A robust SLAM system with compact map

2017 ◽  
Author(s):  
Huiguo Wang ◽  
Xinyu Wu ◽  
Zhiheng Chen
Keyword(s):  
Compact Map

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

scholarly journals Mapping Theorems on Spaces with sn-Network g-Functions

2015 ◽  
Vol 55 (1) ◽  
pp. 199-208
Author(s):  
Luong Quoc Tuyen
Keyword(s):  
Compact Subset ◽  
Topological Spaces ◽  
Metrizable Spaces ◽  
Compact Map

AbstractLet Δ be the sets of all topological spaces satisfying the following conditions.(1) Each compact subset of X is metrizable;(2) There exists an sn-network g-function g on X such that if xn → x and yn ∈ g(n; xn) for all n ∈ N, then x is a clusterpoint of {yn}.In this paper, we prove that if X ∈ Δ, then each sequentially- quotient boundary-compact map on X is pseudo-sequence-covering; if X ∈ Δ and X has a point-countable sn-network, then each sequence-covering boundary-compact map on X is 1-sequence-covering. As the applications, we give that each sequentially-quotient boundary-compact map on g-metrizable spaces is pseudo-sequence-covering, and each sequence-covering boundary-compact on g-metrizable spaces is 1-sequence-covering.

16.—On Uniqueness of Topological Degree for Set-valued Mappings

1976 ◽  
Vol 74 ◽  
pp. 225-229 ◽  
Author(s):  
J. R. L. Webb ◽  
W. N. Everitt
Keyword(s):  
Topological Degree ◽  
Set Valued Mappings ◽  
Compact Map

SynopsisIt is shown that three independent axioms uniquely determine the topological degree of set-valued maps of the form I – G, where G is a convex-valued, limit compact map. This extends earlier work of Amann and Weiss, Nussbaum, and others, in that, apart from dealing with set-valued maps, a larger class of maps is considered even in the single-valued case.

scholarly journals Multi-Scale Bag-of-Features for Scalable Map Retrieval

2012 ◽  
Vol 16 (7) ◽  
pp. 793-799 ◽  
Author(s):  
Kanji Tanaka ◽  
◽  
Kensuke Kondo
Keyword(s):  
Mobile Robot ◽  
Retrieval System ◽  
The Novel ◽  
Large Collection ◽  
Inverted File ◽  
Multi Scale ◽  
Bag Of Features ◽  
Retrieval Problem ◽  
Environment Maps ◽  
Compact Map

Retrieving a large collection of environment maps built by mapper robots is a key problem in mobile robot self-localization. The map retrieval problem is studied from the novel perspective of the multi-scale Bag-Of-Features (BOF) approach in this paper. In general, the multi-scale approach is advantageous in capturing both the global structure and the local details of a given map. BOF map retrieval is advantageous in its compact map representation as well as the efficient map retrieval using an inverted file system. The main contribution of this paper is combining the advantages of both approaches. Our approach is based on multi cue BOF as well as packing BOF, and achieves the efficiency and compactness of the map retrieval system. Experiments evaluate the effectiveness of the techniques presented using a large collection of environment maps.

On the Homotopy Property of Nussbaum's Fixed Point Index

1982 ◽  
Vol 34 (1) ◽  
pp. 44-62
Author(s):  
Gilles Fournier ◽  
Reine Fournier
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Index ◽  
Point Index ◽  
Homotopy Property ◽  
Lefschetz Fixed Point Theorem ◽  
The One ◽  
Compact Map ◽  
General Conditions

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

scholarly journals Every local compact map group is unimodular

1968 ◽  
Vol 19 (5) ◽  
pp. 1079-1079
Author(s):  
H. Leptin ◽  
L. Robertson
Keyword(s):  
Compact Map

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Bogdan Przeradzki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Bounded Set ◽  
Compact Map

AbstractThe existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.

scholarly journals Perfect maps on convergence spaces

1979 ◽  
Vol 20 (3) ◽  
pp. 447-466
Author(s):  
Robert A. Herrmann
Keyword(s):  
Final Section ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Convergence Space ◽  
Covering Property ◽  
Convergence Spaces ◽  
Weakly Continuous ◽  
Perfect Map ◽  
Perfect Maps ◽  
Compact Map

The concept of the perfect map on a convergence space (X, q), where q is a convergence function, is introduced and investigated. Such maps are not assumed to be either continuous or surjective. Some nontrivial examples of well known mappings between topological spaces, nontopological pretopological spaces and nonpseudotopological convergence spaces are shown to be perfect in this new sense. Among the numerous results obtained is a covering property for perfectness and the result that such maps are closed, compact, and for surjections almost-compact. Sufficient conditions are given for a compact (respectively almost-compact) map to be perfect. In the final section, a major result shows that if f: (X, q) → (Y, p) is perfect and g: (X, q) → (Z, s) is weakly-continuous into Hausdorff Z, then (f, g): (X, q) → (Y×Z, p×s) is perfect. This result is given numerous applications.

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