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Symmetry, Volume 13, Issue 10 (October 2021) – 217 articles

Cover Story (view full-size image): Fullerene C60 can form bulky oligomeric molecules (C60)n. Their quantum-chemical description is challenging, so other theoretical approaches complement their digital portrait. We have studied the energy, topology, and symmetry of (C60)n combining density functional theory computations with topological indices and information entropy. The topological indices relate to the reactivities of the atoms, whereas information entropy is indicative in the aspect of the odd–even symmetry oscillations with n. Our findings allow predicting important properties of (C60)n with large n without heavy artillery of quantum chemistry. View this paper
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Article
Mobile Expert System: Exploring Context-Aware Machine Learning Rules for Personalized Decision-Making in Mobile Applications
Symmetry 2021, 13(10), 1975; https://doi.org/10.3390/sym13101975 - 19 Oct 2021
Cited by 2 | Viewed by 1314
Abstract
Expert systems, a form of artificial intelligence (AI), are typically designed to solve many real-world problems by reasoning through knowledge, which is primarily represented as IF–THEN rules, with the information acquired from humans or domain experts. However, to assume such rules for [...] Read more.
Expert systems, a form of artificial intelligence (AI), are typically designed to solve many real-world problems by reasoning through knowledge, which is primarily represented as IF–THEN rules, with the information acquired from humans or domain experts. However, to assume such rules for personalized decision-making in an intelligent, context-aware mobile application is a challenging issue. The reason is that different mobile users may behave differently in various day-to-day situations, i.e., not identical, and thus the rules for personalized services must be reflected according to their symmetrical or asymmetrical behavioral activities. Therefore, our key focus is to solve this issue through adding personalized decision-making intelligence to develop powerful mobile applications to assist the end-users. To achieve our goal, in this paper, we explore on “Mobile Expert System”, where we take into account machine-learning rules as knowledge-base rather than traditional handcrafted static rules. Thus, the concept of a mobile expert system enables the computing and decision-making processes more actionable and intelligent than traditional ones in the domain of mobile analytics and applications. Our experiment section shows that the context-aware machine learning rules discovered from users’ mobile phone data can contribute in building a mobile expert system to solve a particular problem, through making personalized decisions in various context-aware test cases. Full article
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Review
What Are the Synergies between Paleoanthropology and Brain Imaging?
Symmetry 2021, 13(10), 1974; https://doi.org/10.3390/sym13101974 - 19 Oct 2021
Cited by 2 | Viewed by 1620
Abstract
We are interested here in the central organ of our thoughts: the brain. Advances in neuroscience have made it possible to obtain increasing information on the anatomy of this organ, at ever-higher resolutions, with different imaging techniques, on ever-larger samples. At the same [...] Read more.
We are interested here in the central organ of our thoughts: the brain. Advances in neuroscience have made it possible to obtain increasing information on the anatomy of this organ, at ever-higher resolutions, with different imaging techniques, on ever-larger samples. At the same time, paleoanthropology has to deal with partial reflections on the shape of the brain, on fragmentary specimens and small samples in an attempt to approach the morphology of the brain of past human species. It undeniably emerges from the perspective we propose here that paleoanthropology has much to gain from interacting more with the field of neuroimaging. Improving our understanding of the morphology of the endocast necessarily involves studying the external surface of the brain and the link it maintains with the internal surface of the skull. The contribution of neuroimaging will allow us to better define the relationship between brain and endocast. Models of intra- and inter-species variability in brain morphology inferred from large neuroimaging databases will help make the most of the rare endocasts of extinct species. We also conclude that exchanges between these two disciplines will also be beneficial to our knowledge of the Homo sapiens brain. Documenting the anatomy among other human species and including the variation over time within our own species are approaches that offer us a new perspective through which to appreciate what really characterizes the brain of humanity today. Full article
(This article belongs to the Special Issue Symmetry in Human Evolution, from Biology to Behaviours)
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Article
Towards Potential Content-Based Features Evaluation to Tackle Meaningful Citations
Symmetry 2021, 13(10), 1973; https://doi.org/10.3390/sym13101973 - 19 Oct 2021
Cited by 1 | Viewed by 702
Abstract
The scientific community has presented various citation classification models to refute the concept of pure quantitative citation analysis systems wherein all citations are treated equally. However, a small number of benchmark datasets exist, which makes the asymmetric citation data-driven modeling quite complex. These [...] Read more.
