Symmetry

21 pages, 5927 KiB

Open AccessArticle

Atmospheric Temperature Prediction Based on a BiLSTM-Attention Model

by Xueli Hao, Ying Liu, Lili Pei, Wei Li and Yaohui Du

Symmetry 2022, 14(11), 2470; https://doi.org/10.3390/sym14112470 - 21 Nov 2022

Cited by 4 | Viewed by 1776

To address the problem that traditional models are not effective in predicting atmospheric temperature, this paper proposes an atmospheric temperature prediction model based on symmetric BiLSTM (bidirectional long short-term memory)-Attention model. Firstly, the meteorological data from five major stations in Beijing were integrated, [...] Read more.

To address the problem that traditional models are not effective in predicting atmospheric temperature, this paper proposes an atmospheric temperature prediction model based on symmetric BiLSTM (bidirectional long short-term memory)-Attention model. Firstly, the meteorological data from five major stations in Beijing were integrated, cleaned, and normalized to build an atmospheric temperature prediction dataset containing multiple feature dimensions; then, a BiLSTM memory network was used to construct with forward and backward information in the time dimension. And the limitations of the traditional LSTM method in long-term time series analysis were solved by introducing the attention mechanism to achieve the prediction analysis of atmospheric temperature. Finally, by comparing the prediction results with those of BiLSTM, LSTM-Attention, and LSTM, it is revealed that the proposed model has the best prediction effect, with a MAE value of 0.013, which is 0.72%, 0.41%, and 1.24% lower than those of BiLSTM, LSTM-Attention, and LSTM, respectively; the R² value reaches 0.9618, which is 2.73%, 1.23%, and 4.98% higher than BiLSTM, LSTM-Attention, and LSTM, respectively. The results show that the symmetrical BiLSTM-Attention atmospheric temperature prediction model can effectively improve the prediction accuracy of temperature data, and the model can also be used to predict other time series data. Full article

► Show Figures

Figure 1

18 pages, 3964 KiB

Open AccessArticle

Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

by Yongming Liu, Yujian Rui, Zhuanzhe Zhao, Manman Xu and Yang Zhou

Symmetry 2022, 14(11), 2469; https://doi.org/10.3390/sym14112469 - 21 Nov 2022

Viewed by 1161

Abstract

In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that [...] Read more.

In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that continuous Zernike polynomials do not have orthogonality on the discrete coordinates inside the unit circle, which causes the instability of topology optimization results, discrete orthogonal Zernike polynomials are used to characterize the active deformation mirror wave aberrations. Then, the optical and structural deformations are combined to establish an optical-mechanical coupling topology optimization model with the help of the variable density method to derive the sensitivity of the mathematical model. Finally, a wave aberration corrected deformation mirror in an optical machine system is used as an arithmetic example for topology optimization, and the results show that the absolute value of the Zernike coefficient Z₄ after optimization is improved by nearly one order of magnitude compared with the value before optimization, and the vibration characteristics of the optimized structure meet the design requirements. The optimization effect is significant, which improves the optical performance of the deformed mirror and provides a new scheme for the design of the deformed mirror structure which has a certain practical value for engineering. Full article

(This article belongs to the Special Issue Meta-Heuristics for Manufacturing Systems Optimization Ⅱ)

► Show Figures

Figure 1

12 pages, 309 KiB

Open AccessArticle

Ulam Stability of a General Linear Functional Equation in Modular Spaces

by Issam Aboutaib, Chaimaa Benzarouala, Janusz Brzdęk, Zbigniew Leśniak and Lahbib Oubbi

Symmetry 2022, 14(11), 2468; https://doi.org/10.3390/sym14112468 - 21 Nov 2022

Cited by 2 | Viewed by 1408

Abstract

Using the direct method, we prove the Ulam stability results for the general linear functional equation of the form

\sum_{i = 1}^{m} A_{i} (f (φ_{i} (\bar{x}))) = D (\bar{x})

for all [...] Read more.

Using the direct method, we prove the Ulam stability results for the general linear functional equation of the form

\sum_{i = 1}^{m} A_{i} (f (φ_{i} (\bar{x}))) = D (\bar{x})

for all

\bar{x} \in X^{n}

, where f is the unknown mapping from a linear space X over a field

K \in {R, C}

into a linear space Y over field

K

; n and m are positive integers;

φ_{1}, \dots, φ_{m}

are linear mappings from

X^{n}

to X;

A_{1}, \dots, A_{m}

are continuous endomorphisms of Y; and

D : X^{n} \to Y

is fixed. In this paper, the stability inequality is considered with regard to a convex modular on Y, which is lower semicontinuous and satisfies an additional condition (the

Δ_{2}

-condition). Our main result generalizes many similar stability outcomes published so far for modular space. It also shows that there is some kind of symmetry between the stability results for equations in modular spaces and those in classical normed spaces. Full article

(This article belongs to the Section Mathematics)

22 pages, 378 KiB

Open AccessArticle

Distances and Similarity Measures of Q-Rung Orthopair Fuzzy Sets Based on the Hausdorff Metric with the Construction of Orthopair Fuzzy TODIM

by Zahid Hussain, Sahar Abbas and Miin-Shen Yang

Symmetry 2022, 14(11), 2467; https://doi.org/10.3390/sym14112467 - 21 Nov 2022

Cited by 5 | Viewed by 1567

Abstract

In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than [...] Read more.

