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

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>.

Mapping Theorems on Spaces with sn-Network g-Functions

Let 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.

Unsupervised Part-Based Scene Modeling for Map Matching

In exploring the 1-to-Nmap matching problem that exploits a compact map data description, we hope to improve map matching scalability used in robot vision tasks. We propose explicitly targeting fast succinct map matching, which consists of map matching subtasks alone. These tasks include offline map matching attempts to find compact part-based scene models that effectively explain individual maps by using fewer larger parts. These tasks also include online map matching to find correspondence between part-based maps efficiently. Our part-based scene modeling approach is unsupervised and uses common pattern discovery (CPD) between input and known reference maps. Results of our experiments, which use a publicly available radish dataset, confirm the effectiveness of our proposed approach.

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

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.

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

The 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.

Some Results for the Family KKM(X,Y) and the Φ-Mapping in FC-Spaces

We first establish a fixed point theorem for a k-set contraction map on the family KKM(X,X), which does not need to be a compact map. Next, we present the KKM type theorems, matching theorems, coincidence theorems, and minimax theorems on the family KKM(X,Y) and the Φ-mapping in FC-spaces. Our results improve and generalize some recent results.