Symmetry

17 pages, 708 KiB

Open AccessArticle

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

by Muhammad Khalid, Ata-ur-Rahman, Ali Althobaiti, Sayed K. Elagan, Sadah A. Alkhateeb, Ebtehal A. Elghmaz and Samir A. El-Tantawy

Symmetry 2021, 13(11), 2232; https://doi.org/10.3390/sym13112232 - 22 Nov 2021

Cited by 9 | Viewed by 1521

Abstract

In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation [...] Read more.

In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems. Full article

(This article belongs to the Special Issue Mathematical Physics: Topics and Advances)

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18 pages, 479 KiB

Open AccessArticle

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

by Jian Zhang, Ancheng Chang and Gang Yang

Symmetry 2021, 13(11), 2231; https://doi.org/10.3390/sym13112231 - 22 Nov 2021

Cited by 4 | Viewed by 1402

Abstract

The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient [...] Read more.

The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient stability criterion for the existence and global exponential stability of T-periodic solutions on the proposed system is obtained. In addition, an instructive numerical example is arranged to support the present approach. The obtained results broaden the application range of neutral-types inertial neural networks. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications)

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8 pages, 2512 KiB

Open AccessArticle

Terahertz Metamaterial Modulator Based on Phase Change Material VO₂

by Yanfei Dong, Dingwang Yu, Gaosheng Li, Mingtuan Lin and Li-An Bian

Symmetry 2021, 13(11), 2230; https://doi.org/10.3390/sym13112230 - 22 Nov 2021

Cited by 17 | Viewed by 2167

Abstract

In this paper, a new type of terahertz (THz) metamaterial (MM) modulator has been presented with bifunctional properties based on vanadium dioxide (VO₂). The design consists of a VO₂ resonator, polyimide substrate, frequency selective surface (FSS) layer, and VO₂ [...] Read more.

In this paper, a new type of terahertz (THz) metamaterial (MM) modulator has been presented with bifunctional properties based on vanadium dioxide (VO₂). The design consists of a VO₂ resonator, polyimide substrate, frequency selective surface (FSS) layer, and VO₂ film. Based on the metal-insulator transition (MIT) of VO₂, this structure integrated with VO₂ material can achieve the dynamic modulation on both transmission and reflection waves at 2.5 THz by varying the electrical conductivity value of VO₂. Meanwhile, it also exhibits adjustable absorption performance across the whole band from 0.5–7 THz. At the lower conductivity (

σ

= 25 S/m), this structure can act as a bandpass FSS, and, at the high conductivity (

σ

= 2 × 10⁵ S/m), it behaves like a wideband absorber covering 2.52–6.06 THz with absorption A > 0.9, which realizes asymmetric transmission. The surface electric field distributions are illustrated to provide some insight into the physical mechanism of dynamic modulation. From the simulated results, it can be observed that this design has the capability of controlling tunable manipulation on both transmission/reflection responses at a wide frequency band. This proposed design may pave a novel pathway towards thermal imaging, terahertz detection, active modulators, etc. Full article

(This article belongs to the Special Issue Terahertz Communication and Asymmetric Transmission: Advances and Applications)

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12 pages, 2539 KiB

Open AccessArticle

First Principles Calculation of the Topological Phases of the Photonic Haldane Model

by Filipa R. Prudêncio and Mário G. Silveirinha

Symmetry 2021, 13(11), 2229; https://doi.org/10.3390/sym13112229 - 22 Nov 2021

Cited by 4 | Viewed by 1782

Abstract

Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an [...] Read more.

Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter. Full article

(This article belongs to the Special Issue Topological Photonic Structures and Their Symmetries)

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12 pages, 538 KiB

Open AccessArticle

The North–South Asymmetry of Sunspot Relative Numbers Based on Complex Network Technique

by Hengyu Xu, Yu Fei, Chun Li, Jiajuan Liang, Xinan Tian and Zhongjie Wan

Symmetry 2021, 13(11), 2228; https://doi.org/10.3390/sym13112228 - 22 Nov 2021

Cited by 3 | Viewed by 1440

Abstract

Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable [...] Read more.

Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable visibility graphs (LPVG) are applied to implement the mapping of sunspot relative numbers in the northern and southern hemispheres. The results show that these three methods can capture important information of nonlinear dynamics existing in the long-term hemispheric sunspot activity. In the presentation of the results, the network degree sequence of the HVG method changes preferentially to the original data series as well as the VG and the LPVG, while both the VG and the LPVG slightly lag behind the original time series, which provides some new ideas for the nonlinear dynamics of the hemispheric asymmetry in the two hemispheres. Meanwhile, the use of statistical feature-skewness values and complex network visibility graphs can yield some complementary information for mutual verification. Full article

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13 pages, 491 KiB

Open AccessArticle

Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

by Andrey Bochkarev, Aleksandr Zemlyanukhin, Vladimir Erofeev and Aleksandr Ratushny

Symmetry 2021, 13(11), 2227; https://doi.org/10.3390/sym13112227 - 21 Nov 2021

Cited by 2 | Viewed by 1211

Abstract

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. [...] Read more.

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity. Full article

(This article belongs to the Special Issue Dynamical Processes in Heterogeneous and Discrete Media)

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8 pages, 546 KiB

Open AccessArticle

Inter-Limb Asymmetry in Force Accuracy and Steadiness Changes after a 12-Week Strength Training Program in Young Healthy Men

by Rafał Szafraniec, Tadeusz Stefaniak, Dariusz Harmaciński and Michał Kuczyński

Symmetry 2021, 13(11), 2226; https://doi.org/10.3390/sym13112226 - 21 Nov 2021

Cited by 1 | Viewed by 1992

Abstract

The study aimed to investigate the impact of a 12-week strength training program on force accuracy and steadiness changes in lower limbs in young healthy men. Twenty subjects with a dominant right lower limb were included. They performed a force matching task both [...] Read more.

The study aimed to investigate the impact of a 12-week strength training program on force accuracy and steadiness changes in lower limbs in young healthy men. Twenty subjects with a dominant right lower limb were included. They performed a force matching task both pre and post strength training program. The ability to reproduce force was determined by calculating three errors: absolute error (AE), constant error (CE), and variable error (VE). After intervention AE and VE improved in both legs indicating higher improvement in the dominant leg (p = 0.032 for AE and p = 0.005 for VE). However, CE improved only in the dominant leg (p = 0.001). We conclude that strength training improved the accuracy and consistency of force in a force reproduction task. This improvement was more evident in the dominant lower limb. Most likely, the inter-limb asymmetry in changes of force application ability caused by strength training is due to the different mechanisms responsible for the control of voluntary movements in the dominant and non-dominant lower limb. Full article

(This article belongs to the Special Issue New Insights into Motion Analysis)

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22 pages, 3448 KiB

Open AccessArticle

An Equivalent Homogenization Theoretical Method for Composite Sandwich Cylinders Subjected to Pure Bending

by Yang Liu, Fuwei Gu, Mingxuan Li, Xiaofeng Lu and Xiaolei Zhu

Symmetry 2021, 13(11), 2225; https://doi.org/10.3390/sym13112225 - 21 Nov 2021

Cited by 1 | Viewed by 1648

Abstract

An equivalent theoretical homogenization method was proposed for composite sandwich cylinders subjected to pure bending. Firstly, based on a homogeneous orthotropic layer hypothesis, the trapezoidal corrugated sandwich core was found to be equivalent in a homogenization orthotropic layer with the nine equivalent mechanical [...] Read more.

An equivalent theoretical homogenization method was proposed for composite sandwich cylinders subjected to pure bending. Firstly, based on a homogeneous orthotropic layer hypothesis, the trapezoidal corrugated sandwich core was found to be equivalent in a homogenization orthotropic layer with the nine equivalent mechanical properties. Then, Lekhnitskii’s theory, based on a unified connection parameter method, was introduced and applied in the equivalent composite sandwich cylinder. The method developed by Lekhnitskii is suitable for arbitrary combinations of winding layers with different winding angles and materials. Additionally, the bending stiffness of the equivalent sandwich cylinder could be calculated. By developing user subroutine of UMAT, the numerical calculation results were in a good agreement with the results of the proposed method. Further, according to the Hill–Tsai strength criterion and the maximum strain criterion, parametric study was done for specified bending stiffness and specified bending strength. The results show that the influence of core parameters on the specified bending stiffness and strength are lower than that of the skin parameters. Additionally, larger skin thickness and smaller winding angles could improve the specified bending stiffness and specified bending strength of the composite corrugated sandwich cylinders. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry of Composite Materials and Structures)

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16 pages, 2834 KiB

Open AccessArticle

Synchronizability of Multi-Layer-Coupled Star-Composed Networks

by Haiping Gao, Jian Zhu, Xianyong Li and Xing Chen

Symmetry 2021, 13(11), 2224; https://doi.org/10.3390/sym13112224 - 21 Nov 2021

Cited by 3 | Viewed by 1157

Abstract

In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the [...] Read more.

