Editor's Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to authors, or important in this field. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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Article

Article
Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams
Symmetry 2020, 12(12), 1935; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12121935 - 24 Nov 2020
Cited by 17
Abstract
We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. [...] Read more.
We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Article
Tetra- and Penta-Quark Structures in the Constituent Quark Model
Symmetry 2020, 12(11), 1869; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111869 - 13 Nov 2020
Cited by 22
Abstract
With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the [...] Read more.
With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the Gaussian expansion method, has been employed systematically in real- and complex-range investigations. We review herein the double- and fully-heavy tetraquarks, but also the hidden-charm, hidden-bottom and doubly charmed pentaquarks. Several exotic hadrons observed experimentally were well reproduced within our approach; moreover, their possible compositeness and other properties, such as their decay widths and general patterns in the spectrum, are analyzed. Besides, we report also some theoretical predictions of tetra- and penta-quark states which have not seen by experiment yet. Full article
(This article belongs to the Special Issue Advances in Chiral Quark Models)
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Article
On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic
Symmetry 2020, 12(10), 1646; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101646 - 07 Oct 2020
Cited by 10
Abstract
This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability [...] Read more.
This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks. Full article
(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)
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Article
Exploring Possible Triangle Singularities in the Ξ b − → K − J / ψ Λ Decay
Symmetry 2020, 12(10), 1611; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101611 - 28 Sep 2020
Cited by 13
Abstract
We analyze possible singularities in the J/ψΛ invariant mass distribution of the ΞbKJ/ψΛ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop [...] Read more.
We analyze possible singularities in the J/ψΛ invariant mass distribution of the ΞbKJ/ψΛ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with Ξ*-charmonium-Λ intermediate states, the one from the χc1Ξ(2120)Λ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs S- and P-waves in χc1Λ and J/ψΛ systems, respectively, when the quantum numbers of these systems are 1/2+ or 3/2+. When the quantum numbers of the Ξ(2120) are JP=1/2+, 1/2 or 3/2+, the peak structure should be sharper than the other JP choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the Ξ*-charmonium-Λ triangle diagram if structures are observed in the J/ψΛ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the Ds1*(2700) as one of the intermediate particles can also produce singularities in the J/ψΛ distribution, but at higher energies above 4.9 GeV. Full article
(This article belongs to the Special Issue Advances in Chiral Quark Models)
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Article
Clar Covers of Overlapping Benzenoids: Case of Two Identically-Oriented Parallelograms
Symmetry 2020, 12(10), 1599; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101599 - 25 Sep 2020
Cited by 7
Abstract
We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons Rb, parallelograms M, vertically overlapping parallelograms MvM, horizontally [...] Read more.
We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons Rb, parallelograms M, vertically overlapping parallelograms MvM, horizontally overlapping parallelograms MhM, and intersecting parallelograms MxM. All formulas have the form of multiple sums over binomial coefficients. Three of the formulas are given with a proof based on the interface theory of benzenoids, while the remaining two formulas are presented as conjectures verified via extensive numerical tests. Both of the conjectured formulas have the form of a 2×2 determinant bearing close structural resemblance to analogous formulas for the number of Kekulé structures derived from the John-Sachs theory of Kekulé structures. Full article
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Article
A New Approach to Identifying a Multi-Criteria Decision Model Based on Stochastic Optimization Techniques
Symmetry 2020, 12(9), 1551; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091551 - 20 Sep 2020
Cited by 24
Abstract
Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet [...] Read more.
Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet identification of preferences makes it impossible to determine the preferences for new alternatives. In this work, we propose a new approach to identifying a multi-criteria decision model to address this challenge. Our proposal is based on stochastic optimization techniques and the characteristic objects method (COMET). An extensive work comparing the use of hill-climbing, simulated annealing, and particle swarm optimization algorithms are presented in this paper. The paper also contains preliminary studies on initial conditions. Finally, our approach has been demonstrated using a simple numerical example. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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Article
Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods
Symmetry 2020, 12(9), 1549; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091549 - 20 Sep 2020
Cited by 84
Abstract
Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) [...] Read more.
Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) methods. To achieve that, a set of feasible MCDA methods was identified. Based on reference literature guidelines, a simulation experiment was planned. The formal foundations of the authors’ approach provide a reference set of MCDA methods ( Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), and PROMETHEE II: Preference Ranking Organization Method for Enrichment of Evaluations) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). This allowed the generation of a set of models differentiated by the number of attributes and decision variants, as well as similarity research for the obtained rankings sets. As the authors aim to build a complex benchmarking model, additional dimensions were taken into account during the simulation experiments. The aspects of the performed analysis and benchmarking methods include various weighing methods (results obtained using entropy and standard deviation methods) and varied techniques of normalization of MCDA model input data. Comparative analyses showed the detailed influence of values of particular parameters on the final form and a similarity of the final rankings obtained by different MCDA methods. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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Article
Empirical Consequences of Emergent Mass
Symmetry 2020, 12(9), 1468; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091468 - 07 Sep 2020
Cited by 27
Abstract
The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The [...] Read more.
The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD’s self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD’s process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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Article
Increase in Absolute Leaf Water Content Tends to Keep Pace with That of Leaf Dry Mass—Evidence from Bamboo Plants
Symmetry 2020, 12(8), 1345; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081345 - 12 Aug 2020
Cited by 6
Abstract
Leaves, as the most important photosynthetic organ of plants, are intimately associated with plant function and adaptation to environmental changes. The scaling relationship of the leaf dry mass (or the fresh mass) vs. leaf surface area has been referred to as “diminishing returns”, [...] Read more.
