Log in

Relevant bibliographies by topics / Discrete metric / Journal articles

To see the other types of publications on this topic, follow the link: Discrete metric.

Journal articles on the topic 'Discrete metric'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Discrete metric.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Zeng, Wei, Ren Guo, Feng Luo, and Xianfeng Gu. "Discrete heat kernel determines discrete Riemannian metric." Graphical Models 74, no. 4 (July 2012): 121–29. http://dx.doi.org/10.1016/j.gmod.2012.03.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Agarwal, Ravi P., Mohamed Jleli, and Bessem Samet. "Some Integral Inequalities Involving Metrics." Entropy 23, no. 7 (July 8, 2021): 871. http://dx.doi.org/10.3390/e23070871.

Full text

Abstract:

In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.

APA, Harvard, Vancouver, ISO, and other styles

3

Plewik, Szymon, and Marta Walczyńska. "On metric $\sigma$-discrete spaces." Banach Center Publications 108 (2016): 239–53. http://dx.doi.org/10.4064/bc108-0-18.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

MOORS, WARREN B. "FRAGMENTABILITY BY THE DISCRETE METRIC." Bulletin of the Australian Mathematical Society 91, no. 2 (January 5, 2015): 303–10. http://dx.doi.org/10.1017/s0004972714000926.

Full text

Abstract:

AbstractIn a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are ${\it\sigma}$-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.

APA, Harvard, Vancouver, ISO, and other styles

5

Burdyuk, V. Ya, and I. V. Burdyuk. "Discrete and continuous metric spaces." Cybernetics and Systems Analysis 28, no. 6 (November 1992): 950–52. http://dx.doi.org/10.1007/bf01291301.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

HUANG, WEN, JIAN LI, JEAN-PAUL THOUVENOT, LEIYE XU, and XIANGDONG YE. "Bounded complexity, mean equicontinuity and discrete spectrum." Ergodic Theory and Dynamical Systems 41, no. 2 (October 7, 2019): 494–533. http://dx.doi.org/10.1017/etds.2019.66.

Full text

Abstract:

We study dynamical systems that have bounded complexity with respect to three kinds metrics: the Bowen metric $d_{n}$, the max-mean metric $\hat{d}_{n}$ and the mean metric $\bar{d}_{n}$, both in topological dynamics and ergodic theory. It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_{n}$ (respectively $\hat{d}_{n}$) if and only if it is equicontinuous (respectively equicontinuous in the mean). However, we construct minimal systems that have bounded complexity with respect to $\bar{d}_{n}$ but that are not equicontinuous in the mean. It turns out that an invariant measure $\unicode[STIX]{x1D707}$ on $(X,T)$ has bounded complexity with respect to $d_{n}$ if and only if $(X,T)$ is $\unicode[STIX]{x1D707}$-equicontinuous. Meanwhile, it is shown that $\unicode[STIX]{x1D707}$ has bounded complexity with respect to $\hat{d}_{n}$ if and only if $\unicode[STIX]{x1D707}$ has bounded complexity with respect to $\bar{d}_{n}$, if and only if $(X,T)$ is $\unicode[STIX]{x1D707}$-mean equicontinuous and if and only if it has discrete spectrum.

APA, Harvard, Vancouver, ISO, and other styles

7

Khatsymovsky, V. M. "On the discrete Christoffel symbols." International Journal of Modern Physics A 34, no. 30 (October 30, 2019): 1950186. http://dx.doi.org/10.1142/s0217751x19501860.

Full text

Abstract:

The piecewise flat space–time is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine connection form of the Regge action of our previous work, we get a second-order form of the action. This can be expanded over metric variations from simplex to simplex. For a particular periodic simplicial structure and coordinates of the vertices, the leading order over metric variations is found to coincide with a certain finite difference form of the Hilbert–Einstein action.

APA, Harvard, Vancouver, ISO, and other styles

8

Aslanyan, Levon H. "Metric decompositions and the discrete isoperimetry." IFAC Proceedings Volumes 33, no. 20 (July 2000): 457–62. http://dx.doi.org/10.1016/s1474-6670(17)38092-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Barcelo, Hélène, Valerio Capraro, and Jacob A. White. "Discrete homology theory for metric spaces." Bulletin of the London Mathematical Society 46, no. 5 (June 17, 2014): 889–905. http://dx.doi.org/10.1112/blms/bdu043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Fabel, Paul. "Metric spaces with discrete topological fundamental group." Topology and its Applications 154, no. 3 (February 2007): 635–38. http://dx.doi.org/10.1016/j.topol.2006.08.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

KURATA, Hisayasu, and Maretsugu YAMASAKI. "The metric growth of the discrete Laplacian." Hokkaido Mathematical Journal 45, no. 3 (October 2016): 399–417. http://dx.doi.org/10.14492/hokmj/1478487617.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Arrighi, Pablo, Giuseppe Di Molfetta, and Stefano Facchini. "Quantum walking in curved spacetime: discrete metric." Quantum 2 (August 22, 2018): 84. http://dx.doi.org/10.22331/q-2018-08-22-84.

