Symmetry

15 pages, 595 KiB

Open AccessArticle

Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems

by Qian-Qian Xiao, Ying Wang, Fu-Yao Liu, Chen Deng and Wei Sun

Symmetry 2023, 15(1), 253; https://doi.org/10.3390/sym15010253 - 16 Jan 2023

Viewed by 2063

The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and [...] Read more.

The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge–Kutta–Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima’s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima’s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method. Full article

(This article belongs to the Special Issue Symmetry in Gravity Research)

► Show Figures

Figure 1

12 pages, 322 KiB

Open AccessArticle

Time-Dependent 4D Quantum Harmonic Oscillator and Reacting Hydrogen Atom

by Ashot S. Gevorkyan and Aleksander V. Bogdanov

Symmetry 2023, 15(1), 252; https://doi.org/10.3390/sym15010252 - 16 Jan 2023

Cited by 1 | Viewed by 1617

Abstract

With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of [...] Read more.

With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of dynamical symmetry that reduces the equation of motion of a non-stationary oscillator to an autonomous form that does not change with time. By imposing an additional constraint on the wave function of the isotropic oscillator, we have obtained the total wave functions of the reacting hydrogen atom in two different cases: (a) when the non-stationary frequency has two asymptotic values and there is no external field; and (b) when, in addition to the non-stationary frequency, an external force acts on the hydrogen atom. The transition S-matrix elements of various elementary atomic–molecular processes are constructed. The probabilities of quantum transitions of the hydrogen atom to others, including new bound states, are studied in detail, taking into account the influence of external forces. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)

38 pages, 844 KiB

Open AccessArticle

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

by Muhammad Qiyas, Muhammad Naeem, Lazim Abdullah, Muhammad Riaz and Neelam Khan

Symmetry 2023, 15(1), 251; https://doi.org/10.3390/sym15010251 - 16 Jan 2023

Cited by 2 | Viewed by 1643

Abstract

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value [...] Read more.

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between

[0.5, 0.5)

, the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

26 pages, 646 KiB

Open AccessArticle

Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy

by Predrag S. Stanimirović, Branislav Ivanov, Dragiša Stanujkić, Vasilios N. Katsikis, Spyridon D. Mourtas, Lev A. Kazakovtsev and Seyyed Ahmad Edalatpanah

Symmetry 2023, 15(1), 250; https://doi.org/10.3390/sym15010250 - 16 Jan 2023

Cited by 7 | Viewed by 2000

Abstract

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we [...] Read more.

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)

► Show Figures

Figure 1

36 pages, 506 KiB

Open AccessFeature PaperArticle

On Rational Solutions of Dressing Chains of Even Periodicity

by Henrik Aratyn, José Francisco Gomes, Gabriel Vieira Lobo and Abraham Hirsz Zimerman

Symmetry 2023, 15(1), 249; https://doi.org/10.3390/sym15010249 - 16 Jan 2023

Cited by 2 | Viewed by 1508

Abstract

We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under

A_{N - 1}^{(1)}

symmetry. This formalism identifies rational solutions (as well [...] Read more.

We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under

A_{N - 1}^{(1)}

symmetry. This formalism identifies rational solutions (as well as special function solutions) with points on orbits of fundamental shift operators of

A_{N - 1}^{(1)}

affine Weyl groups acting on seed configurations defined as first-order polynomial solutions of the underlying dressing chains. This approach clarifies the structure of rational solutions and establishes an explicit and systematic method towards their construction. For the special case of the

N = 4

dressing chain equations, the method yields all the known rational (and special function) solutions of the Painlevé V equation. The formalism naturally extends to

N = 6

and beyond as shown in the paper. Full article

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

22 pages, 1071 KiB

Open AccessArticle

Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics

by Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Abdulrahman F. AlJohani, Weam Alharbi and Amal F. Alharbi

Symmetry 2023, 15(1), 248; https://doi.org/10.3390/sym15010248 - 16 Jan 2023

Cited by 12 | Viewed by 2234

Abstract

Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and [...] Read more.

Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)

► Show Figures

Figure 1

20 pages, 312 KiB

Open AccessArticle

Some Results on Submodules Using (μ,ν,ω)-Single-Valued Neutrosophic Environment

by Muhammad Shazib Hameed, Esmail Hassan Abdullatif Al-Sabri, Zaheer Ahmad, Shahbaz Ali and Muhammad Usman Ghani

Symmetry 2023, 15(1), 247; https://doi.org/10.3390/sym15010247 - 16 Jan 2023

Cited by 2 | Viewed by 1490

Abstract

The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being [...] Read more.

The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet

(μ, ν, ω)

structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category. Full article

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

13 pages, 310 KiB

Open AccessArticle

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

by Loredana Ciurdariu and Eugenia Grecu

Symmetry 2023, 15(1), 246; https://doi.org/10.3390/sym15010246 - 16 Jan 2023

Cited by 3 | Viewed by 1514

Abstract

A new

(p, q)

-integral identity involving left and right post quantum derivatives, by using three times

(p, q)

-differentiable functions is established and then this identity is used to derive several new post-quantum Ostrowski type integral [...] Read more.

A new

(p, q)

-integral identity involving left and right post quantum derivatives, by using three times

(p, q)

-differentiable functions is established and then this identity is used to derive several new post-quantum Ostrowski type integral inequalities for three times

(p, q)

-differentiable functions. These results are generalizations of corresponding results in the area of integral inequalities. Full article

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

13 pages, 560 KiB

Open AccessArticle

Phonon Blockade in Parametrically Pumped Acoustic Cavity at Finite Temperature

by Zhenglu Duan, Yongkang Shao, Yi Ren and Biao Huang

Symmetry 2023, 15(1), 245; https://doi.org/10.3390/sym15010245 - 16 Jan 2023

Cited by 1 | Viewed by 1508

Abstract

In this study, we investigated the phonon blockade effect in a parametrically driven and dissipative acoustic cavity at finite temperature. With the approximated analytical results based on the steady-state density-matrix master equation, we found that a quantum-interference-induced phonon blockade exists at finite temperature. [...] Read more.

In this study, we investigated the phonon blockade effect in a parametrically driven and dissipative acoustic cavity at finite temperature. With the approximated analytical results based on the steady-state density-matrix master equation, we found that a quantum-interference-induced phonon blockade exists at finite temperature. We found a crossover between the quantum and thermal regimes on the curve of the second-order correlation function of the acoustic mode as the temperature increases. This phenomenon implies an asymmetry about the quantum and classic regimes. We also numerically simulated the single-phonon emission using the Monte Carlo wave function method. The results showed that a wide and deep dip around the zero time delay exists on the curve of the time-delayed second-order correlation function, which implies the possibility of observing a strong phonon blockade with pulse driving. Our study outlines a potential candidate for a efficient single-phonon source and applications in quantum information and phononic quantum networks. Full article

(This article belongs to the Special Issue Advances in Quantum Information)

► Show Figures

Figure 1

15 pages, 1649 KiB

Open AccessArticle

Output Layer Structure Optimization for Weighted Regularized Extreme Learning Machine Based on Binary Method

by Sibo Yang, Shusheng Wang, Lanyin Sun, Zhongxuan Luo and Yuan Bao

Symmetry 2023, 15(1), 244; https://doi.org/10.3390/sym15010244 - 16 Jan 2023

Cited by 3 | Viewed by 1613

Abstract

In this paper, we focus on the redesign of the output layer for the weighted regularized extreme learning machine (WRELM). For multi-classification problems, the conventional method of the output layer setting, named “one-hot method”, is as follows: Let the [...] Read more.

In this paper, we focus on the redesign of the output layer for the weighted regularized extreme learning machine (WRELM). For multi-classification problems, the conventional method of the output layer setting, named “one-hot method”, is as follows: Let the class of samples be r; then, the output layer node number is r and the ideal output of s-th class is denoted by the s-th unit vector in

R^{r}

(

1 \leq s \leq r

). Here, in this article, we propose a “

b i n a r y

m e t h o d

” to optimize the output layer structure: Let

2^{p - 1} < r \leq 2^{p}

, where

p \geq 2

, and p output nodes are utilized and, simultaneously, the ideal outputs are encoded in binary numbers. In this paper, the binary method is employed in WRELM. The weights are updated through iterative calculation, which is the most important process in general neural networks. While in the extreme learning machine, the weight matrix is calculated in least square method. That is, the coefficient matrix of the linear equations we solved is symmetric. For WRELM, we continue this idea. And the main part of the weight-solving process is a symmetry matrix. Compared with the one-hot method, the binary method requires fewer output layer nodes, especially when the number of sample categories is high. Thus, some memory space can be saved when storing data. In addition, the number of weights connecting the hidden and the output layer will also be greatly reduced, which will directly reduce the calculation time in the process of training the network. Numerical experiments are conducted to prove that compared with the one-hot method, the binary method can reduce the output nodes and hidden-output weights without damaging the learning precision. Full article

► Show Figures

Figure 1

17 pages, 326 KiB

Open AccessArticle

Fixed Points of (α, β, F*) and (α, β, F**)-Weak Geraghty Contractions with an Application

by Khairul Habib Alam, Yumnam Rohen and Naeem Saleem

Symmetry 2023, 15(1), 243; https://doi.org/10.3390/sym15010243 - 16 Jan 2023

Cited by 13 | Viewed by 2577

Abstract

This study aims to provide some new classes of

(α, β, F^{*})

-weak Geraghty contraction and

(α, β, F^{* *})

-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we [...] Read more.