The scientific community has presented various citation classification models to refute the concept of pure quantitative citation analysis systems wherein all citations are treated equally. However, a small number of benchmark datasets exist, which makes the asymmetric citation data-driven modeling quite complex. These models classify citations for varying reasons, mostly harnessing metadata and content-based features derived from research papers. Presently, researchers are more inclined toward binary citation classification with the belief that exploiting the datasets of incomplete nature in the best possible way is adequate to address the issue. We argue that contemporary ML citation classification models overlook essential aspects while selecting the appropriate features that hinder elutriating the asymmetric citation data. This study presents a novel binary citation classification model exploiting a list of potential natural language processing (NLP) based features. Machine learning classifiers, including SVM, KLR, and RF, are harnessed to classify citations into important and non-important classes. The evaluation is performed using two benchmark data sets containing a corpus of around 953 paper-citation pairs annotated by the citing authors and domain experts. The study outcomes exhibit that the proposed model outperformed the contemporary approaches by attaining a precision of 0.88. Full article
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Article
On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution
Symmetry 2021, 13(10), 1972; https://doi.org/10.3390/sym13101972 - 19 Oct 2021
Cited by 3 | Viewed by 775
Abstract
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in the terms of the boundary conditions. Uniform equiconvergence [...] Read more.
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in the terms of the boundary conditions. Uniform equiconvergence of spectral expansions related to the second-order differential equations with involution:y(x)+αy(x)+qxyx=λyx,1<x<1, with the boundary conditions y1+b1y1=0,y1+b2y1=0, is obtained. As a corollary, it is proved that the eigenfunctions of the perturbed boundary value problems form the basis in L2(1,1) for any complex-valued coefficient q(x)L1(1,1). Full article
Article
Improving the Convergence of Interval Single-Step Method for Simultaneous Approximation of Polynomial Zeros
Symmetry 2021, 13(10), 1971; https://doi.org/10.3390/sym13101971 - 19 Oct 2021
Viewed by 577
Abstract
This paper describes the extended method of solving real polynomial zeros problems using the single-step method, namely, the interval trio midpoint symmetric single-step (ITMSS) method, which updates the midpoint at each forward-backward-forward step. The proposed algorithm will constantly update the value of the [...] Read more.
This paper describes the extended method of solving real polynomial zeros problems using the single-step method, namely, the interval trio midpoint symmetric single-step (ITMSS) method, which updates the midpoint at each forward-backward-forward step. The proposed algorithm will constantly update the value of the midpoint of each interval of the previous roots before entering the preceding steps; hence, it always generate intervals that decrease toward the polynomial zeros. Theoretically, the proposed method possesses a superior rate of convergence at 16, while the existing methods are known to have, at most, 9. To validate its efficiency, we perform numerical experiments on 52 polynomials, and the results are presented, using performance profiles. The numerical results indicate that the proposed method surpasses the other three methods by fine-tuning the midpoint, which reduces the final interval width upon convergence with fewer iterations. Full article
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
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Article
Matching of Manufacturing Resources in Cloud Manufacturing Environment
Symmetry 2021, 13(10), 1970; https://doi.org/10.3390/sym13101970 - 19 Oct 2021
Cited by 3 | Viewed by 777
Abstract
With the introduction and application of new information technology in manufacturing, various advanced manufacturing models and national strategies have received more and more attention. The goal of cloud manufacturing is to closely link the resources and capabilities of manufacturers through a variety of [...] Read more.
With the introduction and application of new information technology in manufacturing, various advanced manufacturing models and national strategies have received more and more attention. The goal of cloud manufacturing is to closely link the resources and capabilities of manufacturers through a variety of services to create a dedicated platform for complex manufacturing process needs. How to achieve effective matching of various manufacturing resources and capabilities in the form of services will be a common problem in the future. In order to effectively improve cloud manufacturing tasks and resource matching efficiency and save resources, this study considers the common aspects of cloud manufacturing resource matching as service quality indicators, and extends the scope to the requirements of manufacturing resources, and the matching pattern of traditional service resources. There are additional restrictions on the resource service matching process. At the same time, the resource service matching is usually asymmetric. Therefore, we introduce the concept of task complexity of demand resources, and propose a combination system based on task complexity and service quality evaluation. The artificial bee colony algorithm (ABC) is used for analysis and verification. The experimental paper further validates the proposed the feasibility and efficiency of the method. Full article
(This article belongs to the Special Issue Cloud manufacturing and simulation for complex products)
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Article
Fast Computation of Green Function for Layered Seismic Field via Discrete Complex Image Method and Double Exponential Rules
Symmetry 2021, 13(10), 1969; https://doi.org/10.3390/sym13101969 - 19 Oct 2021
Cited by 3 | Viewed by 656
Abstract
A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for [...] Read more.