Full text

Abstract:

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the(1+1)−dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators-differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.

APA, Harvard, Vancouver, ISO, and other styles

13

Gähler, Siegfried, and Donata Matel-Kaminska. "Remarks on Generalized Metric Discrete Convergence Spaces." Mathematische Nachrichten 146, no. 17-20 (1990): 259–69. http://dx.doi.org/10.1002/mana.19901461702.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Bolton, J., P. Gader, and J. N. Wilson. "Discrete Choquet Integral as a Distance Metric." IEEE Transactions on Fuzzy Systems 16, no. 4 (August 2008): 1107–10. http://dx.doi.org/10.1109/tfuzz.2008.924347.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Craizer, Marcos, Henri Anciaux, and Thomas Lewiner. "Discrete affine minimal surfaces with indefinite metric." Differential Geometry and its Applications 28, no. 2 (April 2010): 158–69. http://dx.doi.org/10.1016/j.difgeo.2009.07.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Aalto, Daniel, and Juha Kinnunen. "The discrete maximal operator in metric spaces." Journal d'Analyse Mathématique 111, no. 1 (May 2010): 369–90. http://dx.doi.org/10.1007/s11854-010-0022-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Lledó, Fernando, and Olaf Post. "Eigenvalue bracketing for discrete and metric graphs." Journal of Mathematical Analysis and Applications 348, no. 2 (December 2008): 806–33. http://dx.doi.org/10.1016/j.jmaa.2008.07.029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Wang, Le Yi, and Lin Lin. "On metric dimensions of discrete-time systems." Systems & Control Letters 19, no. 4 (October 1992): 287–91. http://dx.doi.org/10.1016/0167-6911(92)90067-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

ALIMOHAMMADI, M., and A. A. BAGHJARY. "KLEIN–GORDON AND DIRAC PARTICLES IN NONCONSTANT SCALAR-CURVATURE BACKGROUND." International Journal of Modern Physics A 23, no. 10 (April 20, 2008): 1613–26. http://dx.doi.org/10.1142/s0217751x08039463.

Full text

Abstract:

The Klein–Gordon and Dirac equations are considered in a semiinfinite laboratory (x > 0) in the presence of background metrics ds2 = u2(x)ημν dxμ dxν and ds2 = -dt2 + u2(x)ηij dxi dxj with u(x) = e±gx. These metrics have nonconstant scalar-curvatures. Various aspects of the solutions are studied. For the first metric with u(x) = egx, it is shown that the spectra are discrete, with the ground state energy [Formula: see text] for spin-0 particles. For u(x) = e-gx, the spectrums are found to be continuous. For the second metric with u(x) = e-gx, each particle, depends on its transverse-momentum, can have continuous or discrete spectrum. For Klein–Gordon particles, this threshold transverse-momentum is [Formula: see text], while for Dirac particles it is g/2. There is no solution for u(x) = egx case. Some geometrical properties of these metrics are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

20

REQUARDT, MANFRED. "THE CONTINUUM LIMIT OF DISCRETE GEOMETRIES." International Journal of Geometric Methods in Modern Physics 03, no. 02 (March 2006): 285–313. http://dx.doi.org/10.1142/s0219887806001156.

Full text

Abstract:

In various areas of modern physics and in particular in quantum gravity or foundational space–time physics, it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework within the category of general metric spaces by combining recent work of our own and ingeneous ideas of Gromov et al. developed in pure mathematics. A central role is played by two core concepts. For one, the notion of intrinsic scaling dimension of a (discrete) space or, in mathematical terms, the growth degree of a metric space at infinity, on the other hand, the concept of a metrical distance between general metric spaces and an appropriate scaling limit (called by us a geometric renormalization group) performed in this metric space of spaces. In doing this, we prove a variety of physically interesting results about the nature of this limit process, properties of the limit space, e.g., what preconditions qualify it as a smooth classical space–time and, in particular, its dimension.

