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Symmetry, Volume 13, Issue 8 (August 2021) – 242 articles

Cover Story (view full-size image): Topology–symmetry analysis of the OD theory allows revealing the similarity of crystals and assigning them to the common structural family. New iodate Ba(IO3)OH occur unexpectedly and are relative to highly nonlinear optical Bi(IO3)O. The higher tetragonal (!) local symmetry of the central first layer produces a different conjugation in the triple with the second layers, leading to higher or lower optical nonlinearity for two members of family. Such structures may be ordered or have significant disorder. The topology–symmetry analysis of other pairs of iodate AgBi(IO3)4 and iodate-sulfate AgBi(SO4)(IO3) leads to obtaining a semi-quantitatively evaluation of nonlinear optical properties based on structural data. Such an approach is original and promising. View this paper
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16 pages, 6691 KiB  
Article
Web-Browsing Application Using Web Scraping Technology in Korean Network Separation Application
by Won-Chi Jung, Jinsu Kim and Namje Park
Symmetry 2021, 13(8), 1550; https://doi.org/10.3390/sym13081550 - 23 Aug 2021
Cited by 3 | Viewed by 2538
Abstract
Attackers’ intrusion into the Enterprise LAN is increasing every year, and the method is becoming more intelligent and crafty. Various security measures against external network intrusions, such as firewalls, are being studied and applied to protect against external attacks, but it is difficult [...] Read more.
Attackers’ intrusion into the Enterprise LAN is increasing every year, and the method is becoming more intelligent and crafty. Various security measures against external network intrusions, such as firewalls, are being studied and applied to protect against external attacks, but it is difficult to respond to increasing attacks. Most institutions block access from the external network for the safety of the internal network and allow access from the internal network to the external network through some restricted ports. In particular, restricted ports in subject to a variety of security techniques to block intrusion into the internal network, but in the process, access to the internal network is only applied by restricted ports, making it inefficient to handle internal requests. Although various studies have been conducted on network isolation to address these challenges, it is difficult to perform tasks efficiently as security functions, such as detecting whether request data is attacked or not, during actual application. The proposed technique is a network-blocking-based network separation technique that converts data from the external network connected to the Internet into symmetry data from which malicious code is removed through an agent and delivers it to the client of the internal network. We propose a technique to provide access. Full article
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43 pages, 11181 KiB  
Article
Neurofunctional Symmetries and Asymmetries during Voluntary out-of- and within-Body Vivid Imagery Concurrent with Orienting Attention and Visuospatial Detection
by Amedeo D’Angiulli, Darren Kenney, Dao Anh Thu Pham, Etienne Lefebvre, Justin Bellavance and Derrick Matthew Buchanan
Symmetry 2021, 13(8), 1549; https://doi.org/10.3390/sym13081549 - 23 Aug 2021
Cited by 5 | Viewed by 3675
Abstract
We explored whether two visual mental imagery experiences may be differentiated by electroencephalographic (EEG) and performance interactions with concurrent orienting external attention (OEA) to stimulus location and subsequent visuospatial detection. We measured within-subject (N = 10) event-related potential (ERP) changes during out-of-body imagery [...] Read more.
We explored whether two visual mental imagery experiences may be differentiated by electroencephalographic (EEG) and performance interactions with concurrent orienting external attention (OEA) to stimulus location and subsequent visuospatial detection. We measured within-subject (N = 10) event-related potential (ERP) changes during out-of-body imagery (OBI)—vivid imagery of a vertical line outside of the head/body—and within-body imagery (WBI)—vivid imagery of the line within one’s own head. Furthermore, we measured ERP changes and line offset Vernier acuity (hyperacuity) performance concurrent with those imagery, compared to baseline detection without imagery. Relative to OEA baseline, OBI yielded larger N200 and P300, whereas WBI yielded larger P50, P100, N400, and P800. Additionally, hyperacuity dropped significantly when concurrent with both imagery types. Partial least squares analysis combined behavioural performance, ERPs, and/or event-related EEG band power (ERBP). For both imagery types, hyperacuity reduction correlated with opposite frontal and occipital ERP amplitude and polarity changes. Furthermore, ERP modulation and ERBP synchronizations for all EEG frequencies correlated inversely with hyperacuity. Dipole Source Localization Analysis revealed unique generators in the left middle temporal gyrus (WBI) and in the right frontal middle gyrus (OBI), whereas the common generators were in the left precuneus and middle occipital cortex (cuneus). Imagery experiences, we conclude, can be identified by symmetric and asymmetric combined neurophysiological-behavioural patterns in interactions with the width of attentional focus. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Brain Behavior and Perception II)
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13 pages, 271 KiB  
Article
A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
by Xianyong Huang, Shanhe Wu and Bicheng Yang
Symmetry 2021, 13(8), 1548; https://doi.org/10.3390/sym13081548 - 23 Aug 2021
Cited by 2 | Viewed by 1493
Abstract
In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help [...] Read more.
In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
17 pages, 4004 KiB  
Article
Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters
by Xuefen Li and Fangfang Shen
Symmetry 2021, 13(8), 1547; https://doi.org/10.3390/sym13081547 - 23 Aug 2021
Viewed by 1376
Abstract
Because the two-dimensional coupled ecosystem has perfect symmetry, the dynamical behavior of symmetric dynamical system is discussed. The analysis of the dynamical behavior of a two-dimensional coupled ecosystem with stochastic parameters is explored in this paper. Firstly, a two-dimensional coupled ecosystem with stochastic [...] Read more.
Because the two-dimensional coupled ecosystem has perfect symmetry, the dynamical behavior of symmetric dynamical system is discussed. The analysis of the dynamical behavior of a two-dimensional coupled ecosystem with stochastic parameters is explored in this paper. Firstly, a two-dimensional coupled ecosystem with stochastic parameters is established, it is transformed into a deterministic equivalent system by orthogonal polynomial approximation. Then, analysis of the dynamical behaviour of equivalently deterministic coupled ecosystems is performed using stability theory. At last, we analyzed the dynamical behaviour of non-trivial points by means of the mathematics analysis method and found the influence of random parameters on asymptotic stability in coupled ecosystem is prominent. The dynamical behaviour analysis results were verified by numerical simulation. Full article
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28 pages, 1148 KiB  
Article
Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment
by Ashot S. Gevorkyan, Alexander V. Bogdanov and Vladimir V. Mareev
Symmetry 2021, 13(8), 1546; https://doi.org/10.3390/sym13081546 - 23 Aug 2021
Cited by 3 | Viewed by 1806
Abstract
Evolution of a self-consistent joint system (JS), i.e., a quantum system (QS) + thermal bath (TB), is considered within the framework of the Langevin–Schrödinger (L-Sch) type equation. As a tested QS, we considered two linearly coupled quantum oscillators that interact with TB. The [...] Read more.
Evolution of a self-consistent joint system (JS), i.e., a quantum system (QS) + thermal bath (TB), is considered within the framework of the Langevin–Schrödinger (L-Sch) type equation. As a tested QS, we considered two linearly coupled quantum oscillators that interact with TB. The influence of TB on QS is described by the white noise type autocorrelation function. Using the reference differential equation, the original L-Sch equation is reduced to an autonomous form on a random space–time continuum, which reflects the fact of the existence of a hidden symmetry of JS. It is proven that, as a result of JS relaxation, a two-dimensional quantized small environment is formed, which is an integral part of QS. The possibility of constructing quantum thermodynamics from the first principles of non-Hermitian quantum mechanics without using any additional axioms has been proven. A numerical algorithm has been developed for modeling various properties and parameters of the QS and its environment. Full article
(This article belongs to the Special Issue Symmetry in Particle Physics II)
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21 pages, 564 KiB  
Article
A Technology Acceptance Model-Based Analytics for Online Mobile Games Using Machine Learning Techniques
by Shaifali Chauhan, Mohit Mittal, Marcin Woźniak, Swadha Gupta and Rocío Pérez de Prado
Symmetry 2021, 13(8), 1545; https://doi.org/10.3390/sym13081545 - 23 Aug 2021
Cited by 25 | Viewed by 4228
Abstract
In recent years, the enhancement in technology has been envisioning for people to complete tasks in an easier way. Every manufacturing industry requires heavy machinery to accomplish tasks in a symmetric and systematic way, which is much easier with the help of advancement [...] Read more.
In recent years, the enhancement in technology has been envisioning for people to complete tasks in an easier way. Every manufacturing industry requires heavy machinery to accomplish tasks in a symmetric and systematic way, which is much easier with the help of advancement in the technology. The technological advancement directly affects human life as a result. It is found that humans are now fully dependent on it. The online game industry is one example of technology breakthrough. It is now a prominent industry to develop online games at world level. In this paper, our main objective is to analyze major factors which encourage mobile games industry to expand. Analyzing the system and symmetric relations inside can be done into two phases. The first phase is through a TAM Model, which is a very efficient way to solve statistical problems, and the second phase is with machine learning (ML) techniques, such as SVM, logistic regression, etc. Both strategies are popular and efficient in analyzing a system while maintaining the symmetry in a better way. Therefore, according to results from both the TAM model and ML approach, it is clear that perceived usefulness, attitude, and symmetric flow are important factors for game industry. The analytics provide a clear insight that perceived usefulness is an important parameter over behavior intention for the online mobile game industry. Full article
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19 pages, 590 KiB  
Article
Comparative Study of Univariate and Multivariate Long Short-Term Memory for Very Short-Term Forecasting of Global Horizontal Irradiance
by Ashis Kumar Mandal, Rikta Sen, Saptarsi Goswami and Basabi Chakraborty
Symmetry 2021, 13(8), 1544; https://doi.org/10.3390/sym13081544 - 23 Aug 2021
Cited by 5 | Viewed by 2277
Abstract
Accurate global horizontal irradiance (GHI) forecasting is crucial for efficient management and forecasting of the output power of photovoltaic power plants. However, developing a reliable GHI forecasting model is challenging because GHI varies over time, and its variation is affected by changes in [...] Read more.
Accurate global horizontal irradiance (GHI) forecasting is crucial for efficient management and forecasting of the output power of photovoltaic power plants. However, developing a reliable GHI forecasting model is challenging because GHI varies over time, and its variation is affected by changes in weather patterns. Recently, the long short-term memory (LSTM) deep learning network has become a powerful tool for modeling complex time series problems. This work aims to develop and compare univariate and several multivariate LSTM models that can predict GHI in Guntur, India on a very short-term basis. To build the multivariate time series models, we considered all possible combinations of temperature, humidity, and wind direction variables along with GHI as inputs and developed seven multivariate models, while in the univariate model, we considered only GHI variability. We collected the meteorological data for Guntur from 1 January 2016 to 31 December 2016 and built 12 datasets, each containing variability of GHI, temperature, humidity, and wind direction of a month. We then constructed the models, each of which measures up to 2 h ahead of forecasting of GHI. Finally, to measure the symmetry among the models, we evaluated the performances of the prediction models using root mean square error (RMSE) and mean absolute error (MAE). The results indicate that, compared to the univariate method, each multivariate LSTM performs better in the very short-term GHI prediction task. Moreover, among the multivariate LSTM models, the model that incorporates the temperature variable with GHI as input has outweighed others, achieving average RMSE values 0.74 W/m2–1.5 W/m2. Full article
(This article belongs to the Section Computer)
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19 pages, 7167 KiB  
Article
Post-Processing of High Formwork Monitoring Data Based on the Back Propagation Neural Networks Model and the Autoregressive—Moving-Average Model
by Yang Yang, Lin Yang and Gang Yao
Symmetry 2021, 13(8), 1543; https://doi.org/10.3390/sym13081543 - 23 Aug 2021
Cited by 6 | Viewed by 2399
Abstract
Many high formwork systems are currently equipped with health monitoring systems, and the analysis of the data obtained can determine whether high formwork is a hazard. Therefore, the post-processing of monitoring data has become an issue of widespread concern. In this paper, we [...] Read more.
Many high formwork systems are currently equipped with health monitoring systems, and the analysis of the data obtained can determine whether high formwork is a hazard. Therefore, the post-processing of monitoring data has become an issue of widespread concern. In this paper, we discussed the fitting effect of the symmetrical high formwork monitoring data using the autoregressive–moving-average (ARMA) model and the back propagation neural networks (BPNN) combined model to process. In the actual project, the symmetry of the high formwork system allows the analysis of local monitoring results to be well extended to the whole. For the establishment of the ARMA model, the accurate judgment of the model order has a significant impact. In this paper, back propagation neural networks (BPNN) are used to simulate the ARMA process. The order of the ARMA model is estimated by determining the optimal neural network structure, which is suitable for linear or nonlinear sequences. We validated this approach from the ARMA model data simulated in Monte Carlo and compared it with the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The length of the sequence, the coefficients and the order of the ARMA model are considered as factors that influence the judgment effect. Under different conditions, the BPNN always shows an accuracy rate of more than 90%, while the BIC only has a higher accuracy rate when the model order is low and the judgment efficiency of the AIC is below 50%. Finally, the proposed method successfully modeled the stress sequence and obtained the stress change trend. Compared with AIC and BIC, the efficiency of the processing time series is increased by about 50% when an order is obtained by BPNN. Full article
(This article belongs to the Special Issue Symmetry in Structural Health Monitoring)
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22 pages, 1550 KiB  
Article
Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method
by Saima Rashid, Khadija Tul Kubra and Juan Luis García Guirao
Symmetry 2021, 13(8), 1542; https://doi.org/10.3390/sym13081542 - 23 Aug 2021
Cited by 19 | Viewed by 2004
Abstract
In this paper, the Aboodh transform is utilized to construct an approximate analytical solution for the time-fractional Zakharov–Kuznetsov equation (ZKE) via the Adomian decomposition method. In the context of a uniform magnetic flux, this framework illustrates the action of weakly nonlinear ion acoustic [...] Read more.
In this paper, the Aboodh transform is utilized to construct an approximate analytical solution for the time-fractional Zakharov–Kuznetsov equation (ZKE) via the Adomian decomposition method. In the context of a uniform magnetic flux, this framework illustrates the action of weakly nonlinear ion acoustic waves in plasma carrying cold ions and hot isothermal electrons. Two compressive and rarefactive potentials (density fraction and obliqueness) are illustrated. With the aid of the Caputo derivative, the essential concepts of fractional derivatives are mentioned. A powerful research method, known as the Aboodh Adomian decomposition method, is employed to construct the solution of ZKEs with success. The Aboodh transform is a refinement of the Laplace transform. This scheme also includes uniqueness and convergence analysis. The solution of the projected method is demonstrated in a series of Adomian components that converge to the actual solution of the assigned task. In addition, the findings of this procedure have established strong ties to the exact solutions to the problems under investigation. The reliability of the present procedure is demonstrated by illustrative examples. The present method is appealing, and the simplistic methodology indicates that it could be straightforwardly protracted to solve various nonlinear fractional-order partial differential equations. Full article
(This article belongs to the Section Mathematics)
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27 pages, 35345 KiB  
Article
Analytical Fragility Curves for Seismic Design of Glass Systems Based on Cloud Analysis
by Silvana Mattei and Chiara Bedon
Symmetry 2021, 13(8), 1541; https://doi.org/10.3390/sym13081541 - 23 Aug 2021
Cited by 5 | Viewed by 2273
Abstract
Given the growing spread of glass as a construction material, the knowledge of structural response must be ensured, especially under dynamic accidental loads. In this regard, an increasingly popular method to probabilistically characterize the seismic response of a given structure is based on [...] Read more.
Given the growing spread of glass as a construction material, the knowledge of structural response must be ensured, especially under dynamic accidental loads. In this regard, an increasingly popular method to probabilistically characterize the seismic response of a given structure is based on the use of “fragility” or “seismic vulnerability” curves. Most existing applications, however, typically refer to construction and structural members composed of traditional building materials. The present study extends and adapts such a calculation method to innovative structural glass systems, which are characterized by specific material properties and expected damage mechanisms, restraint details, and dynamic features. Suitable Engineering Demand Parameters (EDPs) for seismic design are thus required. In this paper, a major advantage is represented by the use of Cloud Analysis in the Cornell’s reliability method, for the seismic assessment of two different case-study glass systems. Cloud Analysis is known to represent a simple and immediate tool to analytically investigate a given (glass) structure by taking into account variations in seismic motions and uncertainties of structural parameters. Such a method is exploited by means of detailed three-dimensional (3D) Finite Element (FE) numerical models and non-linear dynamic analyses (ABAQUS/Standard). Critical issues and typical failure mechanisms for in-plane seismically loaded glass systems are discussed. The validity of reference EDPs are addressed for the examined solutions. Based on a broad seismic investigation (60 records in total), fragility curves are developed from parametric results, so as to support a multi-hazard performance-based design (PBD) procedure. Full article
(This article belongs to the Special Issue Symmetry Applied in Special Engineering)
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14 pages, 4162 KiB  
Article
An Effective Evaluation of Wavelength Scheduling for Various WDM-PON Network Designs with Traffic Protection Provision
by Rastislav Róka
Symmetry 2021, 13(8), 1540; https://doi.org/10.3390/sym13081540 - 23 Aug 2021
Cited by 8 | Viewed by 1940
Abstract
Recently, metropolitan and access communication networks have markedly developed by utilizing a variety of technologies. Their bearer communication infrastructures will be mostly exploiting the optical transmission medium where wavelength division multiplexing techniques will play an important role. This contribution discusses the symmetric sharing [...] Read more.
Recently, metropolitan and access communication networks have markedly developed by utilizing a variety of technologies. Their bearer communication infrastructures will be mostly exploiting the optical transmission medium where wavelength division multiplexing techniques will play an important role. This contribution discusses the symmetric sharing of common optical network resources in wavelength and time domains. Wavelength-Division Multiplexed Passive Optical Networks (WDM-PON) attract considerable attention regarding the next generation of optical metropolitan and access networks. The main purpose of this contribution is presented by the analysis of possible scheduling of wavelengths for our novel hybrid network topologies considered for WDM-PON networks. This contribution briefly deploys adequate Dynamic Wavelength Allocation (DWA) algorithms for selected WDM-PON network designs with the provision of traffic protection when only passive optical components in remote nodes are utilized. The main part of this study is focused on the use of wavelength scheduling methods for selected WDM-PON network designs. For evaluation of offline and online wavelength scheduling for novel hybrid network topologies, a simulation model realized in the Matlab programming environment allows to analyze interactions between various metropolitan and access parts in the Optical Distribution Network (ODN) related to advanced WDM-PON network designs. Finally, wavelength scheduling methods are compared from a viewpoint of utilization in advanced WDM-PON networks designs. Full article
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12 pages, 382 KiB  
Article
Coloring Properties of Mixed Cycloids
by György Dósa, Nicholas Newman, Zsolt Tuza and Vitaly Voloshin
Symmetry 2021, 13(8), 1539; https://doi.org/10.3390/sym13081539 - 21 Aug 2021
Cited by 2 | Viewed by 1794
Abstract
In this paper, we investigate partitions of highly symmetrical discrete structures called cycloids. In general, a mixed hypergraph has two types of hyperedges. The vertices are colored in such a way that each C-edge has two vertices of the same color, and [...] Read more.
In this paper, we investigate partitions of highly symmetrical discrete structures called cycloids. In general, a mixed hypergraph has two types of hyperedges. The vertices are colored in such a way that each C-edge has two vertices of the same color, and each D-edge has two vertices of distinct colors. In our case, a mixed cycloid is a mixed hypergraph whose vertices can be arranged in a cyclic order, and every consecutive p vertices form a C-edge, and every consecutive q vertices form a D-edge in the ordering. We completely determine the maximum number of colors that can be used for any p3 and any q2. We also develop an algorithm that generates a coloring with any number of colors between the minimum and maximum. Finally, we discuss the colorings of mixed cycloids when the maximum number of colors coincides with its upper bound, which is the largest cardinality of a set of vertices containing no C-edge. Full article
(This article belongs to the Special Issue Research on Symmetry Applied in Graph Theory)
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21 pages, 370 KiB  
Article
Certain Applications of Generalized Kummer’s Summation Formulas for 2F1
by Junesang Choi
Symmetry 2021, 13(8), 1538; https://doi.org/10.3390/sym13081538 - 21 Aug 2021
Cited by 13 | Viewed by 1906
Abstract
We present generalizations of three classical summation formulas 2F1 due to Kummer, which are able to be derived from six known summation formulas of those types. As certain simple particular cases of the summation formulas provided here, we give a number [...] Read more.
We present generalizations of three classical summation formulas 2F1 due to Kummer, which are able to be derived from six known summation formulas of those types. As certain simple particular cases of the summation formulas provided here, we give a number of interesting formulas for double-finite series involving quotients of Gamma functions. We also consider several other applications of these formulas. Certain symmetries occur often in mathematical formulae and identities, both explicitly and implicitly. As an example, as mentioned in Remark 1, evident symmetries are naturally implicated in the treatment of generalized hypergeometric series. Full article
(This article belongs to the Special Issue Various Approaches for Generalized Integral Transforms)
18 pages, 32049 KiB  
Article
Building a Connected Communication Network for UAV Clusters Using DE-MADDPG
by Zixiong Zhu, Nianhao Xie, Kang Zong and Lei Chen
Symmetry 2021, 13(8), 1537; https://doi.org/10.3390/sym13081537 - 20 Aug 2021
Cited by 6 | Viewed by 2715
Abstract
Clusters of unmanned aerial vehicles (UAVs) are often used to perform complex tasks. In such clusters, the reliability of the communication network connecting the UAVs is an essential factor in their collective efficiency. Due to the complex wireless environment, however, communication malfunctions within [...] Read more.
Clusters of unmanned aerial vehicles (UAVs) are often used to perform complex tasks. In such clusters, the reliability of the communication network connecting the UAVs is an essential factor in their collective efficiency. Due to the complex wireless environment, however, communication malfunctions within the cluster are likely during the flight of UAVs. In such cases, it is important to control the cluster and rebuild the connected network. The asymmetry of the cluster topology also increases the complexity of the control mechanisms. The traditional control methods based on cluster consistency often rely on the motion information of the neighboring UAVs. The motion information, however, may become unavailable because of the interrupted communications. UAV control algorithms based on deep reinforcement learning have achieved outstanding results in many fields. Here, we propose a cluster control method based on the Decomposed Multi-Agent Deep Deterministic Policy Gradient (DE-MADDPG) to rebuild a communication network for UAV clusters. The DE-MADDPG improves the framework of the traditional multi-agent deep deterministic policy gradient (MADDPG) algorithm by decomposing the reward function. We further introduce the reward reshaping function to facilitate the convergence of the algorithm in sparse reward environments. To address the instability of the state-space in the reinforcement learning framework, we also propose the notion of the virtual leader–follower model. Extensive simulations show that the success rate of the DE-MADDPG is higher than that of the MADDPG algorithm, confirming the effectiveness of the proposed method. Full article
(This article belongs to the Section Computer)
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11 pages, 300 KiB  
Article
Subclasses of Uniform Univalent Functions Associated with Srivastava and Attiya Operator
by Mohammad Yaseen, Irfan Ali, Sardar Muhammad Hussain and Jong-Suk Ro
Symmetry 2021, 13(8), 1536; https://doi.org/10.3390/sym13081536 - 20 Aug 2021
Viewed by 1395
Abstract
In this paper, we introduce new subclasses kSTs(p,β) and kUKs(p,β) of analytic and univalent functions in the canonical domain associated with the Srivastava and Attiya [...] Read more.
In this paper, we introduce new subclasses kSTs(p,β) and kUKs(p,β) of analytic and univalent functions in the canonical domain associated with the Srivastava and Attiya operator. The radius problems of these subclasses regarding symmetrical points are investigated and compared with previous known results. Certain properties and conditions of these subclasses such as integral representation are also discussed in this work. Full article
(This article belongs to the Special Issue Complex Analysis, in Particular Analytic and Univalent Functions)
28 pages, 1626 KiB  
Article
An Implementation Suite for a Hybrid Public Key Infrastructure
by Jason Chia, Swee-Huay Heng, Ji-Jian Chin, Syh-Yuan Tan and Wei-Chuen Yau
Symmetry 2021, 13(8), 1535; https://doi.org/10.3390/sym13081535 - 20 Aug 2021
Cited by 1 | Viewed by 3635
Abstract
Public key infrastructure (PKI) plays a fundamental role in securing the infrastructure of the Internet through the certification of public keys used in asymmetric encryption. It is an industry standard used by both public and private entities that costs a lot of resources [...] Read more.
Public key infrastructure (PKI) plays a fundamental role in securing the infrastructure of the Internet through the certification of public keys used in asymmetric encryption. It is an industry standard used by both public and private entities that costs a lot of resources to maintain and secure. On the other hand, identity-based cryptography removes the need for certificates, which in turn lowers the cost. In this work, we present a practical implementation of a hybrid PKI that can issue new identity-based cryptographic keys for authentication purposes while bootstrapping trust with existing certificate authorities. We provide a set of utilities to generate and use such keys within the context of an identity-based environment as well as an external environment (i.e., without root trust to the private key generator). Key revocation is solved through our custom naming design which currently supports a few scenarios (e.g., expire by date, expire by year and valid for year). Our implementation offers a high degree of interoperability by incorporating X.509 standards into identity-based cryptography (IBC) compared to existing works on hybrid PKI–IBC systems. The utilities provided are minimalist and can be integrated with existing tools such as the Enterprise Java Bean Certified Authority (EJBCA). Full article
(This article belongs to the Section Computer)
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21 pages, 1385 KiB  
Article
Search of the Shortest Path in a Communication Network with Fuzzy Cost Functions
by Lissette Valdés, Alfonso Ariza, Sira M. Allende, Alicia Triviño and Gonzalo Joya
Symmetry 2021, 13(8), 1534; https://doi.org/10.3390/sym13081534 - 20 Aug 2021
Cited by 3 | Viewed by 1896
Abstract
A communication network management system takes the measurements of its state variables at specific instants of time, considering them constant in the interval between two consecutive measurements. Nevertheless, this assumption is not true, since these variables evolve in real time. Therefore, uncertainty is [...] Read more.
A communication network management system takes the measurements of its state variables at specific instants of time, considering them constant in the interval between two consecutive measurements. Nevertheless, this assumption is not true, since these variables evolve in real time. Therefore, uncertainty is inherent in the processing of the measurements during the intervals so that they cannot be efficiently managed using crisp variables. In this paper, we face this problem by modeling the communications network as a type-V fuzzy graph, where both the nodes and the links are described with precision, but the cost of each link is modeled as a triangular fuzzy number. Different fuzzy cost allocation functions and fuzzy optimization strategies are described and applied to the search for the shortest path between two nodes. An experimental study has been conducted using two representative networks: the backbone network of Nippon Telegraph and Telephone Corporation (NTT) and the National Science Foundation’s Network (NFSNET). In these networks, our fuzzy cost functions and strategies have been compared with the well-known crisp equivalents. The optimal search strategies are based on the proposed Fuzzy Dijkstra Algorithm (FDA), which is described deeply. The simulation results demonstrate that in all cases the fuzzy alternatives surpass or equal the crisp equivalents with statistically significant values. Specifically, the so-called Strategy 8 presents the best throughput, as it significantly exceeds the performance of all those evaluated, achieving a Global Mean Delivery Rate (GMDR) close to 1. Full article
(This article belongs to the Special Issue Graph Algorithms and Graph Theory)
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19 pages, 829 KiB  
Article
Shear-Driven Mechanism of Temperature Gradient Formation in Microfluidic Nematic Devices: Theory and Numerical Studies
by Izabela Śliwa and Alex V. Zakharov
Symmetry 2021, 13(8), 1533; https://doi.org/10.3390/sym13081533 - 20 Aug 2021
Cited by 1 | Viewed by 1466
Abstract
The purpose of this paper is to show some routes in describing the mechanism responsible for the formation of the temperature difference ΔT at the boundaries of the microfluidic hybrid aligned nematic (HAN) channel, initially equal to zero, if one sets up [...] Read more.
The purpose of this paper is to show some routes in describing the mechanism responsible for the formation of the temperature difference ΔT at the boundaries of the microfluidic hybrid aligned nematic (HAN) channel, initially equal to zero, if one sets up the stationary hydrodynamic flow vst or under the effect of an externally applied shear stress (SS) to the bounding surfaces. Calculations based on the nonlinear extension of the classical Ericksen–Leslie theory, supplemented by thermomechanical correction of the SS σzx and Rayleigh dissipation function while accounting for the entropy balance equation, show that the ΔT is proportional to the heat flux q across the HAN channel and grows by up to several degrees under the influence of the externally applied SS. The role of vst=ust(z)i^ with a sharp triangular profile ust(z) across the HAN in the production of the highest ΔT is also investigated. Full article
(This article belongs to the Section Chemistry: Symmetry/Asymmetry)
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18 pages, 3466 KiB  
Article
Design and Catalytic Behaviour of Hosted in Activated Carbon Foam CoxZn1−xFe2O4 Ferrites
by Tanya Tsoncheva, Radostina Ivanova, Nikolay Velinov, Daniela Kovacheva, Ivanka Spassova, Daniela Karashanova and Nartzislav Petrov
Symmetry 2021, 13(8), 1532; https://doi.org/10.3390/sym13081532 - 20 Aug 2021
Viewed by 1870
Abstract
Carbon foams with different surface functionality and tailored texture characteristics were prepared from mixtures containing coal tar pitch and furfural in different proportions. The obtained materials were used as a host matrix for the preparation of zinc- and cobalt-mixed ferrite nanoparticles. The texture, [...] Read more.
Carbon foams with different surface functionality and tailored texture characteristics were prepared from mixtures containing coal tar pitch and furfural in different proportions. The obtained materials were used as a host matrix for the preparation of zinc- and cobalt-mixed ferrite nanoparticles. The texture, morphology, phase composition, and the related redox and catalytic properties of the obtained composites were characterized by low-temperature nitrogen physisorption, XRD, SEM, HRTEM, FTIR, Mössbauer spectroscopy, TPR and catalytic decomposition of methanol to syngas. The impact of the carbon support on the formation of Co- and Zn-mixed ferrites was discussed in detail using KIT-6 silica-based modifications as reference samples. The catalytic behavior of the ferrites was considered in a complex relation to their composition, morphology, location in the porous matrix and metal ions distribution in the spinel sub-lattices. The higher amount of furfural in the carbon foam precursor promoted the formation of cobalt-rich, more accessible and highly active methanol decomposition to syngas spinel particles. Full article
(This article belongs to the Special Issue Heterogeneous Catalysis: Topics and Advances)
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15 pages, 421 KiB  
Review
A Systematic Review on the Interaction between Emotion and Pseudoneglect
by Francesca Strappini, Gaspare Galati and Anna Pecchinenda
Symmetry 2021, 13(8), 1531; https://doi.org/10.3390/sym13081531 - 20 Aug 2021
Cited by 5 | Viewed by 2678
Abstract
Background: A large body of research has shown brain asymmetries in spatial attention. Specifically, there is an attention-processing advantage for the left visual field in healthy, right-handed subjects, known as “pseudoneglect.” Several studies have revealed that emotions modulate this basic spatial phenomenon, [...] Read more.
Background: A large body of research has shown brain asymmetries in spatial attention. Specifically, there is an attention-processing advantage for the left visual field in healthy, right-handed subjects, known as “pseudoneglect.” Several studies have revealed that emotions modulate this basic spatial phenomenon, but the direction of the effect is still unclear. Here we systematically review empirical evidence on the behavioral effects of emotion on pseudoneglect. Methods: We searched through Pubmed, Scopus, PsycINFO, and PsychArticles. Original peer-reviewed articles published until February 2021 were included if they (1) were written in English; (2) were conducted on adults; (3) included at least one task to measure pseudoneglect, and (4) included at least one task with emotional stimuli or employed a measure of emotional state/trait, as they relate to pseudoneglect. Results: Fifteen studies were included, and 784 healthy participants took part in all studies reviewed. Discussion: The results show some evidence of emotion modulation of pseudoneglect, but evidence on the direction of the effect is mixed. We discuss the role of methodological factors that could account for the available findings and the implications for emotion asymmetry hypotheses such as the right-hemisphere hypothesis, the valence-specific hypothesis, as well as neural and arousal frameworks of attention–emotion interactions. Full article
(This article belongs to the Special Issue Symmetry in Cognition and Emotion)
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11 pages, 265 KiB  
Article
Lie Symmetries and Solutions of Reaction Diffusion Systems Arising in Biomathematics
by Mariano Torrisi and Rita Traciná
Symmetry 2021, 13(8), 1530; https://doi.org/10.3390/sym13081530 - 20 Aug 2021
Cited by 8 | Viewed by 1961
Abstract
In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in [...] Read more.
In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in several biological problems and in population dynamics. By using weak equivalence transformation the principal Lie algebra, LP, is written and the classifying equations obtained. Then the extensions of LP are derived and classified with respect to Γ(v) and H(u,v). Some wide special classes of special solutions are carried out. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
14 pages, 598 KiB  
Article
Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations
by Rodica Cimpoiasu, Radu Constantinescu and Alina Streche Pauna
Symmetry 2021, 13(8), 1529; https://doi.org/10.3390/sym13081529 - 19 Aug 2021
Cited by 1 | Viewed by 1628
Abstract
A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It [...] Read more.
A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas. Full article
(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)
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16 pages, 1039 KiB  
Article
Application of Chemical Monitoring and Public Alarm Systems to Reduce Public Vulnerability to Major Accidents Involving Dangerous Substances
by Zsolt Cimer, Gyula Vass, Attila Zsitnyányi and Lajos Kátai-Urbán
Symmetry 2021, 13(8), 1528; https://doi.org/10.3390/sym13081528 - 19 Aug 2021
Cited by 5 | Viewed by 1986
Abstract
As a result of economic development and an increase in the volume of industrial production, the use of dangerous substances is increasing despite the fact that most industrial facilities are committed to the principles of environmental protection and sustainable development. Protection of human [...] Read more.
As a result of economic development and an increase in the volume of industrial production, the use of dangerous substances is increasing despite the fact that most industrial facilities are committed to the principles of environmental protection and sustainable development. Protection of human health and the environment is ensured at the local level by the local safety system. Major accidents typically have an off-site impact that also affects the general public. The most significant asymmetric event is when toxic substances are release into a populated area following a major accident. Early warning systems can significantly reduce the harmful consequences of major accidents that may occur. The operation of a reliable and effective chemical monitoring and public alarm system can be used as a basic device of defence. This ultimately means restoring the symmetry of the local safety system. It was an important scientific objective in Hungary to identify the facilities endangering the population where it is necessary to install chemical monitoring and early warning external protection systems. In this context, the main objective of this study was to present dangerous plant identification methodology and to analyse and evaluate the results of the application of this methodology. Full article
(This article belongs to the Special Issue Symmetry Applied in Special Engineering)
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22 pages, 385 KiB  
Article
Schrödinger Equations in Electromagnetic Fields: Symmetries and Noncommutative Integration
by Alexey Anatolievich Magazev and Maria Nikolaevna Boldyreva
Symmetry 2021, 13(8), 1527; https://doi.org/10.3390/sym13081527 - 19 Aug 2021
Cited by 11 | Viewed by 2756
Abstract
We study symmetry properties and the possibility of exact integration of the time-independent Schrödinger equation in an external electromagnetic field. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra central extensions. Based on [...] Read more.
We study symmetry properties and the possibility of exact integration of the time-independent Schrödinger equation in an external electromagnetic field. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra central extensions. Based on the well-known classification of the subalgebras of the algebra e(3), we classify all electromagnetic fields for which the corresponding time-independent Schrödinger equations admit first-order symmetry algebras. Moreover, we select the integrable cases, and for physically interesting electromagnetic fields, we reduced the original Schrödinger equation to an ordinary differential equation using the noncommutative integration method developed by Shapovalov and Shirokov. Full article
(This article belongs to the Section Physics)
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14 pages, 2147 KiB  
Article
The Kinetic Model of Diffusion and Reactions in Powder Catalysts during Temperature Programmed Oxygen Isotopic Exchange Process
by Arvaidas Galdikas, Muhammad Usman and Matas Galdikas
Symmetry 2021, 13(8), 1526; https://doi.org/10.3390/sym13081526 - 19 Aug 2021
Viewed by 2202
Abstract
The mathematical model of diffusion in powder oxide catalysts during the process of temperature programmed oxygen isotopic exchange is proposed. The diffusion is considered together with the homogeneous and heterogeneous oxygen isotopic exchange processes. The matrix forms of exchange rate equations of simple [...] Read more.
The mathematical model of diffusion in powder oxide catalysts during the process of temperature programmed oxygen isotopic exchange is proposed. The diffusion is considered together with the homogeneous and heterogeneous oxygen isotopic exchange processes. The matrix forms of exchange rate equations of simple and complex heteroexchange, and homoexchange reactions which obtain symmetrical forms are analyzed. The quantitative values of model parameters are found from the fitting of experimental data taken from literature of temperature programmed oxygen isotopic exchange process in catalysts ZrO2 and CeO2. The fittings show a good matching of model results with experimental data. The shapes of kinetic curves registered during temperature programmed oxygen isotopic exchange process are analyzed and the influence of various process parameters such as activation energies of simple and complex heteroexchange, oxygen surface concentration of catalyst, ratio of catalysts surface and volume of reactor, diffusion activation energy is considered. The depth profiles of diffusing oxygen species in oxide catalysts powder are calculated. Full article
(This article belongs to the Collection Feature Papers in Chemistry)
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17 pages, 308 KiB  
Article
Continued Roots, Power Transform and Critical Properties
by Simon Gluzman
Symmetry 2021, 13(8), 1525; https://doi.org/10.3390/sym13081525 - 19 Aug 2021
Cited by 5 | Viewed by 2698
Abstract
We consider the problem of calculation of the critical amplitudes at infinity by means of the self-similar continued root approximants. Region of applicability of the continued root approximants is extended from the determinate (convergent) problem with well-defined conditions studied before by Gluzman and [...] Read more.
We consider the problem of calculation of the critical amplitudes at infinity by means of the self-similar continued root approximants. Region of applicability of the continued root approximants is extended from the determinate (convergent) problem with well-defined conditions studied before by Gluzman and Yukalov (Phys. Lett. A 377 2012, 124), to the indeterminate (divergent) problem my means of power transformation. Most challenging indeterminate for the continued roots problems of calculating critical amplitudes, can be successfully attacked by performing proper power transformation to be found from the optimization imposed on the parameters of power transform. The self-similar continued roots were derived by systematically applying the algebraic self-similar renormalization to each and every level of interactions with their strength increasing, while the algebraic renormalization follows from the fundamental symmetry principle of functional self-similarity, realized constructively in the space of approximations. Our approach to the solution of the indeterminate problem is to replace it with the determinate problem, but with some unknown control parameter b in place of the known critical index β. From optimization conditions b is found in the way making the problem determinate and convergent. The index β is hidden under the carpet and replaced by b. The idea is applied to various, mostly quantum-mechanical problems. In particular, the method allows us to solve the problem of Bose-Einstein condensation temperature with good accuracy. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods)
12 pages, 2102 KiB  
Article
A General Model for Describing the Ovate Leaf Shape
by Peijian Shi, Kexin Yu, Karl J. Niklas, Julian Schrader, Yu Song, Renbin Zhu, Yang Li, Hailin Wei and David A. Ratkowsky
Symmetry 2021, 13(8), 1524; https://doi.org/10.3390/sym13081524 - 19 Aug 2021
Cited by 7 | Viewed by 4269
Abstract
Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry–Rosso–Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for [...] Read more.
Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry–Rosso–Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for convenience), to generate bilaterally symmetrical curves along the x-axis to form ovate leaf shapes. In order to evaluate which of these four equations best describes the ovate leaf shape, we used 14 leaves from 7 Neocinnamomum species (Lauraceae) and 72 leaves from Chimonanthus praecox (Calycanthaceae). Using the AIC and adjusted root mean square error to compare the fitted results, the modified equations fitted the leaf shapes better than the unmodified equations. However, the MLRF equation provided the best overall fit. As the parameters of the MLRF equation represent leaf length, maximum leaf width, and the distance from leaf apex to the point associated with the maximum leaf width along the leaf length axis, these findings are potentially valuable for studying the influence of environmental factors on leaf shape, differences in leaf shape among closely related plant species with ovate leaf shapes, and the extent to which leaves are bilaterally symmetrical. This is the first work in which temperature-dependent developmental equations to describe the ovate leaf shape have been employed, as previous studies lacked similar leaf shape models. In addition, prior work seldom attempted to describe real ovate leaf shapes. Our work bridges the gap between theoretical leaf shape models and empirical leaf shape indices that cannot predict leaf shape profiles. Full article
(This article belongs to the Section Mathematics)
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14 pages, 326 KiB  
Article
The Planar Thirring Model with Kähler-Dirac Fermions
by Simon Hands
Symmetry 2021, 13(8), 1523; https://doi.org/10.3390/sym13081523 - 19 Aug 2021
Cited by 8 | Viewed by 1432
Abstract
Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)U(N) field transformations and [...] Read more.
Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed. Full article
(This article belongs to the Section Physics)
11 pages, 2704 KiB  
Article
Higher Number of Yeast-like Fungi in the Air in 2018 after an Emergency Discharge of Raw Sewage to the Gulf of Gdańsk—Use of Contingency Tables
by Małgorzata Michalska, Piotr Wąż, Monika Kurpas, Roman Marks and Katarzyna Zorena
Symmetry 2021, 13(8), 1522; https://doi.org/10.3390/sym13081522 - 19 Aug 2021
Cited by 1 | Viewed by 1734
Abstract
This study aimed to investigate the differences between the number of yeast-like fungi and molds in the coastal air of five coastal towns of the Gulf of Gdańsk in 2014–2017 vs. 2018, which saw an emergency discharge of sewage. In 2014–2017, a total [...] Read more.
This study aimed to investigate the differences between the number of yeast-like fungi and molds in the coastal air of five coastal towns of the Gulf of Gdańsk in 2014–2017 vs. 2018, which saw an emergency discharge of sewage. In 2014–2017, a total of 62 duplicate samples were collected in the coastal towns of Hel, Puck, Gdynia, Sopot, and Gdańsk-Brzeźno. In 2018, after the emergency disposal of raw sewage, 26 air samples were collected. A Pearson chi-squared test of independence showed that during 2018 in Hel and Sopot, the mean number of molds and yeast-like fungi was higher than in 2014–2017. The result was significantly positive, p ≤ 2.22 × 10−16. The analysis of the General Asymptotic Symmetry Test showed that in Puck and Gdańsk-Brzeźno, the average number of Aspergillus sp. mold fungi was higher in 2018 after an emergency discharge of sewage into the Gulf of Gdańsk compared to the period 2014–2017. The result was not statistically significant. In addition, the average number of Penicillium sp. molds in 2018 in Gdańsk-Brzeźno was higher than in 2014–2017, but statistically insignificant (p = 0.9593). In 2018, the average number of Cladosporium sp. molds in Sopot was higher, but also statistically insignificant (p = 0.2114) compared to 2014–2017. Our results indicate that the study of the number of yeast-like fungi in the air may indicate coastal areas that may be particularly at risk of bacterial or mycological pathogens, e.g., after an emergency discharge of raw sewage. Full article
(This article belongs to the Section Life Sciences)
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26 pages, 1661 KiB  
Article
Modeling and Optimization for Multi-Objective Nonidentical Parallel Machining Line Scheduling with a Jumping Process Operation Constraint
by Guangyan Xu, Zailin Guan, Lei Yue, Jabir Mumtaz and Jun Liang
Symmetry 2021, 13(8), 1521; https://doi.org/10.3390/sym13081521 - 18 Aug 2021
Cited by 2 | Viewed by 1843
Abstract
This paper investigates the nonidentical parallel production line scheduling problem derived from an axle housing machining workshop of an axle manufacturer. The characteristics of axle housing machining lines are analyzed, and a nonidentical parallel line scheduling model with a jumping process operation (NPPLS-JP), [...] Read more.
This paper investigates the nonidentical parallel production line scheduling problem derived from an axle housing machining workshop of an axle manufacturer. The characteristics of axle housing machining lines are analyzed, and a nonidentical parallel line scheduling model with a jumping process operation (NPPLS-JP), which considers mixed model production, machine eligibility constraints, and fuzzy due dates, is established so as to minimize the makespan and earliness/tardiness penalty cost. While the physical structures of the parallel lines in the NPPLS-JP model are symmetric, the production capacities and process capabilities are asymmetric for different models. Different from the general parallel line scheduling problem, NPPLS-JP allows for a job to transfer to another production line to complete the subsequent operations (i.e., jumping process operations), and the transfer is unidirectional. The significance of the NPPLS-JP model is that it meets the demands of multivariety mixed model production and makes full use of the capacities of parallel production lines. Aiming to solve the NPPLS-JP problem, we propose a hybrid algorithm named the multi-objective grey wolf optimizer based on decomposition (MOGWO/D). This new algorithm combines the GWO with the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to balance the exploration and exploitation abilities of the original MOEA/D. Furthermore, coding and decoding rules are developed according to the features of the NPPLS-JP problem. To evaluate the effectiveness of the proposed MOGWO/D algorithm, a set of instances with different job scales, job types, and production scenarios is designed, and the results are compared with those of three other famous multi-objective optimization algorithms. The experimental results show that the proposed MOGWO/D algorithm exhibits superiority in most instances. Full article
(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics)
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