Leaves, as the most important photosynthetic organ of plants, are intimately associated with plant function and adaptation to environmental changes. The scaling relationship of the leaf dry mass (or the fresh mass) vs. leaf surface area has been referred to as “diminishing returns”, suggesting that the leaf area fails to increase in proportion to leaf dry mass (or fresh mass). However, previous studies used materials across different families, and there is lack of studies testing whether leaf fresh mass is proportional to the leaf dry mass for the species in the same family, and examining the influence of the scaling of leaf dry mass vs. fresh mass on two kinds of diminishing returns based on leaf dry mass and fresh mass. Bamboo plants (Poaceae: Bambusoideae) are good materials for doing such a study, which have astonishingly similar leaf shapes across species. Bamboo leaves have a typical parallel venation pattern. In general, a parallel venation pattern tends to produce a more stable symmetrical leaf shape than the pinnate and palmate venation patterns. The symmetrical parallel veins enable leaves to more regularly hold water, which is more likely to result in a proportional relationship between the leaf dry mass and absolute water content, which consequently determines whether the scaling exponent of the leaf dry mass vs. area is significantly different from (or the same as) that of the leaf fresh mass vs. area. In the present study, we used the data of 101 bamboo species, cultivars, forms and varieties (referred to as 101 (bamboo) taxa below for convenience) to analyze the scaling relationships between the leaf dry mass and area, and between leaf fresh mass and area. We found that the confidence intervals of the scaling exponents of the leaf fresh mass vs. dry mass of 68 out of the 101 taxa included unity, which indicates that for most bamboo species (67.3%), the increase in leaf water mass keeps pace with that of leaf dry mass. There was a significant scaling relationship between either leaf dry mass or fresh mass, and the leaf surface area for each studied species. We found that there was no significant difference between the scaling exponent of the leaf dry mass vs. leaf area and that of the leaf fresh mass vs. leaf area when the leaf dry mass was proportional to the leaf fresh mass. The goodness of fit to the linearized scaling relationship of the leaf fresh mass vs. area was better than that of the leaf dry mass vs. area for each of the 101 bamboo taxa. In addition, there were significant differences in the normalized constants of the leaf dry mass vs. fresh mass among the taxa (i.e., the differences in leaf water content), which implies the difference in the adaptabilities to different environments across the taxa. Full article
(This article belongs to the Section Chemistry and Symmetry/Asymmetry)
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Article
Fluctuating Asymmetry in Morphological Characteristics of Betula Pendula Roth Leaf under Conditions of Urban Ecosystems: Evaluation of the Multi-Factor Negative Impact
Symmetry 2020, 12(8), 1317; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081317 - 06 Aug 2020
Cited by 4
Abstract
The fluctuating asymmetry (FA) in Betula pendula Roth was estimated as an integrated measure of five morphometric characteristics of a lamina. Samples were collected in seven cities that differ both in climatic conditions, moderately to sharply continental. In total, 33 ecotopes were distinguished [...] Read more.
The fluctuating asymmetry (FA) in Betula pendula Roth was estimated as an integrated measure of five morphometric characteristics of a lamina. Samples were collected in seven cities that differ both in climatic conditions, moderately to sharply continental. In total, 33 ecotopes were distinguished with various level of anthropogenic load. The statistical data processing involved correlation, one-way and factorial ANOVA, regression analyses, and principal component analysis (PCA). The impact of 25 climatic and anthropogenic factors on the FA value was considered. In most urban ecotopes, the integrated fluctuating asymmetry (IFA) value was higher than in natural biotopes of the same region. No significant inter-annual differences in IFA values were found. FA dependence on traffic load is noted to be statistically significant. The covariation analysis of IFA, climatic, and anthropogenic variables in various urban ecotopes revealed the impact of three groups of factors that together explain 93% of the variance in environmental parameters. The complex analysis clearly arranged the studied ecotopes by pollution gradient and climatic patterns. The primary effect of the total anthropogenic load on the developmental stability of B. pendula results in an IFA increase. IFA can play a key role in bioindication assessment of environmental quality. The climatic factors have no significant effect on the developmental stability of B. pendula in urban conditions. Full article
(This article belongs to the Special Issue Fluctuating Asymmetry as a Measure of Stress)
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Article
Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)
Symmetry 2020, 12(8), 1289; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081289 - 03 Aug 2020
Cited by 10
Abstract
All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as [...] Read more.
All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
Article
Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument
Symmetry 2020, 12(8), 1248; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081248 - 29 Jul 2020
Cited by 8
Abstract
The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important [...] Read more.
The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given. Full article
Article
An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem
Symmetry 2020, 12(8), 1225; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081225 - 26 Jul 2020
Cited by 10
Abstract
A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the [...] Read more.
A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the notion of symmetry is particularly important in multi-criteria decision aid (MCDA) because they are basic characteristics of the binary relationships used in modelling the preferences of decision-makers. The focal point of this study is evaluating the P&R facility system location problem from the experts’ point of view. For this aim, an integrated multicriteria decision-making (MCDM) methodology is proposed to evaluate the location of the facilities of the P&R system. The questionnaire survey was designed and estimated by 10 transport experts in the related field. The famous analytic hierarchy process (AHP) was adopted in a fuzzy environment, where the fuzzy sets have an efficient ability to manage the vague concepts in a specific way; moreover, it can mitigate the evaluator reasoning during decision-making. The hierarchical structure of the problem was established to evaluate a real-life problem in Cuenca city, Ecuador. The outcomes highlighted the “accessibility of public transport” as the most significant issue in the P&R facility location problem. The obtained results provide more flexible facilities than the pure AHP method. Full article
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Article
Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
Symmetry 2020, 12(8), 1210; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081210 - 23 Jul 2020
Cited by 5
Abstract
We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are [...] Read more.