APA, Harvard, Vancouver, ISO, and other styles

21

Khatsymovsky, V. M. "On the discrete version of the Kerr geometry." International Journal of Modern Physics A 36, no. 20 (July 7, 2021): 2150130. http://dx.doi.org/10.1142/s0217751x2150130x.

Full text

Abstract:

In this paper, a Kerr-type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the existence of a length scale at which edge lengths are loosely fixed, as considered in our earlier paper. In addition, we previously considered the Regge action on a simplicial manifold on which the vertices are coordinatized and the corresponding piecewise constant metric is introduced, and found that for the simplest periodic simplicial structure and in the leading order over metric variations between four-simplices, this reduces to a finite-difference form of the Hilbert–Einstein action. The problem of solving the corresponding discrete Einstein equations (classical) with a length scale (having a quantum nature) arises as the problem of determining the optimal background metric for the perturbative expansion generated by the functional integral. Using a one-complex-function ansatz for the metric, which reduces to the Kerr–Schild metric in the continuum, we find a discrete metric that approximates the continuum one at large distances and is nonsingular on the (earlier) singularity ring. The effective curvature [Formula: see text], including where [Formula: see text] (gravity sources), is analyzed with a focus on the vicinity of the singularity ring.

APA, Harvard, Vancouver, ISO, and other styles

22

Zhao, Ping, Yong Wang, Lihong Zhu, and Xiangyun Li. "A frame-independent comparison metric for discrete motion sequences." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 9 (January 23, 2020): 1764–74. http://dx.doi.org/10.1177/0954406219898239.

Full text

Abstract:

To evaluate the kinematic performance of designed mechanisms, a statistical-variance-based metric is proposed in this article to measure the “distance” between two discrete motion sequences: the reference motion and the given task motion. It seeks to establish a metric that is independent of the choice of the fixed frame or moving frame. Quaternions are adopted to represent the rotational part of a spatial pose, and the variance of the set of relative displacements is computed to reflect the difference between two sequences. With this variance-based metric formulation, we show that the comparison results of two spatial discrete motions are not affected by the choice of frames. Both theoretical demonstration and computational example are presented to support this conclusion. In addition, since the deviation error between the task motion and the synthesized motion measured with this metric is independent of the location of frames, those corresponding parameters could be excluded from the optimization algorithm formulated with our frame-independent metric in kinematic synthesis of mechanisms, and the complexity of the algorithm are hereby reduced. An application of a four-bar linkage synthesis problem is presented to illustrate the advantage of the proposed metric.

APA, Harvard, Vancouver, ISO, and other styles

23

Korotyaev, Evgeny, and Natalia Saburova. "Scattering on periodic metric graphs." Reviews in Mathematical Physics 32, no. 08 (February 13, 2020): 2050024. http://dx.doi.org/10.1142/s0129055x20500245.

Full text

Abstract:

We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the fiber metric Laplacian are expressed explicitly in terms of eigenfunctions and eigenvalues of the corresponding fiber discrete Laplacian and eigenfunctions of the Dirichlet problem on the unit interval. We show that all these eigenfunctions are uniformly bounded. We apply these results to the periodic metric Laplacian perturbed by real integrable potentials. We prove the following: (a) the wave operators exist and are complete, (b) the standard Fredholm determinant is well-defined and is analytic in the upper half-plane without any modification for any dimension, (c) the determinant and the corresponding S-matrix satisfy the Birman–Krein identity.

