and Applied Analysis3It is clear that every k-Lipschitz mapping is continuous. Moreover, the Banach contrac-tion principle holds for a closed subset in a complete p-normed space.Definition 2.2 see 3 . Let X, ‖ · ‖p 0 < p ≤ 1 be a p-normed space and 0 < s ≤ p. A setC ⊂ X is said to be s-convex if the following condition is satisfied1 − t x t1/sy ∈ C, whenever x, y ∈ C, t ...

In many important application domains such as Business and Finance, Process Monitoring, and Security, huge and quickly increasing volumes of complex data are collected. Strong efforts are underway developing automatic and interactive analysis tools for mining useful information from these data repositories. Many data analysis algorithms require an appropriate definition of similarity (or distan...

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In [1], an analogue of the Grothendieck compactness principle for the weak topology was used to characterize Banach spaces with the Schur property. Using a different analogue of the Grothendieck compactness principle for the weak topology...

Abstract: In this paper, constraint rotation techniques are considered for preconditioning 0–1 knapsack problems. These techniques permit one to generate new inequalities by means of rotation of the original ones in order to approach the convex hull associated with the feasible integer points. The time and space complexities of Kianfar’s inequality rotation algorithm for combinatorial problems ...

Let T be an aperiodic and repetitive tiling of R with finite local complexity. We present a spectral sequence that converges to the K-theory of T with page-2 isomorphic to the Pimsner cohomology of T . It is a generalization of Serre spectral sequence to a class of spaces which are not fibered. The Pimsner cohomology of T generalizes the cohomology of the base space of a fibration with local co...

objectives: almond (prunus amygdalus) hull and shell are agricultural by-products that are a source of phenolic compounds.the processing of almond produce shell and hull, accounts for more than 50% by dry weight of the almond fruits. recently, more studies have focused on the influence of storage conditions and postharvest handling on the nutritional quality of fruits, especially the antioxidan...

The most successful approaches to extractive text summarization seek to maximize bigram coverage subject to a budget constraint. In this work, we propose instead to maximize semantic volume. We embed each sentence in a semantic space and construct a summary by choosing a subset of sentences whose convex hull maximizes volume in that space. We provide a greedy algorithm based on the GramSchmidt ...

The Shapley-Folkman theorem and its corollaries [ 1, 2, 3, 4, 5, 6, 81 provide strong bounds on the distance between the sum of a family of nonconvex sets and the convex hull of the sum. Proofs of the theorem are nonconstructive, and require moderately advanced analysis. The proof developed below is based on elementary considerations. It provides an approximation sequentially with the successiv...

Point clusters occur in both spatial and non-spatial data. In the former context they may represent segmented particle data, in the latter context they may represent clusters in scatterplots. In order to visualize such point clusters, enclosing surfaces lead to much better comprehension than pure point renderings. We propose a flexible system for the generation of enclosing surfaces for 3D poin...

Let X be a complex manifold and γ a simple closed curve inX . We address the question: What conditions on γ insure the existence of a 1-dimension complex variety Σ with boundary γ in X . When X = C, an answer to this question involves the polynomial hull of gamma. When X = P, complex projective space, the projective hull γ̂ of γ, a generalization of polynomial hull, comes into play. One always h...