Quasitopological vector spaces Yang, Zhongqiang; Hu, Zeying
Topology and its applications,
04/2024, Letnik:
346
Journal Article
Recenzirano
In this paper, motivated by a diffeological vector space with the D-topology, we introduce the concept of quasitopological vector space, which is a vector space with a topology satisfying the ...conditions that the vector addition is separately continuous in each variable, and the scalar multiplication is jointly continuous. The following results are proved: (1) Every quasitopological finite-dimensional vector space is a topological vector space. (2) For each infinite-dimensional vector space, we define a T1 non-Hausdorff topology on it such that it is a quasitopological vector space but is not a topological vector space.
Abstract
In the present work, we introduce the notion of pseudo-seminorm, then we established, a criterion for the metrizability of a pseudo vector space with a pseudo topology . It is specified, ...that for the metrizability of is necessary and sufficient that is first countable. Moreover, a sufficient condition for existence a base for the filter of neighborhoods of zero is proved and demonstrated that this condition introduces a compatible pseudo topology with the algebraic vector space structures.
In set theory without the Axiom of Choice (
$\mathsf {AC}$
), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost ...disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.
Traditional Web news media retrieval technology can only meet the specific requirements of customers. Because of its universal characteristics, it cannot meet the needs of different environments, ...different purposes, and different times simultaneously. Researchers have proposed a search method for online news media, which is used for computing the semantic grouping vector space model. The customer's interest model is analyzed through the characteristics of the user's different classification areas. In this paper, we propose a vector space model that performs semantic grouping based on feature words. The model divides four groups that are relatively independent in the meaning of feature words in a news report: time, place, person, and event, and then forms four vector spaces and calculates the weight value and similarity of each vector space. Theoretical analysis and experimental results show that the improved model is suitable for searching Web news information and improves the calibration rate, query speed, and calibration rate.
In this paper, the notions of (L,M)-fuzzy bornological space and (L,M)-fuzzy bornological vector space are introduced. Some properties are discussed. It is shown that the category of (L,M)-fuzzy ...bornological (vector) spaces, which embeds the category of M-fuzzifying bornological (vector) spaces as a reflective subcategory, is topological category. Further, it is proved that the category of M-fuzzifying bornological spaces can be embedded in the category of stratified (L,M)-fuzzy bornological spaces as a coreflective subcategory.
The aim of this paper is to answer Smarandache conjectures about neutrosophic quadruple vector spaces. This paper depends on the concept of weak n-refined neutrosophic vector space to prove that an ...NQ vector space V defined over the field F is isomorphic to F *F *F *F. Keywords: n-Refined weak neutrosophic vector space, NQ vector space, vector space homomorphism.
A novel space vector modulation (SVM) technique for a three-level five-phase inverter is described based on an optimized five vectors concept. The concept utilizes a novel vector minimization ...technique that reduces the number of vectors in the d 1 - q 1 vector space by identifying candidate vectors in each of the ten sectors that comprise the decagon vector space. The candidate vectors are selected based on the inequality relationship between the five-phase voltages during each switching cycle. Using this technique, the original 243 inverter states are reduced to 113 candidate vectors, and from the remaining states ten possible switching sequences in each sector are utilized to develop the desired voltage reference in the d 1 - q 1 vector space while forcing a null vector in the d 3 - q 3 vector space. A novel region determination technique is also introduced to identify the subregion that the d 1 - q 1 voltage vector occupies. This technique significantly reduces the computational overhead required when implementing SVM techniques with multilevel and multiphase inverters. The space vector technique can utilize redundant vectors to assist in balancing subcycle variation of the dc-link capacitor voltage under unbalanced load conditions. Experiments validate simulation results where the low-order voltage harmonics show that the d 3 - q 3 voltage vector is null.
Cloud computing has emerging as a promising pattern for data outsourcing and high-quality data services. However, concerns of sensitive information on cloud potentially causes privacy problems. Data ...encryption protects data security to some extent, but at the cost of compromised efficiency. Searchable symmetric encryption (SSE) allows retrieval of encrypted data over cloud. In this paper, we focus on addressing data privacy issues using SSE. For the first time, we formulate the privacy issue from the aspect of similarity relevance and scheme robustness. We observe that server-side ranking based on order-preserving encryption (OPE) inevitably leaks data privacy. To eliminate the leakage, we propose a two-round searchable encryption (TRSE) scheme that supports top-k multikeyword retrieval. In TRSE, we employ a vector space model and homomorphic encryption. The vector space model helps to provide sufficient search accuracy, and the homomorphic encryption enables users to involve in the ranking while the majority of computing work is done on the server side by operations only on ciphertext. As a result, information leakage can be eliminated and data security is ensured. Thorough security and performance analysis show that the proposed scheme guarantees high security and practical efficiency.
Fréchet Spaces via Fuzzy Structures Jasim, Ahmad Ghanawi; Al-Nafie, Z. D.
Journal of physics. Conference series,
03/2021, Letnik:
1818, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Abstract
The concept of fuzzy Fréchet space
Z
introduced in two equivalent ways, the first way when
Z
considered as a fuzzy
F
− locally convex topological vector space and the second one when
Z
...defined as a complete fuzzy topological vector space whose fuzzy topology generated by a countable separating collection of fuzzy seminorms. Moreover, many classes of continuous mappings between these spaces are established and specified that the class of continuous, strongly continuous and sequentially continuous mappings between these spaces are equivalent.
PDF