We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are discussed and illustrated by examples. The case of multiple eigenvalues also is considered, and sufficient conditions of instability are obtained. Some issues of the dynamics of a nonlinear system with an unstable linear approximation are discussed. The behavior of trajectories in the case of unstable equilibrium is investigated, and an example of the chaotic behavior versus the case of bounded solutions is presented and discussed. Full article
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Article
Traffic Flow Density Model and Dynamic Traffic Congestion Model Simulation Based on Practice Case with Vehicle Network and System Traffic Intelligent Communication
Symmetry 2020, 12(7), 1172; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071172 - 15 Jul 2020
Cited by 14
Abstract
The massive increase in the number of vehicles has set a precedent in terms of congestion, being one of the important factors affecting the flow of traffic, but there are also effects on the world economy. The studies carried out so far try [...] Read more.
The massive increase in the number of vehicles has set a precedent in terms of congestion, being one of the important factors affecting the flow of traffic, but there are also effects on the world economy. The studies carried out so far try to highlight solutions that will streamline the traffic, as society revolves around transportation and its symmetry. Current research highlights that the increased density of vehicles could be remedied by dedicated short-range communications (DSRC) systems through communications of the type vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I) or vehicle-to-everything (V2X). We can say that wireless communication technologies have the potential to significantly change the efficiency and road safety, thus improving the efficiency of transport systems. An important factor is to comply with the requirements imposed on the use of vehicle safety and transport applications. Therefore, this paper focuses on several simulations on the basis of symmetry models, implemented in practical cases in order to streamline vehicle density and reduce traffic congestion. The scenarios aim at both the communication of the vehicles with each other and their prioritization by the infrastructure, so we can have a report on the efficiency of the proposed models. Full article
(This article belongs to the Special Issue Symmetry and IoT Intelligence in the Post Pandemic Economy)
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Article
Unitarization Technics in Hadron Physics with Historical Remarks
Symmetry 2020, 12(7), 1114; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071114 - 03 Jul 2020
Cited by 14
Abstract
We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, [...] Read more.
We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Padé approximants and the N / D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnés solution, generalization to coupled channels and the Khuri-Treiman formalism, among others. Full article
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Article
Racemic Phospholipids for Origin of Life Studies
Symmetry 2020, 12(7), 1108; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071108 - 03 Jul 2020
Cited by 4
Abstract
Although prebiotic condensations of glycerol, phosphate and fatty acids produce phospholipid esters with a racemic backbone, most experimental studies on vesicles intended as protocell models have been carried out by employing commercial enantiopure phospholipids. Current experimental research on realistic protocell models urgently requires [...] Read more.
Although prebiotic condensations of glycerol, phosphate and fatty acids produce phospholipid esters with a racemic backbone, most experimental studies on vesicles intended as protocell models have been carried out by employing commercial enantiopure phospholipids. Current experimental research on realistic protocell models urgently requires racemic phospholipids and efficient synthetic routes for their production. Here we propose three synthetic pathways starting from glycerol or from racemic solketal (α,β-isopropylidene-dl-glycerol) for the gram-scale production (up to 4 g) of racemic phospholipid ester precursors. We describe and compare these synthetic pathways with literature data. Racemic phosphatidylcholines and phosphatidylethanolamines were obtained in good yields and high purity from 1,2-diacylglycerols. Racemic POPC (rac-POPC, (R,S)-1-palmitoyl-2-oleoyl-3-phosphocholine), was used as a model compound for the preparation of giant vesicles (GVs). Confocal laser scanning fluorescence microscopy was used to compare GVs prepared from enantiopure (R)-POPC), racemic POPC (rac-POPC) and a scalemic mixture (scal-POPC) of (R)-POPC enriched with rac-POPC. Vesicle morphology and size distribution were similar among the different (R)-POPC, rac-POPC and scal-POPC, while calcein entrapments in (R)-POPC and in scal-POPC were significantly distinct by about 10%. Full article
(This article belongs to the Special Issue Chirality and the Origin of Life)
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Article
SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics
Symmetry 2020, 12(7), 1099; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071099 - 02 Jul 2020
Cited by 8
Abstract
In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random [...] Read more.
In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Article
Type 2 Degenerate Poly-Euler Polynomials
Symmetry 2020, 12(6), 1011; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12061011 - 15 Jun 2020
Cited by 7
Abstract
In recent years, many mathematicians have studied the degenerate versions of many special polynomials and numbers. The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithms functions. The paper is divided two parts. First, we introduce a [...] Read more.
In recent years, many mathematicians have studied the degenerate versions of many special polynomials and numbers. The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithms functions. The paper is divided two parts. First, we introduce a new type of the type 2 poly-Euler polynomials and numbers constructed from the modified polyexponential function, the so-called type 2 poly-Euler polynomials and numbers. We show various expressions and identities for these polynomials and numbers. Some of them involving the (poly) Euler polynomials and another special numbers and polynomials such as (poly) Bernoulli polynomials, the Stirling numbers of the first kind, the Stirling numbers of the second kind, etc. In final section, we introduce a new type of the type 2 degenerate poly-Euler polynomials and the numbers defined in the previous section. We give explicit expressions and identities involving those polynomials in a similar direction to the previous section. Full article
Article
Two-Pole Structures in QCD: Facts, Not Fantasy!
Symmetry 2020, 12(6), 981; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060981 - 08 Jun 2020
Cited by 19
Abstract
The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it [...] Read more.
The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the K ¯ p and the other close to the π Σ threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, although it is not yet listed in the summary tables. Here, I discuss the open ends and critically review approaches that cannot deal with this issue. In the meson sector, some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the D 0 * ( 2300 ) , which is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel D π , D η , D s K ¯ scattering in the isospin I = 1 / 2 channel indeed reveal its two-pole structure. Further states in the heavy meson sector with I = 1 / 2 exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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Article
On the Analytical and Numerical Study of a Two-Dimensional Nonlinear Heat Equation with a Source Term
Symmetry 2020, 12(6), 921; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060921 - 02 Jun 2020
Cited by 4
Abstract
The paper deals with two-dimensional boundary-value problems for the degenerate nonlinear parabolic equation with a source term, which describes the process of heat conduction in the case of the power-law temperature dependence of the heat conductivity coefficient. We consider a heat wave propagation [...] Read more.
