Symmetry in Functional Analysis and Engineering Mathematics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 3433

Special Issue Editor


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Special Issue Information

Dear Colleagues,

Symmetries appear in a number of phenomena in nature and science and thus are either the object of study or a requirement when engineering applications are developed. This happens in many scientific and engineering fields including, inter alia, aerospace, agricultural, civil, design, electronic, or mechanical engineering. Sometimes the reason is purely aesthetic to enhance the final perception of the product or construction, quite commonly it is an economical reason as this may lower the design and production costs, but on occasion it is a need, for instance, for aerodynamical reasons.

On the other hand, symmetries also do appear under different features in functional analysis. Sometimes researchers have studied if a given property is kept in a symmetric way under different structural properties, for instance, when continuous linear forms are exchanged with continuous seminorms while studying weak barrelledness conditions. In another setting, quite commonly the symmetric property has been relaxed, for instance, in the definition of metric spaces to obtain some interesting generalizations. However, on occasion the symmetry itself is a requirement, such as in symmetric groups theory.

The study of symmetry is thus a matter of interest in mathematics, engineering, and other scientific fields, opening new lines of research where mathematical tools have been used and developed.

This Special Issue focuses on the most recent advances in functional analysis, engineering, and arising in all fields of science, engineering applications, and other applied fields where symmetry is tackled. 

Prof. Dr. Luis Manuel Sánchez Ruiz
Guest Editor

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Published Papers (2 papers)

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Research

19 pages, 365 KiB  
Article
An Iterative Approach with the Inertial Method for Solving Variational-like Inequality Problems with Multivalued Mappings in a Banach Space
by Mohammad Farid and Saud Fahad Aldosary
Symmetry 2024, 16(2), 139; https://doi.org/10.3390/sym16020139 - 24 Jan 2024
Viewed by 931
Abstract
We formulate an iterative approach employing the inertial technique to approximate the anticipated solution for a generalized mixed variational-like inequality, as well as variational inequality and fixed point problems associated with a relatively nonexpansive multivalued mapping within the context of a real Banach [...] Read more.
We formulate an iterative approach employing the inertial technique to approximate the anticipated solution for a generalized mixed variational-like inequality, as well as variational inequality and fixed point problems associated with a relatively nonexpansive multivalued mapping within the context of a real Banach space. Additionally, we delve into the robust convergence of our suggested algorithm. Furthermore, we highlight certain implications and present numerical observations to underscore the significance of our findings. The proposed theorem extends and consolidates several previously published works. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Engineering Mathematics)
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18 pages, 351 KiB  
Article
Robust Variable Selection Based on Relaxed Lad Lasso
by Hongyu Li, Xieting Xu, Yajun Lu, Xi Yu, Tong Zhao and Rufei Zhang
Symmetry 2022, 14(10), 2161; https://doi.org/10.3390/sym14102161 - 15 Oct 2022
Cited by 2 | Viewed by 1487
Abstract
Least absolute deviation is proposed as a robust estimator to solve the problem when the error has an asymmetric heavy-tailed distribution or outliers. In order to be insensitive to the above situation and select the truly important variables from a large number of [...] Read more.
Least absolute deviation is proposed as a robust estimator to solve the problem when the error has an asymmetric heavy-tailed distribution or outliers. In order to be insensitive to the above situation and select the truly important variables from a large number of predictors in the linear regression, this paper introduces a two-stage variable selection method named relaxed lad lasso, which enables the model to obtain robust sparse solutions in the presence of outliers or heavy-tailed errors by combining least absolute deviation with relaxed lasso. Compared with lasso, this method is not only immune to the rapid growth of noise variables but also maintains a better convergence rate, which is Opn1/2. In addition, we prove that the relaxed lad lasso estimator has the property of consistency at large samples; that is, the model selects the number of important variables with a high probability of convergence to one. Through the simulation and empirical results, we further verify the outstanding performance of relaxed lad lasso in terms of prediction accuracy and the correct selection of informative variables under the heavy-tailed distribution. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Engineering Mathematics)
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