7581866
The orientation number of two complete graphs with linkages
For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any D@?D(G), we denote by d(D) the diameter of D. The orientation number d->(G) of G is defined by d->(G)=min{d(D)|D@?D(G)}. In this paper, we study the orientation numbers of a family of graphs, denoted by G(p,q;m), that are obtained from the disjoint union of two complete graphs K"p and K"q by adding m edges linking them in an arbitrary manner. Define d->(m)=min{d->(G):G@?G(p,q;m)}. We prove that d->(2)=4 and min{m:d->(m)=3}=4. Let @a=min{m:d->(m)=2}. We evaluate the exact value of @a when p==p+4.
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.
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.
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.
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.
27297851
AXMEDIS Programme and Publication Tools Integration with Workflow-Enabled Communication and Process Control
This paper presents the AXMEDIS Programme and Publications (P&P) tools as supported by workflow (WF) integration enabling communication and control in a way that is designed to empower the user to locate digital contents of interest over the AXMEDIS P2P network and to manage and assign the distributions as required. These communications support a large set of interconnections between different sections of the AXMEDIS framework to enable automated processing and integration of digital contents. Following a brief introduction to the overall AXMEDIS framework, this paper presents the functionalities and features of the Programme and Publication (P&P) tools, discusses each individual component, including the P&P Editor and P&P Engine set in the context of the architecture for workflow integration and control for P&P tools within the AXMEDIS Framework
20652786
The iterative development of a tangible pin-board to symmetrically link physical and digital documents
There is an asymmetry in many tangible interfaces: while physical objects can be used to manipulate digital information, the reverse is often not possible—the digital world cannot push back. We introduce a new push-back tangible technology, a pin-board that physically ejects paper documents. This is realized by extending the Pin&Play technology to support ‘pouts’, addressable pin-like devices that can remove themselves from a board using muscle wire actuators. We describe how this technology has been developed through two iterations of prototyping, application and formative study. An initial study revealed how potential mismatches between the physical and digital characteristics of pouts caused difficulties with users predicting pop-out events and reasoning about the state of pouts. This led us to extend pouts to reveal more of their internal state, an approach verified through a second study. It also raises more general issues for the design of pushback tangible technologies and ubiquitous interfaces.