Symmetry

18 pages, 4374 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Analysis of Drill-String Nonlinear Dynamics Using the Lumped-Parameter Method

by Lelya A. Khajiyeva, Igor V. Andrianov, Yuliya F. Sabirova and Askar K. Kudaibergenov

Symmetry 2022, 14(7), 1495; https://doi.org/10.3390/sym14071495 - 21 Jul 2022

Cited by 6 | Viewed by 2274

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string [...] Read more.

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string with a static compressive load at the left end is considered. In this paper, this method is applied to discretize linear and nonlinear models of the lateral vibrations of a vertical drill string under the effect of a supersonic gas flow. The obtained results are verified with the previously published data. The optimal number of the drill-string partitions is determined using the developed application, which allows us to estimate the accuracy of the loaded data. The numerical solution of the model is obtained using the fourth-order Runge–Kutta method. The optimization of the numerical algorithm using parallel-programming tools is carried out, and the efficiency of the method is analyzed. Full article

(This article belongs to the Special Issue Dynamical Processes in Heterogeneous and Discrete Media)

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17 pages, 5432 KiB

Open AccessArticle

Computational Analysis of MHD Nonlinear Radiation Casson Hybrid Nanofluid Flow at Vertical Stretching Sheet

by Nadeem Abbas, Wasfi Shatanawi and Kamaleldin Abodayeh

Symmetry 2022, 14(7), 1494; https://doi.org/10.3390/sym14071494 - 21 Jul 2022

Cited by 71 | Viewed by 3053

Abstract

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The [...] Read more.

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The effect of nonlinear radiation was studied. We considered the SWCNT (signal wall carbon nanotube) and MWCNT (multi-wall carbon nanotube) with base liquid (water). Under the flow suppositions, a mathematical model was settled by means of boundary layer approximations in terms of partial differential equations. The suitable transformation was developed by using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique named bvp4c. The impacts of pertinent flow parameters on skin friction, Nusselt number, and temperature and velocity distributions were depicted through tabular form as well as graphical form. In this study, the Yamada Ota model achieved a higher heat transfer rate compared to the Tiwari Das and Xue hybrid nanofluid models. The skin friction (

C_{fx} {Re}^{- 1 / 2}

) increased and temperature gradient (

{Nu}_{x} {Re}^{- 1 / 2}

) declined due to the increment of solid nanoparticle concentration (

ϕ_{2}

). Physically, skin friction increased because the higher values of the solid nanoparticles increased resistance to the fluid motion. Full article

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22 pages, 549 KiB

Open AccessArticle

Groups and Structures of Commutative Semigroups in the Context of Cubic Multi-Polar Structures

by Anas Al-Masarwah, Mohammed Alqahtani and Majdoleen Abu Qamar

Symmetry 2022, 14(7), 1493; https://doi.org/10.3390/sym14071493 - 21 Jul 2022

Viewed by 1581

Abstract

In recent years, the m-polar fuzziness structure and the cubic structure have piqued the interest of researchers and have been commonly implemented in algebraic structures like groupoids, semigroups, groups, rings and lattices. The cubic m-polar (

C_{m} P

) structure [...] Read more.

In recent years, the m-polar fuzziness structure and the cubic structure have piqued the interest of researchers and have been commonly implemented in algebraic structures like groupoids, semigroups, groups, rings and lattices. The cubic m-polar (

C_{m} P

) structure is a generalization of m-polar fuzziness and cubic structures. The intent of this research is to extend the

C_{m} P

structures to the theory of groups and semigroups. In the present research, we preface the concept of the

C_{m} P

groups and probe many of its characteristics. This concept allows the membership grade and non-membership grade sequence to have a set of m-tuple interval-valued real values and a set of m-tuple real values between zero and one. This new notation of group (semigroup) serves as a bridge among

C_{m} P

structure, classical set and group (semigroup) theory and also shows the effect of the

C_{m} P

structure on a group (semigroup) structure. Moreover, we derive some fundamental properties of

C_{m} P

groups and support them by illustrative examples. Lastly, we vividly construct semigroup and groupoid structures by providing binary operations for the

C_{m} P

structure and provide some dominant properties of these structures. Full article

(This article belongs to the Special Issue The Study of Lattice Theory and Universal Algebra)

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12 pages, 436 KiB

Open AccessArticle

Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions

by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong

Symmetry 2022, 14(7), 1492; https://doi.org/10.3390/sym14071492 - 21 Jul 2022

Cited by 4 | Viewed by 1667

Abstract

Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) [...] Read more.

Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)

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43 pages, 11062 KiB

Open AccessArticle

A Feature-Based Method for Detecting Design Patterns in Source Code

by Mariam Kouli and Abbas Rasoolzadegan

Symmetry 2022, 14(7), 1491; https://doi.org/10.3390/sym14071491 - 21 Jul 2022

Cited by 3 | Viewed by 3901

Abstract

Design patterns are common solutions to existing issues in software engineering. In recent decades, design patterns have been researched intensively because they increase the quality factors of software systems such as flexibility, maintainability, and reusability. Design pattern detection refers to the determination of [...] Read more.

Design patterns are common solutions to existing issues in software engineering. In recent decades, design patterns have been researched intensively because they increase the quality factors of software systems such as flexibility, maintainability, and reusability. Design pattern detection refers to the determination of the symmetry between a code fragment and the definition of a design pattern. One of the major challenges in design pattern detection is how to obtain accurate information about the design patterns used in the software system due to the existence of different design pattern variants. Increasing the number of design pattern variants covered by a detection method is one of the main factors that increase its accuracy. In this paper, a step toward solving this challenge was taken by proposing a new feature-based method that builds on concrete definitions of existing design pattern variants and supports the definition and detection of new variants. In this proposed method, the needed features are extracted from the signatures of the design patterns. This method was applied to the 23 Gang of Four (GoF) design patterns and evaluated using four open-source Java projects. Afterward, it was compared with some previous methods using automatically generated testbeds. The experimental results demonstrated that the proposed method has better performance in terms of precision and recall compared to the other methods. Full article

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20 pages, 428 KiB

Open AccessArticle

Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

by Omid Nikan, Ho Duy Binh, Zakieh Avazzadeh and Le Dinh Long

Symmetry 2022, 14(7), 1490; https://doi.org/10.3390/sym14071490 - 21 Jul 2022

Viewed by 1459

Abstract

The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of

(Φ, g) \in L^{2} (0, T) \times L^{2} (Ω)

, we give a [...] Read more.

The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of

(Φ, g) \in L^{2} (0, T) \times L^{2} (Ω)

, we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in

L^{q} (D)

, with

q \neq 2

under some reasonable Cauchy data assumptions. Full article

(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)

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14 pages, 2868 KiB

Open AccessArticle

Few-Shot Learning for Fault Diagnosis: Semi-Supervised Prototypical Network with Pseudo-Labels

by Jun He, Zheshuai Zhu, Xinyu Fan, Yong Chen, Shiya Liu and Danfeng Chen

Symmetry 2022, 14(7), 1489; https://doi.org/10.3390/sym14071489 - 21 Jul 2022

Cited by 7 | Viewed by 2757

Abstract

Achieving deep learning-based bearing fault diagnosis heavily relies on large labeled training samples. However, in real industry applications, labeled data are scarce or even impossible to obtain. In this study, we addressed a challenging few-shot bearing fault diagnosis problem with few or no [...] Read more.

Achieving deep learning-based bearing fault diagnosis heavily relies on large labeled training samples. However, in real industry applications, labeled data are scarce or even impossible to obtain. In this study, we addressed a challenging few-shot bearing fault diagnosis problem with few or no training labeled samples of novel categories. To tackle this problem, we considered a semi-supervised prototype network based on few-shot bearing fault diagnosis with pseudo-labels. The existing prototypical networks with pseudo-label methods train a pseudo label model to label unlabeled samples using high-dimensional labeled data, which cannot eliminate the instability of the pseudo-label model caused by dimensional labeled features. To mitigate this issue, we used kernel principal component analysis to reduce the dimensions of and remove redundant information from high-dimensional data. Specifically, we used the pseudo-label prediction algorithm with probability distance to label unlabeled samples, aiming to improve the labeling accuracy. We applied two well-known bearing data sets for the validation experiments with symmetry parameters. The findings illustrated that the classification accuracy of the proposed method is higher than that of other existing methods. Full article

(This article belongs to the Special Issue Advances and Applications in Data-Driven Process Monitoring, Fault Diagnosis and Control)

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10 pages, 2976 KiB

Open AccessArticle

Numerical Solution of Radiative and Viscous Dissipative Fluid Flow along an Oscillating Vertical Plate

by Rajaraman Rengasamy and Rajamanickam Muthucumaraswamy

Symmetry 2022, 14(7), 1488; https://doi.org/10.3390/sym14071488 - 21 Jul 2022

Viewed by 1770

Abstract

A numerical analysis of an unsteady radiative and viscous dissipative fluid flow across a semi-infinite oscillating vertical plate with a constant temperature and mass diffusion is examined here. The fluid under consideration is optically thin gray, emitting, heat-retaining, and non-dispersing. A finite-difference approach [...] Read more.

A numerical analysis of an unsteady radiative and viscous dissipative fluid flow across a semi-infinite oscillating vertical plate with a constant temperature and mass diffusion is examined here. The fluid under consideration is optically thin gray, emitting, heat-retaining, and non-dispersing. A finite-difference approach known as the Crank−Nicolson strategy was applied to find the solution to the limitless governing equations. Applications of such engineering problems can be found in fields such as aerospace, solar power, the cooling of nuclear reactors, and chemical and mechanical engineering. Based on the computational solutions, the impacts of distinct physical parameters, such as velocity, concentration, temperature, skin friction, Nusselt number, and Sherwood number profiles, are portrayed pictorially and imparted. The numerical solution of the velocity profile developed in this study fits extremely well with what was previously published and validated. Furthermore, we discovered that plate oscillation, radiation, and viscous dissipation parameters surprisingly influence the flow pattern. Full article

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31 pages, 5580 KiB

Open AccessArticle

A Novel Deep Learning Model for Sea State Classification Using Visual-Range Sea Images

by Muhammad Umair, Manzoor Ahmed Hashmani, Syed Sajjad Hussain Rizvi, Hasmi Taib, Mohd Nasir Abdullah and Mehak Maqbool Memon

Symmetry 2022, 14(7), 1487; https://doi.org/10.3390/sym14071487 - 20 Jul 2022

Cited by 6 | Viewed by 3287

Abstract

Wind-waves exhibit variations both in shape and steepness, and their asymmetrical nature is a well-known feature. One of the important characteristics of the sea surface is the front-back asymmetry of wind-wave crests. The wind-wave conditions on the surface of the sea constitute a [...] Read more.

Wind-waves exhibit variations both in shape and steepness, and their asymmetrical nature is a well-known feature. One of the important characteristics of the sea surface is the front-back asymmetry of wind-wave crests. The wind-wave conditions on the surface of the sea constitute a sea state, which is listed as an essential climate variable by the Global Climate Observing System and is considered a critical factor for structural safety and optimal operations of offshore oil and gas platforms. Methods such as statistical representations of sensor-based wave parameters observations and numerical modeling are used to classify sea states. However, for offshore structures such as oil and gas platforms, these methods induce high capital expenditures (CAPEX) and operating expenses (OPEX), along with extensive computational power and time requirements. To address this issue, in this paper, we propose a novel, low-cost deep learning-based sea state classification model using visual-range sea images. Firstly, a novel visual-range sea state image dataset was designed and developed for this purpose. The dataset consists of 100,800 images covering four sea states. The dataset was then benchmarked on state-of-the-art deep learning image classification models. The highest classification accuracy of 81.8% was yielded by NASNet-Mobile. Secondly, a novel sea state classification model was proposed. The model took design inspiration from GoogLeNet, which was identified as the optimal reference model for sea state classification. Systematic changes in GoogLeNet’s inception block were proposed, which resulted in an 8.5% overall classification accuracy improvement in comparison with NASNet-Mobile and a 7% improvement from the reference model (i.e., GoogLeNet). Additionally, the proposed model took 26% less training time, and its per-image classification time remains competitive. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis)

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15 pages, 5173 KiB

Open AccessArticle

Experimental Study on Dynamic Performance of Tubular Flange Grid-Type Dam under Impact Load

by Xiu-Li Wang, Yong Yao, Sai-Long Wang, Zhu-Jun Feng and Yun-Peng Chu

Symmetry 2022, 14(7), 1486; https://doi.org/10.3390/sym14071486 - 20 Jul 2022

Viewed by 1498

Abstract

As one of the most dangerous geological hazards in the world, debris flows can destroy trees and structures, break electrical, water, and gas lines, and disrupt bridges and roadways in a short period of time, threatening life and property. In particular, fast-moving large [...] Read more.

As one of the most dangerous geological hazards in the world, debris flows can destroy trees and structures, break electrical, water, and gas lines, and disrupt bridges and roadways in a short period of time, threatening life and property. In particular, fast-moving large boulders carried by debris-induced destructive impact loading can strike objects without warning. To resist impact loading caused by rocks in debris, this paper proposed an innovative grid-type debris dam (or Sabo dam) design composed of symmetrical cross-sections of steel tubular flange beams and columns. This paper studied the dynamic performance of the tubular flange columns under impact loading by conducting lab tests and numerical simulations. Moreover, the dynamic response of the grid-type debris dam was simulated under various loading conditions. Comparing three different types of columns with similar configurations under the same loading condition, the tubular flange column proposed in this research exhibits better performance in overall strain, displacement, acceleration, and bending conditions. Furthermore, the results also prove that the proposed structure has excellent interoperability and energy absorption capabilities. When increasing the testing impact load, the failure modes of the dam change from dent at the impact point to local buckling and total failure of the structure, which indicates that the structure has superior performance under impact loading. Full article

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

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18 pages, 470 KiB

Open AccessArticle

Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form

by Gianfranco Cariolaro and Roberto Corvaja

Symmetry 2022, 14(7), 1485; https://doi.org/10.3390/sym14071485 - 20 Jul 2022

Cited by 3 | Viewed by 2565

Abstract

This paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real [...] Read more.

This paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real variables. However, there is a very efficient representation of the CM called the standard form (SF) that reduces the degrees of freedom to four real variables, while preserving all the relevant information on the state. The SF can be easily evaluated using a set of symplectic invariants. The paper starts from the SF, introducing an architecture that implements with primitive components the given two-mode Gaussian state having the CM with the SF. The architecture consists of a beam splitter, followed by the parallel set of two single–mode real squeezers, followed by another beam splitter. The advantage of this architecture is that it gives a precise non-redundant physical meaning of the generation of the Gaussian state. Essentially, all the relevant information is contained in this simple architecture. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

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16 pages, 298 KiB

Open AccessArticle

Extended Convergence of Three Step Iterative Methods for Solving Equations in Banach Space with Applications

by Samundra Regmi, Ioannis K. Argyros, Santhosh George and Christopher I. Argyros

Symmetry 2022, 14(7), 1484; https://doi.org/10.3390/sym14071484 - 20 Jul 2022

Cited by 2 | Viewed by 1135

Abstract

Symmetries are vital in the study of physical phenomena such as quantum physics and the micro-world, among others. Then, these phenomena reduce to solving nonlinear equations in abstract spaces. These equations in turn are mostly solved iteratively. That is why the objective of [...] Read more.

Symmetries are vital in the study of physical phenomena such as quantum physics and the micro-world, among others. Then, these phenomena reduce to solving nonlinear equations in abstract spaces. These equations in turn are mostly solved iteratively. That is why the objective of this paper was to obtain a uniform way to study three-step iterative methods to solve equations defined on Banach spaces. The convergence is established by using information appearing in these methods. This is in contrast to earlier works which relied on derivatives of the higher order to establish the convergence. The numerical example completes this paper. Full article

21 pages, 361 KiB

Open AccessArticle

An Authentication Protocol for the Medical Internet of Things

by Nagwa El-Meniawy, Mohamed R. M. Rizk, Magdy A. Ahmed and Mohamed Saleh

Symmetry 2022, 14(7), 1483; https://doi.org/10.3390/sym14071483 - 20 Jul 2022

Cited by 6 | Viewed by 1905

Abstract

The progress in biomedical sensors, Internet of Things technologies, big data, cloud computing, and artificial intelligence is leading the development of e-health medical systems, offering a range of new and innovative services. One such service is remote patient monitoring, where medical professionals are [...] Read more.

The progress in biomedical sensors, Internet of Things technologies, big data, cloud computing, and artificial intelligence is leading the development of e-health medical systems, offering a range of new and innovative services. One such service is remote patient monitoring, where medical professionals are able to collect and examine a patient’s medical data remotely. Of course, in these systems, security and privacy are of utmost importance and we need to verify the identities of system users before granting them access to sensitive patient-related data. To this end, several authentication protocols have been recently designed specifically for e-health systems. We survey several of these protocols and report on flaws and shortcomings we discovered. Moreover, we propose an authentication protocol that enables a medical professional and the network of sensors used by a patient to authenticate each other and share a cryptographic key to be used for security in a communication session. The protocol also enables the dynamic assignment of patients to doctors in order to control access to patients’ data. We perform a security analysis of the protocol both formally, using the ProVerif protocol analysis tool, and informally, demonstrating its security features. We show that our protocol achieves mutual authentication, secret key establishment, forward secrecy, and anonymity. In terms of performance, the protocol is computationally lightweight, as it relies on symmetric key cryptography. This is demonstrated by comparing the computational cost of our protocol (in terms of execution time) with that of other similar protocols. Full article

(This article belongs to the Section Computer)

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21 pages, 8069 KiB

Open AccessArticle

Image Encryption Algorithm Using 2-Order Bit Compass Coding and Chaotic Mapping

by Jinlin Chen, Yiquan Wu, Yeguo Sun and Chunzhi Yang

Symmetry 2022, 14(7), 1482; https://doi.org/10.3390/sym14071482 - 20 Jul 2022

Cited by 1 | Viewed by 1676

Abstract

This paper proposes a novel image encryption algorithm based on an integer form of chaotic mapping and 2-order bit compass diffusion technique. Chaotic mapping has been widely used in image encryption. If the floating-point number generated by chaotic mapping is applied to image [...] Read more.

This paper proposes a novel image encryption algorithm based on an integer form of chaotic mapping and 2-order bit compass diffusion technique. Chaotic mapping has been widely used in image encryption. If the floating-point number generated by chaotic mapping is applied to image encryption algorithm, it will slow encryption and increase the difficulty of hardware implementation. An innovative pseudo-random integer sequence generator is proposed. In chaotic system, the result of one-iteration is used as the shift value of two binary sequences, the original symmetry relationship is changed, and then XOR operation is performed to generate a new binary sequence. Multiple iterations can generate pseudo-random integer sequences. Here integer sequences have been used in scrambling of pixel positions. Meanwhile, this paper demonstrates that there is an inverse operation in the XOR operation of two binary sequences. A new pixel diffusion technique based on bit compass coding is proposed. The key vector of the algorithm comes from the original image and is hidden by image encryption. The efficiency of our proposed method in encrypting a large number of images is evaluated using security analysis and time complexity. The performance evaluation of algorithm includes key space, histogram differential attacks, gray value distribution(GDV),correlation coefficient, PSNR, entropy, and sensitivity. The comparison between the results of coefficient, entropy, PSNR, GDV, and time complexity further proves the effectiveness of the algorithm. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Data Sciences and Machine Learning for Multidisciplinary Research)

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11 pages, 68430 KiB

Open AccessArticle

Distortion-Corrected Integral Imaging 3D Display System Based on Lens Array Holographic Optical Element

by Jun-Hua Li, Han-Le Zhang, Qing-Lin Ji and Wu-Xiang Zhao

Symmetry 2022, 14(7), 1481; https://doi.org/10.3390/sym14071481 - 20 Jul 2022

Viewed by 1906

Abstract

We propose a distortion-corrected integral imaging (II) 3D display system based on lens array holographic optical element (LAHOE). The LAHOE is used as a projection screen. The projection beam of the LAHOE is parallel light. Hence, the projection system consists of a spatial [...] Read more.

We propose a distortion-corrected integral imaging (II) 3D display system based on lens array holographic optical element (LAHOE). The LAHOE is used as a projection screen. The projection beam of the LAHOE is parallel light. Hence, the projection system consists of a spatial light modulator, a reverse projection lens, a relay optical element, and a telecentric lens. The acquired 3D data and the reconstructed 3D image of II are symmetrically related to each other. Therefore, there is lens distortion in the projection system. To avoid affecting the viewing experience of the viewers, the elemental image array (EIA) is projected obliquely on the LAHOE, causing the lateral distortion of the EIA. There is a position deviation in the projection system, so the projected EIA has geometric deformation. Due to the distortion of the EIA, it is difficult to precisely align the projected EIA and LAHOE, which results in serious flip of the reconstructed 3D images. The distortion of the EIA affects the asymmetry of the 3D image reconstruction. Lens distortion can be solved by the distortion compensation method. Lateral and the geometric deformation can be solved by the perspective transformations in computer graphics. After correction, the undistorted EIA is projected, and the projected EIA on the LAHOE has little distortion. In the process of 3D image reconstruction, the causes of asymmetry affecting 3D image reconstruction are analyzed, and the issues that generate these asymmetric factors are addressed. Experimental results indicate that a better 3D display effect is achieved. Full article

(This article belongs to the Special Issue Advances in 3D Imaging, Display and Security with Symmetry/Asymmetry)

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10 pages, 2324 KiB

Open AccessArticle

Exact Traveling Wave Solutions in a Generalized Harry Dym Type Equation

by Rong Wu and Yan Zhou

Symmetry 2022, 14(7), 1480; https://doi.org/10.3390/sym14071480 - 20 Jul 2022

Cited by 3 | Viewed by 1848

Abstract

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions [...] Read more.

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions in parameter space are examined. It is demonstrated that solitary wave solutions, periodic peakons, pseudo-peakons, and compacton solutions exist. All conceivable exact explicit parametric representations of various solutions are presented. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

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13 pages, 277 KiB

Open AccessArticle

Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function

by Jamiu Olusegun Hamzat, Abiodun Tinuoye Oladipo and Georgia Irina Oros

Symmetry 2022, 14(7), 1479; https://doi.org/10.3390/sym14071479 - 19 Jul 2022

Cited by 6 | Viewed by 1458

Abstract

The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and [...] Read more.

The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and the modified sigmoid function. The results contained in the proved theorems refer to coefficient estimates for the functions in the newly introduced classes. Full article

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

19 pages, 5561 KiB

Open AccessArticle

Mapping Natural Orbits around Io

by Thamis C. F. Carvalho Ferreira, Antonio F. Bertachini A. Prado, Silvia M. Giuliatti Winter and Lucas S. Ferreira

Symmetry 2022, 14(7), 1478; https://doi.org/10.3390/sym14071478 - 19 Jul 2022

Cited by 7 | Viewed by 1866

Abstract

As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural [...] Read more.

As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural satellites Europa and Ganymede. This natural satellite is a good candidate to be visited by future missions. In this sense, the present work has the goal of studying and mapping the best initial orbital conditions for orbits around Io, considering the symmetrical or asymmetical perturbative effects of a third body (Jupiter) and the

J_{2}

term from the mass configuration of Io. The initial orbital parameters of the probe were investigated through a set of numerical simulations. The results showed that although most orbits around Io have lifetimes of less than 6 months, some regions were found where the initial conditions of the orbits provided satisfactory times for the accomplishment of future missions around Io. Full article

(This article belongs to the Special Issue Advances in Mechanics and Control)

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19 pages, 4893 KiB

Open AccessArticle

A Symmetrical Terahertz Triple-Band Metamaterial Absorber Using a Four-Capacitance Loaded Complementary Circular Split Ring Resonator and an Ultra-Thin ZnSe Substrate

by Yadgar I. Abdulkarim, Fatih Özkan Alkurt, Halgurd N. Awl, Olcay Altıntaş, Fahmi F. Muhammadsharif, Bhargav Appasani, Mehmet Bakır, Muharrem Karaaslan, Mohamed Taouzari and Jian Dong

Symmetry 2022, 14(7), 1477; https://doi.org/10.3390/sym14071477 - 19 Jul 2022

Cited by 15 | Viewed by 2619

Abstract

In this research work, a symmetrical four-capacitance loaded complementary circular split ring resonator is proposed, which uses an ultra-thin Zinc Selenide (ZnSe) substrate to realize a low-profile triple-band metamaterial (MTM) perfect absorber for application in the terahertz (THz) frequency range. The electromagnetic properties [...] Read more.

In this research work, a symmetrical four-capacitance loaded complementary circular split ring resonator is proposed, which uses an ultra-thin Zinc Selenide (ZnSe) substrate to realize a low-profile triple-band metamaterial (MTM) perfect absorber for application in the terahertz (THz) frequency range. The electromagnetic properties of the proposed structure were calculated and investigated using the Finite Integration Technique (FIT). The proposed structure exhibited three highly absorptive (nearly perfect) peaks at the resonance frequencies of 15.68 THz, 37.48 THz, and 39.55 THz. Furthermore, the absorber was found to be insensitive to the polarization and incident wave angles, due to its symmetrical design. The effects of the conductor type, substrate thickness, unit cell dimension, resonator gap, and substrate type on the reflection and absorption spectra were investigated. To validate the numerical results, the proposed design was analyzed using High-Frequency Simulation Software (HFSS) and Advanced Design System (ADS). The surface current, electric field, and magnetic field distributions at the three-resonance frequency were analyzed. It was concluded that the overall performance of the proposed MTM structure was superior compared to those reported in the literature. The proposed design could be a good candidate for application in stealth technology, imaging, and thermal energy harvesting. Full article

(This article belongs to the Special Issue Advances in Metamaterial and Symmetry/Asymmetry)

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20 pages, 8262 KiB

Open AccessArticle

A Hybrid RBF Collocation Method and Its Application in the Elastostatic Symmetric Problems

by Ying-Ting Chen, Cheng Li, Lin-Quan Yao and Yang Cao

Symmetry 2022, 14(7), 1476; https://doi.org/10.3390/sym14071476 - 19 Jul 2022

Cited by 2 | Viewed by 1786

Abstract

In this paper, a new hybrid radial basis function collocation method (HRBF-CM) is proposed to help resolve two-dimensional elastostatic symmetric problems. In the new approach, the hybrid radial basis function (HRBF) combines the infinitely smooth RBF and piecewise smooth RBF, containing two parameters [...] Read more.

In this paper, a new hybrid radial basis function collocation method (HRBF-CM) is proposed to help resolve two-dimensional elastostatic symmetric problems. In the new approach, the hybrid radial basis function (HRBF) combines the infinitely smooth RBF and piecewise smooth RBF, containing two parameters (the shape parameter and the weight parameter). Discretization schemes are presented in detail. We use MATLAB to implement the HRBF-CM and produce numerical results which demonstrate the potential of this method. The new method’s accuracy is higher than that of the traditional methods, especially in the case of a more significant number of nodes. We discuss the new method’s effectiveness compared to the widely used traditional RBF and also investigate the effect of parameters on the method’s performance under the new method. Full article

(This article belongs to the Section Engineering and Materials)

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51 pages, 1322 KiB

Open AccessEditor’s ChoiceReview

Symmetric Mass Generation

by Juven Wang and Yi-Zhuang You

Symmetry 2022, 14(7), 1475; https://doi.org/10.3390/sym14071475 - 19 Jul 2022

Cited by 56 | Viewed by 4916

Abstract

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last [...] Read more.

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG. Full article

(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)

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13 pages, 1291 KiB

Open AccessArticle

Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

by Franz H. Harke, Miryam S. Merk and Philipp Otto

Symmetry 2022, 14(7), 1474; https://doi.org/10.3390/sym14071474 - 19 Jul 2022

Cited by 2 | Viewed by 2023

Abstract

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix

W

. However, in practice, the structure of

W

is unknown a priori and difficult to obtain, [...] Read more.

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix

W

. However, in practice, the structure of

W

is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain

W

, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With

W

determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin. Full article

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

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15 pages, 6247 KiB

Open AccessArticle

Joint-Prior-Based Uneven Illumination Image Enhancement for Surface Defect Detection

by Yuanhong Qiu, Shuanlong Niu, Tongzhi Niu, Weifeng Li and Bin Li

Symmetry 2022, 14(7), 1473; https://doi.org/10.3390/sym14071473 - 19 Jul 2022

Cited by 3 | Viewed by 1874

Abstract

Images in real surface defect detection scenes often suffer from uneven illumination. Retinex-based image enhancement methods can effectively eliminate the interference caused by uneven illumination and improve the visual quality of such images. However, these methods suffer from the loss of defect-discriminative information [...] Read more.

Images in real surface defect detection scenes often suffer from uneven illumination. Retinex-based image enhancement methods can effectively eliminate the interference caused by uneven illumination and improve the visual quality of such images. However, these methods suffer from the loss of defect-discriminative information and a high computational burden. To address the above issues, we propose a joint-prior-based uneven illumination enhancement (JPUIE) method. Specifically, a semi-coupled retinex model is first constructed to accurately and effectively eliminate uneven illumination. Furthermore, a multiscale Gaussian-difference-based background prior is proposed to reweight the data consistency term, thereby avoiding the loss of defect information in the enhanced image. Last, by using the powerful nonlinear fitting ability of deep neural networks, a deep denoised prior is proposed to replace existing physics priors, effectively reducing the time consumption. Various experiments are carried out on public and private datasets, which are used to compare the defect images and enhanced results in a symmetric way. The experimental results demonstrate that our method is more conducive to downstream visual inspection tasks than other methods. Full article

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9 pages, 258 KiB

Open AccessArticle

Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings

by Azzh Saad Alshehry, Jebrel M. Habeb, Rashid Abu-Dawwas and Ahmad Alrawabdeh

Symmetry 2022, 14(7), 1472; https://doi.org/10.3390/sym14071472 - 19 Jul 2022

Cited by 2 | Viewed by 1175

Abstract

Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a graded ring which is not commutative, and [...] Read more.

Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a graded ring which is not commutative, and demonstrates that the symmetry is obtained as a lot of the outcomes in commutative graded rings remain in graded rings that are not commutative. Full article

(This article belongs to the Section Mathematics)

11 pages, 286 KiB

Open AccessArticle

A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator

by Abdel Moneim Y. Lashin, Abeer O. Badghaish and Badriah Maeed Algethami

Symmetry 2022, 14(7), 1471; https://doi.org/10.3390/sym14071471 - 19 Jul 2022

Cited by 5 | Viewed by 1611

Abstract

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes [...] Read more.

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes some known results, as well as provides some new ones. Full article

(This article belongs to the Special Issue Complex Analysis, in Particular Analytic and Univalent Functions)

29 pages, 550 KiB

Open AccessArticle

Supervisory Control of Automated Manufacturing Systems Based on State-Tree Structures

by Chan Gu, Junbo Zhao and Zhou He

Symmetry 2022, 14(7), 1470; https://doi.org/10.3390/sym14071470 - 18 Jul 2022

Viewed by 1546

Abstract

The automated manufacturing systems (AMS) can be regarded as a resource allocation system which can be abstracted as discrete event systems (DES) for analysis. Once an effective computational method is put forward to the DES, the corresponding real AMS, connected by networks or [...] Read more.

The automated manufacturing systems (AMS) can be regarded as a resource allocation system which can be abstracted as discrete event systems (DES) for analysis. Once an effective computational method is put forward to the DES, the corresponding real AMS, connected by networks or sensors, can be indirectly controlled. Supervisory control theory (SCT) of DES is developed with the intention of discovering the maximally permissible supervisor of AMS. The state-tree structure (STS) is an extension of SCT, whose application is mainly to solve the SCT state explosion of complicated AMS. The nonblocking supervisory control is investigated on the foundation of predicates in STS, of which the synthesis focuses on the states of the system but ignores the transition between events. In order to effectively solve the above problems, this paper puts forward a novel method based on state feedback control (SFBC) in the STS framework, by which the relation among events is discussed. First, following the definition of the SFBC for predicates, the algorithms to compute the SFBC under reachability, coreachability, and weak controllability are introduced. Second, it is proved that the nonblocking SFBC obtained by the proposed algorithm is equivalent to the one by computing predicates first, which ensures the satisfactory controllers for the supervisory control problems. To demonstrate the contribution of the proposed approach, which is designed considering the symmetry of the system behavior between the real system and its STS model, three examples are illustrated. Full article

(This article belongs to the Special Issue Advanced Materials, Structures, Symmetrical Design and Mechanism in Mechanical Engineering)

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12 pages, 1402 KiB

Open AccessArticle

Parameter Learning of Bayesian Network with Multiplicative Synergistic Constraints

by Yu Zhang and Zhiming Hu

Symmetry 2022, 14(7), 1469; https://doi.org/10.3390/sym14071469 - 18 Jul 2022

Cited by 1 | Viewed by 1711

Abstract

Learning the conditional probability table (CPT) parameters of Bayesian networks (BNs) is a key challenge in real-world decision support applications, especially when there are limited data available. The traditional approach to this challenge is introducing domain knowledge/expert judgments that are encoded as qualitative [...] Read more.

Learning the conditional probability table (CPT) parameters of Bayesian networks (BNs) is a key challenge in real-world decision support applications, especially when there are limited data available. The traditional approach to this challenge is introducing domain knowledge/expert judgments that are encoded as qualitative parameter constraints. In this paper, we focus on multiplicative synergistic constraints. The negative multiplicative synergy constraint and positive multiplicative synergy constraint in this paper are symmetric. In order to integrate multiplicative synergistic constraints into the learning process of Bayesian Network parameters, we propose four methods to deal with the multiplicative synergistic constraints based on the idea of classical isotonic regression algorithm. The four methods are simulated by using the lawn moist model and Asia network, and we compared them with the maximum likelihood estimation (MLE) algorithm. Simulation results show that the proposed methods are superior to the MLE algorithm in the accuracy of parameter learning, which can improve the results of the MLE algorithm to obtain more accurate estimators of the parameters. The proposed methods can reduce the dependence of parameter learning on expert experiences. Combining these constraint methods with Bayesian estimation can improve the accuracy of parameter learning under small sample conditions. Full article

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8 pages, 860 KiB

Open AccessArticle

Dynamics and Exact Traveling Wave Solutions of the Sharma–Tasso–Olver–Burgers Equation

by Yan Zhou and Jinsen Zhuang

Symmetry 2022, 14(7), 1468; https://doi.org/10.3390/sym14071468 - 18 Jul 2022

Cited by 6 | Viewed by 1553

Abstract

In this paper, to study the Sharma–Tasso–Olver–Burgers equation, we focus on the geometric properties and the exact traveling wave solutions. The corresponding traveling system is a cubic oscillator with damping, and it has time-dependent and time-independent first integral. For all bounded orbits of [...] Read more.

In this paper, to study the Sharma–Tasso–Olver–Burgers equation, we focus on the geometric properties and the exact traveling wave solutions. The corresponding traveling system is a cubic oscillator with damping, and it has time-dependent and time-independent first integral. For all bounded orbits of the traveling system, we give the exact explicit kink wave solutions. Full article

(This article belongs to the Special Issue Recent Advances in Symmetries Methods and Other Approaches to Nonlinear Differential Equations)

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29 pages, 6645 KiB

Open AccessFeature PaperReview

Searching for Pairs of Higgs Bosons in the LHC Run 2 Dataset

by Elizabeth Brost and Luca Cadamuro

Symmetry 2022, 14(7), 1467; https://doi.org/10.3390/sym14071467 - 18 Jul 2022

Viewed by 3079

Abstract

The discovery of the Higgs boson confirms the existence of a scalar sector of the standard model, responsible for electroweak symmetry breaking, but the nature and properties of the potential at the origin of this mechanism are still unknown. By studying the production [...] Read more.

The discovery of the Higgs boson confirms the existence of a scalar sector of the standard model, responsible for electroweak symmetry breaking, but the nature and properties of the potential at the origin of this mechanism are still unknown. By studying the production of pairs of Higgs bosons (HH), physicists can directly measure the coupling of the Higgs boson to itself and thus determine the shape of this potential, which has far-reaching implications on the origin and evolution of our Universe. Because of this deep connection to the foundations of electroweak symmetry breaking, HH production is also an ideal place to search for manifestations of yet-unknown physics, such as modifications of the strength of the self-coupling and of the interaction between pairs of vector bosons and Higgs bosons. In this review article, we summarize the current searches for HH production at ATLAS and CMS, using the LHC Run 2 dataset, discuss the implications of our current constraints on physics beyond the standard model, and briefly review prospect for future HH searches. Full article

(This article belongs to the Special Issue Recent Advance in Accelerator and Particle Physics)

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14 pages, 2777 KiB

Open AccessArticle

Vertebral Slip Morphology in Dysplastic Spondylolisthesis as a Criterion for the Choice of the L5/S1 Support (ALIF, PLIF, Fibular Graft) in Surgical Treatment

by Robert Vyskocil, Martin Prymek, Ludek Ryba, Jan Sklensky, Jan Kocanda, Michael Lujc, Petr Vosynek and Martin Repko

Symmetry 2022, 14(7), 1466; https://doi.org/10.3390/sym14071466 - 18 Jul 2022

Cited by 1 | Viewed by 4240

Abstract

Dysplastic spondylolisthesis is a severe pathological condition, based on dysplastic changes in the lumbosacral part of the spine, that causes the asymmetry of the lumbosacral junction. The appropriate therapeutic algorithm remains controversial. As the gold standard, the surgical reposition of the slipped vertebra [...] Read more.

Dysplastic spondylolisthesis is a severe pathological condition, based on dysplastic changes in the lumbosacral part of the spine, that causes the asymmetry of the lumbosacral junction. The appropriate therapeutic algorithm remains controversial. As the gold standard, the surgical reposition of the slipped vertebra and 360° fusion of the affected spinal segment is preferred. Thirty-two patients were operated on between the years 2005 and 2018. Different techniques of 360° fusion, based on the severity of the displacement of the affected vertebral segment, were used. Herein, the advantages and disadvantages of different techniques of interbody fusion are discussed. The slippage and retention after reduction in the vertebrae are evaluated prior to the operation, postoperatively, one year after the surgery, and during follow-up, which was 7 years on average (minimum 2 years for a follow-up). Complications associated with the surgery are evaluated, in addition to the operation time, blood loss, spinopelvic parameters, and patient satisfaction with the surgery. All surgical techniques improved the slippage compared to preoperative conditions. The retention of the reposition was not changed significantly in postoperative controls. The incidence of neurological complications reached 12.5%. Surgical treatment is the only treatment option that successfully addressed the pathological principle of dysplastic spondylolisthesis. All of the surgical methods used led to restoring the symmetry of the lumbar spine, and to the improvement in both radiological parameters and the alleviation of subjective difficulties. The aim of this article is to summarize surgical methods in patients having dysplastic spondylolisthesis with a slip of more than 25%, who were operated on, and to determine the optimal treatment algorithm according to the severity of the slip. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Musculoskeletal Science)

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