Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics); Q1 (Physics and Astronomy); Q1 (Computer Science)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.2 days after submission; acceptance to publication is undertaken in 3.5 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Symmetry.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.7 (2022)
Latest Articles
Schwartz Symmetry Condition for Coherent Diffraction Imaging Patterns
Symmetry 2024, 16(4), 399; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040399 (registering DOI) - 29 Mar 2024
Abstract
We demonstrate a symmetry condition for the mixed partial derivatives of measured data when performing a coherent diffraction imaging (CDI) experiment for differentiable samples under scientific investigation. The proposed condition can be used as a physical restriction to improve real data measurements and
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We demonstrate a symmetry condition for the mixed partial derivatives of measured data when performing a coherent diffraction imaging (CDI) experiment for differentiable samples under scientific investigation. The proposed condition can be used as a physical restriction to improve real data measurements and has been used within the most celebrated phase-retrieval inversion algorithms as an ad hoc constraint without proof. The symmetry relies on John’s ultrahyperbolic equation for the X-ray transform, which is also demonstrated to be valid in the imaging regime for CDI. The obtained conditions are easy to implement and can be used as a constraint by computational imaging methods.
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(This article belongs to the Special Issue Advances in Symmetry and Complex Systems)
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An Improved Sorting Algorithm for Periodic PRI Signals Based on Congruence Transform
by
Huixu Dong, Yuanzheng Ge, Rui Zhou and Hongyan Wang
Symmetry 2024, 16(4), 398; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040398 - 28 Mar 2024
Abstract
Recently, a signal sorting algorithm based on the congruence transform has been proposed, which is effective in dealing with the staggered Pulse Repetition Interval (PRI) signals. It can effectively sort the staggered PRI signals and obtain the sub-PRI sequence directly without sub-PRI ranking,
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Recently, a signal sorting algorithm based on the congruence transform has been proposed, which is effective in dealing with the staggered Pulse Repetition Interval (PRI) signals. It can effectively sort the staggered PRI signals and obtain the sub-PRI sequence directly without sub-PRI ranking, and it is less affected by interfered pulses and pulse loss. Nevertheless, we find that the algorithm causes pseudo-peaks in the remainder histogram when sorting signals such as sliding PRI, sinusoidal PRI, etc. (collectively referred to as periodic PRI signal in this paper) and pseudo-peaks will cause errors in signal sorting. To solve the issue of pseudo-peaks when sorting periodic PRI signals, an improved sorting algorithm based on congruence transform is proposed. According to the analysis of the congruence characteristics of the periodic PRI signal, a novel method is proposed to identify pseudo-peaks based on the histogram peak amplitude and symmetric difference set. The signal sorting algorithm based on congruence transform is improved to achieve a good sorting effect on periodic PRI signals. Simulation experiments demonstrate that the novel algorithm can effectively sort periodic PRI signals and improve Precall, Pd, and Pf by 6.9%, 5.1%, and 3.2%, respectively, compared to the typical similar algorithms.
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(This article belongs to the Special Issue Multidimensional Signal Processing and Deep Learning—Symmetry Approach)
Open AccessArticle
Constraints on Graviton Mass from Schwarzschild Precession in the Orbits of S-Stars around the Galactic Center
by
Predrag Jovanović, Vesna Borka Jovanović, Duško Borka and Alexander F. Zakharov
Symmetry 2024, 16(4), 397; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040397 - 28 Mar 2024
Abstract
In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC).
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In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors.
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(This article belongs to the Special Issue Selected Papers on Nonlinear Dynamics)
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Research on LFD System of Humanoid Dual-Arm Robot
by
Ze Cui, Lang Kou, Zenghao Chen, Peng Bao, Donghai Qian, Lang Xie and Yue Tang
Symmetry 2024, 16(4), 396; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040396 - 28 Mar 2024
Abstract
Although robots have been widely used in a variety of fields, the idea of enabling them to perform multiple tasks in the same way that humans do remains a difficulty. To solve this, we investigate the learning from demonstration (LFD) system with our
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Although robots have been widely used in a variety of fields, the idea of enabling them to perform multiple tasks in the same way that humans do remains a difficulty. To solve this, we investigate the learning from demonstration (LFD) system with our independently designed symmetrical humanoid dual-arm robot. We present a novel action feature matching algorithm. This algorithm accurately transforms human demonstration data into task models that robots can directly execute, considerably improving LFD’s generalization capabilities. In our studies, we used motion capture cameras to capture human demonstration actions, which included combinations of simple actions (the action layer) and a succession of complicated operational tasks (the task layer). For the action layer data, we employed Gaussian mixture models (GMM) for processing and constructing an action primitive library. As for the task layer data, we created a “keyframe” segmentation method to transform this data into a series of action primitives and build another action primitive library. Guided by our algorithm, the robot successfully imitated complex human tasks. Results show its excellent task learning and execution, providing an effective solution for robots to learn from human demonstrations and significantly advancing robot technology.
Full article
(This article belongs to the Special Issue Symmetry Applied in Computer Vision, Automation, and Robotics)
Open AccessArticle
Performance Analysis of a Dual-Inverter-Fed Open-End Winding Induction Machine under Asymmetrical Control: Theoretical Approach and Experimental Validation
by
Mohammed Zerdani, Houcine Chafouk and Sid Ahmed El Mehdi Ardjoun
Symmetry 2024, 16(4), 395; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040395 - 28 Mar 2024
Abstract
Currently, power trains based on an Open-End Winding Induction Machine fed by a Dual Inverter (DI-OEWIM) are attracting a great deal of interest in various modern industrial applications. However, applying symmetrical control to this system (DI-OEWIM), which is symmetrical in nature, will lead
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Currently, power trains based on an Open-End Winding Induction Machine fed by a Dual Inverter (DI-OEWIM) are attracting a great deal of interest in various modern industrial applications. However, applying symmetrical control to this system (DI-OEWIM), which is symmetrical in nature, will lead to malfunction. Therefore, the objective of this paper is to explore the influence of asymmetric control on the performance of this system. The principle of this study is to create an asymmetrical control by integrating a phase-shift angle in the Space Vector Pulse Width Modulation (SVPWM) strategy. We then evaluate the impact of these angles on various performances, such as the Total Harmonic Distortion (THD), power losses, Common Mode Voltage (CMV), Zero-Sequence Voltage (ZSV), rotation speed and torque ripple of this system. This study was carried out in the Matlab/Simulink environment and was validated experimentally using the dSPACE 1104 board. The results show that the different angles have significant effects on the overall performance of this system.
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(This article belongs to the Section Engineering and Materials)
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Symmetry Transformations in Cosmological and Black Hole Analytical Solutions
by
Edgar A. León and Andrés Sandoval-Rodríguez
Symmetry 2024, 16(4), 394; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040394 - 28 Mar 2024
Abstract
We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of
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We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler–Regge, and isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal–Szekeres within this approach, as well as Lemaître coordinates. We use Schwarzschild spacetime as a prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner–Nordström, and Schwarzschild de Sitter, can be readily generalized.
Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
Open AccessArticle
The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation
by
Bilge İnan
Symmetry 2024, 16(4), 393; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040393 - 27 Mar 2024
Abstract
This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method
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This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method to solve this equation, considering the conformable fractional derivative. Furthermore, we analyze the stability of the method through theoretical considerations. The method involves transforming the problem into systems of nonlinear equations at each time since our method is an implicit method, which is then solved by converting them into linear equations systems using the Newton method. To test the accuracy of the method, we compare the results obtained with exact solutions and with those available in the literature. Additionally, we examine the symmetry of the graphs obtained from the solution to examine the results. The findings of our numerical simulations demonstrate the effectiveness and reliability of the proposed approach in solving the generalized fractional-order Fisher equation.
Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
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On Darbo- and Sadovskii-Type Fixed Point Theorems in Banach Spaces
by
Leszek Olszowy and Tomasz Zając
Symmetry 2024, 16(4), 392; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040392 - 27 Mar 2024
Abstract
The paper aims to generalize several known Darbo- and Sadovskii-type fixed point theorems. These generalizations weaken the assumptions used so far. In addition, an example of an application is presented.
Full article
(This article belongs to the Special Issue Nonlinear Differential and Integral Equations and Their Infinite Systems)
Open AccessArticle
New Insights into Aromaticity through Novel Delta Polynomials and Delta Aromatic Indices
by
Krishnan Balasubramanian
Symmetry 2024, 16(4), 391; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040391 - 27 Mar 2024
Abstract
We have developed novel polynomials called delta polynomials, which are, in turn, derived from the characteristic and matching polynomials of graphs associated with polycyclic aromatic compounds. Natural logarithmic aromatic indices are derived from these delta polynomials, which are shown to provide new insights
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We have developed novel polynomials called delta polynomials, which are, in turn, derived from the characteristic and matching polynomials of graphs associated with polycyclic aromatic compounds. Natural logarithmic aromatic indices are derived from these delta polynomials, which are shown to provide new insights into the aromaticity of polycyclic aromatic compounds, including the highly symmetric C60 buckminsterfullerene, several other fullerenes, graphene, kekulene series and other cycloarenes, such as polycyclic circumcoronaphenes and coronoids. The newly developed aromatic index yields a value of 6.77 for graphene, 6.516865 for buckminsterfullerene C60(Ih), 5.914023 for kekulene (D6h symmetry), 6.064420 for coronene (D6h), 6.137828 for circumcoronene (D6h), 6.069668 for dicronylene and so forth. Hence, the novel scaled logarithmic aromatic delta indices developed here appear to provide good quantitative measures of aromaticity, especially when they are used in conjunction with other aromatic indicators.
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(This article belongs to the Collection Feature Papers in Chemistry)
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Theoretical Advances in Beta and Double-Beta Decay
by
Vasile-Alin Sevestrean and Sabin Stoica
Symmetry 2024, 16(4), 390; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040390 - 26 Mar 2024
Abstract
Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the
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Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta ( ). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to obtain the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra, and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta ( ) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes.
Full article
(This article belongs to the Special Issue Recent Advances in Double Beta Decay Investigations: In Honor of Prof. Sabin Stoica at His 70th Anniversary)
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A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs
by
Simeng Li, Dianliang Deng and Yuecai Han
Symmetry 2024, 16(4), 389; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040389 - 26 Mar 2024
Abstract
In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential
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In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).
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(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Functional Data Analysis)
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Optimal Economic Research of Microgrids Based on Multi-Strategy Integrated Sparrow Search Algorithm under Carbon Emission Constraints
by
Yuhao Zhao, Sen Yang, Songlin Liu, Shouming Zhang and Zhenyu Zhong
Symmetry 2024, 16(4), 388; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040388 - 26 Mar 2024
Abstract
In the global transition towards sustainable energy, microgrids are emerging as a core component of distributed energy systems and a pivotal technology driving this transformation. By integrating renewable energy sources such as solar and wind power, microgrids not only enhance energy efficiency and
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In the global transition towards sustainable energy, microgrids are emerging as a core component of distributed energy systems and a pivotal technology driving this transformation. By integrating renewable energy sources such as solar and wind power, microgrids not only enhance energy efficiency and reduce reliance on traditional energy sources but also bolster grid stability and mitigate the risk of widespread power outages. Consequently, microgrids demonstrate significant potential in improving the reliability of power supply and facilitating flexibility in energy consumption. However, the operational planning and optimization of microgrids are faced with complex challenges characterized by multiple objectives and constraints, making the reduction in operational costs a focal point of research. This study fully considers an operational model for a microgrid that incorporates distributed energy resources and comprehensive costs, integrating a battery storage system to ensure three-phase balance. The microgrid model includes photovoltaic power generation, wind power generation, fuel cells, micro-gas turbines, energy storage systems, and loads. The objectives of operating and maintaining this microgrid primarily involve optimizing dispatch, energy consumption, and pollution emissions, aiming to reduce carbon emissions and minimize total costs. To achieve these goals, the study introduces a carbon emission constraint strategy and proposes an improved Multi-Strategy Integrated Sparrow Search Algorithm (MISSA). By applying the MISSA to solve the operational problems of the microgrid and comparing it with other algorithms, the results demonstrate the effectiveness of the carbon emission constraint strategy in the microgrid’s operation. Furthermore, the results prove that the MISSA can achieve the lowest comprehensive operational costs for the microgrid, confirming its effectiveness in addressing the operational challenges of the microgrid.
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(This article belongs to the Section Engineering and Materials)
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Open AccessArticle
Retarded Gravity in Disk Galaxies
by
Yuval Glass, Tomer Zimmerman and Asher Yahalom
Symmetry 2024, 16(4), 387; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040387 - 26 Mar 2024
Abstract
Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years
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Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data.
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(This article belongs to the Section Physics)
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Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator
by
Nur Chamidah, Budi Lestari, I Nyoman Budiantara and Dursun Aydin
Symmetry 2024, 16(4), 386; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040386 - 25 Mar 2024
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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different
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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties.
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Open AccessArticle
On q-Hermite Polynomials with Three Variables: Recurrence Relations, q-Differential Equations, Summation and Operational Formulas
by
Mohammed Fadel, Nusrat Raza and Wei-Shih Du
Symmetry 2024, 16(4), 385; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040385 - 25 Mar 2024
Abstract
In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variables are established, including
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In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variables are established, including their generation function, series description, summation equations, recurrence relationships, q-differential formula and operational rules.
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(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis III)
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Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method
by
Yonggang Mei, Bingbing He, Shangwen He, Xin Ren and Zeqi Zhang
Symmetry 2024, 16(4), 384; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040384 - 24 Mar 2024
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Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature
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Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency.
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Open AccessArticle
Load Calculation Method for Deep-Buried Layered Soft Rock Tunnel Based on Back-Analysis of Structural Deformation
by
Lixin Zhang, Lijun Chen, Jianxun Chen, Yanbin Luo, Huijie Guo, Yang Zhai and Pengkun Wang
Symmetry 2024, 16(4), 383; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040383 - 23 Mar 2024
Abstract
After the excavation and unloading of deep-buried soft rock tunnels, support structures often experience deformation-related disasters such as concrete cracking, steel frame bending and twisting, and primary support instability under different forms of load. Accurately calculating the load borne by the primary support
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After the excavation and unloading of deep-buried soft rock tunnels, support structures often experience deformation-related disasters such as concrete cracking, steel frame bending and twisting, and primary support instability under different forms of load. Accurately calculating the load borne by the primary support structure is the key to ensuring design rationality and construction safety. Especially in layered soft surrounding rock formations, the magnitude and distribution of the loads are different from those of conventional rock and soil masses, resulting in limited applicability of existing load calculation methods to similar formations. Therefore, based on the measured deformation of the tunnel structure, while considering the different geometric forms of the primary support structure during partial excavation, this paper proposes a deformation-structure (D-S) load calculation method. By comparing the calculation results of this method and a large number of sample data for typical deep-buried layered soft rock tunnels, the reliability of the D-S load calculation method is verified. In addition, the variation law of the loads during the tunnel construction period is enunciated, and the magnitude and distribution of the loads acting on the primary support are clarified. The D-S load calculation method provides a theoretical basis for load calculation in deep-buried layered soft rock tunnels.
