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Symmetry, Volume 15, Issue 4 (April 2023) – 179 articles

Cover Story (view full-size image): Continuum Coulomb wavefunctions of hydrogen for different energies plotted as a waterfall plot. They are computed via "single-shot factorization" using the general approach outlined in the article. The factorization constructs the superpotential from the logarithmic derivative of confluent hypergeometric functions, and we illustrate how to solve all known continuum problems using this approach. This work generalizes supersymmetric quantum mechanics from bound states to continuum states. View this paper
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19 pages, 333 KiB  
Article
The Origin of the Difference between Space and Time
by Hrvoje Nikolić
Symmetry 2023, 15(4), 957; https://doi.org/10.3390/sym15040957 - 21 Apr 2023
Viewed by 1892
Abstract
All differences between the role of space and time in nature are explained by proposing principles in which none of the spacetime coordinates has an a priori special role. Spacetime is treated as a non-dynamical manifold, with a fixed global RD topology. [...] Read more.
All differences between the role of space and time in nature are explained by proposing principles in which none of the spacetime coordinates has an a priori special role. Spacetime is treated as a non-dynamical manifold, with a fixed global RD topology. The dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it follows that one coordinate takes a special role. It is proposed that any boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the (1,D1) signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized. Full article
20 pages, 2681 KiB  
Article
The Facial Expression Data Enhancement Method Induced by Improved StarGAN V2
by Baojin Han and Min Hu
Symmetry 2023, 15(4), 956; https://doi.org/10.3390/sym15040956 - 21 Apr 2023
Cited by 3 | Viewed by 2140
Abstract
Due to the small data and unbalanced sample distribution in the existing facial emotion datasets, the effect of facial expression recognition is not ideal. Traditional data augmentation methods include image angle modification, image shearing, and image scrambling. The above approaches cannot solve the [...] Read more.
Due to the small data and unbalanced sample distribution in the existing facial emotion datasets, the effect of facial expression recognition is not ideal. Traditional data augmentation methods include image angle modification, image shearing, and image scrambling. The above approaches cannot solve the problem that is the high similarity of the generated images. StarGAN V2 can generate different styles of images across multiple domains. Nevertheless, there are some defects in gener-ating these facial expression images, such as crooked mouths and fuzzy facial expression images. To service such problems, we improved StarGAN V2 by solving the drawbacks of creating pictures that apply an SENet to the generator of StarGAN V2. The generator’s SENet can concentrate at-tention on the important regions of the facial expression images. Thus, this makes the generated symmetrical expression image more obvious and easier to distinguish. Meanwhile, to further im-prove the quality of the generated pictures, we customized the hinge loss function to reconstruct the loss functions that increase the boundary of real and fake images. The created facial expression pictures testified that our improved model could solve the defects in the images created by the original StarGAN V2. The experiments were conducted on the CK+ and MMI datasets. The correct recognition rate of the facial expressions on the CK+ was 99.2031%, which is a 1.4186% higher accuracy than that of StarGAN V2. The correct recognition rate of the facial expressions on the MMI displays was 98.1378%, which is 5.059% higher than that of the StarGAN V2 method. Furthermore, contrast test outcomes proved that the improved StarGAN V2 performed better than most state-of-the-art methods. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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9 pages, 277 KiB  
Article
Processing Fractional Differential Equations Using ψ-Caputo Derivative
by Mahrouz Tayeb, Hamid Boulares, Abdelkader Moumen and Moheddine Imsatfia
Symmetry 2023, 15(4), 955; https://doi.org/10.3390/sym15040955 - 21 Apr 2023
Cited by 4 | Viewed by 1254
Abstract
Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness of solutions (EUS) for FDEs in [...] Read more.
Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness of solutions (EUS) for FDEs in the sense ψ-Caputo fractional derivative (ψ-CFD) in the second-order 1<α<2. We know that ψ-CFD is a generalization of previously familiar fractional derivatives: Riemann-Liouville and Caputo. By applying the Banach fixed-point theorem (BFPT) and the Schauder fixed-point theorem (SFPT), we obtained the desired results, and to embody the theoretical results obtained, we provided two examples that illustrate the theoretical proofs. Full article
9 pages, 256 KiB  
Article
A Note on Generalized Solitons
by Amira Ishan and Sharief Deshmukh
Symmetry 2023, 15(4), 954; https://doi.org/10.3390/sym15040954 - 21 Apr 2023
Cited by 3 | Viewed by 1050
Abstract
In this paper, we initiate the study of a generalized soliton on a Riemannian manifold, we find a characterization for the Euclidean space, and in the compact case, we find a sufficient condition under which it reduces to a quasi-Einstein manifold. We also [...] Read more.
In this paper, we initiate the study of a generalized soliton on a Riemannian manifold, we find a characterization for the Euclidean space, and in the compact case, we find a sufficient condition under which it reduces to a quasi-Einstein manifold. We also find sufficient conditions under which a compact generalized soliton reduces to an Einstein manifold. Note that Ricci solitons being self-similar solutions of the heat flow, this topic is related to the symmetry in the geometry of Riemannian manifolds. Moreover, generalized solitons being generalizations of Ricci solitons are naturally related to symmetry. Full article
(This article belongs to the Special Issue Symmetry and Geometry in Physics II)
15 pages, 3128 KiB  
Article
An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications
by Yan Zhang, Jiyuan Tao, Yongyao Lv and Guoqiang Wang
Symmetry 2023, 15(4), 953; https://doi.org/10.3390/sym15040953 - 21 Apr 2023
Cited by 2 | Viewed by 1676
Abstract
The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to [...] Read more.
The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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28 pages, 881 KiB  
Article
Chikungunya Transmission of Mathematical Model Using the Fractional Derivative
by Sonal Jain and Dimplekumar N. Chalishajar
Symmetry 2023, 15(4), 952; https://doi.org/10.3390/sym15040952 - 21 Apr 2023
Cited by 2 | Viewed by 2807
Abstract
In this study, a mathematical model that may depict the dynamic transmission of the Chikungunya virus within a specific population has been examined. Various differential operators were considered, ranging from classical to nonlocal operators. We added a stochastic component to each instance and [...] Read more.
In this study, a mathematical model that may depict the dynamic transmission of the Chikungunya virus within a specific population has been examined. Various differential operators were considered, ranging from classical to nonlocal operators. We added a stochastic component to each instance and used the Lipschitz and linear growth criteria to illustrate the existence and uniqueness of the solutions. The most recent numerical method with Newton polynomial (are related symmetrical) interpolations was used to solve each problem numerically using MATLAB. There are some presented numerical simulations which are compared with the Lipschitz and linear growth properties. This new research work emphasizes how the Chikungunya virus model is formulated using fractional ODEs. Full article
(This article belongs to the Section Mathematics)
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45 pages, 6452 KiB  
Review
Time Series Analysis Based on Informer Algorithms: A Survey
by Qingbo Zhu, Jialin Han, Kai Chai and Cunsheng Zhao
Symmetry 2023, 15(4), 951; https://doi.org/10.3390/sym15040951 - 21 Apr 2023
Cited by 5 | Viewed by 5308
Abstract
Long series time forecasting has become a popular research direction in recent years, due to the ability to predict weather changes, traffic conditions and so on. This paper provides a comprehensive discussion of long series time forecasting techniques and their applications, using the [...] Read more.
Long series time forecasting has become a popular research direction in recent years, due to the ability to predict weather changes, traffic conditions and so on. This paper provides a comprehensive discussion of long series time forecasting techniques and their applications, using the Informer algorithm model as a framework. Specifically, we examine sequential time prediction models published in the last two years, including the tightly coupled convolutional transformer (TCCT) algorithm, Autoformer algorithm, FEDformer algorithm, Pyraformer algorithm, and Triformer algorithm. Researchers have made significant improvements to the attention mechanism and Informer algorithm model architecture in these different neural network models, resulting in recent approaches such as wavelet enhancement structure, auto-correlation mechanism, and depth decomposition architecture. In addition to the above, attention algorithms and many models show potential and possibility in mechanical vibration prediction. In recent state-of-the-art studies, researchers have used the Informer algorithm model as an experimental control, and it can be seen that the algorithm model itself has research value. The informer algorithm model performs relatively well on various data sets and has become a more typical algorithm model for time series forecasting, and its model value is worthy of in-depth exploration and research. This paper discusses the structures and innovations of five representative models, including Informer, and reviews the performance of different neural network structures. The advantages and disadvantages of each model are discussed and compared, and finally, the future research direction of long series time forecasting is discussed. Full article
(This article belongs to the Special Issue Machine Learning and Data Analysis)
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15 pages, 333 KiB  
Article
On Correlation Functions as Higher-Spin Invariants
by Adrien Scalea
Symmetry 2023, 15(4), 950; https://doi.org/10.3390/sym15040950 - 21 Apr 2023
Cited by 2 | Viewed by 1028
Abstract
(Chern–Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the n-point correlation functions of the higher-spin currents as higher-spin invariants directly on the CFT side, which [...] Read more.
(Chern–Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the n-point correlation functions of the higher-spin currents as higher-spin invariants directly on the CFT side, which complements earlier results that have a holographic perspective. Full article
(This article belongs to the Section Physics)
22 pages, 4763 KiB  
Article
Effect of the Size of the Superhydrophobic Regions of Biphilic Surfaces on the Bubble Dynamics
by José Pereira, Ricardo Cautela, Ana Moita and António Moreira
Symmetry 2023, 15(4), 949; https://doi.org/10.3390/sym15040949 - 21 Apr 2023
Cited by 1 | Viewed by 1687
Abstract
The current work aims to experimentally evaluate the effect of the size of circular superhydrophobic regions of biphilic surfaces on the bubble dynamics under pool boiling conditions. Biphilic surfaces are structured surfaces with tunable wettability, presenting an array of hydrophobic small spots in [...] Read more.
