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Linear Topological Spaces
Published in Eberhard Malkowsky, Vladimir Rakočević, Advanced Functional Analysis, 2019
Eberhard Malkowsky, Vladimir Rakočević
Let X be a linear space and T be a topology with the property that the algebraic operations of the linear space are continuous. Then the pair (X,T), or X, for short, is called a linear topological space, or topological vector space (TVS). The topology of a linear topological space is referred to as a linear topology.
A Survey of Interest Flooding Attack in Named-Data Networking: Taxonomy, Performance and Future Research Challenges
Published in IETE Technical Review, 2022
Ren-Ting Lee, Yu-Beng Leau, Yong Jin Park, Mohammed Anbar
Kumar et al. [43] applied machine learning to detect IFA with a linear topology in NDN. The author tested variable detection approaches with the generated dataset. They tried on Multilayer Perceptron with Back Propagation (MLP + BP). Next, Radial Bases Function (RBF) with computed k-means clustering and spread of each RBF function corresponding to the node and include the mean of Euclidian distance of all data points from the centroid. Furthermore, the author combined the algorithm with Particle Swarm Optimization (RBF + PSO), RBF + JAYA and Teaching Learning-Based Optimization (RBF + TLBO). Lastly, the author included Support Vector Machine (SVM) and k-nearest neighbours (KNN) to identify IFA. The experiments showed that the neural network-based approaches such as MLP + BP, RBF + PSO, RBF + JAYA, RBF + TLBO has more accurate detection compared with other machine learning approaches such as KNN and SVM.
L 0-convex compactness and its applications to random convex optimization and random variational inequalities
Published in Optimization, 2021
Tiexin Guo, Erxin Zhang, Yachao Wang, Mingzhi Wu
Let be a random locally convex module over K with base . Since the -topology on E is a linear topology, one can speak of -boundedness. It is known and also clear that a subset G of E is -bounded iff for each one can have , namely for each , is bounded in probability (or, probabilistically bounded in terms of [7]). Another notion of boundedness is crucial for this paper: a subset G of E is said to be almost surely bounded if for each , namely is bounded in order for each . According to the resonance theorem in random normed modules [9,14,46], the following result was already obtained and will be used in this paper:
Phytochemical characterization and antioxidant, antibacterial and antimutagenic activities of aqueous extract from leaves of Alchornea glandulosa
Published in Journal of Toxicology and Environmental Health, Part A, 2018
Douglas Costa Gontijo, Marisa Alves Nogueira Diaz, Geraldo Célio Brandão, Pablo Costa Gontijo, Alaíde Braga de Oliveira, Luciano Gomes Fietto, João Paulo Viana Leite
In addition, antigenotoxic results indicated that EAG induced no marked effect at any of the concentrations assessed (Figure 5A). The reduction of supercoiling topology of the plasmid DNA (form I) in lanes treated with genotoxic agent SnCl2 and EAG was significant (Figure 5B). A significant increase of coiling topology (form II) and linear topology (form III), indicative of topological alteration of the plasmidial DNA, was noted. However, at concentrations 285 and 570 μg of EAG (lanes 4 and 5), there is no marked difference between control with absence of SnCl2 (lane 1), possibly signaling a antigenotoxic action of EAG. Thus, it is conceivable that a possible elevation in EAG concentrations might lead to an enhanced antigenotoxic action.