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Selected Papers from the 2nd International Conference on Mathematical Modeling...
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Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020)

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 August 2020) | Viewed by 13993

Special Issue Editors

Prof. Dr. R. RAJA

E-Mail Website
Guest Editor
Alagappa University, Karaikudi, Tamilnadu, India
Interests: Abstract and fractional differential equations; Stability analysis of dynamical systems; Neural networks; Synchronization theory; Mathematical modeling and optimal control of population systems; Multiagent systems; Complex dynamical networks; Genetic regulatory networks
Prof. Dr. Chee Peng Lim

E-Mail Website
Guest Editor
Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia
Interests: data analytics; condition monitoring; optimisation and decision support
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ovidiu Bagdasar

E-Mail Website
Guest Editor
University of Derby, UK
Interests: Number theory; optimization; computational; discrete and industrial mathematics; but also mathematical education; with a focus on maths anxiety

Special Issue Information

Dear Colleagues,

The 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020) which was held in Alagappa University, Karaikudi, Tamilnadu, India, on 22–24 January 2020 was aimed to bring together research scholars, scientists and experts with Mathematics and Computation backgrounds in Science and Engineering. The significance of the conference was to promote interactions between theoretical, experimental and applied areas, so to encourage a rich exchange of ideas in emerging areas within Mathematics, Computer Science and Engineering.

All articles submitted to this Special Issue are expected to contain original ideas and novel approaches. This Special Issue offers researchers worldwide the opportunity to report their most recent developments and ideas in the field, with a special emphasis on the latest theoretical and practical technical advances.

Prof. Dr. R. RAJA
Prof. Dr. Chee Peng Lim
Prof. Dr. Ovidiu Bagdasar
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Applied Algebra
  • Advanced Analysis
  • Applied Mathematics and Modeling
  • Big Data Analytics
  • Coding Theory
  • Dynamical Systems
  • Fuzzy Sets and Logic
  • Numerical Analysis
  • Operations Research
  • Optimization Techniques
  • Scientific Computing
  • Stochastic Processes
  • Soft Computing
  • System Engineering

Published Papers (6 papers)

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Research

24 pages, 1105 KiB  
Article
A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space
by Pasakorn Yordsorn, Poom Kumam, Habib ur Rehman and Abdulkarim Hassan Ibrahim
Mathematics 2020, 8(7), 1165; https://0-doi-org.brum.beds.ac.uk/10.3390/math8071165 - 16 Jul 2020
Cited by 15 | Viewed by 1974
Abstract
In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration [...] Read more.
In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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26 pages, 563 KiB  
Article
Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability
by Usa Humphries, Grienggrai Rajchakit, Pramet Kaewmesri, Pharunyou Chanthorn, Ramalingam Sriraman, Rajendran Samidurai and Chee Peng Lim
Mathematics 2020, 8(5), 815; https://0-doi-org.brum.beds.ac.uk/10.3390/math8050815 - 18 May 2020
Cited by 43 | Viewed by 2258
Abstract
In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion [...] Read more.
In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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27 pages, 420 KiB  
Article
Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks
by Usa Humphries, Grienggrai Rajchakit, Pramet Kaewmesri, Pharunyou Chanthorn, Ramalingam Sriraman, Rajendran Samidurai and Chee Peng Lim
Mathematics 2020, 8(5), 801; https://0-doi-org.brum.beds.ac.uk/10.3390/math8050801 - 14 May 2020
Cited by 68 | Viewed by 2576
Abstract
We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet [...] Read more.
We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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13 pages, 341 KiB  
Article
Complex Intuitionistic Fuzzy Soft Lattice Ordered Group and Its Weighted Distance Measures
by S. Rajareega, J. Vimala and D. Preethi
Mathematics 2020, 8(5), 705; https://doi.org/10.3390/math8050705 - 2 May 2020
Cited by 14 | Viewed by 2131
Abstract
In recent years, the complex fuzzy set theory has intensified the attention of many researchers. This paper focuses on developing the algebraic structures pertaining to lattice ordered groups and lattice ordered subgroups for complex intuitionistic fuzzy soft set theory. Furthermore, some of their [...] Read more.
In recent years, the complex fuzzy set theory has intensified the attention of many researchers. This paper focuses on developing the algebraic structures pertaining to lattice ordered groups and lattice ordered subgroups for complex intuitionistic fuzzy soft set theory. Furthermore, some of their properties and operations are discussed. In addition, the weighted distance measures between two complex intuitionistic fuzzy soft lattice ordered groups such as weighted hamming, weighted normalized hamming, weighted euclidean and weighted normalized euclidean distance measures were introduced and also some of the algebraic properties of the weighted distance measures are verified. Moreover, the application of complex intuitionistic fuzzy soft lattice ordered groups by using the weighted distance measures is analysed. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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25 pages, 944 KiB  
Article
Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator
by Jamilu Abubakar, Poom Kumam, Habib ur Rehman and Abdulkarim Hassan Ibrahim
Mathematics 2020, 8(4), 609; https://0-doi-org.brum.beds.ac.uk/10.3390/math8040609 - 16 Apr 2020
Cited by 24 | Viewed by 2061
Abstract
Two inertial subgradient extragradient algorithms for solving variational inequality problems involving pseudomonotone operator are proposed in this article. The iterative schemes use self-adaptive step sizes which do not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild [...] Read more.
Two inertial subgradient extragradient algorithms for solving variational inequality problems involving pseudomonotone operator are proposed in this article. The iterative schemes use self-adaptive step sizes which do not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we show the weak and strong convergence of the sequences generated by the proposed algorithms. The strong convergence in the second algorithm follows from the use of viscosity method. Numerical experiments both in finite- and infinite-dimensional spaces are reported to illustrate the inertial effect and the computational performance of the proposed algorithms in comparison with the existing state of the art algorithms. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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22 pages, 1142 KiB  
Article
Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties
by Pharunyou Chanthorn, Grienggrai Rajchakit, Sriraman Ramalingam, Chee Peng Lim and Raja Ramachandran
Mathematics 2020, 8(4), 595; https://0-doi-org.brum.beds.ac.uk/10.3390/math8040595 - 15 Apr 2020
Cited by 39 | Viewed by 1941
Abstract
We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued [...] Read more.
We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued systems. We devise an appropriate Lyapunov-Krasovskii functional (LKF) equipped with general integral terms to facilitate the analysis. By exploiting the multiple integral inequality method, the sufficient conditions for the dissipativity of HTCVNN models are obtained via the linear matrix inequalities (LMIs). The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results. Full article
(This article belongs to the Special Issue Selected Papers from the 2nd International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020))
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