In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the synchronizability of these kinds of networks are derived in the case of bounded and unbounded synchronized regions. The relationships among the synchronizability, the number of layers, the length of the paths, the branchings, and the interlayer and intralayer coupling strengths in the two cases are studied. At the same time, the simulation experiments are carried out with the MATLAB software, and the simulated images of the two symmetrical structure networks’ synchronizability are compared. Finally, the factors affecting the synchronizability of multi-layer-coupled star-composed networks are found. On this basis, optimization schemes are given to improve the synchronizability of multi-layer-coupled star-composed networks and the influences of the number of central nodes on the networks’ synchronizability are further studied. Full article

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12 pages, 2602 KiB

Open AccessArticle

Influence of Molding Technology on Thermal Efficiencies and Pollutant Emissions from Household Solid Fuel Combustion during Cooking Activities in Chinese Rural Areas

by Juan Qi, Jianjun Wu and Lei Zhang

Symmetry 2021, 13(11), 2223; https://doi.org/10.3390/sym13112223 - 21 Nov 2021

Cited by 6 | Viewed by 1564

Abstract

Resident combustion of solid fuel has been widely acknowledged as a high potential for pollutant reduction. However, there is a marked asymmetry between more pollutant emission and less burned volatiles of biomass and coal in the combustion process. To study the solid fuel [...] Read more.

Resident combustion of solid fuel has been widely acknowledged as a high potential for pollutant reduction. However, there is a marked asymmetry between more pollutant emission and less burned volatiles of biomass and coal in the combustion process. To study the solid fuel optimum combustion form in a household stove, both the pollution reduction and energy efficient utilization of crop straws and coals were investigated. Taking the molding pressure and clay addition ratio as variable process conditions, the research of bio-coal briquette (made from the mixture of anthracite and biomass) was implemented in the range of 15~35 MP and 5~15%, respectively. Biomass and coal work complementarily for each other’s combustion property development. In particular, the pyrolysis gas produced by biomass low-temperature devolatilization is featured with low ignition point and is distributed in the bio-coal briquette. Its own combustion provides energy for anthracite particle combustion. Consequently, a positive effect was identified when bio-coal briquettes were used as residential fuel, and further improvement manifested in reducing more than 90% of particle matter (PM) and achieving about twice the thermal efficiencies (TEs) compared with the mass-weighted average values of coal briquettes and biomass briquettes. 88.8 ± 11.8%, 136.7 ± 13.7% and 81.4 ± 17.7% more TEs were provided by wheat straw–coal briquettes, rice straw–coal briquettes and maize straw–coal briquettes. 93.3 ± 3.1% (wheat straw–coal), 97.6 ± 0.2% (rice straw–coal) and 90.4 ± 2.2% (maize straw–coal) in terms of PM_2.5 emission factors (EFs) was reduced. For bio-coal briquette, a 25 MPa and 10% addition were determined as the optimum molding pressure and clay addition ratio. Bio-coal briquettes with higher TEs and lower PM EFs will bring about substantial benefits for air quality promotion, human health and energy saving. Full article

(This article belongs to the Special Issue Symmetry in Measurement of Combustion Derived Emissions)

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15 pages, 303 KiB

Open AccessArticle

The Injectivity Theorem on a Non-Compact Kähler Manifold

by Jingcao Wu

Symmetry 2021, 13(11), 2222; https://doi.org/10.3390/sym13112222 - 20 Nov 2021

Viewed by 1138

Abstract

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, [...] Read more.

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in

C^{n}

, hyperconvex bounded domains, and so on. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities 2021)

17 pages, 288 KiB

Open AccessArticle

All Graphs with a Failed Zero Forcing Number of Two

by Luis Gomez, Karla Rubi, Jorden Terrazas and Darren A. Narayan

Symmetry 2021, 13(11), 2221; https://doi.org/10.3390/sym13112221 - 20 Nov 2021

Cited by 5 | Viewed by 2047

Abstract

Given a graph G, the zero forcing number of G,

Z (G)

, is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S. [...] Read more.

Given a graph G, the zero forcing number of G,

Z (G)

, is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u is added to S in the next iteration. Zero forcing numbers have attracted great interest over the past 15 years and have been well studied. In this paper, we investigate the largest size of a set S that does not force all of the vertices in a graph to be in S. This quantity is known as the failed zero forcing number of a graph and will be denoted by

F (G)

. We present new results involving this parameter. In particular, we completely characterize all graphs G where

F (G) = 2

, solving a problem posed in 2015 by Fetcie, Jacob, and Saavedra. Full article

(This article belongs to the Special Issue Graph Algorithms and Graph Theory)

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15 pages, 930 KiB

Open AccessArticle

Impact of Light Stress on the Synthesis of Both Antioxidants Polyphenols and Carotenoids, as Fast Photoprotective Response in Chlamydomonas reinhardtii: New Prospective for Biotechnological Potential of This Microalga

by Cecilia Faraloni, Tiziana Di Lorenzo and Alessandra Bonetti

Symmetry 2021, 13(11), 2220; https://doi.org/10.3390/sym13112220 - 20 Nov 2021

Cited by 9 | Viewed by 2100

Abstract

The aim of this study was to investigate the potential role of the microalga Chlamydomonas reinhardtii as an antioxidant source of enriched biomass. This microalga is a model organism deeply investigated for physiological studies, particularly considering carotenoid synthesis in response to stress, to [...] Read more.

The aim of this study was to investigate the potential role of the microalga Chlamydomonas reinhardtii as an antioxidant source of enriched biomass. This microalga is a model organism deeply investigated for physiological studies, particularly considering carotenoid synthesis in response to stress, to counteract the effects of the formation of free radicals. Less attention has been paid to the profile characterization of other antioxidant compounds, such as polyphenols, which can be synthesized, concomitantly with carotenoids, under photooxidative stress, especially high light. The cultures of C. reinhardtii were exposed to three different light intensities, 70, 800 and 1500 µmoles photons m⁻² s⁻¹. The increasing light intensity symmetrically induced the increasing accumulation of both carotenoids and phenolic compounds. The results showed that exposure to high light intensities caused the accumulation of electrons in the electron transport chain, with a reduction in photosynthetic activity. In the same cultures, high light intensity induced the strong increment of polyphenols such as gallic, chlorogenic and coumaric acids, which resulted 6.2-fold, 4-fold and 3.7-fold higher, respectively, than in cells exposed to the lowest intensities. As expected, at the highest light intensity, the strong induction of the xanthophyll cycle and the largest increment of loroxanthin, lutein, α-carotene and ß-carotene could be detected. Antioxidant properties doubled with respect to the initial time, both in acetone and methanol cellular extracts of these cultures, revealing a new potential role for biotechnological application of this microalga. Full article

(This article belongs to the Special Issue Photosynthetic Microorganisms: Cultivation and Application)

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11 pages, 593 KiB

Open AccessReview

Are We Right about the Right TPJ? A Review of Brain Stimulation and Social Cognition in the Right Temporal Parietal Junction

by Nathira Ahmad, Samantha Zorns, Katherine Chavarria, Janet Brenya, Aleksandra Janowska and Julian Paul Keenan

Symmetry 2021, 13(11), 2219; https://doi.org/10.3390/sym13112219 - 20 Nov 2021

Cited by 4 | Viewed by 8248

Abstract

In the past decade, the functional role of the TPJ (Temporal Parietal Junction) has become more evident in terms of its contribution to social cognition. Studies have revealed the TPJ as a ‘distinguisher’ of self and other with research focused on non-clinical populations [...] Read more.

In the past decade, the functional role of the TPJ (Temporal Parietal Junction) has become more evident in terms of its contribution to social cognition. Studies have revealed the TPJ as a ‘distinguisher’ of self and other with research focused on non-clinical populations as well as in individuals with Autism and Type I Schizophrenia. Further research has focused on the integration of self-other distinctions with proprioception. Much of what we now know about the causal role of the right TPJ derives from TMS (Transcranial Magnetic Stimulation), rTMS repetitive Transcranial Magnetic Stimulation), and tDCS (transcranial Direct Cortical Stimulation). In this review, we focus on the role of the right TPJ as a moderator of self, which is integrated and distinct from ‘other’ and how brain stimulation has established the causal relationship between the underlying cortex and agency. Full article

(This article belongs to the Special Issue Symmetry in Cognition and Emotion)

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13 pages, 2476 KiB

Open AccessArticle

Online Activation and Deactivation of a Petri Net Supervisor

by Sadok Rezig, Nidhal Rezg and Zied Hajej

Symmetry 2021, 13(11), 2218; https://doi.org/10.3390/sym13112218 - 20 Nov 2021

Cited by 3 | Viewed by 1471

Abstract

This paper highlights algebraic and mathematical properties in symmetry with Petri nets in order to control automated systems such as flexible workshops, which represent one of the most important examples in industry and for discrete event systems in general. This project deals with [...] Read more.