In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid Methods in Fuzzy Decision Problems – Part III)

27 pages, 17992 KiB

Open AccessFeature PaperReview

Ensuring the Reliability and EMC by Modal Reservation: A Brief History and Recent Advances

by Adnan Alhaj Hasan and Talgat Rashitovich Gazizov

Symmetry 2022, 14(11), 2466; https://doi.org/10.3390/sym14112466 - 21 Nov 2022

Cited by 7 | Viewed by 1196

Abstract

With the growth of the radioelectronic complexity and the demand for cutting edge devices, the need to protect them and increase their reliability is also rising. There are many methods to provide this. Modal reservation is one of the most effective, reliable, and [...] Read more.

With the growth of the radioelectronic complexity and the demand for cutting edge devices, the need to protect them and increase their reliability is also rising. There are many methods to provide this. Modal reservation is one of the most effective, reliable, and least complicated methods used nowadays. Using this method in tracing and mounting of printed circuit boards can guarantee both electromagnetic compatibility (by using modal filtering) and reliability (by using the cold redundancy) of the final electronic device. Modal reservation was proposed in 2015, and since then, massive research has been conducted on its investigations and development including 18 patents for inventions. Most of these studies have been devoted to modal reservation in terms of conducted emissions. However, up to now, a general and comprehensive review of modal reservation and investigations of its application with respect to radiated emissions has not been performed. Therefore, this paper aimed at presenting such a review on the history and recent research on modal reservation, concentrating on the studies related to radiated emissions. In addition, this paper analyzes current studies on the efficiency of using modal reservation under climatic impact. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

11 pages, 279 KiB

Open AccessArticle

Positive Solutions for a Class of Integral Boundary Value Problem of Fractional q-Difference Equations

by Shugui Kang, Yunfang Zhang, Huiqin Chen and Wenying Feng

Symmetry 2022, 14(11), 2465; https://doi.org/10.3390/sym14112465 - 21 Nov 2022

Cited by 2 | Viewed by 1212

Abstract

This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new property allows us to prove sufficient conditions [...] Read more.

This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new property allows us to prove sufficient conditions for the existence of positive solutions based on the associated parameter. The results are derived from the application of a fixed point theorem on order intervals. Full article

(This article belongs to the Special Issue Symmetry in Quantum Calculus)

14 pages, 1858 KiB

Open AccessArticle

GIS Partial Discharge Pattern Recognition Based on Multi-Feature Information Fusion of PRPD Image

by Kaiyang Yin, Yanhui Wang, Shihai Liu, Pengfei Li, Yaxu Xue, Baozeng Li and Kejie Dai

Symmetry 2022, 14(11), 2464; https://doi.org/10.3390/sym14112464 - 21 Nov 2022

Cited by 8 | Viewed by 2179

Abstract

Partial discharge (PD) pattern recognition is a critical indicator for evaluating the insulation state of gas-insulated switchgear (GIS). Aiming at the disadvantage of traditional PD pattern recognition methods, such as single feature extraction and low recognition accuracy, a pattern recognition method of PD [...] Read more.

Partial discharge (PD) pattern recognition is a critical indicator for evaluating the insulation state of gas-insulated switchgear (GIS). Aiming at the disadvantage of traditional PD pattern recognition methods, such as single feature extraction and low recognition accuracy, a pattern recognition method of PD based on multi-feature information fusion is proposed in this paper. Firstly, a recognition model based on quasi-Hausdorff distance is established according to the statistical characteristics of the phase-resolved partial discharge (PRPD) image, and then a modified convolutional neural network recognition model is established according to the image features of the PRPD image. Finally, Dempster–Shafer (D–S) evidence theory is used to fuse the two pattern recognition results and complement the advantages of the two approaches to improve the accuracy of partial discharge pattern recognition. The experimental results show that the total recognition accuracy rate of this method for four typical PD is more than 94.00%, and the recognition rate is significantly improved compared to support vector machine and normal convolution neural network. Maintaining stability in typical bipedal robots is challenging due to two main reasons. Full article

(This article belongs to the Special Issue Symmetry in Power and Electronic Engineering)

► Show Figures

Figure 1

11 pages, 966 KiB

Open AccessArticle

Interpolating Scaling Functions Tau Method for Solving Space–Time Fractional Partial Differential Equations

by Haifa Bin Jebreen and Carlo Cattani

Symmetry 2022, 14(11), 2463; https://doi.org/10.3390/sym14112463 - 21 Nov 2022

Cited by 1 | Viewed by 1155

Abstract

This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and [...] Read more.

This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and fractional integration operator are used to introduce the operational matrix for the Caputo fractional derivative. Due to some characteristics of ISFs, such as interpolation, computation costs can be significantly reduced. We investigate the convergence of the technique, and some numerical implementations show that the method is effective for solving such equations. Full article

(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)

► Show Figures

Figure 1

13 pages, 408 KiB

Open AccessArticle

A New Numerical Approach for Variable-Order Time-Fractional Modified Subdiffusion Equation via Riemann–Liouville Fractional Derivative

by Dowlath Fathima, Muhammad Naeem, Umair Ali, Abdul Hamid Ganie and Farah Aini Abdullah

Symmetry 2022, 14(11), 2462; https://doi.org/10.3390/sym14112462 - 21 Nov 2022

Cited by 1 | Viewed by 1494

Abstract

Fractional differential equations describe nature adequately because of the symmetry properties that describe physical and biological processes. In this paper, a new approximation is found for the variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on that basis, an efficient numerical approach is formulated [...] Read more.

Fractional differential equations describe nature adequately because of the symmetry properties that describe physical and biological processes. In this paper, a new approximation is found for the variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on that basis, an efficient numerical approach is formulated for VO time-fractional modified subdiffusion equations (TFMSDE). Complete theoretical analysis is performed, such as stability by the Fourier series, consistency, and convergence, and the feasibility of the proposed approach is also discussed. A numerical example illustrates that the proposed scheme demonstrates high accuracy, and that the obtained results are more feasible and accurate. Full article

(This article belongs to the Special Issue Numerical Analysis, Approximation Theory, Differential Equations)

► Show Figures

Figure 1

10 pages, 265 KiB

Open AccessArticle

Ulam–Hyers Stability via Fixed Point Results for Special Contractions in b-Metric Spaces

by Monica-Felicia Bota and Sanda Micula

Symmetry 2022, 14(11), 2461; https://doi.org/10.3390/sym14112461 - 20 Nov 2022

Cited by 7 | Viewed by 990

Abstract

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b [...] Read more.

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b-metric generalizes the one of a metric, as in the third condition, the right-hand side is multiplied by a real number greater than 1. We remark that the second axiom, i.e., the one which shows the symmetry of the b-metric, remains unchanged. The findings presented in this paper extend some recent results which were proved in the context of a metric space. Some open questions are presented at the end of the paper. Full article

(This article belongs to the Special Issue Recent Progress in Studies of Stability of Numerical Schemes)

17 pages, 3194 KiB

Open AccessFeature PaperArticle

Symmetrical Control Law for Chaotization of Platform Vibrations

by Boris Andrievsky and Iuliia Zaitceva

Symmetry 2022, 14(11), 2460; https://doi.org/10.3390/sym14112460 - 20 Nov 2022

Cited by 3 | Viewed by 1060

Abstract

The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, [...] Read more.

The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, mixing of bulk materials, is disclosed. The proposed algorithm was comprehensively experimentally studied with a laboratory vibratory setup, and the results of experiments demonstrating its efficacy are presented. Full article

(This article belongs to the Special Issue Symmetry in Dynamic Systems)

► Show Figures

Figure 1

0 pages, 322 KiB

Open AccessArticle

On Some Asymptotic Expansions for the Gamma Function

by Mansour Mahmoud and Hanan Almuashi

Symmetry 2022, 14(11), 2459; https://doi.org/10.3390/sym14112459 - 20 Nov 2022

Cited by 3 | Viewed by 1429

Abstract

Inequalities play a fundamental role in both theoretical and applied mathematics and contain many patterns of symmetries. In many studies, inequalities have been used to provide estimates of some functions based on the properties of their symmetry. In this paper, we present the [...] Read more.

Inequalities play a fundamental role in both theoretical and applied mathematics and contain many patterns of symmetries. In many studies, inequalities have been used to provide estimates of some functions based on the properties of their symmetry. In this paper, we present the following new asymptotic expansion related to the ordinary gamma function

Γ (1 + w) \sim \sqrt{2 π w} {(w / e)}^{w} {(\frac{w^{2} + \frac{7}{60}}{w^{2} - \frac{1}{20}})}^{w / 2} exp (\sum_{r = 1}^{\infty}, \frac{μ_{r}}{w^{r}}), w \to \infty

, with the recurrence relation of coefficients

μ_{r}

. Furthermore, we use Padé approximants and our new asymptotic expansion to deduce the new bounds of

Γ (w)

better than some of its recent ones. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials)

17 pages, 320 KiB

Open AccessArticle

A Novel Software Trustworthiness Evaluation Strategy via Relationships between Criteria

by Hongwei Tao, Qiaoling Cao, Haoran Chen, Yang Xian, Songtao Shang and Xiaoxu Niu

Symmetry 2022, 14(11), 2458; https://doi.org/10.3390/sym14112458 - 20 Nov 2022

Cited by 2 | Viewed by 1007

Abstract

Software trustworthiness evaluation is regarded as a multi-criteria decision-making problem. However, most current software trustworthiness evaluation methods do not consider the relationships between criteria. In this paper, we present a software trustworthiness evaluation strategy via the relationships between criteria. Because the trustworthy attribute [...] Read more.

Software trustworthiness evaluation is regarded as a multi-criteria decision-making problem. However, most current software trustworthiness evaluation methods do not consider the relationships between criteria. In this paper, we present a software trustworthiness evaluation strategy via the relationships between criteria. Because the trustworthy attribute degree is evaluated by a criterion, a trustworthy attribute measurement method based on fuzzy theory is first proposed, and the relationships between criteria are described by cooperative and conflicting degrees between criteria. Then, a measure formula for the symmetric substitutivity between criteria is proposed, and the cooperative degree between criteria is taken as the approximation of the symmetric substitutivity between criteria. With the help of the symmetric substitutivity between criteria, the software trustworthiness measurement model obtained by axiomatic approaches is applied to aggregate the degree to which each optional software product meets each objective. Finally, the candidate software products are sorted according to the trustworthiness aggregation results, and the optimal product is obtained from the alternative software products on the basis of the sorting results. The theoretical rationality of the measurement model is validated by proving that it satisfies the desirable properties of software trustworthiness measures, and its effectiveness is demonstrated through a case study. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)

15 pages, 1661 KiB

Open AccessArticle

Design, Synthesis, and In Vitro Antiproliferative Screening of New Hydrazone Derivatives Containing cis-(4-Chlorostyryl) Amide Moiety

by Tarfah Al-Warhi, Leena S. Alqahtani, Matokah Abualnaja, Saba Beigh, Ola A. Abu Ali, Fahmy G. Elsaid, Ali A. Shati, Rasha Mohammed Saleem, Ali Hassan Ahmed Maghrabi, Amani Abdulrahman Alharthi, Amal Alyamani, Eman Fayad, Ali H. Abu Almaaty, Islam Zaki and Shaimaa Hamouda

Symmetry 2022, 14(11), 2457; https://doi.org/10.3390/sym14112457 - 19 Nov 2022

Cited by 5 | Viewed by 1424

Abstract

Hydrazones are regarded as a distinctive category of organic compounds because of their tremendous characteristics and potential uses in analytical, chemical, and medicinal chemistry. In the present study, a new series of Hydrazone Derivatives bearing cis-(4-chlorostyryl) amide moiety were designed and synthesized. [...] Read more.

Hydrazones are regarded as a distinctive category of organic compounds because of their tremendous characteristics and potential uses in analytical, chemical, and medicinal chemistry. In the present study, a new series of Hydrazone Derivatives bearing cis-(4-chlorostyryl) amide moiety were designed and synthesized. In vitro cytotoxicity screening showed that compounds 3i, 3l, 3m, and 3n revealed potent anticancer activity against MCF-7 cancer cell line with IC₅₀ values between 2.19–4.37 μM compared with Staurosporin as a reference compound. The antiproliferative activity of these compounds appears to be correlated well with their ability to inhibit the VEGFR-2 kinase enzyme. Activation of the damage response pathway leads to cellular cycle arrest at the G1 phase. Fluorochrome Annexin V/PI staining indicated that cell death proceeds through the apoptotic pathway mechanism. The mechanistic pathway was confirmed by a significant increase in the level of active caspase 9 compared with control untreated MCF-7 cells. Full article

(This article belongs to the Special Issue Asymmetry and Symmetry in Organic Chemistry 2021)

► Show Figures

Figure 1

9 pages, 250 KiB

Open AccessArticle

Double Contingency of Communications in Bayesian Learning

by Atsuhide Mori

Symmetry 2022, 14(11), 2456; https://doi.org/10.3390/sym14112456 - 19 Nov 2022

Viewed by 1192

Abstract

In previous work, we described the geometry of Bayesian learning on a manifold. In this paper, inspired by the notion of modified double contingency of communications from sociologist Niklas Luhmann, we take two manifolds in equal parts and a potential function on their [...] Read more.

In previous work, we described the geometry of Bayesian learning on a manifold. In this paper, inspired by the notion of modified double contingency of communications from sociologist Niklas Luhmann, we take two manifolds in equal parts and a potential function on their product to set up mutual Bayesian learning. Particularly, given a parametric statistical model, we consider mutual learning between two copies of the parameter space. Here, we associate the potential with the relative entropy (i.e., the Kullback–Leibler divergence). Although the mutual learning forgets all elements about the model except the relative entropy, it still substitutes for the usual Bayesian estimation of the parameter in a certain case. We propose it as a globalization of the information geometry. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology)

11 pages, 541 KiB

Open AccessArticle

Cross-Layer Optimization-Based Asymmetric Medical Video Transmission in IoT Systems

by Yu Wang, Weijia Han, Xiao Ma, Qiuzhi Wang and Fengsen Chen

Symmetry 2022, 14(11), 2455; https://doi.org/10.3390/sym14112455 - 19 Nov 2022

Viewed by 965

Abstract

At present, Internet of Things (IoT) networks are attracting much attention since they provide emerging opportunities and applications. In IoT networks, the asymmetric and symmetric studies on medical and biomedical video transmissions have become an interesting topic in both academic and industrial communities. [...] Read more.

At present, Internet of Things (IoT) networks are attracting much attention since they provide emerging opportunities and applications. In IoT networks, the asymmetric and symmetric studies on medical and biomedical video transmissions have become an interesting topic in both academic and industrial communities. Especially, the transmission process shows the characteristics of asymmetry: the symmetric video-encoding and -decoding processes become asymmetric (affected by modulation and demodulation) once a transmission error occurs. In such an asymmetric condition, the quality of service (QoS) of such video transmissions is impacted by many different factors across the physical (PHY-), medium access control (MAC-), and application (APP-) layers. To address this, we propose a cross-layer optimization-based strategy for asymmetric medical video transmission in IoT systems. The proposed strategy jointly utilizes the video-coding structure in the APP- layer, the power control and channel allocation in the MAC- layer, and the modulation and coding schemes in the PHY- layer. To obtain the optimum configuration efficiently, the proposed strategy is formulated and proofed by a quasi-convex problem. Consequently, the proposed strategy could not only outperform the classical algorithms in terms of resource utilization but also improve the video quality under the resource-limited network efficiently. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Study on Fundamental 6G Technologies for Industrial IoT)

► Show Figures

Figure 1

24 pages, 337 KiB

Open AccessArticle

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

by P. Agilan, K. Julietraja, Nabil Mlaiki and Aiman Mukheimer

Symmetry 2022, 14(11), 2454; https://doi.org/10.3390/sym14112454 - 19 Nov 2022

Cited by 5 | Viewed by 963

Abstract

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the [...] Read more.

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated. Full article

(This article belongs to the Section Mathematics)

8 pages, 450 KiB

Open AccessArticle

Design of the Algorithm for Packaging of Water Molecules in a Fixed Volume

by Ekaterina M. Lorits, Elena A. Gubar and Alexander S. Novikov

Symmetry 2022, 14(11), 2453; https://doi.org/10.3390/sym14112453 - 19 Nov 2022

Cited by 2 | Viewed by 1143

Abstract

The question about the closest symmetrical packing of chemical substance species (molecules, ions, polymer chains, nanoparticles, etc.) is a subproblem of predicting the structure of matter, in particular, the structure of a crystal, information about which makes it possible to predict almost all [...] Read more.

The question about the closest symmetrical packing of chemical substance species (molecules, ions, polymer chains, nanoparticles, etc.) is a subproblem of predicting the structure of matter, in particular, the structure of a crystal, information about which makes it possible to predict almost all of its properties. The design of mathematical models for the closest symmetrical packing is an important and a challenging task for the practical application of optimization theory in theoretical chemistry. Here, we report about the development of the algorithm for water molecules’ symmetrical packing in a closed space of rectangular parallelepiped. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

► Show Figures

Figure 1

17 pages, 1649 KiB

Open AccessArticle

A Reliable Way to Deal with the Coupled Fractional Korteweg-De Vries Equations within the Caputo Operator

by Thongchai Botmart, Badriah M. Alotaibi, Rasool Shah, Lamiaa S. El-Sherif and Samir A. El-Tantawy

Symmetry 2022, 14(11), 2452; https://doi.org/10.3390/sym14112452 - 18 Nov 2022

Cited by 4 | Viewed by 1311

Abstract

The development of numeric-analytic solutions and the construction of fractional order mathematical models for practical issues are of the highest concern in a variety of physics, applied mathematics, and engineering applications. The nonlinear Kersten–Krasil’shchik-coupled Korteweg–de Vries-modified Korteweg–de Vries (KdV-mKdV) system is treated analytically [...] Read more.

The development of numeric-analytic solutions and the construction of fractional order mathematical models for practical issues are of the highest concern in a variety of physics, applied mathematics, and engineering applications. The nonlinear Kersten–Krasil’shchik-coupled Korteweg–de Vries-modified Korteweg–de Vries (KdV-mKdV) system is treated analytically in this paper using a unique method, known as the Laplace residual power series (LRPS) approach to find some approximate solutions. The RPS methodology and the Laplace transform operator are combined in the LRPS method. We provide a detailed introduction to the proposed method for dealing with fractional Kersten–Krasil’shchik-linked KdV-mKdV models. When compared to exact solutions, the approach provides analytical solutions with good accuracy. We demonstrate the effectiveness of the current strategy compared to alternative methods for solving nonlinear equations using an illustrative example. The LRPS technique’s results show and highlight that the method may be used for a variety of time-fractional models of physical processes with simplicity and computing effectiveness. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

14 pages, 1581 KiB

Open AccessArticle

Theoretical Study of Complexes of Tetravalent Actinides with DOTA

by Attila Kovács

Symmetry 2022, 14(11), 2451; https://doi.org/10.3390/sym14112451 - 18 Nov 2022

Viewed by 1482

Abstract

1,4,7,10-Tetraazacyclododecane-N,N′,N″,N‴-tetraacetic acid (H₄DOTA) is a prominent chelating ligand with potential applications in various fields, from radiotherapy to the separation of fission products. The present study explores the stability, structure, and bonding properties of its complexes with tetravalent actinides (An = Th, [...] Read more.

1,4,7,10-Tetraazacyclododecane-N,N′,N″,N‴-tetraacetic acid (H₄DOTA) is a prominent chelating ligand with potential applications in various fields, from radiotherapy to the separation of fission products. The present study explores the stability, structure, and bonding properties of its complexes with tetravalent actinides (An = Th, U, Np, Pu) using density functional theory and relativistic multireference calculations. Neutral complexes prefer to form symmetric (C₄) structures with DOTA. The first coordination sphere of the actinide ions is readily saturated by a weakly bonded H₂O ligand. The latter ligand reduces the molecular symmetry while exerting only marginal effects on the properties of the parent complex. An-ligand bonding is mainly electrostatic, but there are also significant charge-transfer contributions from DOTA to the An 6d/5f orbitals. The charge-transfer interactions and the covalent character of bonding increase gradually in the order of Th < U < Np < Pu, as indicated by analysis of the electron density distribution using the Quantum Theory of Atoms in Molecules. Full article

(This article belongs to the Special Issue Symmetry in Coordination Chemistry in 2021)

► Show Figures

Figure 1

24 pages, 453 KiB

Open AccessArticle

Survivability of AIDS Patients via Fractional Differential Equations with Fuzzy Rectangular and Fuzzy b-Rectangular Metric like Spaces

by Naeem Saleem, Salman Furqan, Hossam A. Nabwey and Reny George

Symmetry 2022, 14(11), 2450; https://doi.org/10.3390/sym14112450 - 18 Nov 2022

Cited by 1 | Viewed by 1115

Abstract

As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be [...] Read more.

As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using

α - ψ

-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique. Full article

(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)

► Show Figures

Figure 1

15 pages, 3083 KiB

Open AccessArticle

Dynamic Load Identification for Structures with Unknown Parameters

by Hongzhi Tang, Jinhui Jiang, M. Shadi Mohamed, Fang Zhang and Xu Wang

Symmetry 2022, 14(11), 2449; https://doi.org/10.3390/sym14112449 - 18 Nov 2022

Cited by 4 | Viewed by 1250

Abstract

The inverse problem and the direct problem are symmetrical to each other. As a mathematical method for inverse problems, dynamic load identification is applicable to the situation when the load acting on the structure is difficult to measure directly. In addition, in most [...] Read more.

The inverse problem and the direct problem are symmetrical to each other. As a mathematical method for inverse problems, dynamic load identification is applicable to the situation when the load acting on the structure is difficult to measure directly. In addition, in most practical fields, the exact value of the structural parameters cannot be obtained precisely, which makes the inverse problem beyond the capabilities of traditional dynamic load identification methods. Hence, in this work, we propose a dynamic load identification algorithm based on the extended Kalman filter (EKF) for a structure with unknown parameters. The algorithm is discussed under different conditions where the unknown parameters are either the stiffness or the mass of the structure. Such a case has not been considered in other literature yet. In order to verify the advantages of the proposed method, the recursive least square method was also used to compare the results. A 5-Dof symmetric system with unknown coefficients was selected for numerical simulation examples, and the influence of noise on the algorithm was also considered in the simulation. The results show that the proposed algorithm is effective for structures with unknown mass and stiffness coefficients. Compared with the recursive least square method, the method proposed in this paper has the higher accuracy and a wider application scope. Full article

(This article belongs to the Special Issue Advanced Mathematical and Simulation Methods for Inverse Problems)

► Show Figures

Figure 1

8 pages, 2549 KiB

Open AccessArticle

MoO₃ Interlayer Modification on the Electronic Structure of Co/BP Interface

by Baoxing Liu, Haipeng Xie, Yuan Zhao, Dongmei Niu and Yongli Gao

Symmetry 2022, 14(11), 2448; https://doi.org/10.3390/sym14112448 - 18 Nov 2022

Cited by 2 | Viewed by 1407

Abstract

The modification by molybdenum trioxide (MoO₃) buffer layer on the electronic structure between Co and black phosphorus (BP) was investigated with ultraviolet photoemission spectroscopy (UPS) and X-ray photoemission spectroscopy (XPS). It was found that the MoO₃ buffer layer could effectively [...] Read more.

The modification by molybdenum trioxide (MoO₃) buffer layer on the electronic structure between Co and black phosphorus (BP) was investigated with ultraviolet photoemission spectroscopy (UPS) and X-ray photoemission spectroscopy (XPS). It was found that the MoO₃ buffer layer could effectively prevent the destruction of the outermost BP lattice during the Co deposition, with the symmetry of the lattice remaining maintained. There is a noticeable interfacial charge transfer in addition to the chemical reaction between Co and MoO₃. The growth pattern of Co deposited onto the MoO₃/BP film is the island growth mode. The observations reveal the significance of a MoO₃ buffer layer on the electronic structure between Co and black phosphorus and provide help for the design of high-performance Co/BP-based spintronic devices. Full article

(This article belongs to the Special Issue Chirality Applied in Spintronics, Ferroics and Light–Matter Interactions)

► Show Figures

Figure 1

10 pages, 630 KiB

Open AccessArticle

A Lateral Control Method of Intelligent Vehicles Based on Shared Control

by Gang Li, Pengfei Shang, Changbing Zheng and Dehui Sun

Symmetry 2022, 14(11), 2447; https://doi.org/10.3390/sym14112447 - 18 Nov 2022

Cited by 2 | Viewed by 1324

Abstract

This paper studies the lateral control problem for intelligent vehicles based on the concept of shared control. Considering the participation of drivers in the control loop, a shared control-based lateral controller is designed, which consists of two differed controllers: one is an LQR-based [...] Read more.

This paper studies the lateral control problem for intelligent vehicles based on the concept of shared control. Considering the participation of drivers in the control loop, a shared control-based lateral controller is designed, which consists of two differed controllers: one is an LQR-based autonomous driving controller and the other is a driver’s intention-based fuzzy controller. For the vehicle dynamic model with two-degrees of freedom, an autonomous driving controller based on LQR and a driver’s intention-based fuzzy controller are designed. Then, the lateral controller based on shared control is constructed, which integrates the aforementioned two controllers. Finally, the co-simulation by MATLAB/Simulink and Carsim is presented. Furthermore, simulation results show that the designed lateral controller can track the desired path with better performance than the LQR-based autonomous driving controller. Full article

(This article belongs to the Section Engineering and Materials)

► Show Figures

Figure 1

11 pages, 1867 KiB

Open AccessArticle

Cheney–Sharma Type Operators on a Triangle with Straight Sides

by Teodora Cătinaş

Symmetry 2022, 14(11), 2446; https://doi.org/10.3390/sym14112446 - 18 Nov 2022

Cited by 1 | Viewed by 892

Abstract

We consider two types of Cheney–Sharma operators for functions defined on a triangle with all straight sides. We construct their product and Boolean sum, we study their interpolation properties and the orders of accuracy and we give different expressions of the corresponding remainders, [...] Read more.

We consider two types of Cheney–Sharma operators for functions defined on a triangle with all straight sides. We construct their product and Boolean sum, we study their interpolation properties and the orders of accuracy and we give different expressions of the corresponding remainders, highlighting the symmetry between the methods. We also give some illustrative numerical examples. Full article

(This article belongs to the Special Issue Numerical Analysis, Approximation Theory, Differential Equations)

► Show Figures

Figure 1

9 pages, 3591 KiB

Open AccessArticle

The Reappearance of Poetic Beauty in Chaos

by Suqiao Sheng, Huiyu Wen, Guangfu Xie and Yongxin Li

Symmetry 2022, 14(11), 2445; https://doi.org/10.3390/sym14112445 - 18 Nov 2022

Cited by 2 | Viewed by 1391

Abstract

Different forms of attractors, or basins of attraction, in chaotic systems often bring people the enjoyment of beauty. This attraction is reminiscent of ancient Chinese poetry and introduces people to a poetic and magical world, bringing them a sense of wonder and enlightenment. [...] Read more.

Different forms of attractors, or basins of attraction, in chaotic systems often bring people the enjoyment of beauty. This attraction is reminiscent of ancient Chinese poetry and introduces people to a poetic and magical world, bringing them a sense of wonder and enlightenment. In this work, some cases of the beauty of chaos, including forms of symmetry, asymmetry, conditional symmetry, and extension, are demonstrated. The chaos theory of science and engineering and the art of literature are innovatively combined and integrated here. The unique charm of chaotic attractors is revealed and endowed to the artistic realm of ancient Chinese poetry, helping people to understand the poetic beauty of the chaotic world. Through bold association and imagination, chaotic attractors are endowed with fresh vitality, thus showing people a world of artistic space that is full of fantasy. Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)

► Show Figures

Figure 1

12 pages, 676 KiB

Open AccessFeature PaperArticle

Particle Production in Strong Electromagnetic Fields and Local Approximations

by Ivan A. Aleksandrov, Denis G. Sevostyanov and Vladimir M. Shabaev

Symmetry 2022, 14(11), 2444; https://doi.org/10.3390/sym14112444 - 18 Nov 2022

Cited by 4 | Viewed by 1178

Abstract

We investigate the phenomenon of electron–positron pair production in intense external backgrounds within the strong-field regime. We perform nonperturbative calculations by solving the quantum kinetic equations, and obtain the momentum distributions of particles created and the total number of pairs. In particular, we [...] Read more.

We investigate the phenomenon of electron–positron pair production in intense external backgrounds within the strong-field regime. We perform nonperturbative calculations by solving the quantum kinetic equations, and obtain the momentum distributions of particles created and the total number of pairs. In particular, we analyze the validity of the locally constant field approximation (LCFA), which represents a powerful method for treating inhomogeneous external backgrounds. We consider a combination of two consecutive time-dependent Sauter pulses and thoroughly examine the effects of quantum interference and the role of the Pauli exclusion principle. It is shown that the latter can be approximately incorporated within the LCFA when computing the momentum distributions, while the closed-form LCFA expression for the total particle yield completely disregards Pauli blocking. It is demonstrated that in the presence of multiple turning points of classical electron trajectories, one observes interference patterns in the particle spectra, and the LCFA may significantly overestimate the number of pairs. To further elaborate this issue, we perform the analogous calculations in the case of scalar QED. It is shown that the quantum statistics effects enhance the number of bosons produced. Full article

(This article belongs to the Special Issue Nonperturbative and Symmetry Methods in QFT: Applications to Actual Physical Problems, in Particular, to Physics of Nanostructures)

► Show Figures

Figure 1

10 pages, 625 KiB

Open AccessArticle

A Modified Wei-Hua-He Digital Signature Scheme Based on Factoring and Discrete Logarithm

by Elumalai R and G. S. G. N. Anjaneyulu

Symmetry 2022, 14(11), 2443; https://doi.org/10.3390/sym14112443 - 17 Nov 2022

Viewed by 1395

Abstract

A symmetric cipher such as AES in cryptography is much faster than an asymmetric cipher but digital signatures often use asymmetric key ciphers because they provides the sender’s identity and data integrity. In this paper, a modified-He digital signature scheme is proposed using [...] Read more.

A symmetric cipher such as AES in cryptography is much faster than an asymmetric cipher but digital signatures often use asymmetric key ciphers because they provides the sender’s identity and data integrity. In this paper, a modified-He digital signature scheme is proposed using a one-way hash function. The proposed scheme, unlike the He signature technique, employs Euclid’s Division Lemma with large prime moduli p. Its security is built on large integer factoring, discrete logarithms and expanded root problems. The time complexity of the proposed scheme is

O (l o g^{3} p)

. The proposed modified-He scheme is efficient, as evidenced by the analytical results with key lengths greater than 512 bits. Full article

(This article belongs to the Special Issue Recent Advances in the Application of Symmetry Group)

► Show Figures

Figure 1

16 pages, 3536 KiB

Open AccessArticle

Fermatean Neutrosophic Topological Spaces and an Application of Neutrosophic Kano Method

by Nazmiye Gonul Bilgin, Dragan Pamučar and Muhammad Riaz

Symmetry 2022, 14(11), 2442; https://doi.org/10.3390/sym14112442 - 17 Nov 2022

Cited by 3 | Viewed by 1560

Abstract

The main objective of this paper is to redefine the concept of Fermatean neutrosophic sets as well as to introduce topological structure on Fermatean neutrosophic sets. The idea of Fermatean neutrosophic sets is the hybrid model of Fermatean fuzzy sets and neutrosophic sets [...] Read more.

The main objective of this paper is to redefine the concept of Fermatean neutrosophic sets as well as to introduce topological structure on Fermatean neutrosophic sets. The idea of Fermatean neutrosophic sets is the hybrid model of Fermatean fuzzy sets and neutrosophic sets to utilize key features of these structures. Topological data analysis for indeterminate and uncertain information is a rapidly developing field. Motivated by this recent trend, the idea of Fermatean neutrosophic topology is proposed, which is an extension of neutrosophic topology and Fermatean fuzzy topology. Some fundamental properties of Fermatean neutrosophic topology are explored and related results are investigated. Certain properties provided in the classical topological space that may not be valid in this space is one of the factors that makes the study important. Moreover, an application is made for the problem of seeking reasonable solutions to customer expectations by using the neutrosophic Kano method, which is an interesting illustration of neutrosophic decision making. Full article

(This article belongs to the Special Issue Recent Advances in Fuzzy Optimization Methods and Models)

13 pages, 5037 KiB

Open AccessArticle

Vbswp-CeaH: Vigorous Buyer-Seller Watermarking Protocol without Trusted Certificate Authority for Copyright Protection in Cloud Environment through Additive Homomorphism

by Ashwani Kumar, Mohit Kumar, Sahil Verma, Kavita, N. Z. Jhanjhi and Rania M. Ghoniem

Symmetry 2022, 14(11), 2441; https://doi.org/10.3390/sym14112441 - 17 Nov 2022

Cited by 8 | Viewed by 1287

Abstract

Cloud-based storage ensures the secure dissemination of media. Authentication and integrity are important aspects in the distribution of digital media. Encryption-based techniques shelter this media between the communicating parties which are involved in a transaction. The challenge is how to restrict the digital [...] Read more.

Cloud-based storage ensures the secure dissemination of media. Authentication and integrity are important aspects in the distribution of digital media. Encryption-based techniques shelter this media between the communicating parties which are involved in a transaction. The challenge is how to restrict the digital media which is illegally redistributed by the authorized users. However, the digital watermarking technique and encryption-based methods are also not sufficient enough to provide copyright protection. The watermarking protocol is used to provide intellectual property for the customer and the service provider. This research paper provides a vigorous buyer-seller watermarking protocol without trusted certificate authority for copyright protection in the cloud environment. This research work uses the cloud environment which enables the cloud as a service infrastructural provider for storing credentials such as public and private secret keys and the digital certificates of interacting parties. The scheme uses additive homomorphism encryption with an effective key exchange algorithm for exchanging digital media. This proposed approach addresses the problems of anonymity and copy deterrence and protects the digital rights of the buyer and seller; these most up-to-date issues are related to information security. Furthermore, the experiment results conclude that the proposed protocol is flexible and secure even in a non-secure communication channel. We have used performance measures such as PSNR, NCC and cost in time methods for checking the integrity of the proposed protocol. The conducted experiments show a stronger robustness and high imperceptibility for the watermark and watermarked images. Full article

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry, Volume 14, Issue 11 (November 2022) – 247 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI