non-Euclidean spaces." Russian Journal of Mathematical Physics 23, no. 4 (2016): 431–54. http://dx.doi.org/10.1134/s1061920816040026.

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7

Capecchi, Danilo, and Giuseppe Ruta. "Beltrami's continuum mechanics in non-Euclidean spaces." PAMM 15, no. 1 (2015): 703–4. http://dx.doi.org/10.1002/pamm.201510341.

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8

Midler, Jean-Claude. "Non-Euclidean Geographic Spaces: Mapping Functional Distances." Geographical Analysis 14, no. 3 (2010): 189–203. http://dx.doi.org/10.1111/j.1538-4632.1982.tb00068.x.

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9

Dörfel, B.-D. "Non-commutative Euclidean structures in compact spaces." Journal of Physics A: Mathematical and General 34, no. 12 (2001): 2583–94. http://dx.doi.org/10.1088/0305-4470/34/12/306.

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10

Schwarz, Binyamin, and Abraham Zaks. "Non-Euclidean motions in projective matrix spaces." Linear Algebra and its Applications 137-138 (August 1990): 351–61. http://dx.doi.org/10.1016/0024-3795(90)90134-x.

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11

Orsingher, Enzo, and Bruno Toaldo. "Shooting randomly against a line in Euclidean and non-Euclidean spaces." Stochastics 86, no. 1 (2013): 16–45. http://dx.doi.org/10.1080/17442508.2012.749260.

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12

Brandolini, Luca, Leonardo Colzani, and Andrea Torlaschi. "Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces." Tohoku Mathematical Journal 53, no. 3 (2001): 467–78. http://dx.doi.org/10.2748/tmj/1178207421.

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13

Agmon, Shmuel. "Spectral theory of schrödinger operators on euclidean and on non-euclidean spaces." Communications on Pure and Applied Mathematics 39, S1 (1986): S3—S16. http://dx.doi.org/10.1002/cpa.3160390703.

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14

CAMARINHA, M., F. SILVA LEITE, and P. CROUCH. "Splines of class Ck on non-euclidean spaces." IMA Journal of Mathematical Control and Information 12, no. 4 (1995): 399–410. http://dx.doi.org/10.1093/imamci/12.4.399.

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15

Wang, Shanshan, and Jin Zhang. "Programing Two-Dimensional Materials in Non-Euclidean Spaces." Chem 6, no. 4 (2020): 829–31. http://dx.doi.org/10.1016/j.chempr.2020.03.022.

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16

Capecchi, Danilo, and Giuseppe Ruta. "Beltrami and mathematical physics in non-Euclidean spaces." Meccanica 51, no. 4 (2015): 747–62. http://dx.doi.org/10.1007/s11012-015-0237-6.

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17

Meda, Stefano. "On non-isotropic homogeneous Lipschitz spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 2 (1989): 240–55. http://dx.doi.org/10.1017/s1446788700031670.

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AbstractWe prove that in a non-isotropic Euclidean space, homogeneous Lipschitz spaces of distributions, defined in terms of (generalized) Weierstrass integrals, can be characterized by means of higher order difference operators.
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18

Yang, Qi, and Chuanming Zong. "Multiple Lattice Tilings in Euclidean Spaces." Canadian Mathematical Bulletin 62, no. 4 (2018): 923–29. http://dx.doi.org/10.4153/s0008439518000103.

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AbstractIn 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean plane if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves the following results. Except for parallelograms and centrally symmetric hexagons, there are no other convex domains that can form two-, three- or four-fold lattice tilings in the Euclidean plane. However, there are both octagons and decagons that can form five-fold lattice tilings. Whenever $n\geqslant 3$, there are non-parallelohedral polytopes that can form five-fold lattice tilings in the $n$-dimensional Euclidean space.
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19

Tuo-Yeong. "MULTIPLIERS FOR SOME NON-ABSOLUTE INTEGRALS IN EUCLIDEAN SPACES." Real Analysis Exchange 24, no. 1 (1998): 149. http://dx.doi.org/10.2307/44152945.

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20

Bannai, Eiichi, Osamu Shimabukuro, and Hajime Tanaka. "Finite analogues of non-Euclidean spaces and Ramanujan graphs." European Journal of Combinatorics 25, no. 2 (2004): 243–59. http://dx.doi.org/10.1016/s0195-6698(03)00110-0.