A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for the computation of the finite part. Estimation of signal parameters via rotational invariance techniques (ESPRIT) is used to improve the accuracy and efficiency of extracting DCIM compared to the generalized pencil of function (GPOF). Due to the symmetry of the horizontal layered media, the Green function, representing the seismic fields due to a point source, can be written in the form of Sommerfeld integral in cylindrical coordinate system and be calculated by the proposed method. The performance of the method is then compared to the DE rules with weighted average partition extrapolation (WA), which shows a good agreement, with computational time reduced by about 40%. Full article
(This article belongs to the Topic Applied Metaheuristic Computing)
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Review
Multifractal Model for Transient Phenomena Analysis in Laser Produced Plasmas
Symmetry 2021, 13(10), 1968; https://doi.org/10.3390/sym13101968 - 19 Oct 2021
Cited by 1 | Viewed by 740
Abstract
The pulsed laser deposition process is a complex one, encompassing a wide range of physical phenomena that act at different time scales, ranging from laser absorption to melting, plasma formation, and thin film deposition. In the past 15 years, there has been an [...] Read more.
The pulsed laser deposition process is a complex one, encompassing a wide range of physical phenomena that act at different time scales, ranging from laser absorption to melting, plasma formation, and thin film deposition. In the past 15 years, there has been an exponential increase in theoretical models for different aspects of laser ablation phenomena, especially laser-produced plasmas. Among these. new types of models based on multifractal physics have been proposed. The models aim to describe the various dynamics reported for laser-produced plasmas in both the multifractal-type Schrodinger representation and in the multifractal-type hydrodynamic representation. The two approaches are complementary, as the Schrodinger representation uses operation procedures (invariance groups, variational principles, harmonic maps, etc.) while the hydrodynamic representation translates the dynamics of the laser-produced plasma into fluid motion of a multifractal type. The aim of this review is to report on the wide range of dynamics that can be discussed within the framework of a multifractal approach to plasma dynamics. Full article
(This article belongs to the Special Issue Exploring Transient Phenomena at Various Interaction Scales)
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Review
On Markov Moment Problem, Polynomial Approximation on Unbounded Subsets, and Mazur–Orlicz Theorem
Symmetry 2021, 13(10), 1967; https://doi.org/10.3390/sym13101967 - 18 Oct 2021
Viewed by 679
Abstract
We review earlier and recent results on the Markov moment problem and related polynomial approximation on unbounded subsets. Such results allow proving the existence and uniqueness of the solutions for some Markov moment problems. This is the first aim of the paper. Our [...] Read more.
We review earlier and recent results on the Markov moment problem and related polynomial approximation on unbounded subsets. Such results allow proving the existence and uniqueness of the solutions for some Markov moment problems. This is the first aim of the paper. Our solutions have a codomain space a commutative algebra of (linear) symmetric operators acting from the entire real or complex Hilbert space H to H; this algebra of operators is also an order complete Banach lattice. In particular, Hahn–Banach type theorems for the extension of linear operators having a codomain such a space can be applied. The truncated moment problem is briefly discussed by means of reference citations. This is the second purpose of the paper. In the end, a general extension theorem for linear operators with two constraints is recalled and applied to concrete spaces. Here polynomial approximation plays no role. This is the third aim of this work. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods)
Article
Approximation Solution of the Nonlinear Circular Sitnikov Restricted Four–Body Problem
Symmetry 2021, 13(10), 1966; https://doi.org/10.3390/sym13101966 - 18 Oct 2021
Cited by 4 | Viewed by 724
Abstract
In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated [...] Read more.
In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt–Poincaré method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt–Poincaré method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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Article
Research on the New Topology and Coordinated Control Strategy of Renewable Power Generation Connected MMC-Based DC Power Grid Integration System
Symmetry 2021, 13(10), 1965; https://doi.org/10.3390/sym13101965 - 18 Oct 2021
Cited by 3 | Viewed by 1119
Abstract
The modular multilevel converter (MMC) station connected to the islanded renewable energy generation system needs to adopt the voltage frequency (VF) control to provide AC voltage. The single-pole converter fault will unbalance the input and output power of the DC power grid, which [...] Read more.
The modular multilevel converter (MMC) station connected to the islanded renewable energy generation system needs to adopt the voltage frequency (VF) control to provide AC voltage. The single-pole converter fault will unbalance the input and output power of the DC power grid, which causes the DC voltage or the bridge arm current of the non-fault pole to exceed the protection value in the time scale of tens to hundreds of milliseconds, leading to cascading failures. To realize the fault ride-through (FRT) of single-pole converter fault, this paper analyzes the electrical characteristic of the system. Based on the analysis, the existing topology is optimized and the reasonable operation reserved margin is designed. Furthermore, the corresponding control strategy is proposed, which can not only ensure the single-pole converter block fault ride-through but can also realize economic, stable, and resilient power supply and address asymmetrical problems. Finally, the simulation model is built in PSCAD/EMTDC and the simulation results validate the effectiveness of the proposed control strategy. Full article
(This article belongs to the Special Issue Advanced Technologies in Electrical and Electronic Engineering)
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Article
Further Results on the IDCPE Class of Life Distributions
Symmetry 2021, 13(10), 1964; https://doi.org/10.3390/sym13101964 - 18 Oct 2021
Viewed by 612
Abstract
Navarro et al. (2010) proposed the increasing dynamic cumulative past entropy (IDCPE) class of life distributions. In this paper, we investigate some characterizations of this class. Closure and reversed closure properties of the IDCPE class are obtained. As applications of a main result, [...] Read more.
