Symmetry

19 pages, 71330 KiB

Open AccessArticle

Magnetic Circuit Analysis of Halbach Array and Improvement of Permanent Magnetic Adsorption Device for Wall-Climbing Robot

by Shilong Jiao, Xiaojun Zhang, Xuan Zhang, Jidong Jia and Minglu Zhang

Symmetry 2022, 14(2), 429; https://doi.org/10.3390/sym14020429 - 21 Feb 2022

Cited by 13 | Viewed by 3211

Abstract

To solve the problems that the theoretical analysis of Halbach array magnetic circuit is insufficient and that calculating the magnetic adsorption force of a permanent magnet by using the magnetic node method is complex, the magnetic flux density of a Halbach array magnetic [...] Read more.

To solve the problems that the theoretical analysis of Halbach array magnetic circuit is insufficient and that calculating the magnetic adsorption force of a permanent magnet by using the magnetic node method is complex, the magnetic flux density of a Halbach array magnetic circuit composed of multiple permanent magnets with perpendicular magnetization directions is calculated. On the basis of the concentrated magnetic phenomenon of the ferromagnetic material and the end effect of the permanent magnet, a method for calculating the magnetic adsorption force of the Halbach array magnetic circuit by using the equivalent magnetic flux density is proposed, and the variation trend of magnetic adsorption force after changing the parameters of the magnetic circuit is obtained. ANSYS software is used to analyze several magnetic circuits that produce large magnetic adsorption force, a magnetic circuit structure that produces the largest magnetic adsorption force is determined, and the permanent magnetic adsorption device of the wall-climbing robot is improved. The magnetic adsorption force of the wall-climbing robot before and after the improvement of the permanent magnetic adsorption device is measured through experiments. The experimental results show that the magnetic adsorption force after the improvement is increased by 24.63% compared to before the improvement. Full article

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26 pages, 868 KiB

Open AccessArticle

Important Study on the ∇ Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

by Ahmed A. El-Deeb, Omar Bazighifan and Clemente Cesarano

Symmetry 2022, 14(2), 428; https://doi.org/10.3390/sym14020428 - 21 Feb 2022

Cited by 1 | Viewed by 1312

Abstract

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert-type on time scales. We present and prove very important generalized results with the help of the Fenchel–Legendre transform, submultiplicative functions, and Hölder’s and Jensen’s inequality on [...] Read more.

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert-type on time scales. We present and prove very important generalized results with the help of the Fenchel–Legendre transform, submultiplicative functions, and Hölder’s and Jensen’s inequality on time scales. We obtain some well-known time scale inequalities due to Hardy–Hilbert inequalities. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Symmetry plays an essential role in determining the correct methods for solutions to dynamic inequalities Full article

12 pages, 299 KiB

Open AccessArticle

Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions

by Alina Alb Lupaş and Georgia Irina Oros

Symmetry 2022, 14(2), 427; https://doi.org/10.3390/sym14020427 - 21 Feb 2022

Cited by 4 | Viewed by 1531

Abstract

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions [...] Read more.

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions

A_{n} = \{f \in H (U) : f (z) = z +

a_{n + 1} z^{n + 1} + \dots, z \in U\}

written simply

A

when

n = 1

, the newly introduced class involves functions

f \in A

considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties. Full article

(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis II)

24 pages, 757 KiB

Open AccessArticle

Robust Adaptive Estimation of Graph Signals Based on Welsch Loss

by Wenyuan Wang and Qiang Sun

Symmetry 2022, 14(2), 426; https://doi.org/10.3390/sym14020426 - 21 Feb 2022

Cited by 4 | Viewed by 1910

Abstract

This paper considers the problem of adaptive estimation of graph signals under the impulsive noise environment. The existing least mean squares (LMS) approach suffers from severe performance degradation under an impulsive environment that widely occurs in various practical applications. We present a novel [...] Read more.

This paper considers the problem of adaptive estimation of graph signals under the impulsive noise environment. The existing least mean squares (LMS) approach suffers from severe performance degradation under an impulsive environment that widely occurs in various practical applications. We present a novel adaptive estimation over graphs based on Welsch loss (WL-G) to handle the problems related to impulsive interference. The proposed WL-G algorithm can efficiently reconstruct graph signals from the observations with impulsive noises by formulating the reconstruction problem as an optimization based on Welsch loss. An analysis on the performance of the WL-G is presented to develop effective sampling strategies for graph signals. A novel graph sampling approach is also proposed and used in conjunction with the WL-G to tackle the time-varying case. The performance advantages of the proposed WL-G over the existing LMS regarding graph signal reconstruction under impulsive noise environment are demonstrated. Full article

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9 pages, 5197 KiB

Open AccessArticle

Buoyancy-Marangoni Fingering of a Miscible Spreading Drop

by Alireza Hooshanginejad and Sunghwan Jung

Symmetry 2022, 14(2), 425; https://doi.org/10.3390/sym14020425 - 21 Feb 2022

Cited by 3 | Viewed by 2979

Abstract

We experimentally investigate the interfacial instability that emerges when a water droplet is deposited on a bath of glycerol-water solution. Despite the absence of surface tension to stabilize short-wavelength undulations, we observe finite-size fingers that grow and pinch off from the drop. We [...] Read more.

