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Symmetry
Special Issues
Symmetry Applications in Uncertain Differential Equations
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Symmetry Applications in Uncertain Differential Equations

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 1627

Special Issue Editors

Dr. Anshui Li

E-Mail Website
Guest Editor
School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China
Interests: uncertain statistics; bayesian inference
Dr. Waichon Lio

E-Mail Website
Guest Editor
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: uncertainty theory; mathematical programming
Prof. Dr. Baoding Liu

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Interests: uncertainty theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

An uncertain differential equation is a type of differential equation involving uncertain processes. Nowadays, the study of uncertain differential equations is in a period of rapid development, and it involves fields including finance, optimal control, game theory, accelerated degradation test, birth rate, chemical reaction, crude oil price, drug metabolism, electric circuit, epidemic spread, gas futures price, heat conduction, liquid seepage, population, rumor spread, software reliability, spring vibration, and string vibration. The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results involving their symmetry properties, both from a theoretical and an applied point of view.

The topics of interest for this Special Issue include but are not limited to:

  1. uncertain differential equation;
  2. uncertain statistics;
  3. uncertain programming;
  4. uncertain calculus;
  5. uncertain finance.

Dr. Anshui Li
Dr. Waichon Lio
Prof. Dr. Baoding Liu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • uncertain differential equation
  • uncertain statistics
  • uncertainty theory
  • uncertain finance
  • symmetry
  • uncertain process
  • uncertain renewal process
  • uncertain calculus

Published Papers (2 papers)

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Research

15 pages, 3504 KiB  
Article
Least Squares Estimation of Multifactor Uncertain Differential Equations with Applications to the Stock Market
by Nanxuan Wu and Yang Liu
Symmetry 2024, 16(7), 904; https://doi.org/10.3390/sym16070904 - 16 Jul 2024
Viewed by 741
Abstract
Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, [...] Read more.
Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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15 pages, 362 KiB  
Article
A Symmetric Fourth Party Logistics Routing Problem with Multiple Distributors in Uncertain Random Environments
by Xinyu Gao, Xin Gao and Yang Liu
Symmetry 2024, 16(6), 701; https://doi.org/10.3390/sym16060701 - 6 Jun 2024
Viewed by 328
Abstract
Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In [...] Read more.
Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer’s supply, and distributor’s demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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