The paper deals with two-dimensional boundary-value problems for the degenerate nonlinear parabolic equation with a source term, which describes the process of heat conduction in the case of the power-law temperature dependence of the heat conductivity coefficient. We consider a heat wave propagation problem with a specified zero front in the case of two spatial variables. The solution existence and uniqueness theorem is proved in the class of analytic functions. The solution is constructed as a power series with coefficients to be calculated by a proposed constructive recurrent procedure. An algorithm based on the boundary element method using the dual reciprocity method is developed to solve the problem numerically. The efficiency of the application of the dual reciprocity method for various systems of radial basis functions is analyzed. An approach to constructing invariant solutions of the problem in the case of central symmetry is proposed. The constructed solutions are used to verify the developed numerical algorithm. The test calculations have shown the high efficiency of the algorithm. Full article
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Article
Keep a Left Profile, Baby! The Left-Cradling Bias Is Associated with a Preference for Left-Facing Profiles of Human Babies
Symmetry 2020, 12(6), 911; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060911 - 01 Jun 2020
Cited by 6
Abstract
The left-cradling bias (LCB) refers to the (typically female) preference to hold an infant on the left side of one’s own body. Among the three main accounts proposed for such a phenomenon, namely the “handedness”, “heartbeat” and “hemispheric asymmetry” hypotheses, the latter has [...] Read more.
The left-cradling bias (LCB) refers to the (typically female) preference to hold an infant on the left side of one’s own body. Among the three main accounts proposed for such a phenomenon, namely the “handedness”, “heartbeat” and “hemispheric asymmetry” hypotheses, the latter has met with the greatest empirical success. Accordingly, the LCB would facilitate the communication of socio-emotional information through the right hemisphere of both the cradled and the cradling individual, and should emerge mainly in face-to-face interactions. In this regard, it should be noticed that when the infant’s body is oriented toward the cradler, the left or right side of their face is relatively more visible to left- and right-cradlers, respectively. Therefore, we hypothesized that the LCB might also be associated with a preference for left-facing profiles (i.e., those showing the left, and more expressive, hemiface/cheek) of human babies. In order to test our hypothesis, we assessed the cradling-side preferences of female participants, as well as their preference for the left- or right-facing profile of a human infant depicted in a drawing. Left-cradlers exhibited a significantly larger preference for the left-facing version of the drawing compared with right-cradlers, a finding further corroborating the right-hemisphere hypothesis. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Brain Behavior and Perception)
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Article
Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations
Symmetry 2019, 11(12), 1523; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11121523 - 16 Dec 2019
Cited by 11
Abstract
A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a [...] Read more.
A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers. Full article
(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics)
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Article
Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity
Symmetry 2019, 11(12), 1462; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11121462 - 28 Nov 2019
Cited by 19
Abstract
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper, we use Noether symmetry approach for a modified teleparallel theory of gravity labeled as f ( T , B ) gravity where T is the scalar torsion [...] Read more.
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper, we use Noether symmetry approach for a modified teleparallel theory of gravity labeled as f ( T , B ) gravity where T is the scalar torsion and B the boundary term. Using Noether theorem, we were able to find exact spherically symmetric solutions for different forms of the function f ( T , B ) coming from Noether symmetries. Full article
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
Article
Short vs. Standard Length Cone Morse Connection Implants: An In Vitro Pilot Study in Low Density Polyurethane Foam
Symmetry 2019, 11(11), 1349; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11111349 - 01 Nov 2019
Cited by 15
Abstract
The aim of the investigation was to evaluate the insertion torque, pull-out torque and implant stability quotient (ISQ) of short implants (SI) and standard length implants (ST) inserted into linearly elastic and constitutive isotropic symmetry polyurethane foam blocks. Short dental titanium implants with [...] Read more.
The aim of the investigation was to evaluate the insertion torque, pull-out torque and implant stability quotient (ISQ) of short implants (SI) and standard length implants (ST) inserted into linearly elastic and constitutive isotropic symmetry polyurethane foam blocks. Short dental titanium implants with a Cone Morse connection and a conical shape (test implants: Test Implant A—diameter 5.5 mm and length 6 mm) (Test Implant B—diameter 5.5 mm and length 5 mm) were used for the present in vitro investigation. ST implants (4 mm diameter and 10 mm length), with a Cone Morse connection and a conical shape, were used as Control Implant A and as Control Implants B. These two latter implants had a different macro design. A total of 20 implants (5 Test A, 5 Test B, 5 Control A and 5 Control B) were used for the present research. The results were similar when comparing the Test A and Test B implants. The test implants had very good stability in polyurethane 14.88–29.76 kgm3 density blocks. The insertion torque values were very high for both types of test implant (25–32 Ncm on 14.88 kgm blocks, and up to 45 Ncm in 29.76 kgm3 blocks). The pull-out test values were very similar to the insertion torque values. The ISQ values were significantly high with 75–80 in 14.88 kgm3 blocks, and 78–83 in 29.76 kgm3 blocks. No differences were found in the values of the Control A and Control B implants. In both these implants, the insertion torque was quite low in the 14.88 kgm3 blocks (16–28 Ncm). Better results were found in the 29.76 kgm3 blocks. The pull-out values for these control implants were slightly lower than the insertion torque values. High ISQ values were found in both control implants (57–80). When comparing SI and ST implants, the SI had a similar if not better performance in low quality polyurethane foam blocks (14.88–29.76 kgm), corresponding to D3 and D4 bone. Full article
(This article belongs to the Special Issue Dental Implant Macrogeometry and Biomaterials)
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Article
The Quantum Cosmological Constant
Symmetry 2019, 11(9), 1130; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11091130 - 05 Sep 2019
Cited by 11
Abstract
We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time [...] Read more.