This paper highlights algebraic and mathematical properties in symmetry with Petri nets in order to control automated systems such as flexible workshops, which represent one of the most important examples in industry and for discrete event systems in general. This project deals with the problem of forbidden state transition by using a new application of the theory of regions for supervisory control. In the literature, most control synthesis methods suffer greatly from a cumbersome calculation burden of the Petri net supervisor given the complex exploration of the state graph. Our new methodology lightens the computational load of the Petri net supervisor by choosing specific regions on the reachability graph, on which the control is calculated offline using CPLEX. The determined controller is activated online if the process enters the chosen region, and deactivated otherwise. All our experiments were applied in a flexible workshop implemented in our research laboratory, which was used to engrave selected models on glass blocks of different colors. Full article

(This article belongs to the Special Issue Graph Algorithms and Graph Theory)

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18 pages, 1396 KiB

Open AccessArticle

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

by Khaled S. Al Noufaey

Symmetry 2021, 13(11), 2217; https://doi.org/10.3390/sym13112217 - 19 Nov 2021

Cited by 6 | Viewed by 1597

Abstract

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation [...] Read more.

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications)

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13 pages, 51365 KiB

Open AccessArticle

A Driver and Control Method for Primary Stator Discontinuous Segmented-PMLSM

by Mingyi Wang, Kai Kang, Chengming Zhang and Liyi Li

Symmetry 2021, 13(11), 2216; https://doi.org/10.3390/sym13112216 - 19 Nov 2021

Cited by 2 | Viewed by 1253

Abstract

In recent years, with the development of the permanent magnet linear synchronous motor (PMLSM), the application of PMLSM has not been limited only to the high-end equipment field; the primary stator discontinuous segmented-PMLSM (DSPMLSM), which consists of multiple primary stators and one mover, [...] Read more.

In recent years, with the development of the permanent magnet linear synchronous motor (PMLSM), the application of PMLSM has not been limited only to the high-end equipment field; the primary stator discontinuous segmented-PMLSM (DSPMLSM), which consists of multiple primary stators and one mover, has also been applied in long-distance transportation systems, such as electromagnetic launch, high precision material transport, etc. Compared with the symmetry phase parameters of conventional PMLSM, the stationary electrical parameters vary when the mover enters and leaves the primary stators (the inter-segment region). At the same time, due to the sectional power supply, there will be primary suction or pulling force when the mover enters and exits the inter-segment region, which will lead to large thrust fluctuation and result in lager position error. This paper proposed a related drive and control strategy about the DSPMLSM system, which improved the position tracking accuracy during the full range of DSPMLSM. First, the parameter variation between stator segments has been analyzed through finite element simulation of DSPMLSM. Then, a double closed-loop series control structure of position-current is designed, in which a PI-Lead controller was adopted for the position loop and a PI controller was adopted for the current loop. In order to improve the position tracking accuracy of DSPMLSM, a thrust fluctuation extended state observer (TFESO) was adopted to observe and compensate the complex thrust disturbances such as cogging force, friction and other unmodeled thrust fluctuation. At last, the DSPMLSM experimental stage was established, and the experimental results show that the proposed driver and control theory can effectively improve the position tracking accuracy of the whole stroke of DSPMLSM. Full article

(This article belongs to the Special Issue Research on Motor and Special Electromagnetic Device of Symmetry)

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12 pages, 324 KiB

Open AccessArticle

Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

by Haji Gul, Sajjad Ali, Kamal Shah, Shakoor Muhammad, Thanin Sitthiwirattham and Saowaluck Chasreechai

Symmetry 2021, 13(11), 2215; https://doi.org/10.3390/sym13112215 - 19 Nov 2021

Cited by 5 | Viewed by 1423

Abstract

In this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the [...] Read more.

In this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases . For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit. Full article

(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications II)

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22 pages, 7152 KiB

Open AccessArticle

Multi-Criteria Analysis of a People-Oriented Urban Pedestrian Road System Using an Integrated Fuzzy AHP and DEA Approach: A Case Study in Harbin, China

by Hongliang Li, Yu Lin, Yuming Wang, Jing Liu, Shan Liang, Shulin Guo and Tiangang Qiang

Symmetry 2021, 13(11), 2214; https://doi.org/10.3390/sym13112214 - 19 Nov 2021

Cited by 9 | Viewed by 1910

Abstract

Increasingly, cities worldwide are striving for green travel and slow traffic, and vigorously developing people-oriented urban pedestrian traffic with sustainability has become a fixture in recent discourse. This paper comprehensively considers the sidewalk’s facilities environment and the status of pedestrian traffic flow; divides [...] Read more.

Increasingly, cities worldwide are striving for green travel and slow traffic, and vigorously developing people-oriented urban pedestrian traffic with sustainability has become a fixture in recent discourse. This paper comprehensively considers the sidewalk’s facilities environment and the status of pedestrian traffic flow; divides the urban pedestrian road system (UPRS) into five subsystems around the underpass, overpass, crosswalk, sidewalk, and road crosswalk; and introduces the basic structure as well as the function of each system. Then, the indicators are classified into two types of crosswalk facilities and sidewalk facilities, and a comprehensive pedestrian road indicator system with the combination of subjective and objective is established. Consequently, the integration of the fuzzy AHP and DEA-based symmetrical technique for the subjective evaluation indicator combined with pedestrian traffic characteristics is developed. A nine-step semantics scale of relative importance was used so that the symmetry of the response of pedestrian satisfaction was maintained. Fuzzy evaluation based on AHP is further modeled, and the DEA is employed to achieve an overall evaluation of the quality of service (QoS) for UPRS. The applicability of the established evaluation system is finally verified through a real case study in Harbin, China. The serviceability assessment method in this paper provides a new idea for planners to conduct sustainability evaluation for UPRS in future urban renewal development. Full article

(This article belongs to the Special Issue Advanced Transportation Technologies and Symmetries in Intelligent Transportation Systems)

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18 pages, 4157 KiB

Open AccessArticle

An Efficient and Robust Improved A* Algorithm for Path Planning

by Huanwei Wang, Xuyan Qi, Shangjie Lou, Jing Jing, Hongqi He and Wei Liu

Symmetry 2021, 13(11), 2213; https://doi.org/10.3390/sym13112213 - 19 Nov 2021

Cited by 24 | Viewed by 4200

Abstract

Path planning plays an essential role in mobile robot navigation, and the A* algorithm is one of the best-known path planning algorithms. However, the conventional A* algorithm and the subsequent improved algorithms still have some limitations in terms of robustness and efficiency. These [...] Read more.

Path planning plays an essential role in mobile robot navigation, and the A* algorithm is one of the best-known path planning algorithms. However, the conventional A* algorithm and the subsequent improved algorithms still have some limitations in terms of robustness and efficiency. These limitations include slow algorithm efficiency, weak robustness, and collisions when robots are traversing. In this paper, we propose an improved A*-based algorithm called EBHSA* algorithm. The EBHSA* algorithm introduces the expansion distance, bidirectional search, heuristic function optimization and smoothing into path planning. The expansion distance extends a certain distance from obstacles to improve path robustness by avoiding collisions. Bidirectional search is a strategy that searches for a path from the start node and from the goal node at the same time. Heuristic function optimization designs a new heuristic function to replace the traditional heuristic function. Smoothing improves path robustness by reducing the number of right-angle turns. Moreover, we carry out simulation tests with the EBHSA* algorithm, and the test results show that the EBHSA* algorithm has excellent performance in terms of robustness and efficiency. In addition, we transplant the EBHSA* algorithm to a robot to verify its effectiveness in the real world. Full article

(This article belongs to the Special Issue Advanced Decision-Making Techniques in Dynamic Industry 4.0 Sustainable Engineering Processes)

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15 pages, 328 KiB

Open AccessArticle

Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions

by Thongchai Dumrongpokaphan, Sotiris K. Ntouyas and Thanin Sitthiwirattham

Symmetry 2021, 13(11), 2212; https://doi.org/10.3390/sym13112212 - 19 Nov 2021

Cited by 2 | Viewed by 1029

Abstract

In this paper, we study a boundary value problem involving

(p, q)

-integrodifference equations, supplemented with nonlocal fractional

(p, q)

-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a [...] Read more.

In this paper, we study a boundary value problem involving

(p, q)

-integrodifference equations, supplemented with nonlocal fractional

(p, q)

-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of

(p, q)

-integral that are used in our study. Full article

(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)

22 pages, 2275 KiB

Open AccessArticle

An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data

by Siti Zahariah, Habshah Midi and Mohd Shafie Mustafa

Symmetry 2021, 13(11), 2211; https://doi.org/10.3390/sym13112211 - 19 Nov 2021

Cited by 2 | Viewed by 1130

Abstract

Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where

p > > n

. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least [...] Read more.

Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where

p > > n

. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects. Full article

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20 pages, 7482 KiB

Open AccessArticle

Detection of Road Images Containing a Counterlight Using Multilevel Analysis

by JongBae Kim

Symmetry 2021, 13(11), 2210; https://doi.org/10.3390/sym13112210 - 19 Nov 2021

Cited by 1 | Viewed by 1238

Abstract

In this paper, a method for detecting real-time images that include counterlight produced by the sun, is proposed. It involves applying a multistep analysis of the size, location, and distribution of bright areas in the image. In general, images containing counterlight have a [...] Read more.

In this paper, a method for detecting real-time images that include counterlight produced by the sun, is proposed. It involves applying a multistep analysis of the size, location, and distribution of bright areas in the image. In general, images containing counterlight have a symmetrically high brightness value at a specific location spread over an extremely large region. In addition, the distribution and change in brightness in that specific region have a symmetrically large difference compared with other regions. Through a multistep analysis of these symmetrical features, it is determined whether counterlight is included in the image. The proposed method presents a processing time of approximately 0.7 s and a detection accuracy of 88%, suggesting that the approach can be applied to a safe driving support system for autonomous vehicles. Full article

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19 pages, 326 KiB

Open AccessArticle

Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

by Soubhagya Kumar Sahoo, Muhammad Tariq, Hijaz Ahmad, Ayman A. Aly, Bassem F. Felemban and Phatiphat Thounthong

Symmetry 2021, 13(11), 2209; https://doi.org/10.3390/sym13112209 - 19 Nov 2021

Cited by 9 | Viewed by 1380

Abstract

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory [...] Read more.

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities II)

20 pages, 6534 KiB

Open AccessArticle

Trajectory Tracking Control for Underactuated USV with Prescribed Performance and Input Quantization

by Kunyi Jiang, Lei Mao, Yumin Su and Yuxin Zheng

Symmetry 2021, 13(11), 2208; https://doi.org/10.3390/sym13112208 - 19 Nov 2021

Cited by 9 | Viewed by 1894

Abstract

This paper is devoted to the problem of prescribed performance trajectory tracking control for symmetrical underactuated unmanned surface vessels (USVs) in the presence of model uncertainties and input quantization. By combining backstepping filter mechanisms and adaptive algorithms, two robust control architectures are investigated [...] Read more.

This paper is devoted to the problem of prescribed performance trajectory tracking control for symmetrical underactuated unmanned surface vessels (USVs) in the presence of model uncertainties and input quantization. By combining backstepping filter mechanisms and adaptive algorithms, two robust control architectures are investigated for surge motion and yaw motion. To guarantee the prespecified performance requirements for position tracking control, the constrained error dynamics are transformed to unconstrained ones by virtue of a tangent-type nonlinear mapping function. On the other hand, the inaccurate model can be identified through radial basis neural networks (RBFNNs), where the minimum learning parameter (MLP) algorithm is employed with a low computational complexity. Furthermore, quantization errors can be effectively reduced even when the parameters of the quantizer remain unavailable to designers. Finally, the effectiveness of the proposed controllers is verified via theoretical analyses and numerical simulations. Full article

(This article belongs to the Special Issue Recent Progress in Robot Control Systems: Theory and Applications)

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18 pages, 2251 KiB

Open AccessArticle

Performance Estimation in V2X Networks Using Deep Learning-Based M-Estimator Loss Functions in the Presence of Outliers

by Ali R. Abdellah, Abdullah Alshahrani, Ammar Muthanna and Andrey Koucheryavy

Symmetry 2021, 13(11), 2207; https://doi.org/10.3390/sym13112207 - 19 Nov 2021

Cited by 5 | Viewed by 1842

Abstract

Recently, 5G networks have emerged as a new technology that can control the advancement of telecommunication networks and transportation systems. Furthermore, 5G networks provide better network performance while reducing network traffic and complexity compared to current networks. Machine-learning techniques (ML) will help symmetric [...] Read more.

Recently, 5G networks have emerged as a new technology that can control the advancement of telecommunication networks and transportation systems. Furthermore, 5G networks provide better network performance while reducing network traffic and complexity compared to current networks. Machine-learning techniques (ML) will help symmetric IoT applications become a significant new data source in the future. Symmetry is a widely studied pattern in various research areas, especially in wireless network traffic. The study of symmetric and asymmetric faults and outliers (anomalies) in network traffic is an important topic. Nowadays, deep learning (DL) is an advanced approach in challenging wireless networks such as network management and optimization, anomaly detection, predictive analysis, lifetime value prediction, etc. However, its performance depends on the efficiency of training samples. DL is designed to work with large datasets and uses complex algorithms to train the model. The occurrence of outliers in the raw data reduces the reliability of the training models. In this paper, the performance of Vehicle-to-Everything (V2X) traffic was estimated using the DL algorithm. A set of robust statistical estimators, called M-estimators, have been proposed as robust loss functions as an alternative to the traditional MSE loss function, to improve the training process and robustize DL in the presence of outliers. We demonstrate their robustness in the presence of outliers on V2X traffic datasets. Full article

(This article belongs to the Section Computer)

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18 pages, 316 KiB

Open AccessArticle

Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

by Arshad Ali Khan and Basit Ali

Symmetry 2021, 13(11), 2206; https://doi.org/10.3390/sym13112206 - 19 Nov 2021

Cited by 5 | Viewed by 1266

Abstract

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of

b -

metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness [...] Read more.

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of

b -

metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of

b -

metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Fixed Point Theory)

10 pages, 266 KiB

Open AccessArticle

Integrable Nonlocal PT-Symmetric Modified Korteweg-de Vries Equations Associated with so(3, \({\mathbb{R}}\))

by Wen-Xiu Ma

Symmetry 2021, 13(11), 2205; https://doi.org/10.3390/sym13112205 - 19 Nov 2021

Cited by 9 | Viewed by 1329

Abstract

We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra

so (3, R)

. The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal complex reverse-spacetime and real reverse-spacetime modified Korteweg-de Vries equations [...] Read more.

We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra

so (3, R)

. The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal complex reverse-spacetime and real reverse-spacetime modified Korteweg-de Vries equations associated with

so (3, R)

. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials)

24 pages, 12362 KiB

Open AccessArticle

The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

by Xin Yang, Guangjun Zhang, Xueren Li and Dong Wang

Symmetry 2021, 13(11), 2204; https://doi.org/10.3390/sym13112204 - 18 Nov 2021

Cited by 4 | Viewed by 1489

Abstract

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. [...] Read more.

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order

q

and the feedback gain parameter

k_{1}

. In addition, the fractional-order or the parameter

k_{1}

can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by

q

or parameter

k_{1}

are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter

β

of the electromagnetic radiation,

k_{1}

and

q

, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of

k_{1}

and

q

can be summarized into three cases:

β > 0.02

,

- 0.06 < β < 0.02

and

β < - 0.06

. The influence rules and some interesting phenomena are investigated. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

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15 pages, 2490 KiB

Open AccessArticle

Extended Graph of the Fuzzy Topographic Topological Mapping Model

by Muhammad Zillullah Mukaram, Tahir Ahmad, Norma Alias, Noorsufia Abd Shukor and Faridah Mustapha

Symmetry 2021, 13(11), 2203; https://doi.org/10.3390/sym13112203 - 18 Nov 2021

Cited by 2 | Viewed by 1118

Abstract

Fuzzy topological topographic mapping (

F T T M

) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM,

F T T M_{n}

, is [...] Read more.

Fuzzy topological topographic mapping (

F T T M

) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM,

F T T M_{n}

, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of

F T T M

, namely the homeomorphisms between its components, allows the generation of new

F T T M

. The generated

F T T M

s can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the

F T T M

components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated

F T T M

pseudo degree zero with respect to n number of components and k number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture. Full article

(This article belongs to the Special Issue Research on Symmetry Applied in Graph Theory)

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