The current work aims to experimentally evaluate the effect of the size of circular superhydrophobic regions of biphilic surfaces on the bubble dynamics under pool boiling conditions. Biphilic surfaces are structured surfaces with tunable wettability, presenting an array of hydrophobic small spots in a hydrophilic surface or vice versa. The factors that affect the bubble dynamics are of geometric nature such as the diameters of the bubbles, their volume, and the height of the centroid, and of more complex nature such as the departure frequency of the bubbles and the rate of evaporation mass transfer. In this study, the bubble dynamics and boiling performance were evaluated by adjusting the diameter of the single circular superhydrophobic regions. A stainless steel AISI 304 foil was used as the base hydrophilic region, and the superhydrophobic regions were made by spray coating the NeverWet® superhydrophobic solution over well-defined masks. The main conclusion was that the bubble dynamics are clearly affected by the diameter of the superhydrophobic spots. The smaller spots favored the generation of more uniform and stable bubbles, mainly due to the border surface tension forces’ dominance. With the increase in the diameter of the bubbles, the surface tension acting at the border with the much larger hydrophilic region impacts the process less. Thus, the smaller superhydrophobic regions had higher evaporation mass transfer rates. The region with the best pool boiling performance along with improved bubble dynamics was the superhydrophobic region with an 0.8 mm diameter, corresponding to a superhydrophobic area to total area ratio of 0.11%. Moreover, this experimental work confirmed that the bubble dynamics’ impacting factors such as the diameter at the various stages of development of the bubbles can be modulated according to the final objectives of the design and fabrication of the biphilic surfaces. The research significance and novelty of this work come from the comprehensive study of the geometrical pattern of the heat transfer surface in pool boiling conditions and its impact on the bubble dynamics and heat transfer capability. We also suggest further studies considering nanoscale superhydrophobic spot arrangements and the future usage of different working fluids such as nanofluids. Full article
(This article belongs to the Special Issue Symmetry in Power Systems and Thermal Engineering)
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16 pages, 1478 KiB  
Communication
Symmetry in Regression Analysis: Perpendicular Offsets—The Case of a Photovoltaic Cell
by Lorentz Jäntschi
Symmetry 2023, 15(4), 948; https://doi.org/10.3390/sym15040948 - 21 Apr 2023
Cited by 3 | Viewed by 1410
Abstract
It is known that, for paired measurements subjected to experimental error, better suited linear regression is obtained by using perpendicular offsets. Even so, the great majority of statistical software still uses classical vertical offsets for reasons of convenience. The same convenience leads to [...] Read more.
It is known that, for paired measurements subjected to experimental error, better suited linear regression is obtained by using perpendicular offsets. Even so, the great majority of statistical software still uses classical vertical offsets for reasons of convenience. The same convenience leads to the preference of the least squares method in the favor of maximum-likelihood estimation. The treatise for perpendicular offsets for simple linear regression is slightly trickier than the corresponding one for vertical offsets. However, there is no general treatise for perpendicular offsets for nonlinear cases to date. In this work, a typical case of nonlinear dependence—potential versus intensity of current produced by a photovoltaic cell—is subjected to study. A series of paired potential/current data was collected from a commercial photovoltaic device and served for introducing the perpendicular offsets approach in the case of a nonlinear regression. Photovoltaic cell parameters—internal resistance, short-circuit current intensity, potential of open-circuit, and the maximum power point—have been determined by using the perpendicular offsets approach. Several issues were addressed in this work, such as exploring the intrinsic symmetry in the treatment of current versus potential diagrams, the suitability of perpendicular offsets in obtaining of the regression coefficients, and the implementation of nonlinear regression models with perpendicular offsets. Even if both the treatises of perpendicular offsets and nonlinear regression are known for some time now, there is no report in the literature of using both. Furthermore, since both potential and current measurements are affected by errors, it is more natural to use the proposed approach of perpendicular offsets. Full article
(This article belongs to the Section Physics)
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15 pages, 935 KiB  
Article
On the Nature of Bondi–Metzner–Sachs Transformations
by Zahra Mirzaiyan and Giampiero Esposito
Symmetry 2023, 15(4), 947; https://doi.org/10.3390/sym15040947 - 21 Apr 2023
Viewed by 1251
Abstract
This paper investigates, as a first step, the four branches of BMS transformations, motivated by the classification into elliptic, parabolic, hyperbolic and loxodromic proposed a few years ago in the literature. We first prove that to each normal elliptic transformation of the complex [...] Read more.
This paper investigates, as a first step, the four branches of BMS transformations, motivated by the classification into elliptic, parabolic, hyperbolic and loxodromic proposed a few years ago in the literature. We first prove that to each normal elliptic transformation of the complex variable ζ used in the metric for cuts of null infinity, there is a corresponding BMS supertranslation. We then study the conformal factor in the BMS transformation of the u variable as a function of the squared modulus of ζ. In the loxodromic and hyperbolic cases, this conformal factor is either monotonically increasing or monotonically decreasing as a function of the real variable given by the modulus of ζ. The Killing vector field of the Bondi metric is also studied in correspondence with the four admissible families of BMS transformations. Eventually, all BMS transformations are re-expressed in the homogeneous coordinates suggested by projective geometry. It is then found that BMS transformations are the restriction to a pair of unit circles of a more general set of transformations. Within this broader framework, the geometry of such transformations is studied by means of its Segre manifold. Full article
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12 pages, 3786 KiB  
Article
Heat and Mass Transfer on Magnetohydrodynamics Casson Carbon Nanotubes Nanofluid Flow in an Asymmetrical Channel via Porous Medium
by Wan Nura’in Nabilah Noranuar, Ahmad Qushairi Mohamad, Sharidan Shafie and Lim Yeou Jiann
Symmetry 2023, 15(4), 946; https://doi.org/10.3390/sym15040946 - 20 Apr 2023
Cited by 4 | Viewed by 1342
Abstract
The rapid development of nanotechnology in our emerging industries has drawn the interest of numerous researchers and scientists, especially in experimental and numerical studies. Therefore, the present analytical study will help reduce time and costs and validate the numerical study. However, the analytical [...] Read more.
The rapid development of nanotechnology in our emerging industries has drawn the interest of numerous researchers and scientists, especially in experimental and numerical studies. Therefore, the present analytical study will help reduce time and costs and validate the numerical study. However, the analytical research of carbon nanotubes with Casson fluid in a channel is still limited. Therefore, the current analytical study inspected the consequences of carbon nanotubes (CNTs) nanoparticles on the heat and mass transfer of magnetohydrodynamics (MHD) Casson nanofluid flow induced by a moving vertical plate with a porous region inside an asymmetrical channel. Dimensional governing equations are used for the modelling, which is then expressed in a dimensionless form by employing dimensionless variables. The analytical solutions for the velocity, temperature, and concentration are tackled using the Laplace transform technique. The temperature and velocity are significantly enhanced when increasing the nanoparticle volume fraction. This is due to the outstanding characteristic of nanofluid thermal conductivity, which results in an efficient heat transfer. This result has the potential to be applied to various nanofluid cooling technologies. Since the solutions are determined in an analytical form, this study could be used as a reference for other numerical and experimental works and a guide for several industries. Full article
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18 pages, 349 KiB  
Article
Gauging Fractons and Linearized Gravity
by Erica Bertolini, Alberto Blasi, Andrea Damonte and Nicola Maggiore
Symmetry 2023, 15(4), 945; https://doi.org/10.3390/sym15040945 - 20 Apr 2023
Cited by 6 | Viewed by 1158
Abstract
We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the [...] Read more.
We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the paradigm that quantum field theories are defined by their symmetries, fractons unavoidably come together with linearized gravity. The standard Faddeev–Popov procedure to gauge fix the theory leads to a scalar gauge condition, which has two important drawbacks: it is frozen in the Landau gauge and linearized gravity cannot be obtained as a limit. In this paper, we adopt a tensorially alternative gauge fixing, which avoids both problems. In particular, this allows to show that important physical features, such as counting of the degrees of freedom, do not depend on a particular gauge choice, as expected. Moreover, the resulting gauge fixed theory contains both fractons and linearized gravity as a limit, differently from the standard scalar choice. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2023)
19 pages, 8019 KiB  
Article
Study on the Anisotropy of Strength Properties of Columnar Jointed Rock Masses Using a Geometric Model Reconstruction Method Based on a Single-Random Movement Voronoi Diagram of Uniform Seed Points
by Zhende Zhu, Luxiang Wang, Shu Zhu and Junyu Wu
Symmetry 2023, 15(4), 944; https://doi.org/10.3390/sym15040944 - 20 Apr 2023
Cited by 6 | Viewed by 1310
Abstract
The unique structural characteristics and special symmetry of columnar jointed rock mass result in its complex mechanical properties and strong anisotropy, which seriously affects the safety of engineering construction. To better simulate natural columnar jointed rock mass, a geometric model reconstruction method based [...] Read more.
The unique structural characteristics and special symmetry of columnar jointed rock mass result in its complex mechanical properties and strong anisotropy, which seriously affects the safety of engineering construction. To better simulate natural columnar jointed rock mass, a geometric model reconstruction method based on a single-random movement Voronoi diagram of uniform seed points using the feasible geological parameters of horizontal polygon density, irregular factor, dip angle, strike angle, transverse joint spacing, and transverse joint penetration rate is proposed in this paper. Based on this method, numerical simulation of CJRM models with varying strike angles, dip angles, and irregular factors under uniaxial compression were conducted. The results show that the uniaxial compression strengths versus strike angle and dip angle both decrease with the increase in the irregular factor, showing a U-shape and a gentle W-shape, respectively. The strength anisotropy of the strike angle decreases from 1.1057 to 1.0395 with the increase in the irregular factor, indicating relatively isotropy. With the increase int the irregular factor, the strength anisotropy of the dip angle increases from 4.3381 to 6.7953, indicating an increasing strong anisotropy at a high degree, and the effect of the irregular factor on strength behavior has the strongest and weakest impact at the dip angles of 60° and 90°, respectively. Full article
(This article belongs to the Topic Mathematical Modeling)
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10 pages, 283 KiB  
Article
On Generalized Bivariate (p,q)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (p,q)-Bernoulli–Lucas Polynomials
by Hao Guan, Waseem Ahmad Khan and Can Kızılateş
Symmetry 2023, 15(4), 943; https://doi.org/10.3390/sym15040943 - 20 Apr 2023
Cited by 3 | Viewed by 1021
Abstract
Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations. In this paper, we define the generalized (p,q)-Bernoulli–Fibonacci [...] Read more.
Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations. In this paper, we define the generalized (p,q)-Bernoulli–Fibonacci and generalized (p,q)-Bernoulli–Lucas polynomials and numbers by using the (p,q)-Bernoulli numbers, unified (p,q)-Bernoulli polynomials, h(x)-Fibonacci polynomials, and h(x)-Lucas polynomials. We also introduce the generalized bivariate (p,q)-Bernoulli–Fibonacci and generalized bivariate (p,q)-Bernoulli–Lucas polynomials and numbers. Then, we derive some properties of these newly established polynomials and numbers by using their generating functions with their functional equations. Finally, we provide some families of bilinear and bilateral generating functions for the generalized bivariate (p,q)-Bernoulli–Fibonacci polynomials. Full article
14 pages, 19001 KiB  
Article
Chromatic Differentiation of Functional Mappings of the Composition of Nucleic Acids
by Ivan V. Stepanyan and Mihail Y. Lednev
Symmetry 2023, 15(4), 942; https://doi.org/10.3390/sym15040942 - 20 Apr 2023
Cited by 1 | Viewed by 1148
Abstract
Color visualization of the DNA of diverse living beings can help in the exploration of the issue of chromatic differentiation of functional mappings of the nucleotide composition of DNA molecules. By “chromatic differentiation”, we mean the coloring of these mappings. Algorithms for coloring [...] Read more.
Color visualization of the DNA of diverse living beings can help in the exploration of the issue of chromatic differentiation of functional mappings of the nucleotide composition of DNA molecules. By “chromatic differentiation”, we mean the coloring of these mappings. Algorithms for coloring genetic representations improve the perception of complex genetic information using color. Methodologically, to build the chromatic differentiation of functional mappings of the nucleotide composition of DNA, we employed the system of nucleotide Walsh functions and the Chaos Game Representation (CGR) algorithm. The authors compared these two approaches and proposed a modified CGR algorithm. The work presents various algorithms of chromatic differentiation based on the nucleotide Walsh functions at a specific location of the fragment in the nucleotide chain and on the frequencies of those fragments. The results of the analysis provide examples of chromatic differentiation in a variety of parametric spaces. The paper describes various approaches to coloring and video animation of DNA molecules in their chromatically differentiated spans of physicochemical parameters. Full article
(This article belongs to the Section Life Sciences)
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18 pages, 7664 KiB  
Article
Cell-Dependent Mechanical Properties of Asymmetric Crosslinked Metallic Wire Mesh with Hybrid Patterns Based on Arbitrary Poisson’s Ratio
by Fang Wu, Zeyu Li, Congcong Lin, Shaoxiang Ge and Xin Xue
Symmetry 2023, 15(4), 941; https://doi.org/10.3390/sym15040941 - 20 Apr 2023
Cited by 1 | Viewed by 1369
Abstract
Metallic wire mesh has gained attention as a potential material for lightweight aircraft structures, e.g., a metallic frame of morphing wings, due to its customizable mechanical properties associated with cell structures. However, the relationship between the pattern design of cell structures and the [...] Read more.
Metallic wire mesh has gained attention as a potential material for lightweight aircraft structures, e.g., a metallic frame of morphing wings, due to its customizable mechanical properties associated with cell structures. However, the relationship between the pattern design of cell structures and the mechanical characteristics of metallic wire mesh remains unclear. The present work aims to investigate the mechanical behavior of asymmetric crosslinked metallic wire mesh with a hybrid Poisson’s ratio pattern, which has the potentials of arbitrary Poisson’s ratios. Two typical designs of cell arrangement for asymmetric crosslinked metallic wire mesh were proposed, namely negative Poisson’s ratio cells (NPRC) and positive Poisson’s ratio cells (PPRC). The in-plane Poisson’s ratio of asymmetric crosslinked metallic wire mesh was calculated based on the Euler beam theory. The effects of hybrid Poisson’s pattern and interwoven joint on mechanical properties, including macroscopic Poisson’s ratio and elastic bending recovery, were analyzed using numerical and experimental methods. The results demonstrate that the analytical Poisson’s ratio obtained from the proposed theoretical model agrees well with the simulation result. The hybrid structure which consisted of NPRC and PPRC could effectively control transverse shrinkage and become one of the most efficient potentials for promising structures with the arbitrary Poisson’s ratio phenomenon. Full article
(This article belongs to the Special Issue Symmetry Methods in Mechanics of Materials)
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20 pages, 1541 KiB  
Review
Why Are Most Humans Right-Handed? The Modified Fighting Hypothesis
by Matz Larsson, Astrid Schepman and Paul Rodway
Symmetry 2023, 15(4), 940; https://doi.org/10.3390/sym15040940 - 19 Apr 2023
Cited by 2 | Viewed by 8771
Abstract
Humans show a population-level preference for using the right hand. The fighting hypothesis is an influential theory that suggests that left-handedness persists because its rarity provides a surprise advantage in fighting interactions, and that left-handedness is less frequent because it has a health [...] Read more.
Humans show a population-level preference for using the right hand. The fighting hypothesis is an influential theory that suggests that left-handedness persists because its rarity provides a surprise advantage in fighting interactions, and that left-handedness is less frequent because it has a health cost. However, evidence for the health cost of left-handedness is unsubstantiated, leaving the greater frequency of right-handers unexplained. Research indicates that homicide may have been common in early hominins. We propose that the hand used to hold a weapon by early hominins could have influenced the outcome of a fight, due to the location of the heart and aorta. A left-handed unilateral grip exposes the more vulnerable left hemithorax towards an opponent, whereas a right-hand unilateral grip exposes the less vulnerable right hemithorax. Consequently, right-handed early ancestors, with a preference for using the right forelimb in combat, may have had a lower risk of a mortal wound, and a fighting advantage. This would explain their greater frequency. In accordance with the original fighting hypothesis, we also suggest that left-handed fighters have a surprise advantage when they are rare, explaining their persistence. We discuss evidence for the modified fighting hypothesis, its predictions, and ways to test the theory. Full article
(This article belongs to the Special Issue Individual Differences in Behavioral and Neural Lateralization)
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15 pages, 329 KiB  
Article
Results on Second-Order Hankel Determinants for Convex Functions with Symmetric Points
by Khalil Ullah, Isra Al-Shbeil, Muhammad Imran Faisal, Muhammad Arif and Huda Alsaud
Symmetry 2023, 15(4), 939; https://doi.org/10.3390/sym15040939 - 19 Apr 2023
Cited by 6 | Viewed by 1408
Abstract
One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some [...] Read more.
One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some sharp estimates of problems involving coefficients for the family of convex functions with respect to symmetric points and associated with a hyperbolic tangent function. These problems include the first four initial coefficients, the Fekete–Szegö and Zalcman inequalities, and the second-order Hankel determinant. Additionally, the inverse and logarithmic coefficients of the functions belonging to the defined class are also studied in relation to the current problems. Full article
(This article belongs to the Special Issue Symmetry in Pure Mathematics and Real and Complex Analysis)
10 pages, 284 KiB  
Article
The n-Point Composite Fractional Formula for Approximating Riemann–Liouville Integrator
by Iqbal M. Batiha, Shameseddin Alshorm, Abdallah Al-Husban, Rania Saadeh, Gharib Gharib and Shaher Momani
Symmetry 2023, 15(4), 938; https://doi.org/10.3390/sym15040938 - 19 Apr 2023
Cited by 6 | Viewed by 1140
Abstract
In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized Taylor’s formula, a novel three-point central fractional formula is established [...] Read more.
In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized Taylor’s formula, a novel three-point central fractional formula is established for approximating a Riemann–Liouville fractional integrator. Such a new formula, which emerges clearly from the symmetrical aspects of the proposed numerical approach, is then further extended to formulate an n-point composite fractional formula for approximating the same operator. Several numerical examples are introduced to validate our findings. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
9 pages, 259 KiB  
Article
On Some Bounds for the Gamma Function
by Mansour Mahmoud, Saud M. Alsulami and Safiah Almarashi
Symmetry 2023, 15(4), 937; https://doi.org/10.3390/sym15040937 - 19 Apr 2023
Cited by 2 | Viewed by 963
Abstract
Both theoretical and applied mathematics depend heavily on inequalities, which are rich in symmetries. In numerous studies, estimations of various functions based on the characteristics of their symmetry have been provided through inequalities. In this paper, we study the monotonicity of certain functions [...] Read more.
Both theoretical and applied mathematics depend heavily on inequalities, which are rich in symmetries. In numerous studies, estimations of various functions based on the characteristics of their symmetry have been provided through inequalities. In this paper, we study the monotonicity of certain functions that involve Gamma functions. We were able to obtain some of the bounds of Γ(v) that are more accurate than some recently published inequalities. Full article
20 pages, 365 KiB  
Article
On the Ideal Convergent Sequences in Fuzzy Normed Space
by Nifeen H. Altaweel, Mohammad H. M. Rashid, Olayan Albalawi, Maryam G. Alshehri, Nidal H. E. Eljaneid and Razan Albalawi
Symmetry 2023, 15(4), 936; https://doi.org/10.3390/sym15040936 - 19 Apr 2023
Cited by 2 | Viewed by 1322
Abstract
This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster points of a sequence in a fuzzy normed [...] Read more.
This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster points of a sequence in a fuzzy normed linear space are investigated. In a fuzzy normed space, we investigated additional effects, such as describing compactness in terms of ideal cluster points and other relevant but previously unresearched ideal convergence and adjoint ideal convergence aspects of sequences and nets. The countable compactness of a fuzzy normed space and its link to it were also defined. The terms ideal and its adjoint divergent sequences are then introduced, and specific aspects of them are explored in a fuzzy normed space. Our study supports the importance of condition (AP) in examining summability via ideals. It is suggested to use a fuzzy point symmetry-based genetic clustering method to automatically count the number of clusters in a data set and determine how well the data are fuzzy partitioned. As long as the clusters have the attribute of symmetry, they can be any size, form, or convexity. One of the crucial ways that symmetry is used in fuzzy systems is in the solution of the linear Fuzzy Fredholm Integral Equation (FFIE), which has symmetric triangular (Fuzzy Interval) output and any fuzzy function input. Full article
(This article belongs to the Section Mathematics)
19 pages, 4067 KiB  
Article
Industrial Machinery Components Classification: A Case of D-S Pooling
by Amina Batool, Yaping Dai, Hongbin Ma and Sijie Yin
Symmetry 2023, 15(4), 935; https://doi.org/10.3390/sym15040935 - 19 Apr 2023
Cited by 1 | Viewed by 2704
Abstract
Industries are increasingly shifting towards unmanned and intelligent systems that require efficient processing and monitoring of structures across various applications, ranging from machine manufacturing to waste disposal. In order to achieve the goal of intelligent processing, it is crucial to accurately classify and [...] Read more.
Industries are increasingly shifting towards unmanned and intelligent systems that require efficient processing and monitoring of structures across various applications, ranging from machine manufacturing to waste disposal. In order to achieve the goal of intelligent processing, it is crucial to accurately classify and differentiate various components and parts. However, existing studies have not focused on simultaneously classifying electro-mechanical machinery components. This poses a challenge as these components, including capacitors, transistors, ICs, inductors, springs, locating pins, washers, nuts, and bolts, exhibit high intra- and inter-class similarity, making their accurate classification a tedious task. Furthermore, many of these components have symmetrical shapes but are asymmetrical among different classes. To address these challenges, this article introduces a new double-single (D-S) pooling method that focuses on the higher resemblance of seventeen electro-mechanical component classifications with minimum trainable parameters and achieves maximum accuracy. The industrial machine component classification model (IMCCM) consists of two convolutional neural network (CNN) blocks designed with a D-S pooling method that facilitates the model to effectively highlight the differences for the higher similar classes, and one block of grey-level co-occurrence matrix (GLCM) to strengthen the classification outcome. The extracted fused features from these three blocks are then forwarded to the random forest classifier to distinguish components. The accuracy achieved by this proposed model is 98.15%—outperforming the existing state of the arts (SOTAs) models, and has 141,346 trainable parameters– hence, highly effective for industrial implementation. Full article
(This article belongs to the Special Issue Artificial Intelligence, Adaptation and Symmetry/Asymmetry)
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2 pages, 168 KiB  
Editorial
Review of Contributions to the Special Edition: Symmetry in Integrable Systems: Theory and Application
by Bo Ren
Symmetry 2023, 15(4), 934; https://doi.org/10.3390/sym15040934 - 19 Apr 2023
Viewed by 889
Abstract
Nonlinear partial differential equations (NPDEs) are widely used to describe complex phenomena in various fields of science [...] Full article
(This article belongs to the Special Issue Symmetry in Integrable Systems: Theory and Application)
3 pages, 160 KiB  
Editorial
Noether and Space-Time Symmetries in Physics
by Ugur Camci, Bobomurat Ahmedov and Ashfaque H. Bokhari
Symmetry 2023, 15(4), 933; https://doi.org/10.3390/sym15040933 - 18 Apr 2023
Viewed by 1156
Abstract
Symmetry is the most common and important principle of those which guide efforts to construct realistic theories in science [...] Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics)
19 pages, 8142 KiB  
Article
Symmetrically Construction Monitoring Analysis and Completed State Evaluation of a Tied Steel Box Arch Bridge Based on Finite Element Method
by Jian Pan, Xirui Wang, Kainan Huang and Wensheng Wang
Symmetry 2023, 15(4), 932; https://doi.org/10.3390/sym15040932 - 18 Apr 2023
Cited by 1 | Viewed by 2434
Abstract
Because of their beautiful appearance, strong crossing ability, and reasonable stress performance, the application of tied steel box arch bridges is becoming more and more extensive. Bridge construction monitoring can control and adjust the deviation state to ensure the stress and linear state [...] Read more.
Because of their beautiful appearance, strong crossing ability, and reasonable stress performance, the application of tied steel box arch bridges is becoming more and more extensive. Bridge construction monitoring can control and adjust the deviation state to ensure the stress and linear state of the bridge after completion. This study carried out a symmetrical construction monitoring analysis and completed state evaluation of the newly built Dafeng River Bridge in Guangxi Province based on the finite element method. MIDAS Civil finite element software is used for simulation analysis to calculate the deformation and stress of the tied steel box arch bridge at the construction and completion stages. The tensile and compressive stress of the main arch and transverse brace, as well as the cumulative displacements of the main arch and lattice beam, are symmetrically distributed. The maximum tensile and compressive stresses are 15.1 MPa and 74.6 MPa, respectively, less than the specification’s allowable value. Meanwhile, for the completed bridge under the loading combinations of serviceability limit state and bearing capacity ultimate limit state, the stress of the main arch, transverse brace, and lattice beam meets the specification requirements. The maximum cable forces of the suspender and tie rod under the bearing capacity ultimate limit state are 2189.4 kN and 2991.2 kN, and their corresponding minimum safety factors are 3.2 and 2.7. In addition, the deviations between the on-site monitoring and the finite element theoretical values are within the specification allowable range for the cable force of the suspender and tie rod and the bridge deck alignment. It indicates that the bridge construction monitoring effect is reasonable and ideal, and the symmetrically finite element simulation analysis can provide a theoretical basis for construction monitoring. Full article
(This article belongs to the Special Issue Symmetry in the Finite Element Method and Finite Element Analysis)
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14 pages, 781 KiB  
Article
Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique
by Mohamed Adel, Mohamed M. Khader, Taghreed A. Assiri and Wajdi Kallel
Symmetry 2023, 15(4), 931; https://doi.org/10.3390/sym15040931 - 18 Apr 2023
Cited by 11 | Viewed by 1169
Abstract
The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation [...] Read more.
The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach’s accuracy and utility, and it is presented in symmetric forms. Full article
(This article belongs to the Section Mathematics)
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18 pages, 355 KiB  
Article
Feng-Liu’s Approach to Fixed Point Results of Intuitionistic Fuzzy Set-Valued Maps
by Mohammed Shehu Shagari, Trad Alotaibi, Rehana Tabassum, Awad A. Bakery, OM Kalthum S. K. Mohamed and Arafa O. Mustafa
Symmetry 2023, 15(4), 930; https://doi.org/10.3390/sym15040930 - 18 Apr 2023
Viewed by 1034
Abstract
The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. [...] Read more.
The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. Hence, the aim of this paper is to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. To this effect, the technique of κ-contraction and Feng-Liu’s approach are combined to establish new versions of intuitionistic fuzzy functional equations. One of the distinguishing ideas of this article is the study of fixed point theorems of intuitionistic fuzzy set-valued mappings without using the conventional Pompeiu–Hausdorff metric. Some of our obtained results are applied to examine their analogues in ordered metric-like spaces endowed with an order and binary relation as well as invariant point results of crisp set-valued mappings. By using a comparative example, it is observed that a few important corresponding notions in the existing literature are complemented, unified and generalized. Full article
(This article belongs to the Special Issue New Trends in Fixed Point Theory with Emphasis on Symmetry)
2 pages, 157 KiB  
Editorial
Mathematical Aspects in Non-Equilibrium Thermodynamics
by Róbert Kovács, Patrizia Rogolino and Francesco Oliveri
Symmetry 2023, 15(4), 929; https://doi.org/10.3390/sym15040929 - 17 Apr 2023
Viewed by 992
(This article belongs to the Special Issue Mathematical Aspects in Non-equilibrium Thermodynamics)
12 pages, 307 KiB  
Article
Fractional Stochastic Evolution Inclusions with Control on the Boundary
by Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy G. El-Sayed and Alaa Y. Elbadrawi
Symmetry 2023, 15(4), 928; https://doi.org/10.3390/sym15040928 - 17 Apr 2023
Cited by 4 | Viewed by 1055
Abstract
Symmetry in systems arises as a result of natural design and provides a pivotal mechanism for crucial system properties. In the field of control theory, scattered research has been carried out concerning the control of group-theoretic symmetric systems. In this manuscript, the principles [...] Read more.
Symmetry in systems arises as a result of natural design and provides a pivotal mechanism for crucial system properties. In the field of control theory, scattered research has been carried out concerning the control of group-theoretic symmetric systems. In this manuscript, the principles of stochastic analysis, the fixed-point theorem, fractional calculus, and multivalued map theory are implemented to investigate the null boundary controllability (NBC) of stochastic evolution inclusion (SEI) with the Hilfer fractional derivative (HFD) and the Clarke subdifferential. Moreover, an example is depicted to show the effect of the obtained results. Full article
(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)
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