We experimentally investigate the interfacial instability that emerges when a water droplet is deposited on a bath of glycerol-water solution. Despite the absence of surface tension to stabilize short-wavelength undulations, we observe finite-size fingers that grow and pinch off from the drop. We show that the fingering patterns formed in the experiments resultes from a balance between the outward buoyancy effect and inward Marangoni flow. This induced Marangoni flow inhibits small perturbations and acts as an effective surface tension on the miscible interface of the spreading drop. To characterize the final size and shape of the drop, we perform systematic experiments by varying the drop volume and the glycerol-water volume fraction. In addition, we have developed scaling arguments for the drop’s final radius using key physical forces, and show that the final wavelength is inversely proportional to the Bond number. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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23 pages, 8508 KiB

Open AccessArticle

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

by Tsafack Nestor, Akram Belazi, Bassem Abd-El-Atty, Md Nazish Aslam, Christos Volos, Nkapkop Jean De Dieu and Ahmed A. Abd El-Latif

Symmetry 2022, 14(2), 424; https://doi.org/10.3390/sym14020424 - 21 Feb 2022

Cited by 38 | Viewed by 3001

Abstract

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically [...] Read more.

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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16 pages, 19857 KiB

Open AccessArticle

The Role of Art Expertise and Symmetry on Facial Aesthetic Preferences

by Luis Carlos Pereira Monteiro, Victória Elmira Ferreira do Nascimento, Amanda Carvalho da Silva, Ana Catarina Miranda, Givago Silva Souza and Rachel Coelho Ripardo

Symmetry 2022, 14(2), 423; https://doi.org/10.3390/sym14020423 - 20 Feb 2022

Cited by 6 | Viewed by 4729

Abstract

Humans, like other species, have a preference for symmetrical visual stimuli, a preference that is influenced by factors such as age, sex, and artistic training. In particular, artistic training seems to decrease the rejection of asymmetry in abstract stimuli. However, it is not [...] Read more.

Humans, like other species, have a preference for symmetrical visual stimuli, a preference that is influenced by factors such as age, sex, and artistic training. In particular, artistic training seems to decrease the rejection of asymmetry in abstract stimuli. However, it is not known whether the same trend would be observed in relation to concrete stimuli such as human faces. In this article, we investigated the role of expertise in visual arts, music, and dance, in the perceived beauty and attractiveness of human faces with different asymmetries. With this objective, the beauty and attractiveness of 100 photographs of faces with different degrees of asymmetry were evaluated by 116 participants with different levels of art expertise. Expertise in visual arts and dance was associated with the extent to which facial asymmetry influenced the beauty ratings assigned to the faces. The greater the art expertise in visual arts and dance, the more indifferent to facial asymmetry the participant was to evaluate beauty. The same effect was not found for music and neither for attractiveness ratings. These findings are important to help understand how face aesthetic evaluation is modified by artistic training and the difference between beauty and attractiveness evaluations. Full article

(This article belongs to the Section Life Sciences)

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10 pages, 271 KiB

Open AccessArticle

Topological Sigma-Semiring Separation and Ordered Measures in Noetherian Hyperconvexes

by Susmit Bagchi

Symmetry 2022, 14(2), 422; https://doi.org/10.3390/sym14020422 - 20 Feb 2022

Cited by 1 | Viewed by 2022

Abstract

The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed [...] Read more.

The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed in a sigma-semiring in a NHC under a topological ordering of NHCs. The topological ordering relation maintains the irreflexive and anti-symmetric algebraic properties while retaining the homeomorphism of NHCs. The monotonic measure sequence in a NHC determines the convexity and compactness of topological subspaces. Interestingly, the topological ordering in NHCs in two isomorphic topological spaces induces the corresponding ordering of measures in sigma-semirings. Moreover, the uniform topological measure spaces of NHCs need not always preserve the pushforward measures, and a NHC semiring is functionally separable by a set of inner-measurable functions. Full article

(This article belongs to the Special Issue Topological Structures and Analysis with Applications)

17 pages, 2218 KiB

Open AccessArticle

Functional Evaluation Using Fuzzy FMEA for a Non-Invasive Measurer for Methane and Carbone Dioxide

by Lidilia Cruz-Rivero, María Leonor Méndez-Hernández, Carlos Eusebio Mar-Orozco, Alberto A. Aguilar-Lasserre, Alfonso Barbosa-Moreno and Josué Sánchez-Escobar

Symmetry 2022, 14(2), 421; https://doi.org/10.3390/sym14020421 - 20 Feb 2022

Cited by 10 | Viewed by 2088

Abstract

This paper combines the use of two tools: Failure Mode and Effect Analysis (FMEA) and Fuzzy Logic (FL), to evaluate the functionality of a quantifier prototype of Methane gas (CH₄) and Carbon Dioxide (CO₂), developed specifically to measure the [...] Read more.

This paper combines the use of two tools: Failure Mode and Effect Analysis (FMEA) and Fuzzy Logic (FL), to evaluate the functionality of a quantifier prototype of Methane gas (CH₄) and Carbon Dioxide (CO₂), developed specifically to measure the emissions generated by cattle. Unlike previously reported models for the same purpose, this device reduces damage to the integrity of the animal and does not interfere with the activities of livestock in their development medium. FMEA and FL are used to validate the device’s functionality, which involves identifying possible failure modes that represent a more significant impact on the operation and prevent the prototype from fulfilling the function for which it was created. As a result, this document presents the development of an intelligent fuzzy system type Mamdani, supported in the Fuzzy Inference System Toolbox of MatLabR2018b^®, for generating a risk priority index. A Fuzzy FMEA model was obtained to validate the prototype for measuring Methane and Carbon Dioxide emissions, which allows considering this prototype as a reliable alternative for the reliable measurement of these gases. This study was necessary as a complementary part in the validation of the design of the prototype quantifier of CH₄ and CO₂ emissions. The methods used (classic FMEA and Fuzzy FMEA) to evaluate the RPN show asymmetric graphs due to data disparity. Values in the classical method are mostly lower than the Mamdani model results due to the description of the criteria with which it is evaluated. Full article

(This article belongs to the Special Issue Computational Intelligence and Soft Computing: Recent Applications)

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13 pages, 3219 KiB

Open AccessArticle

A Poset-Based Approach to Curvature of Hypergraphs

by Yasharth Yadav, Areejit Samal and Emil Saucan

Symmetry 2022, 14(2), 420; https://doi.org/10.3390/sym14020420 - 20 Feb 2022

Cited by 4 | Viewed by 2602

Abstract

In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a [...] Read more.

In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a two-dimensional simplicial complex associated with a hypergraph, such that the vertices of the simplicial complex represent the vertices and hyperedges of the original hypergraph. We then define the Forman–Ricci curvature of the vertices and the hyperedges as the scalar curvature of the associated vertices in the simplicial complex. Remarkably, Forman–Ricci curvature has a simple combinatorial expression and it can effectively capture the variation in symmetry or asymmetry over a hypergraph. Finally, we perform an empirical study involving computation and analysis of the Forman–Ricci curvature of hyperedges in several real-world hypergraphs. We find that Forman–Ricci curvature shows a moderate to high absolute correlation with standard hypergraph measures such as eigenvector centrality and cardinality. Our results suggest that the notion of Forman–Ricci curvature extended to hypergraphs in this work can be used to gain novel insights on the organization of higher-order interactions in real-world hypernetworks. Full article

(This article belongs to the Special Issue Topological Graph Theory and Discrete Geometry)

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10 pages, 259 KiB

Open AccessArticle

New Applications of Fractional Integral for Introducing Subclasses of Analytic Functions

by Alina Alb Lupaş

Symmetry 2022, 14(2), 419; https://doi.org/10.3390/sym14020419 - 20 Feb 2022

Cited by 2 | Viewed by 1252

Abstract

The fractional integral is prolific in giving rise to interesting outcomes when associated with different operators. For the study presented in this paper, the fractional integral is associated with the convolution product of multiplier transformation and the Ruscheweyh derivative. Using the operator obtained [...] Read more.

The fractional integral is prolific in giving rise to interesting outcomes when associated with different operators. For the study presented in this paper, the fractional integral is associated with the convolution product of multiplier transformation and the Ruscheweyh derivative. Using the operator obtained as a result of this association and inspired by previously published results obtained with similarly introduced operators, the class of analytic functions

IR (μ, λ, β, γ, α, l, m, n)

is defined and investigated concerning various characteristics such as distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to this class. Full article

(This article belongs to the Section Mathematics)

17 pages, 319 KiB

Open AccessArticle

On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by a Generalized Operator

by Waggas Galib Atshan, Rajaa Ali Hiress and Sahsene Altınkaya

Symmetry 2022, 14(2), 418; https://doi.org/10.3390/sym14020418 - 19 Feb 2022

Cited by 14 | Viewed by 2041

Abstract

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in

U = {z \in ℂ : | z | < 1}

involving the generalized operator [...] Read more.

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in

U = {z \in ℂ : | z | < 1}

involving the generalized operator

I_{α, β}^{j} f

. The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems. Full article

(This article belongs to the Special Issue Symmetry in Pure Mathematics and Real and Complex Analysis)

14 pages, 1701 KiB

Open AccessArticle

Fault Diagnosis of Crack on Gearbox Using Vibration-Based Approaches

by Sufyan A. Mohammed, Nouby M. Ghazaly and Jamil Abdo

Symmetry 2022, 14(2), 417; https://doi.org/10.3390/sym14020417 - 19 Feb 2022

Cited by 17 | Viewed by 3663

Abstract

This study experimentally investigates vibration-based approaches for fault diagnosis of automotive gearboxes. The primary objective is to identify methods that can detect gear-tooth cracks, a common fault in gearboxes. Vibrational signals were supervised on a gearbox test rig under different operating conditions of [...] Read more.

This study experimentally investigates vibration-based approaches for fault diagnosis of automotive gearboxes. The primary objective is to identify methods that can detect gear-tooth cracks, a common fault in gearboxes. Vibrational signals were supervised on a gearbox test rig under different operating conditions of gears with three symmetrical crack depths (1, 2, and 3 mm). The severity of the gear-tooth cracks was predicted from the vibrational signal dataset using an artificial feedforward multilayer neural network with backpropagation (NNBP). The vibration amplitudes were the greatest when the crack size in the high-speed shaft was 3 mm, and the root mean square of its vibration speed was below 3.5 mm/s. The vibration amplitudes of the gearbox increased with increasing depth of the tooth cracks under different operating conditions. The NNBP predicted the states of gear-tooth cracks with an average recognition rate of 80.41% under different conditions. In some cases, the fault degree was difficult to estimate via time-domain analysis as the vibration level increases were small and not easily noticed. Results also showed that when using the same statistical features, the time-domain analysis can better detect crack degree compared to the neural network technique. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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14 pages, 2585 KiB

Open AccessArticle

The Mechanistic Integration and Thermodynamic Optimality of a Nanomotor

by Ruizheng Hou

Symmetry 2022, 14(2), 416; https://doi.org/10.3390/sym14020416 - 19 Feb 2022

Cited by 1 | Viewed by 1337

Abstract

The performance of artificial nanomotors is still far behind nature-made biomolecular motors. A mechanistic disparity between the two categories exists: artificial motors often rely on a single mechanism to rectify directional motion, but biomotors integrate multiple mechanisms for better performance. This study proposes [...] Read more.

The performance of artificial nanomotors is still far behind nature-made biomolecular motors. A mechanistic disparity between the two categories exists: artificial motors often rely on a single mechanism to rectify directional motion, but biomotors integrate multiple mechanisms for better performance. This study proposes a design for a motor-track system and shows that by introducing asymmetric compound foot-track interactions, both selective foot detachment and biased foot-track binding arise from the mechanics of the system. The two mechanisms are naturally integrated to promote the motility of the motor towards being unidirectional, while each mechanism alone only achieves 50% directional fidelity at most. Based on a reported theory, the optimization of the motor is conducted via maximizing the directional fidelity. Along the optimization, the directional fidelity of the motor is raised by parameters that concentrate more energy on driving selective-foot detachment and biased binding, which in turn promotes work production due to the two energies converting to work via a load attached. However, the speed of the motor can drop significantly after the optimization because of energetic competition between speed and directional fidelity, which causes a speed-directional fidelity tradeoff. As a case study, these results test thermodynamic correlation between the performances of a motor and suggest that directional fidelity is an important quantity for motor optimization. Full article

(This article belongs to the Special Issue Symmetry in Computational Mathematics and Biophysics)

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18 pages, 1052 KiB

Open AccessArticle

A Distributed and Privacy-Preserving Random Forest Evaluation Scheme with Fine Grained Access Control

by Yang Zhou, Hua Shen and Mingwu Zhang

Symmetry 2022, 14(2), 415; https://doi.org/10.3390/sym14020415 - 19 Feb 2022

Cited by 2 | Viewed by 2307

Abstract

Random forest is a simple and effective model for ensemble learning with wide potential applications. Implementation of random forest evaluations while preserving privacy for the source data is demanding but also challenging. In this paper, we propose a practical and fault-tolerant privacy-preserving random [...] Read more.

Random forest is a simple and effective model for ensemble learning with wide potential applications. Implementation of random forest evaluations while preserving privacy for the source data is demanding but also challenging. In this paper, we propose a practical and fault-tolerant privacy-preserving random forest evaluation scheme based on asymmetric encryption. The user can use asymmetric encryption to encrypt the data outsourced to the cloud platform and specify who can access the final evaluation results. After receiving the encrypted inputs from the user, the cloud platform evaluates via a random forest model and outputs the aggregated results where only the designated recipient can decrypt them. Threat analyses prove that the proposed scheme achieves the desirable security properties, such as correctness, confidentiality and robustness. Moreover, efficiency analyses demonstrate that the scheme is practical for real-world applications. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Securing Data Sharing)

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17 pages, 6008 KiB

Open AccessArticle

A Novel Method for Friction Coefficient Calculation in Metal Sheet Forming of Axis-Symmetric Deep Drawing Parts

by Jiansheng Xia, Jun Zhao, Shasha Dou and Xing Shen

Symmetry 2022, 14(2), 414; https://doi.org/10.3390/sym14020414 - 19 Feb 2022

Cited by 8 | Viewed by 2189

Abstract

Friction is one of the important factors in sheet metal forming. It greatly affects dynamic behaviors of metal sheets and stress and strain distributions in the metal sheets. In this study, deformation characteristics, stress–strain distribution, and change law of symmetrical parts in the [...] Read more.

Friction is one of the important factors in sheet metal forming. It greatly affects dynamic behaviors of metal sheets and stress and strain distributions in the metal sheets. In this study, deformation characteristics, stress–strain distribution, and change law of symmetrical parts in the process of deep drawing are analyzed using a new theoretical model based on the plastic flow law and partitioning the forming area. In the model, the least-square method is used to linearize the friction coefficient in nonlinear problems and reverse the calculation of friction coefficients to interpret the friction coefficient. To evaluate the model, the friction coefficient in sheet metal drawing of axis-symmetric deep drawing parts under various friction conditions was measured using a self-developed measuring system. The comparison between the experimental results and the calculation using the model shows a good agreement. The results show that the drawing force increases with the increase in punch depth; the friction coefficient decreases with the rise in punch depth. The friction coefficient obtained by fitting is relatively stable, and the average error is less than 3%. Using the friction coefficient model in finite element simulation analysis, it shows that the thickness and blank shape errors are less than 5%. The novel method studied in this paper shows great significance in support for theoretical research, numerical simulation research, and sheet metal stamping performance evaluation. Full article

(This article belongs to the Section Engineering and Materials)

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13 pages, 3277 KiB

Open AccessArticle

Spontaneous Symmetry Breaking: The Case of Crazy Clock and Beyond

by Maja C. Pagnacco, Jelena P. Maksimović, Marko Daković, Bojana Bokic, Sébastien R. Mouchet, Thierry Verbiest, Yves Caudano and Branko Kolaric

Symmetry 2022, 14(2), 413; https://doi.org/10.3390/sym14020413 - 19 Feb 2022

Cited by 4 | Viewed by 2663

Abstract

In this work, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs–Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, [...] Read more.

In this work, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs–Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, this is the first time that crazy-clock behavior is linked and explained with the symmetry-breaking phenomenon, highlighting the entire process in a novel way. The presented phenomenon has been thoroughly investigated by running more than 60 experiments, and evaluated by using statistical cluster K-means analysis. The mixing rate, as well as the magnetic bar shape and dimensions, have a strong influence on the transition appearance. Although the transition for both mixing and no-mixing conditions are taking place completely randomly, by using statistical cluster analysis we obtain different numbers of clusters (showing the time-domains where the transition is more likely to occur). In the case of stirring, clusters are more compact and separated, revealed new hidden details regarding the chemical dynamics of nonlinear processes. The significance of the presented results is beyond oscillatory reaction kinetics since the described example belongs to the small class of chemical systems that shows intrinsic randomness in their response and it might be considered as a real example of a classical liquid random number generator. Full article

(This article belongs to the Special Issue Symmetry in Many-Body Physics)

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18 pages, 1860 KiB

Open AccessArticle

Hybrid Precoding-Based Millimeter Wave Massive MIMO-NOMA Systems

by Zaoxing Zhu, Honggui Deng, Fuxin Xu, Wenjuan Zhang, Gang Liu and Yinhao Zhang

Symmetry 2022, 14(2), 412; https://doi.org/10.3390/sym14020412 - 19 Feb 2022

Cited by 7 | Viewed by 2056

Abstract

A symmetry-based hybrid precoder and combiner is a high spectral efficiency structure in millimeter-wave (mmWave) massive multiple-input multiple-output (mMIMO) non-orthogonal multiple access (NOMA) system. To improve the spectral efficiency of the mmWave mMIMO-NOMA system, we first propose a user grouping scheme to suppress [...] Read more.

A symmetry-based hybrid precoder and combiner is a high spectral efficiency structure in millimeter-wave (mmWave) massive multiple-input multiple-output (mMIMO) non-orthogonal multiple access (NOMA) system. To improve the spectral efficiency of the mmWave mMIMO-NOMA system, we first propose a user grouping scheme to suppress the strong inter-user interference caused by NOMA, then the hybrid precoder based on user channel alignment and the zero-forcing algorithm is constructed to further improve the signal-to-interference-plus-noise ratio (SINR) of the receiver. Subsequently, the non-convex spectral efficiency optimization problem is transformed into a convex optimization problem of inter-cluster power allocation and the closed-form solution for the optimal power under the minimum rate constraint is obtained by solving the KKT condition to further improve the spectral efficiency. The simulation results show that the proposed scheme can achieve higher spectral efficiency compared to orthogonal multiple access (OMA), fixed power allocation (FPA), K-means, and cluster head selection (CHS). Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Wireless Communication and Sensor Networks)

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12 pages, 3102 KiB

Open AccessArticle

On a Surface Associated with Pascal’s Triangle

by Valeriu Beiu, Leonard Dăuş, Marilena Jianu, Adela Mihai and Ion Mihai

Symmetry 2022, 14(2), 411; https://doi.org/10.3390/sym14020411 - 19 Feb 2022

Cited by 3 | Viewed by 2321

Abstract

An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the [...] Read more.

An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the classical discrete Pascal’s triangle (comprising all the binomial coefficients) to a continuous version (exhibiting infinitely many values in between the binomial coefficients) might be geometrically helpful and revealing. That is why we have decided to investigate the geometric properties of a continuous extension of Pascal’s triangle including: Gauss curvatures, mean curvatures, geodesics, and level curves, as well as their symmetries. Full article

(This article belongs to the Special Issue Topological Graph Theory and Discrete Geometry)

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16 pages, 1152 KiB

Open AccessArticle

by Muhammad Nabeel Abid, Miin-Shen Yang, Hanen Karamti, Kifayat Ullah and Dragan Pamucar

Symmetry 2022, 14(2), 410; https://doi.org/10.3390/sym14020410 - 18 Feb 2022

Cited by 26 | Viewed by 2244

Abstract

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited [...] Read more.

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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15 pages, 3530 KiB

Open AccessArticle

Mixtures of Semi-Parametric Generalised Linear Models

by Salomon M. Millard and Frans H. J. Kanfer

Symmetry 2022, 14(2), 409; https://doi.org/10.3390/sym14020409 - 18 Feb 2022

Cited by 1 | Viewed by 1534

Abstract

The mixture of generalised linear models (MGLM) requires knowledge about each mixture component’s specific exponential family (EF) distribution. This assumption is relaxed and a mixture of semi-parametric generalised linear models (MSPGLM) approach is proposed, which allows for unknown distributions of the EF for [...] Read more.

The mixture of generalised linear models (MGLM) requires knowledge about each mixture component’s specific exponential family (EF) distribution. This assumption is relaxed and a mixture of semi-parametric generalised linear models (MSPGLM) approach is proposed, which allows for unknown distributions of the EF for each mixture component while much of the parametric structure of the traditional MGLM is retained. Such an approach inherently allows for both symmetric and non-symmetric component distributions, frequently leading to non-symmetrical response variable distributions. It is assumed that the random component of each mixture component follows an unknown distribution of the EF. The specific member can either be from the standard class of distributions or from the broader set of admissible distributions of the EF which is accessible through the semi-parametric procedure. Since the inverse link functions of the mixture components are unknown, the MSPGLM estimates each mixture component’s inverse link function using a kernel smoother. The MSPGLM algorithm alternates the estimation of the regression parameters with the estimation of the inverse link functions. The properties of the proposed MSPGLM are illustrated through a simulation study on the separable individual components. The MSPGLM procedure is also applied on two data sets. Full article

(This article belongs to the Special Issue Symmetry in Multivariate Analysis)

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17 pages, 6745 KiB

Open AccessArticle

Propagation Prediction of Body Waves in Fluid-Saturated Soils with Flow-Independent Viscosity

by Bo Wang, Xingyuan Zhang and Bo Sun

Symmetry 2022, 14(2), 408; https://doi.org/10.3390/sym14020408 - 18 Feb 2022

Cited by 3 | Viewed by 1674

Abstract

A systematic study of wave theory in thermoviscoelastic soil is essential for engineering applications such as geophysical exploration. In the present work, the influences of flow-independent viscosity of the soil skeleton and the thermal effect on elastic waves are considered, and the propagation [...] Read more.

A systematic study of wave theory in thermoviscoelastic soil is essential for engineering applications such as geophysical exploration. In the present work, the influences of flow-independent viscosity of the soil skeleton and the thermal effect on elastic waves are considered, and the propagation behaviors of body waves in thermoviscoelastic saturated soil are investigated. Firstly, the thermoviscoelastic dynamic coupling model of saturated soil were established by employing the Biot model, the generalized thermoelastic theory, and the Kelvin–Voigt linear viscoelastic model. Secondly, the dispersion equations of body waves in thermoviscoelastic saturated soil were theoretically derived with structural symmetry considered. Finally, the variations of wave velocity and the attenuation coefficient of the body waves with the thermophysical parameters are discussed. The results revealed that the enhancement of the relaxation time of soil caused an increase of wave velocity and the attenuation coefficient of P₁, P₂, and S waves, and a decrease of the wave velocity and attenuation coefficient of the thermal wave. Different ranges of the permeability coefficient and frequency have different effects on the P₁, P₂, and S waves. The variation of thermal conductivity and the phase-lags of heat flux and temperature gradient only affect the thermal wave. Full article

(This article belongs to the Special Issue Symmetry in Applied Mechanics Analysis on Smart Optical Fiber Sensors)

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17 pages, 315 KiB

Open AccessArticle

Simplification of Galactic Dynamic Equations

by Ying-Qiu Gu

Symmetry 2022, 14(2), 407; https://doi.org/10.3390/sym14020407 - 18 Feb 2022

Viewed by 1651

Abstract

Galactic dynamics is the foundation for simulating galactic structure and for solving other problems. However, the traditional dynamic equations include some unreasonable assumptions and are therefore scientifically invalid. In this paper, by introducing the following three working assumptions, we established the galactic dynamics [...] Read more.

Galactic dynamics is the foundation for simulating galactic structure and for solving other problems. However, the traditional dynamic equations include some unreasonable assumptions and are therefore scientifically invalid. In this paper, by introducing the following three working assumptions, we established the galactic dynamics of high precision and convenient formalism. 1. In the research of large-scale structure, the retarded potential of the gravitational field should be taken into account, and the weak field and low velocity approximation of Einstein’s field equation should be adopted. 2. The stars in a fully developed galaxy should be zero-pressure and inviscid fluid, and the equation of motion is different from that of ordinary continuum mechanics. Stars move along geodesics. 3. The structure of the galaxy is only related to the total mass density distribution. The equation of state of dark halo is different from that of ordinary luminous interstellar matter, so their trajectories are also very different. In a galaxy, the dark halo and the ordinary matter are automatically separated. The total mass density distribution can be presupposed according to the observation data, and then it can be determined by comparing the solution of the equations with the observed data. These assumptions and treatments are supported by theory and observation. The variables of the equations of simplified galactic dynamics are separated from each other, and the equations are well-posed and can be solved according to a definite procedure. The solution explains the Tully–Fisher relation. Therefore, this simplified dynamic equation system provides a more reasonable and practical framework for the further study of galactic structure, and can solve many practical problems. In addition, it is closely related to the study of dark matter halo in galaxy. Full article

(This article belongs to the Section Physics)

18 pages, 4541 KiB

Open AccessArticle

Electromagnetic Flow of SWCNT/MWCNT Suspensions in Two Immiscible Water- and Engine-Oil-Based Newtonian Fluids through Porous Media

by Ahmad Zeeshan, Nasir Shehzad, Muhammad Atif, Rahmat Ellahi and Sadiq M. Sait

Symmetry 2022, 14(2), 406; https://doi.org/10.3390/sym14020406 - 18 Feb 2022

Cited by 53 | Viewed by 3778

Abstract

This article deals with steady-state laminar, electrically conducting immiscible fluids. The Newtonian fluid considered passes between two parallel vertical plates in a porous medium. The channel consists of two regions, one of them filled with engine-oil-based carbon nanotubes (CNTs) and the second region [...] Read more.

This article deals with steady-state laminar, electrically conducting immiscible fluids. The Newtonian fluid considered passes between two parallel vertical plates in a porous medium. The channel consists of two regions, one of them filled with engine-oil-based carbon nanotubes (CNTs) and the second region filled with water through a porous medium. The assumptions for the channel walls are electrically non-conducting and are at two different temperatures. Mathematical formulation is formed using rules for the conservation of mass, momentum and energy in both regions. Continuous conditions are used for velocity, temperature and also for shear pressure at the crossing area. The governing equations are first transformed in a non-dimensional form by using appropriate transformations, and then the subsequent differential equations are solved using a topological approach by means of the homotopy analysis method. It is found that the impact of the actual boundaries utilized in the issue is directed, and the outcomes are introduced graphically and discussed. It is noted that the engine-oil SWCNTs experience a significant increase in temperature profiles as compared to the engine-oil MWCNTs, while the movement of fluid slowdown in the nanofluid region due to the concentration of nanoparticles and the thickness of the thermal boundary layer increases by increasing the volume fraction of the carbon nanotubes. Full article

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16 pages, 291 KiB

Open AccessArticle

Some New James Type Geometric Constants in Banach Spaces

by Bingren Chen, Zhijian Yang, Qi Liu and Yongjin Li

Symmetry 2022, 14(2), 405; https://doi.org/10.3390/sym14020405 - 18 Feb 2022

Viewed by 1529

Abstract

We will introduce four new geometric constants closely related to the James constant

J (X)

, which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the [...] Read more.

We will introduce four new geometric constants closely related to the James constant

J (X)

, which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the calculation of several values on some specific spaces. In addition, we will characterize geometric properties of

J_{1} (X)

, such as uniform non-squareness and uniformly normal structure. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)

13 pages, 456 KiB

Open AccessArticle

Independent Roman Domination: The Complexity and Linear-Time Algorithm for Trees

by Zhixing Duan, Huiqin Jiang, Xinyue Liu, Pu Wu and Zehui Shao

Symmetry 2022, 14(2), 404; https://doi.org/10.3390/sym14020404 - 18 Feb 2022

Viewed by 1542

Abstract

For a graph

G = (V, E)

, an independent Roman dominating function (IRDF) is a function

f : V \to {0, 1, 2}

having the property that: (1) every vertex assigned a value of 0 [...] Read more.

For a graph

G = (V, E)

, an independent Roman dominating function (IRDF) is a function

f : V \to {0, 1, 2}

having the property that: (1) every vertex assigned a value of 0 is adjacent to at least one vertex assigned a value of 2, (2) there are no two adjacent vertices with positive assignments. The weight of an IRDF (

w (f)

) is the sum of assignments for all vertices. The minimum weight of an independent Roman dominating function on graph G is the independent Roman domination number, denoted by

i_{R} (G)

. In this paper, we prove that the decision problem of minimum IRDF is

N P

-complete for chordal bipartite graphs. Then, we research the difference in complexity between the decision problem of RDF and IRDF. Finally, we propose a linear-time algorithm for computing the minimum weight of an independent Roman dominating function in trees. Full article

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20 pages, 385 KiB

Open AccessArticle

Inference for Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring

by Liang Wang, Ying Zhou, Yuhlong Lio and Yogesh Mani Tripathi

Symmetry 2022, 14(2), 403; https://doi.org/10.3390/sym14020403 - 17 Feb 2022

Cited by 10 | Viewed by 1740

Abstract

In this paper, generalized progressive hybrid censoring is discussed, while a scheme is designed to provide a flexible and symmetrical scenario to collect failure information in the whole life cycle of units. When the lifetime of units follows Kumaraswamy distribution, inference is investigated [...] Read more.

In this paper, generalized progressive hybrid censoring is discussed, while a scheme is designed to provide a flexible and symmetrical scenario to collect failure information in the whole life cycle of units. When the lifetime of units follows Kumaraswamy distribution, inference is investigated under classical and Bayesian approaches. The maximum likelihood estimates and associated existence and uniqueness properties are established and the confidence intervals for unknown parameters are provided by using a large sample size based on asymptotic theory. Moreover, the Bayes estimates along with highest probability density credible intervals are also developed through the Monte-Carlo Markov Chain sampling technique to approximate the associated posteriors. Simulation studies and a real-life example are presented for illustration purposes. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Probability)

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20 pages, 300 KiB

Open AccessArticle

Several Isospectral and Non-Isospectral Integrable Hierarchies of Evolution Equations

by Shiyin Zhao, Yufeng Zhang and Jian Zhou

Symmetry 2022, 14(2), 402; https://doi.org/10.3390/sym14020402 - 17 Feb 2022

Viewed by 1346

Abstract

By introducing a

3 \times 3

matrix Lie algebra and employing the generalized Tu scheme, a AKNS isospectral–nonisospectral integrable hierarchy is generated by using a third-order matrix Lie algebra. Through a matrix transformation, we turn the

3 \times 3

matrix Lie algebra into [...] Read more.

By introducing a

3 \times 3

matrix Lie algebra and employing the generalized Tu scheme, a AKNS isospectral–nonisospectral integrable hierarchy is generated by using a third-order matrix Lie algebra. Through a matrix transformation, we turn the

3 \times 3

matrix Lie algebra into a

2 \times 2

matrix case for which we conveniently enlarge it into two various expanding Lie algebras in order to obtain two different expanding integrable models of the isospectral–nonisospectral AKNS hierarchy by employing the integrable coupling theory. Specially, we propose a method for generating nonlinear integrable couplings for the first time, and produce a generalized KdV-Schrödinger integrable system and a nonlocal nonlinear Schrödinger equation, which indicates that we unite the KdV equation and the nonlinear Schrödinger equation as an integrable model by our method. This method presented in the paper could apply to investigate other integrable systems. Full article

(This article belongs to the Section Mathematics)

18 pages, 663 KiB

Open AccessArticle

Cross-Project Defect Prediction Considering Multiple Data Distribution Simultaneously

by Yu Zhao, Yi Zhu, Qiao Yu and Xiaoying Chen

Symmetry 2022, 14(2), 401; https://doi.org/10.3390/sym14020401 - 17 Feb 2022

Cited by 15 | Viewed by 4014

Abstract

Software testing is the main method for finding software defects at present, and symmetric testing and other methods have been widely used, but these testing methods will cause a lot of waste of resources. Software defect prediction methods can reasonably allocate testing resources [...] Read more.

Software testing is the main method for finding software defects at present, and symmetric testing and other methods have been widely used, but these testing methods will cause a lot of waste of resources. Software defect prediction methods can reasonably allocate testing resources by predicting the defect tendency of software modules. Cross-project defect prediction methods have huge advantages when faced with missing datasets. However, most cross-project defect prediction methods are designed based on the settings of a single source project and a single target project. As the number of public datasets continues to grow, the number of source projects and defect information is increasing. Therefore, in the case of multi-source projects, this paper explores the problems existing when using multi-source projects for defect prediction. There are two problems. First, in practice, it is not possible to know in advance which source project is used to build the model to obtain the best prediction performance. Second, if an inappropriate source project is used in the experiment to build the model, it can lead to lower performance issues. According to the problems found in the experiment, the paper proposed a multi-source-based cross-project defect prediction method MSCPDP. Experimental results on the AEEEM dataset and PROMISE dataset show that the proposed MSCPDP method effectively solves the above two problems and outperforms most of the current state-of-art cross-project defect prediction methods on F1 and AUC. Compared with the six cross-project defect prediction methods, the F1 median is improved by 3.51%, 3.92%, 36.06%, 0.49%, 17.05%, and 9.49%, and the ACU median is improved by −3.42%, 8.78%, 0.96%, −2.21%, −7.94%, and 5.13%. Full article

(This article belongs to the Special Issue Recent Advances in Software for Symmetry)

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11 pages, 278 KiB

Open AccessArticle

Application of Lie Symmetry to a Mathematical Model that Describes a Cancer Sub-Network

by Maba Boniface Matadi

Symmetry 2022, 14(2), 400; https://doi.org/10.3390/sym14020400 - 17 Feb 2022

Cited by 3 | Viewed by 1733

Abstract

In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the [...] Read more.

In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor (

P 27^{K i p 1}

). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities II)

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Symmetry, Volume 14, Issue 2 (February 2022) – 248 articles

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