Full article
(This article belongs to the Special Issue Physically Data-Driven Research on Symmetry/Asymmetry in Underground Engineering Construction and Maintenance)
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Open AccessReview
Syntheses of Azulene Embedded Polycyclic Compounds
by
Alexandru C. Razus
Symmetry 2024, 16(4), 382; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040382 - 22 Mar 2024
Abstract
This review focuses on obtaining embedded azulene polycyclic molecules treated according to their particular structure. The division of material into the azulene unit grafted only on one or two bonds and poly-fused azulene compounds was suggested with the intention of facilitating the presentation
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This review focuses on obtaining embedded azulene polycyclic molecules treated according to their particular structure. The division of material into the azulene unit grafted only on one or two bonds and poly-fused azulene compounds was suggested with the intention of facilitating the presentation and assimilation of information. The similarity of some structural features in the compounds included in different analyzed classes results in the presence of the same synthesis protocol in several places. Obtaining benz[a]azulenes, azulene-fused acenes, and helicenes or azulene-embedded nanographene, along with other compounds, is presented.
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(This article belongs to the Section Chemistry: Symmetry/Asymmetry)
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Open AccessArticle
Index for Quantifying ‘Order’ in Three-Dimensional Shapes
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Takahiro Shimizu, Masaya Okamoto, Yuto Ieda and Takeo Kato
Symmetry 2024, 16(4), 381; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16040381 - 22 Mar 2024
Abstract
In this study, we focused on assessing the symmetry of shapes and quantifying an index of ‘order’ in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was
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In this study, we focused on assessing the symmetry of shapes and quantifying an index of ‘order’ in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was calculated for the distribution of the Casorati curvatures in both segments to determine the similarity between them. This was proposed as an indicator of the ‘order’ exhibited by the shape. To validate the effectiveness of the proposed index, sensory evaluation experiments were conducted on three shapes: extruded, rotated, and vase. For the rotated shape, the coefficient of determination between the proposed index and the sensory evaluation value of ‘order’ on a 5-point Likert scale was found to be less than 0.1. The reason for the poor correlation coefficient of determination may be attributed to the bias in human perception, where individuals tend to perceive mirror symmetry with respect to the plane that includes the vertical axis when recognizing the mirror symmetry of an object. In contrast, for the extruded and vase shapes, the coefficients of determination were 0.36 and 0.66, respectively, supporting the validity of the proposed index. Nonetheless, the coefficient of determination decreased slightly for familiar extruded shapes and asymmetric vase shapes. In future research, our aim is to quantify ‘aesthetic preference’ by combining the ‘order’ and ‘complexity’ indexes.
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(This article belongs to the Special Issue New Trends in Symmetry/Asymmetry of Image Processing and Computer Vision)
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Open AccessArticle
An Exploration of Multitasking Scheduling Considering Interruptible Job Assignments, Machine Aging Effects, the Influence of Deteriorating Maintenance, and Symmetry
by
Li Zeng
Symmetry 2024, 16(3), 380; https://0-doi-org.brum.beds.ac.uk/10.3390/sym16030380 - 21 Mar 2024
Abstract
The unique topic of allocating and scheduling tasks on a single machine in a multitasking environment is the main emphasis of this research, which also takes into account the effects of worsening maintenance and job-dependent aging effects. In this scenario, the performance and
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The unique topic of allocating and scheduling tasks on a single machine in a multitasking environment is the main emphasis of this research, which also takes into account the effects of worsening maintenance and job-dependent aging effects. In this scenario, the performance and efficiency of the machine in handling different tasks should be symmetric, without significant bias due to the nature or size of the tasks. In a multitasking environment, waiting for jobs can disrupt the processing of the primary job being currently handled. As a result, the actual time required to complete a task becomes erratic and contingent upon the duration of the disruption. In addition to figuring out the best time for maintenance, where to put the due-window, and how big it should be in a multitasking environment, the primary objective is to minimize the costs associated with meeting due-window regulations. To tackle this problem, we propose two optimal algorithms. Additionally, we conduct numerical experiments to compare our approach with the classic due date assignment problem. Interestingly, we observe that in most cases, the average and minimum percentage costs tend to increase as the quantity of jobs increases. However, it is noteworthy that, when the number of jobs is relatively small, specifically when it does not exceed 20, there are instances where these costs decrease with an increase in the number of jobs.
Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)
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