2275351
On best uniform restricted range approximation in complex-valued continuous function spaces
We investigate the problem of best restricted range approximation of complex-valued continuous functions for a very general system of restrictions. Our results, including the characterizations, uniqueness and strong uniqueness, extend all recent results due to Smirnovs.
17566608
Porosity of mutually nearest and mutually furthest points in Banach spaces
Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X. Let B(X) (resp. K(X)) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BG(X) denote the closure of the set {A ∈ B(X) : A ∩ G = φ} and KG(X) = BG(X)∩K(X). We introduce the admissible family A of B(X) and prove that EAo(G) (resp. EoA(G)), the set of all subsets F ∈ A ⊆ BG(X) (resp. F ∈ A ⊆ BG(X)) such that the minimization problem min(F, G) (resp. the maximization problem max(F, G)) is well-posed, is a dense Gδ-subset of A. Furthermore, when X is uniformly convex, we prove that A\EAo(G) and A\EoA(G) are σ-porous in A.
2028079
Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space
Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG (F) < rx (F), where rG (F) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ≥ 2 in the case when X is a complex Banach space.
10976471
Derivatives of Generalized Distance Functions and Existence of Generalized Nearest Points
The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or -1, then the generalized nearest points to x from G exist. We also give a partial answer (Theorem 3.5) to the open problem put forward by S. Fitzpatrick (1989, Bull. Austral. Math. Soc.39, 233-238).
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.
7000090
On isomorphisms of finite Cayley graphs--a survey
The isomorphism problem for Cayley graphs has been extensively investigated over the past 30 years. Recently, substantial progress has been made on the study of this problem, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained, and methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the finite simple group classification, through to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.
157891
ROLEX: relational on-line exchange with XML
1. OVERVIEW ROLEX is a research system for closely coupled XML-relational interoperation [2]. Whereas typical XML-based applications interoperate with existing relational databases via a “shred-and-publish” approach, the ROLEX system seeks to provide direct access to relational data via XML interfaces at the speed of cached XML data. To achieve this, ROLEX is integrated tightly with both the DBMS and the application through a standard interface supported by most XML parsers, the Document Object Model (DOM). Thus, in general, an application need not be modified to be used with ROLEX. With the DBMS providing performance qualitatively similar to cached data, XML applications can rely on it for concurrency control and recovery services. To support our integration model and performance goals, ROLEX is built on the DataBlitz Main-Memory Database System, allowing us to capitalize on low-latency access to data while still providing concurrency control and recovery [1]. The DOM interface supports the expected navigation functions: parent-to-child, child-to-parent, and sibling-to-sibling. A DOM interface to an XML view query supports all the DOM operations and behaves as if the user were navigating the XML document resulting from the query. In ROLEX, we implement a virtual DOM tree that goes a step further by providing the same interface without creating a physical DOM tree. A novelty of ROLEX is that it uses a navigational profile for the user or application when it optimizes view-query plans. While navigational profiles can, in principle, be quite complex, we currently adopt a very simple model. If n is a node in the schema tree with parent p, the navigation profile stores the probability that some node in the DOM tree generated by n will be visited given that its parent, generated by p, has been visited. Query output is produced by a navigable query plan. It provides, for each node n in the schema tree of a view query, two entities: (1) a subplan for evaluating the tag query for n, and (2) a navigation index. The navigation index serves to materialize the output of the tag query and supports efficient lookup based on parameter values,
2190827
Chosen-Plaintext Cryptanalysis of a Clipped-Neural-Network-Based Chaotic Cipher
At ISNN'04, a novel symmetric cipher was proposed, by combining a chaotic signal and a clipped neural network (CNN) for encryption. The present paper analyzes the security of this chaotic cipher against chosen-plaintext attacks, and points out that this cipher can be broken by a chosen-plaintext attack. Experimental analyses are given to support the feasibility of the proposed attack.
15126663
Semi-fragile watermarking scheme for authentication of JPEG images
With the increasing popularity of JPEG images, a need arises to devise effective watermarking techniques which consider JPEG compression as an acceptable manipulation. In this paper, we present a semi-fragile watermarking scheme which embeds a watermark in the quantized DCT domain. It is tolerant to JPEG compression to a pre-determined lowest quality factor, but is sensitive to all other malicious attacks, either in spatial or transform domains. Feature codes are extracted based on the relative sign and magnitudes of coefficients, and these are invariant due to an important property of JPEG compression. The employment of a nine-neighborhood mechanism ensures that non-deterministic block-wise dependence is achieved. Analysis and experimental results are provided to support the effectiveness of the scheme.
13583163
On certain convex matrix sets
Abstract We study some nonnegative matrix sets and investigate the relations between their extreme points. The results obtained answer a question posed by Marshall and Olkin and extend a result of Fulkerson concerning permutation matrices.