APA, Harvard, Vancouver, ISO, and other styles

24

Thakkar, Dhaval, and Ruchi Das. "On Nonautonomous Discrete Dynamical Systems." International Journal of Analysis 2014 (June 2, 2014): 1–6. http://dx.doi.org/10.1155/2014/538691.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Naor, Assaf. "Discrete Riesz transforms and sharp metric X_p inequalities." Annals of Mathematics 184, no. 3 (November 1, 2016): 991–1016. http://dx.doi.org/10.4007/annals.2016.184.3.9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Nicosia, Gaia, and Andrea Pacifici. "Exact algorithms for a discrete metric labeling problem." Electronic Notes in Discrete Mathematics 17 (October 2004): 223–27. http://dx.doi.org/10.1016/j.endm.2004.03.043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Cieslik, Dietmar. "The Steiner ratio of several discrete metric spaces." Discrete Mathematics 260, no. 1-3 (January 2003): 189–96. http://dx.doi.org/10.1016/s0012-365x(02)00762-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Ma, Lei, Hongliang Li, Fanman Meng, Qingbo Wu, and King Ngi Ngan. "Discriminative deep metric learning for asymmetric discrete hashing." Neurocomputing 380 (March 2020): 115–24. http://dx.doi.org/10.1016/j.neucom.2019.11.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Manuilov, V. M. "Roe Bimodules as Morphisms of Discrete Metric Spaces." Russian Journal of Mathematical Physics 26, no. 4 (October 2019): 470–78. http://dx.doi.org/10.1134/s1061920819040058.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Liu, Wanping, Xiaofan Yang, Xinzhi Liu, and Stevo Stević. "Part-metric and its applications in discrete systems." Applied Mathematics and Computation 228 (February 2014): 320–28. http://dx.doi.org/10.1016/j.amc.2013.11.073.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Bobylev, N. A., S. V. Emel'yanov, and S. K. Korovin. "Attractors of discrete controlled systems in metric spaces." Computational Mathematics and Modeling 11, no. 4 (October 2000): 321–26. http://dx.doi.org/10.1007/bf02359296.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Dailey, David P. "On the graphical containment of discrete metric spaces." Discrete Mathematics 131, no. 1-3 (August 1994): 51–66. http://dx.doi.org/10.1016/0012-365x(94)90372-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Alfieri, Arianna, Gaia Nicosia, and Andrea Pacifici. "Exact algorithms for a discrete metric labeling problem." Discrete Optimization 3, no. 3 (September 2006): 181–94. http://dx.doi.org/10.1016/j.disopt.2006.05.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Eilat, Matan, and Bo’az Klartag. "Rigidity of Riemannian embeddings of discrete metric spaces." Inventiones mathematicae 226, no. 1 (May 4, 2021): 349–91. http://dx.doi.org/10.1007/s00222-021-01048-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Manuilov, Vladimir Markovich. "Hilbert C*-modules related to discrete metric spaces." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 5 (2021): 55–63. http://dx.doi.org/10.26907/0021-3446-2021-5-55-63.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Manuilov, V. M. "Hilbert $C^*$-Modules Related to Discrete Metric Spaces." Russian Mathematics 65, no. 5 (May 2021): 40–47. http://dx.doi.org/10.3103/s1066369x21050078.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Luo, Songting, Shingyu Leung, and Jianliang Qian. "An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria." Communications in Computational Physics 10, no. 5 (November 2011): 1113–31. http://dx.doi.org/10.4208/cicp.020210.311210a.

Full text

Abstract:

AbstractThe equilibrium metric for minimizing a continuous congested traffic model is the solution of a variational problem involving geodesic distances. The continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrop’s equilibrium. We propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous formulation. The method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium metric and the resulting geodesic distances. The geodesic distance needed for the state equation is computed by solving a factored eikonal equation, and the adjoint state equation is solved by a fast sweeping method. Numerical examples demonstrate that the proposed adjoint state method produces desired equilibrium metrics and outperforms the subgradient marching method for computing such equilibrium metrics.

APA, Harvard, Vancouver, ISO, and other styles

38

Nešetřil, Jaroslav. "Metric spaces are Ramsey." European Journal of Combinatorics 28, no. 1 (January 2007): 457–68. http://dx.doi.org/10.1016/j.ejc.2004.11.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Horak, P. "Tilings in Lee metric." European Journal of Combinatorics 30, no. 2 (February 2009): 480–89. http://dx.doi.org/10.1016/j.ejc.2008.04.007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Mayor, Gaspar, and Oscar Valero. "Metric aggregation functions revisited." European Journal of Combinatorics 80 (August 2019): 390–400. http://dx.doi.org/10.1016/j.ejc.2018.02.037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Patriarca, Riccardo, Tianya Hu, Francesco Costantino, Giulio Di Gravio, and Massimo Tronci. "A System-Approach for Recoverable Spare Parts Management Using the Discrete Weibull Distribution." Sustainability 11, no. 19 (September 21, 2019): 5180. http://dx.doi.org/10.3390/su11195180.

Full text

Abstract:

Optimal spare parts management strategies allow sustaining a system’s availability, while ensuring timely and effective maintenance. Following a systemic perspective, this paper starts from the Multi-Echelon Technique for Recoverable Item Control (METRIC) to investigate the potential use of a Weibull distribution for modelling items’ demand in case of failure. Adapting the analytic formulation of METRIC through a Discrete Weibull distribution, this study originally proposes a METRIC-based model (DW-METRIC) to be used for modelling the stochastic demand in multi-item systems, in order to ensure process sustainability. The DW-METRIC has been tested in a case study related to an industrial plant constituted by 98 items in a passive redundancy configuration. Comparing the results via a simulation model, the outcomes of the study allow defining applicability criteria for the DW-METRIC, in those settings where the DW-METRIC offers more accurate estimations than the traditional METRIC.