We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere. Full article
(This article belongs to the Special Issue Modified Theories of Gravity)
Article
Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange
Symmetry 2019, 11(8), 1055; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11081055 - 16 Aug 2019
Cited by 10
Abstract
We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are [...] Read more.
We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed. Full article
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Article
Revisiting a Negative Cosmological Constant from Low-Redshift Data
Symmetry 2019, 11(8), 1035; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11081035 - 10 Aug 2019
Cited by 45
Abstract
Persisting tensions between high-redshift and low-redshift cosmological observations suggest the dark energy sector of the Universe might be more complex than the positive cosmological constant of the Λ CDM model. Motivated by string theory, wherein symmetry considerations make consistent AdS backgrounds (i.e., maximally-symmetric [...] Read more.
Persisting tensions between high-redshift and low-redshift cosmological observations suggest the dark energy sector of the Universe might be more complex than the positive cosmological constant of the Λ CDM model. Motivated by string theory, wherein symmetry considerations make consistent AdS backgrounds (i.e., maximally-symmetric spacetimes with a negative cosmological constant) ubiquitous, we explore a scenario where the dark energy sector consists of two components: a negative cosmological constant, with a dark energy component with equation of state w ϕ on top. We test the consistency of the model against low-redshift baryon acoustic oscillation and Type Ia supernovae distance measurements, assessing two alternative choices of distance anchors: the sound horizon at baryon drag determined by the Planck collaboration and the Hubble constant determined by the SH0ES program. We find no evidence for a negative cosmological constant and mild indications for an effective phantom dark energy component on top. A model comparison analysis reveals that the Λ CDM model is favoured over our negative cosmological constant model. While our results are inconclusive, should low-redshift tensions persist with future data, it would be worth reconsidering and further refining our toy negative cosmological constant model by considering realistic string constructions. Full article
(This article belongs to the Special Issue Anomalies and Tensions of the Cosmic Microwave Background)
Communication
The Eigenproblem Translated for Alignment of Molecules
Symmetry 2019, 11(8), 1027; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11081027 - 09 Aug 2019
Cited by 20
Abstract
Molecular conformation as a subproblem of the geometrical shaping of the molecules is essential for the expression of biological activity. It is well known that from the series of all possible sugars, those that are most naturally occurring and usable by living organisms [...] Read more.
Molecular conformation as a subproblem of the geometrical shaping of the molecules is essential for the expression of biological activity. It is well known that from the series of all possible sugars, those that are most naturally occurring and usable by living organisms as a source of energy—because they can be phosphorylated by hexokinase, the first enzyme in the glycolysis pathway—are D-sugars (from the Latin dextro). Furthermore, the most naturally occurring amino acids in living cells are L-sugars (from the Latin laevo). However, a problem arises in dealing with the comparison of their conformers. One alternative way to compare sugars is via their molecular alignment. Here, a solution to the eigenproblem of molecular alignment is communicated. The Cartesian system is rotated, and eventually translated and reflected until the molecule arrives in a position characterized by the highest absolute values of the eigenvalues observed on the Cartesian coordinates. The rotation alone can provide eight alternate positions relative to the reflexes of each coordinate. Full article
(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)
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Article
Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics
Symmetry 2019, 11(8), 1024; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11081024 - 08 Aug 2019
Cited by 10
Abstract
In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = 1 ). The essential role [...] Read more.
In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = 1 ). The essential role is played by the symmetric nature of interactions. The class may be related to the mesoscopic scale of description. This means that we are going to statistically describe an individual state of an agent of the system. We show that the corresponding equations result at the macroscopic scale in two different pictures: anti-diffusive ( σ = 1 ) and diffusive ( σ = 1 ). We provide a rigorous result on the convergence. The result captures the macroscopic behavior resulting from the mesoscopic one. In numerical examples, we observe both unipolar and bipolar behavior known in political sciences. Full article
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Article
Around the Model of Infection Disease: The Cauchy Matrix and Its Properties
Symmetry 2019, 11(8), 1016; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11081016 - 06 Aug 2019
Cited by 10
Abstract
In this paper the model of infection diseases by Marchuk is considered. Mathematical questions which are important in its study are discussed. Among them there are stability of stationary points, construction of the Cauchy matrices of linearized models, estimates of solutions. The novelty [...] Read more.
In this paper the model of infection diseases by Marchuk is considered. Mathematical questions which are important in its study are discussed. Among them there are stability of stationary points, construction of the Cauchy matrices of linearized models, estimates of solutions. The novelty we propose is in a distributed feedback control which affects the antibody concentration. We use this control in the form of an integral term and come to the analysis of nonlinear integro-differential systems. New methods for the study of stability of linearized integro–differential systems describing the model of infection diseases are proposed. Explicit conditions of the exponential stability of the stationary points characterizing the state of the healthy body are obtained. The method of the paper is based on the symmetry properties of the Cauchy matrices which allow us their construction. Full article
Article
CMB Tensions with Low-Redshift H0 and S8 Measurements: Impact of a Redshift-Dependent Type-Ia Supernovae Intrinsic Luminosity
Symmetry 2019, 11(8), 986; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11080986 - 02 Aug 2019
Cited by 25
Abstract
With the recent increase in precision of our cosmological datasets, measurements of Λ CDM model parameter provided by high- and low-redshift observations started to be in tension, i.e., the obtained values of such parameters were shown to be significantly different in a statistical [...] Read more.
With the recent increase in precision of our cosmological datasets, measurements of Λ CDM model parameter provided by high- and low-redshift observations started to be in tension, i.e., the obtained values of such parameters were shown to be significantly different in a statistical sense. In this work we tackle the tension on the value of the Hubble parameter, H 0 , and the weighted amplitude of matter fluctuations, S 8 , obtained from local or low-redshift measurements and from cosmic microwave background (CMB) observations. We combine the main approaches previously used in the literature by extending the cosmological model and accounting for extra systematic uncertainties. With such analysis we aim at exploring non standard cosmological models, implying deviation from a cosmological constant driven acceleration of the Universe expansion, in the presence of additional uncertainties in measurements. In more detail, we reconstruct the Dark Energy equation of state as a function of redshift, while we study the impact of type-Ia supernovae (SNIa) redshift-dependent astrophysical systematic effects on these tensions. We consider a SNIa intrinsic luminosity dependence on redshift due to the star formation rate in its environment, or the metallicity of the progenitor. We find that the H 0 and S 8 tensions can be significantly alleviated, or even removed, if we account for varying Dark Energy for SNIa and CMB data. However, the tensions remain when we add baryon acoustic oscillations (BAO) data into the analysis, even after the addition of extra SNIa systematic uncertainties. This points towards the need of either new physics beyond late-time Dark Energy, or other unaccounted systematic effects (particulary in BAO measurements), to fully solve the present tensions. Full article
(This article belongs to the Special Issue Anomalies and Tensions of the Cosmic Microwave Background)
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Article
On the Complex Interaction between Collective Learning and Social Dynamics
Symmetry 2019, 11(8), 967; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11080967 - 01 Aug 2019
Cited by 14
Abstract
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between [...] Read more.
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between learning dynamics and other types of dynamics which can be modeled by kinetic theory methods. The contents are presented in three parts. First, a general description of different theories of learning dynamics within the framework of cognitive sciences is critically analyzed with the aim of capturing the main features of the system towards modeling. Subsequently, the class of systems which are the object of the modeling approach is defined by showing how the previous structure can be developed, thanks to new conceptual ideas, including the concept of symmetric and asymmetric learning, towards modeling. Finally, some applications are selected to show how the approach can be methodologically applied. Full article
Article
Smart Contract-Based Pool Hopping Attack Prevention for Blockchain Networks
Symmetry 2019, 11(7), 941; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11070941 - 19 Jul 2019
Cited by 20
Abstract
Pool hopping attack is the result of miners leaving the pool when it offers fewer financial rewards and joining back when the rewards of mining yield higher rewards in blockchain networks. This act of leaving and rejoining the pool only during the good [...] Read more.
Pool hopping attack is the result of miners leaving the pool when it offers fewer financial rewards and joining back when the rewards of mining yield higher rewards in blockchain networks. This act of leaving and rejoining the pool only during the good times results in the miner receiving more rewards than the computational power they contribute. Miners exiting the pool deprive it of its collective hash power, which leaves the pool unable to mine the block successfully. This results in its competitors mining the block before they can finish mining. Existing research shows pool hopping resistant measures and detection strategies; however, they do not offer any robust preventive solution to discourage miners from leaving the mining pool. To prevent pool hopping attacks, a smart contract-based pool hopping attack prevention model is proposed. The main objective of our research is maintaining the symmetrical relationship between the miners by requiring them all to continually contribute their computational power to successfully mine a block. We implement a ledger containing records of all miners, in the form of a miner certificate, which tracks the history of the miner’s earlier behavior. The certificate enables a pool manager to better initiate terms of the smart contract, which safeguards the interests of existing mining pool members. The model prevents frequent mine hoppers from pool hopping as they submit coins in the form of an escrow and risk losing them if they abandon the pool before completing mining of the block. The key critical factors that every pool hopping attack prevention solution must address and a study of comparative analysis with existing solutions are presented in the paper. Full article
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Article
The Immobilization of Oxindole Derivatives with Use of Cube Rhombellane Homeomorphs
Symmetry 2019, 11(7), 900; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11070900 - 10 Jul 2019
Cited by 6
Abstract
A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used [...] Read more.
A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used substances and often extending their bioavailability. Through the application of docking methods, the possibility of using cube rhombellanes as potential carriers for two oxindole derivatives was analyzed. In the studies, compounds identified as inhibitors of the CDK2 enzyme and a set of nanostructures proposed by the Topo Cluj Group were used. The popular fullerene molecule C60 was used as the reference system. The estimated binding affinities and structures of obtained complexes show that use of functionalized cube rhombellanes containing hydrogen bond donors and acceptors in their external molecular shell significantly increases ligand affinity toward considered nanocariers, compared to classic fullerenes. The presented values also allow to state that an important factor determining the mutual affinity of the tested ligands and nanostructures is the symmetry of the analyzed nanocarriers and its influence on the distribution of binding groups (aromatic systems, donors and acceptors of hydrogen bonds) on the surface of nanoparticles. Full article
(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)
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Article
Docking of Cisplatin on Fullerene Derivatives and Some Cube Rhombellane Functionalized Homeomorphs
Symmetry 2019, 11(7), 874; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11070874 - 03 Jul 2019
Cited by 6
Abstract
Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed [...] Read more.
Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals. This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus. That is why it seems to be important to connect CisPt with nanostructures and in this way prevent the drug from combining with the B vitamins. As a proposal for a new nanodrug, an attempt was made to implement Cispaltin (CisPt) ligand on functionalized C60 fullerenes and on a cube rhombellane homeomorphic surface. The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers. The behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C60, in terms of their (interacting) energy, geometry and topology was studied and a detailed analysis of structural properties after docking showed many interesting features. Full article
(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)
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Article
On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
Symmetry 2019, 11(7), 863; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11070863 - 02 Jul 2019
Cited by 99
Abstract
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based [...] Read more.
