14909738
Regularities and their relations to error bounds
Abstract.In this paper, we mainly study various notions of regularity for a finite collection {C1,⋯,Cm} of closed convex subsets of a Banach space X and their relations with other fundamental concepts. We show that a proper lower semicontinuous function f on X has a Lipschitz error bound (resp., ϒ-error bound) if and only if the pair {epi(f),X×{0}} of sets in the product space X×ℝ is linearly regular (resp., regular). Similar results for multifunctions are also established. Next, we prove that {C1,⋯,Cm} is linearly regular if and only if it has the strong CHIP and the collection {NC1(z),⋯,NCm(z)} of normal cones at z has property (G) for each z∈C:=∩i=1mCi. Provided that C1 is a closed convex cone and that C2=Y is a closed vector subspace of X, we show that {C1,Y} is linearly regular if and only if there exists α>0 such that each positive (relative to the order induced by C1) linear functional on Y of norm one can be extended to a positive linear functional on X with norm bounded by α. Similar characterization is given in terms of normal cones.
16910052
On best restricted range approximation in continuous complex-valued function spaces
To provide a Kolmogorov-type condition for characterizing a best approximation in a continuous complex-valued function space, it is usually assumed that the family of closed convex sets in the complex plane used to restrict the range satisfies a strong interior-point condition, and this excludes the interesting case when some @W"t is a line-segment or a singleton. The main aim of the present paper is to remove this restriction by virtue of a study of the notion of the strong CHIP for an infinite system of closed convex sets in a continuous complex-valued function space.
2203951
Ontology Management for Agent Development
The content of agent messages is often defined according to some ontology through which agents can communicate with each other based on a common vocabulary. However, when ontology evolves, the existing agents may not be able to communicate properly with new agents built on the evolved ontology unless existing agents are re-designed or re-implemented. In this paper, we propose an ontology management platform called OntoWrap with three distinct components. Firstly it maintains an ontology repository which keeps track of changes to ontology so that the relationship between different versions of ontology and their extensions are maintained. Secondly, it maintains a service repository which links ontology with agent service specifications so that different implantations of an ontology are also maintained. Thirdly, based on the ontology versioning and service specifications, a wrapping service framework is provided for the automatic generation of adapter agents for existing agents to make use of new services.
31564735
Improve the service quality of multi-agent system: ontology management
The association of ontology with services enables service providers to export their services and also enables clients to declare desired services so that new service providers can serve existing clients. Changes and enhancements can be kept track of through the ontology management. The ontology management platform in our system not only declares semantics of agent services, but also provides interface specification for clients to use such a system with semantic information provided.
41815623
Looking for Arbitrage or Term Structures in Frictional Markets
In this paper we consider a frictional market with finitely many securities and finite and discrete future times. The frictions under consideration include fixed and proportional transaction costs, bid-ask spreads, and taxes. In such a market, we find that whether there exists an arbitrage opportunity does not dependent on the fixed transaction costs. Under a reasonable assumption, the no-arbitrage is equivalent to the condition that the optimal value of some linear programming problem is zero, and to the existence of a so-called consistent term structure. These results permit us to identify and to find arbitrage and consistent term structures in polynomial time. Two linear programming problems are proposed, each of which can identify and find the arbitrage opportunity or the consistent term structure if either exists.
27124087
An Autonomous Sensor for 3D Reconstruction
We describe an automated approach to the reconstruction of 3D interiors from laser range data and digital images. This is achieved using a scanning laser rangefinder and digital camera that are mounted on an autonomous mobile platform known as the AEST. The objective is to reproduce complete interiors that are accurate enough for surveying, virtual studio and Augmented Reality applications. The AEST selects and navigates to a series of capture points to progressively reconstruct a 3D textured model to the required degree of accuracy. Navigation and structural information is used to register the data from each new capture point relative to the partial model. The user interface is a web browser with a radio link to the AEST. Results can be viewed in a VRML window as they are obtained. The AEST has been developed in EU-ACTS project RESOLV.
29024680
On optimal orientation of cycle vertex multiplications
For a bridgeless connected graph G, let D(G) be the family of its strong orientations; and for any [email protected]?D(G), we denote by d(D) its diameter. The orientation number d->(G) of G is defined by d->(G)=min{d(D)|[email protected]?D(G)}. For a connected graph G of order n and for any sequence of n positive integers (s"i), let G(s"1,s"2,...,s"n) denote the graph with vertex set V^* and edge set E^* such that V^*[email protected]?"i"="1^nV"i, where V"i's are pairwise disjoint sets with |V"i|=s"i, i=1,2,...,n, and for any two distinct vertices x, y in V^*, [email protected]?E^* if and only if [email protected]?V"i and [email protected]?V"j for some i,[email protected]?{1,2,...,n} with i j such that v"iv"[email protected]?E(G). We call the graph G(s"1,s"2,...,s"n) a G vertex multiplication. In this paper, we determine the orientation numbers of various cycle vertex multiplications.