Navarro et al. (2010) proposed the increasing dynamic cumulative past entropy (IDCPE) class of life distributions. In this paper, we investigate some characterizations of this class. Closure and reversed closure properties of the IDCPE class are obtained. As applications of a main result, we explore the preservation and reversed preservation properties of this class in several stochastic models. We also investigate preservation and reversed preservation of the IDCPE class for coherent systems with dependent and identically distributed components. Full article
Article
Exact Closed-Form Solutions of the Motion in Non-Inertial Reference Frames, Using the Properties of Lie Groups SO3 and SE3
Symmetry 2021, 13(10), 1963; https://doi.org/10.3390/sym13101963 - 18 Oct 2021
Viewed by 740
Abstract
The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group [...] Read more.
The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group of the rigid body displacements, SE3. We obtain a simplified form of the initial value problem that models the non-inertial motion using a tensor instrument introduced in this paper. Thus, the study of the motion in a non-inertial reference frame is transferred into the study of a classical motion in an inertial reference frame. The applications of this method refer to solving the relative motion problem and deriving the straightforward solution to classical theoretical mechanics problems. The motion in a uniform gravitational force field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, the exact solution of the relative rigid body motion in the non-inertial reference frame are studied. Using this symbolic method in studying the motion in a non-inertial reference frame reduces the number of computations. In addition, it offers, in some essential particular cases, exact closed-form coordinate-free analytical solutions. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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Article
Double Integral of the Product of the Exponential of an Exponential Function and a Polynomial Expressed in Terms of the Lerch Function
Symmetry 2021, 13(10), 1962; https://doi.org/10.3390/sym13101962 - 18 Oct 2021
Viewed by 718
Abstract
In this work, the authors use their contour integral method to derive an application of the Fourier integral theorem given by [...] Read more.
In this work, the authors use their contour integral method to derive an application of the Fourier integral theorem given by emxmyexey+y(log(a)+xy)kdxdy in terms of the Lerch function. This integral formula is then used to derive closed solutions in terms of fundamental constants and special functions. Almost all Lerch functions have an asymmetrical zero distribution. There are some useful results relating double integrals of certain kinds of functions to ordinary integrals for which we know no general reference. Thus, a table of integral pairs is given for interested readers. All of the results in this work are new. Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications)
Article
Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics
Symmetry 2021, 13(10), 1961; https://doi.org/10.3390/sym13101961 - 18 Oct 2021
Cited by 3 | Viewed by 546
Abstract
In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the [...] Read more.
In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
Article
Further Results of the TTT Transform Ordering of Order n
Symmetry 2021, 13(10), 1960; https://doi.org/10.3390/sym13101960 - 18 Oct 2021
Viewed by 512
Abstract
To compare the variability of two random variables, we can use a partial order relation defined on a distribution class, which contains the anti-symmetry. Recently, Nair et al. studied the properties of total time on test (TTT) transforms of order n and examined [...] Read more.
To compare the variability of two random variables, we can use a partial order relation defined on a distribution class, which contains the anti-symmetry. Recently, Nair et al. studied the properties of total time on test (TTT) transforms of order n and examined their applications in reliability analysis. Based on the TTT transform functions of order n, they proposed a new stochastic order, the TTT transform ordering of order n (TTT-n), and discussed the implications of order TTT-n. The aim of the present study is to consider the closure and reversed closure of the TTT-n ordering. We examine some characterizations of the TTT-n ordering, and obtain the closure and reversed closure properties of this new stochastic order under several reliability operations. Preservation results of this order in several stochastic models are investigated. The closure and reversed closure properties of the TTT-n ordering for coherent systems with dependent and identically distributed components are also obtained. Full article
Article
Study of the Association between Postural Misalignments in School Students
Symmetry 2021, 13(10), 1959; https://doi.org/10.3390/sym13101959 - 18 Oct 2021
Viewed by 851
Abstract
Nowadays, postural misalignments prevalence in students is increasingly evident and its early detection is the best way to prevent complications in adulthood. It is also known that postural problems appear to have association between them. The aim of this study was to characterize [...] Read more.
Nowadays, postural misalignments prevalence in students is increasingly evident and its early detection is the best way to prevent complications in adulthood. It is also known that postural problems appear to have association between them. The aim of this study was to characterize and study the association between spine, scapular and pelvic girdles postural misalignments in 213 school students (124 males and 89 females), aged between 10 and 20 years, from Escola Básica e Secundária de Santa Maria (EBSSM). To understand the relation between postural misalignments we compare the head positioning with the shoulder girdle, the shoulder girdle with the dorsal spine and the lumbar spine with the pelvic girdle. The postural assessment was made by visual scan analysis in a symmetrograph based on photogrammetry and the Adams. We found high percentages of postural misalignments in all subjects. High prevalence was observed in the posterior view of the frontal plane in the head lateral flexion, shoulders vertical asymmetry, scoliosis and in the presence of gibbosity, whereas, in the right view of the sagittal plane forward head posture and protracted shoulders were observed. The lumbar scoliosis was more prevalent in subjects with iliac crest’s asymmetry (p < 0.001) and forward head posture was significantly related to the subjects with protracted shoulders (p = 0.010). The protracted shoulders were more prevalent in subjects with dorsal hyperkyphosis (p = 0.048) and lumbar hyperlordosis was related to the subjects with pelvic anteversion (p < 0.001). The students’ postural assessment showed a wide variety of postural misalignments. It also seems evident that there is a relationship between their occurrences. It should be highlighted the importance of postural assessment in physical education (PE) classes to determine postural misalignments among school students. Full article
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Article
Comparison Study on the Performance of a Novel and Traditional Energy Piles by Laboratory Tests
Symmetry 2021, 13(10), 1958; https://doi.org/10.3390/sym13101958 - 18 Oct 2021
Cited by 2 | Viewed by 797
Abstract
Phase change material (PCM) is a substance that can absorb or release sufficient latent heat at phase transition. By encapsulating phase change paraffin in hollow steel balls in the concrete, an energy pile with PCM was innovatively produced to improve energy efficiency for [...] Read more.
Phase change material (PCM) is a substance that can absorb or release sufficient latent heat at phase transition. By encapsulating phase change paraffin in hollow steel balls in the concrete, an energy pile with PCM was innovatively produced to improve energy efficiency for the ground heat pumping system. Laboratory tests were carried out on both PCM energy pile and traditional concrete pile to evaluate the thermo mechanical performance. Two piles were heated and cooled through inside tubes at a constant flow rate. The laboratory tests on the two piles were symmetrical for the two horizontal directions in geometry, and heat transfer process follows conservation laws of energy. The temperature response of the pile and soil, internal strain, pile displacement, pore pressure, and soil pressure under heating-cooling cycles were examined. Compared with the traditional concrete pile, the PCM energy pile can effectively reduce the surrounding soil temperature. The use of PCM in the pile can improve the capacity of heat storage and make the pile more effective in heat exchange. Non-uniform thermal strain and accumulations of heat and irrecoverable displacement were observed in the repeated heating-cooling process. The study can provide references for the practical implication of PCM energy piles. Full article
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Article
An Ulm-Type Inverse-Free Iterative Scheme for Fredholm Integral Equations of Second Kind
Symmetry 2021, 13(10), 1957; https://doi.org/10.3390/sym13101957 - 17 Oct 2021
Viewed by 565
Abstract
In this paper, we present an iterative method based on the well-known Ulm’s method to numerically solve Fredholm integral equations of the second kind. We support our strategy in the symmetry between two well-known problems in Numerical Analysis: the solution of linear integral [...] Read more.
In this paper, we present an iterative method based on the well-known Ulm’s method to numerically solve Fredholm integral equations of the second kind. We support our strategy in the symmetry between two well-known problems in Numerical Analysis: the solution of linear integral equations and the approximation of inverse operators. In this way, we obtain a two-folded algorithm that allows us to approximate, with quadratic order of convergence, the solution of the integral equation as well as the inverses at the solution of the derivative of the operator related to the problem. We have studied the semilocal convergence of the method and we have obtained the expression of the method in a particular case, given by some adequate initial choices. The theoretical results are illustrated with two applications to integral equations, given by symmetric non-separable kernels. Full article
(This article belongs to the Special Issue Recent Advances and Application of Iterative Methods)
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Article
Identification of Ship Dynamics Model Based on Sparse Gaussian Process Regression with Similarity
Symmetry 2021, 13(10), 1956; https://doi.org/10.3390/sym13101956 - 17 Oct 2021
Cited by 3 | Viewed by 851
Abstract
The system identification of a ship dynamics model is crucial for the intelligent navigation and design of the ship’s controller. The fluid dynamic effect and the complicated geometry of the hull surface cause a nonlinear or asymmetrical behavior, and it is extremely difficult [...] Read more.
The system identification of a ship dynamics model is crucial for the intelligent navigation and design of the ship’s controller. The fluid dynamic effect and the complicated geometry of the hull surface cause a nonlinear or asymmetrical behavior, and it is extremely difficult to establish a ship dynamics model. A nonparametric model based on sparse Gaussian process regression with similarity was proposed for the dynamic modeling of a ship. It solves the problem, wherein the kernel method is difficult to apply to big data, using similarity to sparse large sample datasets. In addition, the experimental data of the KVLCC2 ship are used to verify the validity of the proposed method. The results show that sparse Gaussian process regression with similarity can be applied to the learning of a large sample data, in order to obtain ship motion prediction with higher accuracy than the parameterized model. Moreover, in the case of sensor signal loss, the identified model continues to provide accurate ship speed and trajectory information in the future, and the maximum prediction error of the motion trajectory within 100 s is only 0.59 m. Full article
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Article
A Study of Improving Running Safety of a Railway Wagon with an Independently Rotating Wheel’s Flange
Symmetry 2021, 13(10), 1955; https://doi.org/10.3390/sym13101955 - 17 Oct 2021
Cited by 2 | Viewed by 820
Abstract
The main objective of this work is to study the possibilities of improving the running safety of a railway wagon with independently rotating wheels by changing their design symmetrically mounted on an axle. The article provides a discussion of the advantages and disadvantages [...] Read more.
The main objective of this work is to study the possibilities of improving the running safety of a railway wagon with independently rotating wheels by changing their design symmetrically mounted on an axle. The article provides a discussion of the advantages and disadvantages of using the independently rotating wheels in a bogie of railway wagons. Their increasing tendency of derailment is described. The influence of a perspective constructive scheme (PKS) of railway wagon wheels in comparison with a traditional constructive scheme (TKS) on running safety due to the climbing of a wheel flange onto a rail is studied. This work introduces a conceptual proposition of a technical solution to railway wheel design as well as containing the results of both analytical calculations as well as the results of multibody simulations. A PKS wheel design for a railway wheel is designed that allows independent rotation of its tread surface and of a guiding surface (i.e., of a flange) to each other, which both are arranged symmetrically on a wheelset axle. It brings features of the distribution of friction forces generating in a flange contact when the wheel with a TKS and with PKS move on a rail. It is possible to conclude with the help of the obtained results that the use of wheels with the PKS is advisable for the reduction of the running resistance as well as for increasing the running safety of railway wagons. Full article
(This article belongs to the Section Computer Science and Symmetry/Asymmetry)
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Article
Modelling Heterogeneity and Super Spreaders of the COVID-19 Spread through Malaysian Networks
Symmetry 2021, 13(10), 1954; https://doi.org/10.3390/sym13101954 - 16 Oct 2021
Viewed by 965
Abstract
Malaysia is multi-ethnic and diverse country. Heterogeneity, in terms of population interactions, is ingrained in the foundation of the country. Malaysian policies and social distancing measures are based on daily infections and R0 (average number of infections per infected person), estimated from the [...] Read more.
Malaysia is multi-ethnic and diverse country. Heterogeneity, in terms of population interactions, is ingrained in the foundation of the country. Malaysian policies and social distancing measures are based on daily infections and R0 (average number of infections per infected person), estimated from the data. Models of the Malaysian COVID-19 spread are mostly based on the established SIR compartmental model and its variants. These models usually assume homogeneity and symmetrical full mixing in the population; thus, they are unable to capture super-spreading events which naturally occur due to heterogeneity. Moreover, studies have shown that when heterogeneity is present, R0 may be very different and even possibly misleading. The underlying spreading network is a crucial element, as it introduces heterogeneity for a more representative and realistic model of the spread through specific populations. Heterogeneity introduces more complexities in the modelling due to its asymmetrical nature of infection compared to the relatively symmetrical SIR compartmental model. This leads to a different way of calculating R0 and defining super-spreaders. Quantifying a super-spreader individual is related to the idea of importance in a network. The definition of a super-spreading individual depends on how super-spreading is defined. Even when the spreading is defined, it may not be clear that a single centrality always correlates with super-spreading, since centralities are network dependent. We proposed using a measure of super-spreading directly related to R0 and that will give a measure of ‘spreading’ regardless of the underlying network. We captured the vulnerability for varying degrees of heterogeneity and initial conditions by defining a measure to quantify the chances of epidemic spread in the simulations. We simulated the SIR spread on a real Malaysian network to illustrate the effects of this measure and heterogeneity on the number of infections. We also simulated super-spreading events (based on our definition) within the bounds of heterogeneity to demonstrate the effectiveness of the newly defined measure. We found that heterogeneity serves as a natural curve-flattening mechanism; therefore, the number of infections and R0 may be lower than expected. This may lead to a false sense of security, especially since heterogeneity makes the population vulnerable to super-spreading events. Full article
(This article belongs to the Special Issue Topological Graph Theory and Discrete Geometry)
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Article
Cortical Activation in Mental Rotation and the Role of the Corpus Callosum: Observations in Healthy Subjects and Split-Brain Patients
Symmetry 2021, 13(10), 1953; https://doi.org/10.3390/sym13101953 - 16 Oct 2021
Cited by 1 | Viewed by 927
Abstract
The mental rotation (MR) is an abstract mental operation thanks to which a person imagines rotating an object or a body part to place it in an other position. The ability to perform MR was belived to belong to the right hemisphere for [...] Read more.
The mental rotation (MR) is an abstract mental operation thanks to which a person imagines rotating an object or a body part to place it in an other position. The ability to perform MR was belived to belong to the right hemisphere for objects, and to the left for one’s ownbody images. Mental rotation is considered to be basic for imitation with the anatomical perspective, which in turn is needed for social interactions and learning. Altered imitative performances have been reported in patients with resections or microstructure alterations of the corpus callosum (CC). These patients also display a reduced MR ability compared to control subjects, as shown in a recent behavioral study. The difference was statistically significant, leading us to hypothesize a role of the CC to integrate the two hemispheres’ asymmetric functions. The present study was designed to detect, by means of a functional MRI, the cortical activation evoked during an MR task in healthy control subjects and callosotomized patients. The results suggest that performing MR requires activation of opercular cortex and inferior parietal lobule in either hemispheres, and likely the integrity of the CC, thus confirming that the main brain commissure is involved in cognitive functions. Full article
(This article belongs to the Special Issue Brain, Behavior and Cognition)
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Article
Security and Privacy Analysis of Vinoth et al.’s Authenticated Key Agreement Scheme for Industrial IoT
Symmetry 2021, 13(10), 1952; https://doi.org/10.3390/sym13101952 - 16 Oct 2021
Cited by 1 | Viewed by 796
Abstract
Vinoth et al. proposed an authenticated key agreement scheme for industrial IoT (Internet of Things) applications. Vinoth et al.’s scheme aimed to protect the remote sensing data of industrial IoT devices under hostile environments. The scheme is interesting because the authorized user is [...] Read more.
Vinoth et al. proposed an authenticated key agreement scheme for industrial IoT (Internet of Things) applications. Vinoth et al.’s scheme aimed to protect the remote sensing data of industrial IoT devices under hostile environments. The scheme is interesting because the authorized user is allowed simultaneously to access the multiple IoT sensing devices. Therefore, we carefully analyzed the security and privacy implications of Vinoth et al.’s scheme. Our findings are summarized as follows. One, Vinoth et al.’s scheme failed to defeat user impersonation attacks. Second, Vinoth et al.’s scheme did not prevent IoT sensing device impersonation attacks. Third, Vinoth et al.’s scheme suffered from replay attacks. Fourth, Vinoth et al.’s scheme was vulnerable to desynchronization attacks. Fifth, Vinoth et al.’s scheme could not maintain user privacy. As a case study, our analysis results enlighten researchers and engineers on the design of robust and efficient authenticated key agreement schemes for IoT applications. Full article
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Article
Preliminary Study on the Loss Laws of Bearing Capacity of Tunnel Structure
Symmetry 2021, 13(10), 1951; https://doi.org/10.3390/sym13101951 - 16 Oct 2021
Cited by 2 | Viewed by 611
Abstract
The bearing capacity of the tunnel structure is the essential basis for the structural safety of tunnel engineering. Due to the unpredictability and uncertainty in the tunnel’s surrounding environment, a systematic and unambiguous study on the bearing capacity of the tunnel structure is [...] Read more.
The bearing capacity of the tunnel structure is the essential basis for the structural safety of tunnel engineering. Due to the unpredictability and uncertainty in the tunnel’s surrounding environment, a systematic and unambiguous study on the bearing capacity of the tunnel structure is still lacking. The analysis framework of the bearing capacity of the tunnel structure is discussed and a method describing the bearing capacity loss of the tunnel structure is proposed in this paper. Furthermore, the loss laws of the tunnel structure bearing capacity under various characteristic factors are preliminarily investigated, and suggestions on the research of bearing capacity are put forward. First, the current research contents and methods of the tunnel structure technical status, mechanical characteristics, and bearing performance (directly mentioned) are summarized, the relevant concepts related to tunnel structure bearing capacity are analyzed, and it is clarified that the bearing capacity loss of the tunnel structure can be considered according to the technical status of lining damage preliminary. Then, based on analysis of main causes and influence path of the bearing capacity loss, the influencing factors of the bearing capacity of the tunnel structure are attributed to external load action (i.e., all external causes acting on the tunnel structure in the form of external loads) and material deterioration (i.e., all internal causes leading to the decrease in mechanical properties such as structure strength/stiffness). Several typical factors are listed with specific examples, respectively. Considering the uncertainty of the absolute value of the bearing capacity caused by the surrounding environment of the tunnel, a method describing the bearing capacity of the tunnel structure using relative loss rate and relative value of index is proposed based on the current relevant analysis data of mechanical characteristics of the tunnel structure. Based on the given definitions and rules, the related data on the quantitative analysis of mechanical characteristics of lining structure reported in the literature are statistically analyzed again from the view of loss laws of the bearing capacity. Taking three factors including crack, insufficient lining thickness, and cavity as examples, the corresponding model of the bearing capacity loss is preliminarily analyzed and interpreted. The simplest linear model can be employed to preliminarily describe the relationship between defect indexes and relative loss rate of the bearing capacity, especially pertinent mechanical data collected from numerical analysis. Moreover, the loss laws of the bearing capacity in practical analysis and model tests (especially when the variation range of factors is wide) can be simulated by a logistic growth model. Through the analysis of the typical factor model, the key points of the research on the bearing capacity of the tunnel structure are discussed, and some suggestions are put forward for the follow-up related research. Full article
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Article
DFT Insights into the Hydrodenitrogenation and Ring-Opening of Indole on an M (M = Ni, Pt, Ni–Pt) Slab Model
Symmetry 2021, 13(10), 1950; https://doi.org/10.3390/sym13101950 - 16 Oct 2021
Viewed by 775
Abstract
Density functional theory (DFT) calculation has been used to study the hydrodenitrogenation (HDN) and ring-opening of indole on an M (M = Ni, Pt, Ni–Pt) slab surface. The possible reaction pathway of indole hydrogenation has been investigated in order to reveal the bimetallic [...] Read more.
Density functional theory (DFT) calculation has been used to study the hydrodenitrogenation (HDN) and ring-opening of indole on an M (M = Ni, Pt, Ni–Pt) slab surface. The possible reaction pathway of indole hydrogenation has been investigated in order to reveal the bimetallic synergistic effects of an M slab surface. Compared to the mechanism of indole hydrogenation on an M slab surface, it was found that a PtNi(111) surface favors indole hydrogenation. According to the results of DFT calculation, it suggests that the bimetallic effect of the M surface plays an important role in indole hydrogenation. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
DNA Structure and the Golden Ratio Revisited
Symmetry 2021, 13(10), 1949; https://doi.org/10.3390/sym13101949 - 16 Oct 2021
Cited by 1 | Viewed by 2109
Abstract
B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing [...] Read more.
B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life. Full article
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Article
On (2-d)-Kernels in Two Generalizations of the Petersen Graph
Symmetry 2021, 13(10), 1948; https://doi.org/10.3390/sym13101948 - 16 Oct 2021
Cited by 1 | Viewed by 708
Abstract
A subset J is a (2-d)-kernel of a graph if J is independent and 2-dominating simultaneously. In this paper, we consider two different generalizations of the Petersen graph and we give complete characterizations of these graphs which have [...] Read more.
A subset J is a (2-d)-kernel of a graph if J is independent and 2-dominating simultaneously. In this paper, we consider two different generalizations of the Petersen graph and we give complete characterizations of these graphs which have (2-d)-kernel. Moreover, we determine the number of (2-d)-kernels of these graphs as well as their lower and upper kernel number. The property that each of the considered generalizations of the Petersen graph has a symmetric structure is useful in finding (2-d)-kernels in these graphs. Full article
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Article
On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain
Symmetry 2021, 13(10), 1947; https://doi.org/10.3390/sym13101947 - 16 Oct 2021
Cited by 9 | Viewed by 741
Abstract
Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to [...] Read more.
Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class kSTqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class kSTqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included. Full article
(This article belongs to the Special Issue Complex Analysis, in Particular Analytic and Univalent Functions)
Article
Inner Product Groups and Riesz Representation Theorem
Symmetry 2021, 13(10), 1946; https://doi.org/10.3390/sym13101946 - 15 Oct 2021
Cited by 1 | Viewed by 619
Abstract
In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and describe [...] Read more.
In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and describe the norms induced by such inner products. Among other results, Hilbert groups, midconvex and orthogonal subgroups are presented, and a Riesz representation theorem on divisible Hilbert groups is proved. Full article
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
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