APA, Harvard, Vancouver, ISO, and other styles

42

Liu, Heng, Fengchun Lei, and Lidong Wang. "Li-Yorke Sensitivity of Set-Valued Discrete Systems." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/260856.

Full text

Abstract:

Consider the surjective, continuous mapf:X→Xand the continuous mapf¯of𝒦(X)induced byf, whereXis a compact metric space and𝒦(X)is the space of all nonempty compact subsets ofXendowed with the Hausdorff metric. In this paper, we give a short proof that iff¯is Li-Yoke sensitive, thenfis Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity offdoes not imply Li-Yorke sensitivity off¯.

APA, Harvard, Vancouver, ISO, and other styles

43

Dzhunushaliev, Vladimir, and Vladimir Folomeev. "Spinor field solutions in F(B2) modified Weyl gravity." International Journal of Modern Physics D 29, no. 13 (September 3, 2020): 2050094. http://dx.doi.org/10.1142/s0218271820500947.

Full text

Abstract:

We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coordinates is obtained. It is demonstrated that this class of conformally equivalent metrics contains the following: (a) a metric describing a toroidal wormhole without exotic matter; (b) a cosmological solution with a bounce and inflation and (c) a transition with a change in metric signature. A physical discussion of the results is given.

APA, Harvard, Vancouver, ISO, and other styles

44

Malicki, Maciej. "An example of a polish group." Journal of Symbolic Logic 73, no. 4 (December 2008): 1173–78. http://dx.doi.org/10.2178/jsl/1230396912.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Rodríuez-Velázquez, Juan. "Lexicographic metric spaces: Basic properties and the metric dimension." Applicable Analysis and Discrete Mathematics 14, no. 1 (2020): 20–32. http://dx.doi.org/10.2298/aadm180627004r.

Full text

Abstract:

In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric dimension of any lexicographic metric space.

APA, Harvard, Vancouver, ISO, and other styles

46

Conant, Jim, Victoria Curnutte, Corey Jones, Conrad Plaut, Kristen Pueschel, Maria Lusby, and Jay Wilkins. "Discrete homotopy theory and critical values of metric spaces." Fundamenta Mathematicae 227, no. 2 (2014): 97–128. http://dx.doi.org/10.4064/fm227-2-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Blanchard, Ph, and D. Volchenkov. "Probabilistic embedding of discrete sets as continuous metric spaces." Stochastics 81, no. 3-4 (June 2009): 259–68. http://dx.doi.org/10.1080/17442500902917326.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

MUBAYI, DHRUV, and CAROLINE TERRY. "DISCRETE METRIC SPACES: STRUCTURE, ENUMERATION, AND 0-1 LAWS." Journal of Symbolic Logic 84, no. 4 (August 19, 2019): 1293–325. http://dx.doi.org/10.1017/jsl.2019.52.

Full text

Abstract:

AbstractFix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots ,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left( {\matrix{ n \cr 2 \cr } } \right) + o\left( {n^2 } \right)} .$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is even, our structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left( {n^2 } \right)$ to $o\left( 1 \right)$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$ . In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots ,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws.

APA, Harvard, Vancouver, ISO, and other styles

49

Gotsman, C., and M. Lindenbaum. "On the metric properties of discrete space-filling curves." IEEE Transactions on Image Processing 5, no. 5 (May 1996): 794–97. http://dx.doi.org/10.1109/83.499920.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

LANG, URS. "INJECTIVE HULLS OF CERTAIN DISCRETE METRIC SPACES AND GROUPS." Journal of Topology and Analysis 05, no. 03 (August 25, 2013): 297–331. http://dx.doi.org/10.1142/s1793525313500118.

Full text

Abstract:

Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the '60s Isbell showed that every metric space X has an injective hull E (X). Here it is proved that if X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E (X) is a locally finite polyhedral complex with finitely many isometry types of n-cells, isometric to polytopes in [Formula: see text], for each n. This applies to a class of finitely generated groups Γ, including all word hyperbolic groups and abelian groups, among others. Then Γ acts properly on E(Γ) by cellular isometries, and the first barycentric subdivision of E(Γ) is a model for the classifying space [Formula: see text] for proper actions. If Γ is hyperbolic, E(Γ) is finite dimensional and the action is cocompact. In particular, every hyperbolic group acts properly and cocompactly on a space of non-positive curvature in a weak (but non-coarse) sense.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!