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
Article
A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested
Symmetry 2019, 11(6), 835; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11060835 - 25 Jun 2019
Cited by 19
Abstract
One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling [...] Read more.
One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Article
Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept
Symmetry 2019, 11(6), 755; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11060755 - 04 Jun 2019
Cited by 7
Abstract
Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, [...] Read more.
Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, in addition to criteria such as punctuality, the frequency of departures, and the number of transfers, a travelling comfort level is an important element for passengers. An overcrowded bus may discourage travelers from choosing this mode of transport and induce them to use a private car despite the existence of many other facilities offered by a given public transport system. Therefore, the forecasting of bus passenger demand, as well as bus occupancy at individual bus stops, is currently an important research direction. The main goal of the article is to present the conceptual framework for the Advanced Travel Information System with the prediction module. The proposed approach assumes that the prediction module is based on the use of the Markov Chain concept. The efficiency and accuracy of the obtained prediction were presented based on a real-life example, where the measurements of passengers boarding and alighting at bus stops were made in a selected Cracow bus line. The methodology presented in the paper and the obtained results can significantly contribute to the development of solutions and systems for a better management as well as a cost and energy consumption optimisation in the public transport system. Current and forecasted information related to bus occupancy, when properly used in the travel information system, may have a positive impact on the development of urban mobility patterns by encouraging the use of public transport. This article addresses the current and practical research problem using an adequate theoretical mathematical tool to describe it, reflecting the characteristics and nature of the phenomenon being studied. To the best of the authors’ knowledge, the article deals for the first time with the problem of prediction of onboard bus comfort levels based on in-vehicle occupancy. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
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Article
Conservation Laws and Stability of Field Theories of Derived Type
Symmetry 2019, 11(5), 642; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11050642 - 07 May 2019
Cited by 9
Abstract
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time [...] Read more.
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern–Simons theory. Full article
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
Article
Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials
Symmetry 2019, 11(5), 613; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11050613 - 02 May 2019
Cited by 14
Abstract
The main purpose of this paper is to give several identities of symmetry for type 2 Bernoulli and Euler polynomials by considering certain quotients of bosonic p-adic and fermionic p-adic integrals on Z p , where p is an odd prime [...] Read more.
The main purpose of this paper is to give several identities of symmetry for type 2 Bernoulli and Euler polynomials by considering certain quotients of bosonic p-adic and fermionic p-adic integrals on Z p , where p is an odd prime number. Indeed, they are symmetric identities involving type 2 Bernoulli polynomials and power sums of consecutive odd positive integers, and the ones involving type 2 Euler polynomials and alternating power sums of odd positive integers. Furthermore, we consider two random variables created from random variables having Laplace distributions and show their moments are given in terms of the type 2 Bernoulli and Euler numbers. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)
Article
The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Geometric Modeling and Virtual Reconstruction
Symmetry 2019, 11(4), 589; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040589 - 24 Apr 2019
Cited by 13
Abstract
This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at [...] Read more.
This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at different levels. Autodesk Inventor Professional software has been used to obtain the 3D CAD model of this historical invention and its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Also, because the single sheet does not have a scale, it has been necessary to adopt a graphic scale so that the dimensions of the different elements are coherent. Furthermore, it has been necessary to establish some dimensional, geometric, and movement restrictions (degrees of freedom) so that the set will work properly. One of the main conclusions is that William Reynolds designed a mechanism seeking a longitudinal symmetry so that, from a single continuous movement, the mechanism allows two vessels to ascend and descend simultaneously. This engineering solution facilitated a doubling of the working capacity of the device, as well as a reduction of the energy needs of the system. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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Article
Hadronic and Hadron-Like Physics of Dark Matter
Symmetry 2019, 11(4), 587; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040587 - 23 Apr 2019
Cited by 19
Abstract
The problems of simple elementary weakly interacting massive particles (WIMPs) appeal to extend the physical basis for nonbaryonic dark matter. Such extension involves more sophisticated dark matter candidates from physics beyond the Standard Model (BSM) of elementary particles. We discuss several models of [...] Read more.
The problems of simple elementary weakly interacting massive particles (WIMPs) appeal to extend the physical basis for nonbaryonic dark matter. Such extension involves more sophisticated dark matter candidates from physics beyond the Standard Model (BSM) of elementary particles. We discuss several models of dark matter, predicting new colored, hyper-colored or techni-colored particles and their accelerator and non-accelerator probes. The nontrivial properties of the proposed dark matter candidates can shed new light on the dark matter physics. They provide interesting solutions for the puzzles of direct and indirect dark matter search. Full article
(This article belongs to the Special Issue Cosmological Inflation, Dark Matter and Dark Energy)
Article
Fully Metallic Flat Lens Based on Locally Twist-Symmetric Array of Complementary Split-Ring Resonators
Symmetry 2019, 11(4), 581; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040581 - 22 Apr 2019
Cited by 10
Abstract
In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of [...] Read more.
In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of complementary split-ring resonators. In this specific design, the twist symmetry is local, as it is only applied to the unit cell of the array. Moreover, the twist symmetry is an approximation, as it is only applied to part of the unit cell. First, we demonstrate that, by varying the order of twist symmetry, the phase delay experienced by a wave propagating through the array can be accurately controlled. Secondly, a lens is designed by tailoring the unit cells throughout the aperture of the lens in order to obtain the desired phase delay. Simulation and measurement results demonstrate that the lens successfully transforms a spherical wave emanating from the focal point into a plane wave at the opposite side of the lens. The demonstrated concepts find application in future wireless communication networks where fully-metallic directive antennas are desired. Full article
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Article
A Scalable and Hybrid Intrusion Detection System Based on the Convolutional-LSTM Network
Symmetry 2019, 11(4), 583; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040583 - 22 Apr 2019
Cited by 47
Abstract
With the rapid advancements of ubiquitous information and communication technologies, a large number of trustworthy online systems and services have been deployed. However, cybersecurity threats are still mounting. An intrusion detection (ID) system can play a significant role in detecting such security threats. [...] Read more.
With the rapid advancements of ubiquitous information and communication technologies, a large number of trustworthy online systems and services have been deployed. However, cybersecurity threats are still mounting. An intrusion detection (ID) system can play a significant role in detecting such security threats. Thus, developing an intelligent and accurate ID system is a non-trivial research problem. Existing ID systems that are typically used in traditional network intrusion detection system often fail and cannot detect many known and new security threats, largely because those approaches are based on classical machine learning methods that provide less focus on accurate feature selection and classification. Consequently, many known signatures from the attack traffic remain unidentifiable and become latent. Furthermore, since a massive network infrastructure can produce large-scale data, these approaches often fail to handle them flexibly, hence are not scalable. To address these issues and improve the accuracy and scalability, we propose a scalable and hybrid IDS, which is based on Spark ML and the convolutional-LSTM (Conv-LSTM) network. This IDS is a two-stage ID system: the first stage employs the anomaly detection module, which is based on Spark ML. The second stage acts as a misuse detection module, which is based on the Conv-LSTM network, such that both global and local latent threat signatures can be addressed. Evaluations of several baseline models in the ISCX-UNB dataset show that our hybrid IDS can identify network misuses accurately in 97.29% of cases and outperforms state-of-the-art approaches during 10-fold cross-validation tests. Full article
(This article belongs to the Special Issue Symmetry-Adapted Machine Learning for Information Security)
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Article
Imaginary Chemical Potential, NJL-Type Model and Confinement–Deconfinement Transition
Symmetry 2019, 11(4), 562; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040562 - 18 Apr 2019
Cited by 8
Abstract
In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss [...] Read more.
In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss periodicity and the transition. We summarize how these properties play a crucial role in understanding QCD properties at finite temperature and density. This review covers several topics in the investigation of the QCD phase diagram based on the imaginary chemical potential. Full article
(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)
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Article
Hyers-Ulam Stability for Linear Differences with Time Dependent and Periodic Coefficients
Symmetry 2019, 11(4), 512; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040512 - 09 Apr 2019
Cited by 10
Abstract
Let q 2 be a positive integer and let ( a j ) , ( b j ) , and ( c j ) (with j a non-negative integer) be three given C -valued and q-periodic sequences. Let [...] Read more.
Let q 2 be a positive integer and let ( a j ) , ( b j ) , and ( c j ) (with j a non-negative integer) be three given C -valued and q-periodic sequences. Let A ( q ) : = A q 1 A 0 , where A j is as is given below. Assuming that the “monodromy matrix” A ( q ) has at least one multiple eigenvalue, we prove that the linear scalar recurrence x n + 3 = a n x n + 2 + b n x n + 1 + c n x n , n Z + is Hyers-Ulam stable if and only if the spectrum of A ( q ) does not intersect the unit circle Γ : = { w C : | w | = 1 } . Connecting this result with a recently obtained one it follows that the above linear recurrence is Hyers-Ulam stable if and only if the spectrum of A ( q ) does not intersect the unit circle. Full article
(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)
Article
Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2 + 1) Polyakov-Nambu-Jona-Lasinio Model
Symmetry 2019, 11(4), 507; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040507 - 08 Apr 2019
Cited by 6
Abstract
We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ( T , μ B ) -plane, with its isentropic trajectories, paying [...] Read more.
We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ( T , μ B ) -plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search. Full article
(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)
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Article
Time-reversal Symmetry in Antenna Theory
Symmetry 2019, 11(4), 486; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040486 - 04 Apr 2019
Cited by 6
Abstract
Here, I discuss some implications of the time-reversal invariance of lossless radiating systems. I highlight that time-reversal symmetry provides a rather intuitive explanation for the conditions of polarization and impedance matching of a receiving antenna. Furthermore, I describe a solution to generate the [...] Read more.
Here, I discuss some implications of the time-reversal invariance of lossless radiating systems. I highlight that time-reversal symmetry provides a rather intuitive explanation for the conditions of polarization and impedance matching of a receiving antenna. Furthermore, I describe a solution to generate the time-reversed electromagnetic field through the illumination of a matched receiving antenna with a Herglotz wave. Full article
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Article
One-Plane Glide-Symmetric Holey Structures for Stop-Band and Refraction Index Reconfiguration
Symmetry 2019, 11(4), 495; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11040495 - 04 Apr 2019
Cited by 9
Abstract
This work presents a new configuration to create glide-symmetric structures in a single plane, which facilitates fabrication and avoids alignment problems in the assembly process compared to traditional glide-symmetric structures based on several planes. The proposed structures can be printed on the metal [...] Read more.
This work presents a new configuration to create glide-symmetric structures in a single plane, which facilitates fabrication and avoids alignment problems in the assembly process compared to traditional glide-symmetric structures based on several planes. The proposed structures can be printed on the metal face of a dielectric substrate, which acts as a support. The article includes a parametric study based on dispersion diagrams on the appearance of stop-bands and phase-shifting by breaking the symmetry. In addition, a procedure to regenerate symmetry is proposed that may be useful for reconfigurable devices. Finally, the measured and simulated S parameters of 10 × 10 unit-cell structures are presented to illustrate the attenuation in these stop-bands and the refractive index of the propagation modes. The attenuation obtained is greater than 30 dB in the stop-band for the symmetry-broken prototype. Full article
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