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21

Dulio, Paolo, and Carla Peri. "Uniqueness theorems for convex bodies in non‐Euclidean spaces." Mathematika 49, no. 1-2 (2002): 13–31. http://dx.doi.org/10.1112/s0025579300016016.

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22

Kadak, Uğur, and Hakan Efe. "The Construction of Hilbert Spaces over the Non-Newtonian Field." International Journal of Analysis 2014 (October 21, 2014): 1–10. http://dx.doi.org/10.1155/2014/746059.

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Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of *-calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the *-norm properties of complex structures, we examine Cauchy-Schwarz and triangle inequalities.
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23

Urdapilleta, Eugenio, Francesca Troiani, Federico Stella, and Alessandro Treves. "Can rodents conceive hyperbolic spaces?" Journal of The Royal Society Interface 12, no. 107 (2015): 20141214. http://dx.doi.org/10.1098/rsif.2014.1214.

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The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane.
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24

Krasnov, V. A. "Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature." Contemporary Mathematics. Fundamental Directions 66, no. 4 (2020): 558–679. http://dx.doi.org/10.22363/2413-3639-2020-66-4-558-679.

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Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and preserving its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevsky who found the volume of the so-called ideal tetrahedron in hyperbolic space (all vertices of this tetrahedron are on the absolute).In this survey, we present main results on volumes of arbitrary non-Euclidean tetrahedra and polyhedra of special types (both tetrahedra and polyhedra of more complex combinatorial structure) in 3-dimensional spherical and hyperbolic spaces of constant curvature K = 1 and K = -1, respectively. Moreover, we consider the new method by Sabitov for computation of volumes in hyperbolic space (described by the Poincare model in upper half-space). This method allows one to derive explicit volume formulas for polyhedra of arbitrary dimension in terms of coordinates of vertices. Considering main volume formulas for non-Euclidean polyhedra, we will give proofs (or sketches of proofs) for them. This will help the reader to get an idea of basic methods for computation of volumes of bodies in non-Euclidean spaces of constant curvature.
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25

Chen, Bang-Yen, and Sharief Deshmukh. "Some results about concircular vector fields on Riemannian manifolds." Filomat 34, no. 3 (2020): 835–42. http://dx.doi.org/10.2298/fil2003835c.

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In this article, we show that the presence of a concircular vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian and Kaehler manifolds. More precisely, we find new geometrical characterizations of spheres, Euclidean spaces as well as of complex Euclidean spaces using non-trivial concircular vector fields.
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26

Zhu, Songhao, Juanjuan Hu, Baoyun Wang, and Shuhan Shen. "Image annotation using high order statistics in non-Euclidean spaces." Journal of Visual Communication and Image Representation 24, no. 8 (2013): 1342–48. http://dx.doi.org/10.1016/j.jvcir.2013.09.004.

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27

Ma, Hongjuan, and Aiping Wang. "Revolution Surfaces with Constant Mean Curvature in Non-Euclidean Spaces." British Journal of Mathematics & Computer Science 8, no. 1 (2015): 16–24. http://dx.doi.org/10.9734/bjmcs/2015/9987.

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28

González, Jesús, and Mark Grant. "Sequential motion planning of non-colliding particles in Euclidean spaces." Proceedings of the American Mathematical Society 143, no. 10 (2015): 4503–12. http://dx.doi.org/10.1090/proc/12443.

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29

Zhu, Songhao, Xiangxiang Li, and Zhiwei Liang. "High Order Statistics in Non-Euclidean Spaces Based Image Classification." National Academy Science Letters 37, no. 3 (2014): 253–59. http://dx.doi.org/10.1007/s40009-013-0217-0.

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30

Dostert, Maria, and Alexander Kolpakov. "Kissing number in non-Euclidean spaces of constant sectional curvature." Mathematics of Computation 90, no. 331 (2021): 2507–25. http://dx.doi.org/10.1090/mcom/3622.

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This paper provides upper and lower bounds on the kissing number of congruent radius r > 0 r > 0 spheres in hyperbolic H n \mathbb {H}^n and spherical S n \mathbb {S}^n spaces, for n ≥ 2 n\geq 2 . For that purpose, the kissing number is replaced by the kissing function κ H ( n , r ) \kappa _H(n, r) , resp. κ S ( n , r ) \kappa _S(n, r) , which depends on the dimension n n and the radius r r . After we obtain some theoretical upper and lower bounds for κ H ( n , r ) \kappa _H(n, r) , we study their asymptotic behaviour and show, in particular, that κ H ( n , r ) ∼ ( n − 1 ) ⋅ d n − 1 ⋅ B ( n − 1 2 , 1 2 ) ⋅ e ( n − 1 ) r \kappa _H(n,r) \sim (n-1) \cdot d_{n-1} \cdot B(\frac {n-1}{2}, \frac {1}{2}) \cdot e^{(n-1) r} , where d n d_n is the sphere packing density in R n \mathbb {R}^n , and B B is the beta-function. Then we produce numeric upper bounds by solving a suitable semidefinite program, as well as lower bounds coming from concrete spherical codes. A similar approach allows us to locate the values of κ S ( n , r ) \kappa _S(n, r) , for n = 3 , 4 n= 3,\, 4 , over subintervals in [ 0 , π ] [0, \pi ] with relatively high accuracy.
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31

Georgiadis, Athanasios G., and George Kyriazis. "Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators." Analysis and Geometry in Metric Spaces 8, no. 1 (2020): 418–29. http://dx.doi.org/10.1515/agms-2020-0120.

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Abstract We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization. We prove embedding theorems between Triebel-Lizorkin spaces associated with operators. Embeddings for non-classical Triebel-Lizorkin and (both classical and non-classical) Besov spaces are proved as well. Our result generalize the Euclidean case and are new for many settings of independent interest such as the ball, the interval and Riemannian manifolds.
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32

Bray, William, and Mark Pinsky. "Growth properties of the Fourier transform." Filomat 26, no. 4 (2012): 755–60. http://dx.doi.org/10.2298/fil1204755b.

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In a recent paper by the authors, growth properties of the Fourier transform on Euclidean space and the Helgason Fourier transform on rank one symmetric spaces of non-compact type were proved and expressed in terms of a modulus of continuity based on spherical means. The methodology employed first proved the result on Euclidean space and then, via a comparison estimate for spherical functions on rank one symmetric spaces to those on Euclidean space, we obtained the results on symmetric spaces. In this note, an analytically simple, yet overlooked refinement of our estimates for spherical Bessel functions is presented which provides significant improvement in the growth property estimates.
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33

Crater, Horace W., and Luca Lusanna. "Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics." International Journal of Geometric Methods in Modern Physics 11, no. 10 (2014): 1450086. http://dx.doi.org/10.1142/s0219887814500868.

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After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.
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34

BERTRAND, JÉRÔME, and BENOÎT KLOECKNER. "A GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACES." Journal of Topology and Analysis 04, no. 04 (2012): 515–42. http://dx.doi.org/10.1142/s1793525312500227.

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Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein space [Formula: see text]. In this paper we investigate the geometry of [Formula: see text] when X is a Hadamard space, by which we mean that X has globally non-positive sectional curvature and is locally compact. Although it is known that, except in the case of the line, [Formula: see text] is not non-positively curved, our results show that [Formula: see text] have large-scale properties reminiscent of that of X. In particular we define a geodesic boundary for [Formula: see text] that enables us to prove a non-embeddablity result: if X has the visibility property, then the Euclidean plane does not admit any isometric embedding in [Formula: see text].
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35

Gaifullin, Alexander A. "The Bellows Conjecture for Small Flexible Polyhedra in Non-Euclidean Spaces." Moscow Mathematical Journal 17, no. 2 (2017): 269–90. http://dx.doi.org/10.17323/1609-4514-2017-17-2-269-290.

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36

HONG, GUIXIANG. "Non-commutative ergodic averages of balls and spheres over Euclidean spaces." Ergodic Theory and Dynamical Systems 40, no. 2 (2018): 418–36. http://dx.doi.org/10.1017/etds.2018.40.

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In this paper, we establish a non-commutative analogue of Calderón’s transference principle, which allows us to deduce the non-commutative maximal ergodic inequalities from the special case—operator-valued maximal inequalities. As applications, we deduce the non-commutative Stein–Calderón maximal ergodic inequality and the dimension-free estimates of the non-commutative Wiener maximal ergodic inequality over Euclidean spaces. We also show the corresponding individual ergodic theorems. To show Wiener’s pointwise ergodic theorem, following a somewhat standard way we construct a dense subset on which pointwise convergence holds. To show Jones’ pointwise ergodic theorem, we use again the transference principle together with the Littlewood–Paley method, which is different from Jones’ original variational method that is still unavailable in the non-commutative setting.
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37

Yu, Yue, Behçet Açıkmeşe, and Mehran Mesbahi. "Mass–spring–damper networks for distributed optimization in non-Euclidean spaces." Automatica 112 (February 2020): 108703. http://dx.doi.org/10.1016/j.automatica.2019.108703.

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38

Zhang, Yandan, Dashan Fan, and Jiecheng Chen. "Transference on some non-convolution operators from euclidean spaces to torus." Chinese Annals of Mathematics, Series B 32, no. 1 (2010): 59–68. http://dx.doi.org/10.1007/s11401-010-0624-1.

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39

Liu, Jiancheng, and Qiuyan Zhang. "Non-existence of stable currents in submanifolds of the Euclidean spaces." Journal of Geometry 96, no. 1-2 (2009): 125–33. http://dx.doi.org/10.1007/s00022-010-0024-4.

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40

ÔIKE, Hiroshi. "Non-existence of higher order non-singular immersions of complex hypersurfaces into Euclidean spaces." Hokkaido Mathematical Journal 16, no. 2 (1987): 191–200. http://dx.doi.org/10.14492/hokmj/1381517926.

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41

Bhattacharya, Rabi, and Lizhen Lin. "Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces." Proceedings of the American Mathematical Society 145, no. 1 (2016): 413–28. http://dx.doi.org/10.1090/proc/13216.

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42

DEKSTER, BORIS V. "A SPHERICAL MAPPING AND BORSUK CONJECTURE IN RIEMANNIAN AND NON-EUCLIDEAN SPACES." Tamkang Journal of Mathematics 25, no. 2 (1994): 149–55. http://dx.doi.org/10.5556/j.tkjm.25.1994.4436.

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We introduce an analog of the spherical mapping for convex bodies in a Riemannian $n$-manifold, and then use this construction to prove the Borsuk conjecture for some types of such bodies. The Borsuk conjecture is that each bounded set $X$ in the Euclidean $n$-space can be covered by $n +1$ sets of smaller diameter. The conjecture was disproved recently by Kahn and Kalai. However Hadwiger proved the Borsuk conjecture under the additional assumption that the set $X$ is a smooth convex body. Here we extend this result to convex bodies in Riemannian manifolds under some further restrictions.
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LORENT, ANDREW. "RECTIFIABILITY OF MEASURES WITH LOCALLY UNIFORM CUBE DENSITY." Proceedings of the London Mathematical Society 86, no. 1 (2003): 153–249. http://dx.doi.org/10.1112/s0024611502013710.

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The conjecture that Radon measures in Euclidean space with positive finite density are rectifiable was a central problem in Geometric Measure Theory for fifty years. This conjecture was positively resolved by Preiss in 1986, using methods entirely dependent on the symmetry of the Euclidean unit ball. Since then, due to reasons of isometric immersion of metric spaces into $l_{\infty}$ and the uncommon nature of the sup norm even in finite dimensions, a popular model problem for generalising this result to non-Euclidean spaces has been the study of 2-uniform measures in $l^{3}_{\infty}$. The rectifiability or otherwise of these measures has been a well-known question.In this paper the stronger result that locally 2-uniform measures in $l^{3}_{\infty}$ are rectifiable is proved. This is the first result that proves rectifiability, from an initial condition about densities, for general Radon measures of dimension greater than 1 outside Euclidean space.2000 Mathematical Subject Classification: 28A75.
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NIELSEN, FRANK, and RICHARD NOCK. "APPROXIMATING SMALLEST ENCLOSING BALLS WITH APPLICATIONS TO MACHINE LEARNING." International Journal of Computational Geometry & Applications 19, no. 05 (2009): 389–414. http://dx.doi.org/10.1142/s0218195909003039.

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In this paper, we first survey prior work for computing exactly or approximately the smallest enclosing balls of point or ball sets in Euclidean spaces. We classify previous work into three categories: (1) purely combinatorial, (2) purely numerical, and (3) recent mixed hybrid algorithms based on coresets. We then describe two novel tailored algorithms for computing arbitrary close approximations of the smallest enclosing Euclidean ball. These deterministic heuristics are based on solving relaxed decision problems using a primal-dual method. The primal-dual method is interpreted geometrically as solving for a minimum covering set, or dually as seeking for a minimum piercing set. Finally, we present some applications in machine learning of the exact and approximate smallest enclosing ball procedure, and discuss about its extension to non-Euclidean information-theoretic spaces.
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45

Sławianowski, J. J., and B. Gołubowska. "Motion of test bodies with internal degrees of freedom in non-Euclidean spaces." Reports on Mathematical Physics 65, no. 3 (2010): 379–422. http://dx.doi.org/10.1016/s0034-4877(10)00018-2.

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46

Pintea, Cornel. "A measure of non-immersability of the Grassmann manifolds in some euclidean spaces." Proceedings of the Edinburgh Mathematical Society 41, no. 1 (1998): 197–205. http://dx.doi.org/10.1017/s0013091500019507.

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LetGk, n, be the Grassmann manifold consisting in all non-orientedk-dimensional vector subspaces of the spaceRk+n. In this paper we will show that any differentiable mappingf:Gk, n→Rm, has infinitely many critical points for suitable choices of the numbersm,n,k.
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47

Kumar, Ashisha, and Swagato K. Ray. "End point estimates for Radon transform of radial functions on non-Euclidean spaces." Monatshefte für Mathematik 174, no. 1 (2014): 41–75. http://dx.doi.org/10.1007/s00605-014-0620-8.

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48

Arora, Subhash C., Gopal Datt, and Satish Verma. "Weighted composition operators on Orlicz-Sobolev spaces." Journal of the Australian Mathematical Society 83, no. 3 (2007): 327–34. http://dx.doi.org/10.1017/s1446788700037952.

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AbstractFor an open subset Ω of the Euclidean space Rn, a measurable non-singular transformation T: Ω → Ω and a real-valued measurable function u on Rn, we study the weighted composition operator uCτ: f ↦ u · (f º T) on the Orlicz-Sobolev space W1·Ψ (Ω) consxsisting of those functions of the Orlicz space LΨ (Ω) whose distributional derivatives of the first order belong to LΨ (Ω). We also discuss a sufficient condition under which uCτ is compact.
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49

Dilworth, S. J. "The dimension of Euclidean subspaces of quasi-normed spaces." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 2 (1985): 311–20. http://dx.doi.org/10.1017/s030500410006285x.

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The purpose of this article is to extend certain results which are known to hold for convex bodies to a class of non-convex bodies occurring in the theory of topological vector spaces. In the first section after this introduction an analogue of F. John's Theorem on the distance of a finite dimensional space from Euclidean space is obtained, and the result is shown to be best possible. The Dvoretzky-Rogers Lemma on the points of contact of a symmetric convex body with the ellipsoid of maximum volume contained within it is discussed for certain non-convex bodies. In the next part the Dvoretzky Theorem on the existence of ellipsoidal sections is shown to hold with the best possible estimate for the dimension of the sections. It follows from estimates involving cotype constants that the finite dimensional subspaces of Lp (0 < p < 1) possess large almost Hilbertian subspaces. The final section extends the theorem of S. Szarek relating the volume of a body to the existence of ellipsoidal sections.
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50

Oussi, Lahcen, and Janusz Wysoczański. "bm-Central Limit Theorems associated with non-symmetric positive cones." Probability and Mathematical Statistics 39, no. 1 (2019): 183–97. http://dx.doi.org/10.19195/0208-4147.39.1.12.

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Analogues of the classical Central Limit Theorem are proved in the noncommutative setting of random variables which are bmindependent and indexed by elements of positive non-symmetric cones, such as the circular cone, sectors in Euclidean spaces and the Vinberg cone. The geometry of the cones is shown to play a crucial role and the related volume characteristics of the cones is shown.
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