This study aims to provide some new classes of

(α, β, F^{*})

-weak Geraghty contraction and

(α, β, F^{* *})

-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem. Full article

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

21 pages, 14356 KiB

Open AccessArticle

Design and Development of a Macro to Compare Sections of Planes to Parts Using Programming with Visual Basic for Applications in CATIA

by José Ignacio Rojas-Sola, Gloria del Río-Cidoncha, Rafael Ortíz-Marín and José Antonio Moya-Ocaña

Symmetry 2023, 15(1), 242; https://doi.org/10.3390/sym15010242 - 16 Jan 2023

Cited by 2 | Viewed by 3273

Abstract

This article presents an application for educational purposes in the field of engineering graphics, which corrects the dihedral projections of the sections of a plane for a part by comparing the solution provided by the student with that obtained through 3D CAD modelling [...] Read more.

This article presents an application for educational purposes in the field of engineering graphics, which corrects the dihedral projections of the sections of a plane for a part by comparing the solution provided by the student with that obtained through 3D CAD modelling software. Said application is generated as a macro in CATIA (Computer-Aided Three-Dimensional Interactive Application), which is included as a tool in the ‘Part Design’ module. The code of this macro is written in the CATVBA language, utilizes the CATIA internal editor, and takes advantage of the capabilities offered by Visual Basic for Applications (VBA) in the design of Graphical User Interfaces (GUI). The operation of the macro consists of obtaining the section in the 3D CAD model, projecting it onto three dihedral projections of the part (elevation, plan, and profile), and calculating the visible and hidden lines by means of a numerical process based on dividing the lines into discrete sections. Likewise, to obtain numerical results, the section obtained in CATIA (reference section) is compared with the section provided by the student (section that needed to be corrected) by means of a spreadsheet (Microsoft Excel). The data of the coordinates of the points of the reference section are exported to said spreadsheet as is the data of the coordinates of the section that needed to be corrected, which is contained in a file with a dxf format (Drawing eXchange Format). From these data, by programming the appropriate formulae in the cells of the spreadsheet, the numerical values of the errors are obtained, thereby locating said errors in the dihedral projections of the section which needed to be corrected. Likewise, the application can be programmed to compare the central symmetry of both of the sections. Full article

(This article belongs to the Special Issue Advances on Engineering Graphics: Improvements and New Proposals, Volume 2)

► Show Figures

Figure 1

13 pages, 1247 KiB

Open AccessArticle

On Thermodynamically Consistent Quasiparticle Model at Finite Chemical Potential

by Wei-Liang Qian, Hong-Hao Ma, Shaoyu Yin and Ping Wang

Symmetry 2023, 15(1), 241; https://doi.org/10.3390/sym15010241 - 16 Jan 2023

Viewed by 1815

Abstract

We explore the quasiparticle model at the finite chemical potential related to Ru-Keng Su’s distinguished contributions to the topic. In addition, we discuss the recent developments in the model, and in particular, one argues that the effective mass of the quasiparticle might attain [...] Read more.

We explore the quasiparticle model at the finite chemical potential related to Ru-Keng Su’s distinguished contributions to the topic. In addition, we discuss the recent developments in the model, and in particular, one argues that the effective mass of the quasiparticle might attain a specific form as a function of momentum, in addition to its dependence on the temperature and chemical potential. Unlike the approaches based on the properties of underlying symmetry or the renormalization group, the momentum dependence emerges as a special solution to an integro-differential equation resulting from the underlying thermodynamic consistency. Moreover, this special solution to the problem is shown to be more general than previously explored in the literature. Instead of fitting to the lattice QCD data at the vanishing chemical potential, in this work, we adopt a “bottom-up” approach by assuming some analytic ansatzes that are manifestly thermodynamically consistent. The remaining physical quantities are subsequently derived, and possible implications are also addressed. Full article

(This article belongs to the Special Issue Heavy-Ion Collisions and Multiparticle Production)

► Show Figures

Figure 1

7 pages, 227 KiB

Open AccessArticle

A Study on k-Hyperideals in Ordered Semihyperrings

by Zheng Kou, Mehdi Gheisari and Saber Omidi

Symmetry 2023, 15(1), 240; https://doi.org/10.3390/sym15010240 - 16 Jan 2023

Cited by 2 | Viewed by 1332

Abstract

In this study, we propose the concept of left extension of a hyperideal by generalizing the concept of k-hyperideals in ordered semihyperrings with symmetrical hyper-operation ⊕. By using the notion of extension of a k-hyperideal, we prove some results in ordered [...] Read more.

In this study, we propose the concept of left extension of a hyperideal by generalizing the concept of k-hyperideals in ordered semihyperrings with symmetrical hyper-operation ⊕. By using the notion of extension of a k-hyperideal, we prove some results in ordered semihyperrings. The results of this paper can be viewed as a generalization for k-ideals of semirings. Full article

13 pages, 590 KiB

Open AccessArticle

Lie Bialgebra Structures on the Lie Algebra

L

Related to the Virasoro Algebra

by Xue Chen, Yihong Su and Jia Zheng

Symmetry 2023, 15(1), 239; https://doi.org/10.3390/sym15010239 - 15 Jan 2023

Viewed by 1393

Abstract

A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the structure of a Lie coalgebra, and some compatibility condition. Moreover, Lie brackets have skew symmetry. Because of the close relation between Lie bialgebras and quantum [...] Read more.

A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the structure of a Lie coalgebra, and some compatibility condition. Moreover, Lie brackets have skew symmetry. Because of the close relation between Lie bialgebras and quantum groups, it is interesting to consider the Lie bialgebra structures on the Lie algebra

L

related to the Virasoro algebra. In this paper, the Lie bialgebras on

L

are investigated by computing

Der (L, L \otimes L)

. It is proved that all such Lie bialgebras are triangular coboundary, and the first cohomology group

H^{1} (L, L \otimes L)

is trivial. Full article

(This article belongs to the Section Mathematics)

29 pages, 5993 KiB

Open AccessArticle

Short-Term Photovoltaic Power Forecasting Based on a Novel Autoformer Model

by Yuanshao Huang and Yonghong Wu

Symmetry 2023, 15(1), 238; https://doi.org/10.3390/sym15010238 - 15 Jan 2023

Cited by 6 | Viewed by 2687

Abstract

Deep learning techniques excel at capturing and understanding the symmetry inherent in data patterns and non-linear properties of photovoltaic (PV) power, therefore they achieve excellent performance on short-term PV power forecasting. In order to produce more precise and detailed forecasting results, this research [...] Read more.

Deep learning techniques excel at capturing and understanding the symmetry inherent in data patterns and non-linear properties of photovoltaic (PV) power, therefore they achieve excellent performance on short-term PV power forecasting. In order to produce more precise and detailed forecasting results, this research suggests a novel Autoformer model with De-Stationary Attention and Multi-Scale framework (ADAMS) for short-term PV power forecasting. In this approach, the multi-scale framework is applied to the Autoformer model to capture the inter-dependencies and specificities of each scale. Furthermore, the de-stationary attention is incorporated into an auto-correlation mechanism for more efficient non-stationary information extraction. Based on the operational data from a 1058.4 kW PV facility in Central Australia, the ADAMS model and the other six baseline models are compared with 5 min and 1 h temporal resolution PV power data predictions. The results show in terms of four performance measurements, the proposed method can handle the task of projecting short-term PV output more effectively than other methods. Taking the result of predicting the PV energy in the next 24 h based on the 1 h resolution data as an example, MSE is 0.280, MAE is 0.302, RMSE is 0.529, and adjusted R-squared is 0.824. Full article

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

► Show Figures

Figure 1

19 pages, 1037 KiB

Open AccessArticle

Numerical Analysis of Fractional-Order Parabolic Equation Involving Atangana–Baleanu Derivative

by Meshari Alesemi

Symmetry 2023, 15(1), 237; https://doi.org/10.3390/sym15010237 - 15 Jan 2023

Cited by 3 | Viewed by 1372

Abstract

In this study, the suggested q-homotopy analysis transform method is used to compute a numerical solution of a fractional parabolic equation, and the solution is obtained in a fast convergent series. The leverage and efficacy of the suggested technique are demonstrated by the [...] Read more.

In this study, the suggested q-homotopy analysis transform method is used to compute a numerical solution of a fractional parabolic equation, and the solution is obtained in a fast convergent series. The leverage and efficacy of the suggested technique are demonstrated by the test examples provided. The results that were acquired are graphically displayed. The series solution in a sizable admissible domain is handled in an extreme way by the current method. It provides us with a simple means of modifying the solution’s convergence zone. The effectiveness and potential of the suggested algorithm are explicitly shown in the results using graphs. Full article

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

► Show Figures

Figure 1

11 pages, 3401 KiB

Open AccessArticle

K₂CdGe₃S₈: A New Infrared Nonlinear Optical Sulfide

by Zi-Xuan Wu, Wen-Fa Chen, Bin-Wen Liu, Xiao-Ming Jiang and Guo-Cong Guo

Symmetry 2023, 15(1), 236; https://doi.org/10.3390/sym15010236 - 15 Jan 2023

Cited by 3 | Viewed by 2046

Abstract

A quaternary metal chalcogenide, namely K₂CdGe₃S₈ (I), is obtained through a high-temperature solid-state approach. Compound I crystallizes with the non-centrosymmetric space group P2₁2₁2₁. It features a 2D layer structure [...] Read more.

A quaternary metal chalcogenide, namely K₂CdGe₃S₈ (I), is obtained through a high-temperature solid-state approach. Compound I crystallizes with the non-centrosymmetric space group P2₁2₁2₁. It features a 2D layer structure with [CdGe₃S₈] layers consisting of tetrahedral GeS₄ and CdS₄ units, and counter K⁺ embedded between the layers. The compound exhibits a powder second-harmonic generation (SHG) response of ~0.1 times that of KH₂PO₄ (KDP) with phase-matchable character at the laser wavelength of 1064 nm. Remarkably, it has a wide band gap (3.20 eV), which corresponds to a favorable high laser-induced damage threshold of 6.7 times that of AgGaS₂. In addition, the calculated birefringence (Δn) is 0.039 at the wavelength of 1064 nm, which satisfies the Δn criteria for a promising infrared NLO material. Full article

(This article belongs to the Special Issue Advances in Nonlinear Optics and Symmetry)

► Show Figures

Figure 1

18 pages, 649 KiB

Open AccessArticle

On New Symmetric Schur Functions Associated with Integral and Integro-Differential Functional Expressions in a Complex Domain

by Samir B. Hadid and Rabha W. Ibrahim

Symmetry 2023, 15(1), 235; https://doi.org/10.3390/sym15010235 - 14 Jan 2023

Cited by 5 | Viewed by 1247

Abstract

The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is defined and then used to determine the geometric [...] Read more.

The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is defined and then used to determine the geometric and symmetric interpretations of mathematical expressions in a complex symmetric domain (the open unit disk). To obtain more symmetric properties involving NSSP, we consider a symmetric differential operator. The outcome is a symmetric convoluted operator. Geometrically, studies are presented for the suggested operator. Our method is based on the theory of differential subordination. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Functional Equations)

► Show Figures

Figure 1

13 pages, 11462 KiB

Open AccessFeature PaperArticle

Influence of Physical Symmetries on the Magnetization Dynamics in Magnetic Fibers

by Tomasz Blachowicz, Pawel Steblinski and Andrea Ehrmann

Symmetry 2023, 15(1), 234; https://doi.org/10.3390/sym15010234 - 13 Jan 2023

Viewed by 1764

Abstract

Magnetic nanofibers belong to the geometries which are intensively investigated in simulations and experiments due to their unique magnetic properties, varying in their lengths, cross-sections, and bending radii. Besides basic research of different magnetization reversal processes and magnetization dynamics in bent nanofibers, these [...] Read more.

Magnetic nanofibers belong to the geometries which are intensively investigated in simulations and experiments due to their unique magnetic properties, varying in their lengths, cross-sections, and bending radii. Besides basic research of different magnetization reversal processes and magnetization dynamics in bent nanofibers, these structures are of potential interest for data storage applications, data transport, or other tasks in spintronics devices. While previous simulations concentrated on the domain wall transport through coupled bent nanofibers, creating networks with many in- and outputs to establish nanofiber-based domain wall logics, here we show the influence of the constricted area, in which a rotating magnetic field is applied in the middle of bent or straight magnetic nanofibers, on the magnetization dynamics. Our micromagnetic simulations, performed by Magpar, reveal a strong impact not only of this area, but also of the curvature of the nanofiber as well as of an additional Dzyaloshinskii–Moriya interaction (DMI). Full article

(This article belongs to the Special Issue Chiral Symmetry and Spin Dynamics)

► Show Figures

Figure 1

20 pages, 1322 KiB

Open AccessArticle

Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators

by Meshari Alesemi, Jameelah S. Al Shahrani, Naveed Iqbal, Rasool Shah and Kamsing Nonlaopon

Symmetry 2023, 15(1), 233; https://doi.org/10.3390/sym15010233 - 13 Jan 2023

Cited by 5 | Viewed by 2124

Abstract

The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natural [...] Read more.

The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natural transformation to discover the solution to a system of fractional-order partial differential equations. Using certain examples, the efficacy of the proposed technique is demonstrated. The exact and approximate solutions were shown to be in close contact in the graphical representation of the obtained results. We also examine whether the proposed method can achieve a quick convergence with a minimal number of calculations. The present approaches are also used to calculate solutions in various fractional orders. It has been proven that fractional-order solutions converge to integer-order solutions to problems. The current technique can be modified for various fractional-order problems due to its simple and straightforward implementation. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

22 pages, 5888 KiB

Open AccessArticle

Isokinetic Rehabilitation Trajectory Planning of an Upper Extremity Exoskeleton Rehabilitation Robot Based on a Multistrategy Improved Whale Optimization Algorithm

by Fumin Guo, Hua Zhang, Yilu Xu, Genliang Xiong and Cheng Zeng

Symmetry 2023, 15(1), 232; https://doi.org/10.3390/sym15010232 - 13 Jan 2023

Cited by 3 | Viewed by 1642

Abstract

Upper extremity exoskeleton rehabilitation robots have become a significant piece of rehabilitation equipment, and planning their motion trajectories is essential in patient rehabilitation. In this paper, a multistrategy improved whale optimization algorithm (MWOA) is proposed for trajectory planning of upper extremity exoskeleton rehabilitation [...] Read more.

Upper extremity exoskeleton rehabilitation robots have become a significant piece of rehabilitation equipment, and planning their motion trajectories is essential in patient rehabilitation. In this paper, a multistrategy improved whale optimization algorithm (MWOA) is proposed for trajectory planning of upper extremity exoskeleton rehabilitation robots with emphasis on isokinetic rehabilitation. First, a piecewise polynomial was used to construct a rough trajectory. To make the trajectory conform to human-like movement, a whale optimization algorithm (WOA) was employed to generate a bounded jerk trajectory with the minimum running time as the objective. The search performance of the WOA under complex constraints, including the search capability of trajectory planning symmetry, was improved by the following strategies: a dual-population search, including a new communication mechanism to prevent falling into the local optimum; a mutation centroid opposition-based learning, to improve the diversity of the population; and an adaptive inertia weight, to balance exploration and exploitation. Simulation analysis showed that the MWOA generated a trajectory with a shorter run-time and better symmetry and robustness than the WOA. Finally, a pilot rehabilitation session on a healthy volunteer using an upper extremity exoskeleton rehabilitation robot was completed safely and smoothly along the trajectory planned by the MWOA. The proposed algorithm thus provides a feasible scheme for isokinetic rehabilitation trajectory planning of upper extremity exoskeleton rehabilitation robots. Full article

(This article belongs to the Special Issue Algorithms for Optimization 2022)

► Show Figures

Figure 1

10 pages, 1961 KiB

Open AccessEditor’s ChoiceArticle

A New Program to Estimate the Parameters of Preston’s Equation, a General Formula for Describing the Egg Shape of Birds

by Peijian Shi, Lin Wang, Brady K. Quinn and Johan Gielis

Symmetry 2023, 15(1), 231; https://doi.org/10.3390/sym15010231 - 13 Jan 2023

Cited by 6 | Viewed by 2468

Abstract

Preston’s equation is a general model describing the egg shape of birds. The parameters of Preston’s equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg’s actual length to two. This method assumes that the straight line through [...] Read more.

Preston’s equation is a general model describing the egg shape of birds. The parameters of Preston’s equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg’s actual length to two. This method assumes that the straight line through the two points on an egg’s profile separated by the maximum distance (i.e., the longest axis of an egg’s profile) is the mid-line. It hypothesizes that the photographed egg’s profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston’s equation considers an angle of deviation for the longest axis of an egg’s profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg’s center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg’s profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston’s equation by automatically searching for the optimal mid-line of an egg’s profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston’s equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg’s profile) and the egg’s maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations. Full article

(This article belongs to the Section Life Sciences)

► Show Figures

Figure 1

15 pages, 329 KiB

Open AccessArticle

A Quadratic Surface Minimax Probability Machine for Imbalanced Classification

by Xin Yan, Zhouping Xiao and Zheng Ma

Symmetry 2023, 15(1), 230; https://doi.org/10.3390/sym15010230 - 13 Jan 2023

Viewed by 1270

Abstract

In this paper, a kernel-free minimax probability machine model for imbalanced classification is proposed. In this model, a quadratic surface is adopted directly for separating the data points into two classes. By using two symmetry constraints to define the two worst-case classification accuracy [...] Read more.

In this paper, a kernel-free minimax probability machine model for imbalanced classification is proposed. In this model, a quadratic surface is adopted directly for separating the data points into two classes. By using two symmetry constraints to define the two worst-case classification accuracy rates, the model of maximizing both the

F_{1}

value of the minority class and the classification accuracy rate of all the data points is proposed. The proposed model corresponds to a fractional programming problem. Since the two worst-case classification accuracy rates are the symmetry, the proposed model can be further simplified. After this, the alternating descent algorithm is adopted for efficiently solving. The proposed method reduces the computational costs by both using the kernel-free technique and adopting the efficient algorithm. Some numerical tests on benchmark datasets are conducted to investigate the classification performance of the proposed method. The numerical results demonstrate that the proposed method performs better when compared with the other state-of-the-art methods, especially for classifying the imbalanced datasets. The better performance for the imbalanced classification is also demonstrated on a Wholesale customers dataset. This method can provide methodological support for the research in areas such as customer segmentation. Full article

(This article belongs to the Section Computer)

► Show Figures

Figure 1

11 pages, 290 KiB

Open AccessArticle

A Class of Smoothing Modulus-Based Iterative Methods for Solving the Stochastic Mixed Complementarity Problems

by Cong Guo, Yingling Liu and Chenliang Li

Symmetry 2023, 15(1), 229; https://doi.org/10.3390/sym15010229 - 13 Jan 2023

Viewed by 1281

Abstract

In this paper, we present a smoothing modulus-based iterative method for solving the stochastic mixed complementarity problems (SMCP). The main idea is that we firstly transform the expected value model of SMCP into an equivalent nonsmooth system of equations, then obtain an approximation [...] Read more.

In this paper, we present a smoothing modulus-based iterative method for solving the stochastic mixed complementarity problems (SMCP). The main idea is that we firstly transform the expected value model of SMCP into an equivalent nonsmooth system of equations, then obtain an approximation smooth system of equations by using a smoothing function, and finally solve it by the Newton method. We give the convergence analysis, and the numerical results show the effectiveness of the new method for solving the SMCP with symmetry coefficient matrices. Full article

(This article belongs to the Section Mathematics)

14 pages, 841 KiB

Open AccessArticle

A Family of Higher Order Scheme for Multiple Roots

by Tajinder Singh, Himani Arora and Lorentz Jäntschi

Symmetry 2023, 15(1), 228; https://doi.org/10.3390/sym15010228 - 13 Jan 2023

Cited by 4 | Viewed by 1948

Abstract

We have developed a two-point iterative scheme for multiple roots that achieves fifth order convergence by using two function evaluations and two derivative evaluations each iteration. Weight function approach is utilized to frame the scheme. The weight function named as [...] Read more.

We have developed a two-point iterative scheme for multiple roots that achieves fifth order convergence by using two function evaluations and two derivative evaluations each iteration. Weight function approach is utilized to frame the scheme. The weight function named as

R (υ_{t})

is used, which is a function of

υ_{t}

, and

υ_{t}

is a function of

ω_{t}

, i.e.,

υ_{t} = \frac{ω_{t}}{1 + a ω_{t}},

where a is a real number and

ω_{t} = {(\frac{g (y_{t})}{g (x_{t})})}^{\frac{1}{\tilde{m}}}

is a multi-valued function. The consistency of the newly generated methods is ensured numerically and through the basins of attraction. Four complex functions are considered to compare the new methods with existing schemes via basins of attraction, and all provided basins of attraction possess reflection symmetry. Further, five numerical examples are used to verify the theoretical results and to contrast the presented schemes with some recognized schemes of fifth order. The results obtained have proved that the new schemes are better than the existing schemes of the same nature. Full article

► Show Figures

Figure 1

10 pages, 282 KiB

Open AccessArticle

Quantum Geometry of Spacetime and Quantum Equilibrium

by Yuri Shtanov

Symmetry 2023, 15(1), 227; https://doi.org/10.3390/sym15010227 - 13 Jan 2023

Cited by 1 | Viewed by 1751

Abstract

We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focus on the [...] Read more.

We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focus on the ergodic approach to its resolution. Full article

(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))

16 pages, 5014 KiB

Open AccessArticle

A Computational Study of the Immobilization of New 5-Nitroisatine Derivatives with the Use of C60-Based Functionalized Nanocarriers

by Przemysław Czeleń, Beata Szefler and Agnieszka Skotnicka

Symmetry 2023, 15(1), 226; https://doi.org/10.3390/sym15010226 - 13 Jan 2023

Cited by 1 | Viewed by 1727

Abstract

Isatin-based compounds are a large group of drugs used as competitive inhibitors of ATP. The 5-nitroisatin derivatives studied in this work are inhibitors of the CDK2 enzyme, which can be used in the development of new anti-cancer therapies. One of the basic activities [...] Read more.

Isatin-based compounds are a large group of drugs used as competitive inhibitors of ATP. The 5-nitroisatin derivatives studied in this work are inhibitors of the CDK2 enzyme, which can be used in the development of new anti-cancer therapies. One of the basic activities that often allows for an increase in biological activity while reducing the undesirable effects associated with the toxicity of medicinal substances is immobilization based on carriers. In this work, fifty nanocarriers derived from C60 fullerene, containing a bound phenyl ring on their surfaces, were used in the process of the immobilization of isatin derivatives. Based on flexible docking methods, the binding capacities of the drugs under consideration were determined using a wide range of nanocarriers containing symmetric and asymmetric modifications of the phenyl ring, providing various types of interactions. Based on the data collected for each of the tested drugs, including the binding affinity and the structure and stability of complexes, the best candidates were selected in terms of the type of substituent that modified the nanoparticle and its location. Among the systems with the highest affinity are the dominant complexes created by functionalized fullerenes containing substituents with a symmetrical location, such as R₂-R₆ and R₃-R₅. Based on the collected data, nanocarriers with a high potential for immobilization and use in the development of targeted therapies were selected for each of the tested drugs. Full article

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

► Show Figures

Figure 1

11 pages, 306 KiB

Open AccessArticle

(β,γ)-Skew QC Codes with Derivation over a Semi-Local Ring

by Mohammad Ashraf, Amal S. Alali, Mohd Asim and Ghulam Mohammad

Symmetry 2023, 15(1), 225; https://doi.org/10.3390/sym15010225 - 13 Jan 2023

Cited by 1 | Viewed by 1705

Abstract

In this article, we consider a semi-local ring

S = F_{q} + u F_{q}

, where

u^{2} = u

,

q = p^{s}

and p is a prime number. We define a multiplication [...] Read more.

In this article, we consider a semi-local ring

S = F_{q} + u F_{q}

, where

u^{2} = u

,

q = p^{s}

and p is a prime number. We define a multiplication

y b = β (b) y + γ (b)

, where

β

is an automorphism and

γ

is a

β

-derivation on

S

so that

S [y; β, γ]

becomes a non-commutative ring which is known as skew polynomial ring. We give the characterization of

S [y; β, γ]

and obtain the most striking results that are better than previous findings. We also determine the structural properties of 1-generator skew cyclic and skew-quasi cyclic codes. Further, We demonstrate remarkable results of the above-mentioned codes over

S

. Finally, we find the duality of skew cyclic and skew-quasi cyclic codes using a symmetric inner product. These codes are further generalized to double skew cyclic and skew quasi cyclic codes and a table of optimal codes is calculated by MAGMA software. Full article

(This article belongs to the Special Issue The Advances in Algebraic Coding Theory)

19 pages, 724 KiB

Open AccessArticle

Event-Triggered Sliding Mode Impulsive Control for Lower Limb Rehabilitation Exoskeleton Robot Gait Tracking

by Yang Liu, Shiguo Peng, Jiajun Zhang, Kan Xie, Zhuoyi Lin and Wei-Hsin Liao

Symmetry 2023, 15(1), 224; https://doi.org/10.3390/sym15010224 - 12 Jan 2023

Cited by 4 | Viewed by 1995

Abstract

Lower limb rehabilitation exoskeleton robots (LLRERs) play an important role in lower limb rehabilitation training and assistance walking for patients with lower limb movement disorders. In order to reduce and eliminate adverse effects on the accuracy of human motion gait tracking during walking [...] Read more.

Lower limb rehabilitation exoskeleton robots (LLRERs) play an important role in lower limb rehabilitation training and assistance walking for patients with lower limb movement disorders. In order to reduce and eliminate adverse effects on the accuracy of human motion gait tracking during walking with an LLRER, which is caused by the gravity and friction, the periodic ground shock force, and the human–exoskeleton interaction force, this paper proposes a feedforward–feedback hybrid control strategy of sliding mode impulsive control with gravity and friction compensation, based on the event-triggered mechanism of Lyapunov function. Firstly, to realize high-precision gait tracking with bounded error, some constraints on controller parameters are deduced by analyzing the Lyapunov-based stability. Secondly, the Zeno behavior of impulsive event triggers is excluded by the analysis of three different cases of the triggering time sequence. Finally, the effectiveness of the proposed hybrid controller is verified by the numerical simulation of the LLRER human–exoskeleton integrated system based on a three-link simplified model. It shows that an event-triggered sliding mode impulsive control strategy with gravity and friction compensation can achieve complete gait tracking with bounded error and has excellent dynamic performance under the constraints. Full article

(This article belongs to the Special Issue Biomechanics and Energetics of Human Motion When Walking with Lower Limb Orthoses, Prosthesis, and Exoskeletons)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry, Volume 15, Issue 1 (January 2023) – 253 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI