Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, and many other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 13.3 days after submission; acceptance to publication is undertaken in 3.7 days (median values for papers published in this journal in the first half of 2021).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our authors say about Symmetry.
- Sections: Published in five topical sections.
Impact Factor:
2.713 (2020)
;
5-Year Impact Factor:
2.612 (2020)
Latest Articles
The Search for μ→eγ with 10-14 Sensitivity: The Upgrade of the MEG Experiment++
Symmetry 2021, 13(9), 1591; https://doi.org/10.3390/sym13091591 (registering DOI) - 29 Aug 2021
Abstract
The MEG experiment took data at the Paul Scherrer Institute in the years 2009–2013 to test the violation of the lepton flavor conservation law, which originates from an accidental symmetry that the Standard Model of elementary particle physics has, and published the most
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The MEG experiment took data at the Paul Scherrer Institute in the years 2009–2013 to test the violation of the lepton flavor conservation law, which originates from an accidental symmetry that the Standard Model of elementary particle physics has, and published the most stringent limit on the charged lepton flavor violating decay : BR( ) at confidence level. The MEG detector has been upgraded in order to reach a sensitivity of . The basic principle of MEG II is to achieve the highest possible sensitivity using the full muon beam intensity at the Paul Scherrer Institute ( muons/s) with an upgraded detector. The main improvements are better rate capability of all sub-detectors and improved resolutions while keeping the same detector concept. In this paper, we present the current status of the preparation, integration and commissioning of the MEG II detector in the recent engineering runs.
Full article
(This article belongs to the Special Issue Upgrades in High Energy Physics Experiments)
Open AccessArticle
Different Drop Heights in Bilateral Asymmetry and Interjoint Coordination during Repetitive Drop-Jumps
Symmetry 2021, 13(9), 1590; https://doi.org/10.3390/sym13091590 (registering DOI) - 29 Aug 2021
Abstract
The difference of drop heights will affect the biomechanics of lower extremities during drop-jump (DJ) landing. Therefore, this study explored the effects of drop heights and training volumes on interjoint coordination and the side-to-side asymmetry of the lower extremities during landing. Twenty males
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The difference of drop heights will affect the biomechanics of lower extremities during drop-jump (DJ) landing. Therefore, this study explored the effects of drop heights and training volumes on interjoint coordination and the side-to-side asymmetry of the lower extremities during landing. Twenty males were randomly assigned to perform 200 DJs (DJs200) from 30, 40 and 50 cm (drop-jump height (DJH) 30, DJH40 and DJH50) platform. One-way ANOVA repeated measure, using MATLAB software, was used to compare the differences of interjoint coordination, side-to-side asymmetry of ground contact time (GCT) and the maximum impact in vertical ground-reaction forces peak (I-vGRFpeak) in the 1st, 50th, 100th, 150th and 200th jumps (DJ1, DJs50, DJs100, DJs150 and DJs200). To examine whether significant differences exist, the least significant difference’s (LSD) method was used for post-hoc comparison. The mean absolute relative phase (MARP) and deviation phase (DP) of hip–knee were lower than DJH50 at DJH30 and DJH40, while side-to-side asymmetry of GCT and I-vGRFpeak were greater than DJH30 and DJH40 at DJH50 within DJs200 (all p <0.05). However, there was no significant difference in MARP and DP of hip–ankle and knee–ankle. Therefore, training at DJH30 may effectively improve jumping performance and reduce musculoskeletal injury risk.
Full article
(This article belongs to the Special Issue Symmetry Applied in Biomechanics and Mechanical Engineering)
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Open AccessArticle
On PID Design Constraints in Relation to Control of Strictly Metzler Linear MIMO Systems
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and
Symmetry 2021, 13(9), 1589; https://doi.org/10.3390/sym13091589 (registering DOI) - 29 Aug 2021
Abstract
For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the
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For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present.
Full article
(This article belongs to the Special Issue PID Control and Symmetry)
Open AccessArticle
A Weight Assignment Algorithm for Incomplete Traffic Information Road Based on Fuzzy Random Forest Method
Symmetry 2021, 13(9), 1588; https://doi.org/10.3390/sym13091588 (registering DOI) - 29 Aug 2021
Abstract
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One of the keys in time-dependent routing is determining the weight for each road network link based on symmetrical and complete traffic information. To facilitate travel planning considering traffic situations based on historical global position system (GPS) trajectory data which uncover the whole
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One of the keys in time-dependent routing is determining the weight for each road network link based on symmetrical and complete traffic information. To facilitate travel planning considering traffic situations based on historical global position system (GPS) trajectory data which uncover the whole road network, this paper proposes a fuzzy random forest-based road section data estimation method, which uses the third law of geography as the core idea. For different time periods, road grade, tidal lane, proximity to infrastructure (main places that affect traffic, such as schools, hospitals), and accident road sections were selected as indicators that influence the traffic. The random forest algorithm is used to build the mapping relationship between attribute data with average traffic which is obtained based on GPS data. Subsequently, the fuzzy reasoning method is used to obtain the weight of road links missing traffic information by calculating their similarities with typical road section samples. Using the road network of Suzhou City as an example, the proposed method was used to analyze estimate the average driving speeds of road sections with missing traffic information for different time periods. Experimental results show that this method can effectively avoid congested road sections and obtain high-speed travel routes.
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Open AccessArticle
Null Homology Groups and Stable Currents in Warped Product Submanifolds of Euclidean Spaces
Symmetry 2021, 13(9), 1587; https://doi.org/10.3390/sym13091587 (registering DOI) - 28 Aug 2021
Abstract
In this paper, we prove that, for compact warped product submanifolds in an Euclidean space , there are no stable p-currents, homology groups are vanishing, and is homotopic to the Euclidean sphere
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In this paper, we prove that, for compact warped product submanifolds in an Euclidean space , there are no stable p-currents, homology groups are vanishing, and is homotopic to the Euclidean sphere under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds.
Full article
Open AccessArticle
Body Balance after Fascial Therapy in Athletes with Soft Lower Limb Muscle Injuries
by
, , , , , , , , and
Symmetry 2021, 13(9), 1586; https://doi.org/10.3390/sym13091586 (registering DOI) - 28 Aug 2021
Abstract
Background: Most injuries in competitive sports are due to overstrain and excessive muscular and fascial tension. This study aimed to assess the effects of a single session of fascial therapy on balance and lower limb weight-bearing in professional athletes following a lower limb
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Background: Most injuries in competitive sports are due to overstrain and excessive muscular and fascial tension. This study aimed to assess the effects of a single session of fascial therapy on balance and lower limb weight-bearing in professional athletes following a lower limb soft-tissue injury. Methods: A pedobarographic platform was used to assess the weight-bearing on both lower limbs and corporal balance. A total of 41 athletes with an acute soft-tissue injury involving the quadriceps femoris muscle were included in the study. Each patient underwent myofascial therapy in the injured limb only. The therapy was intended to release tension and improve proprioception. Results: The injured and healthy limbs showed significant asymmetry in body weight distribution. Before treatment, the patients bore less weight on the injured limb than on the healthy limb. After fascial therapy, eyes-closed tests showed an improved weight distribution symmetry between the two lower limbs. There were no significant differences in the values of the evaluated balance parameters between those measured at baseline and those measured after the therapy, measured after the rehabilitation session. Conclusions: A single fascial therapy session has a beneficial effect on corporal balance in runners with an injured lower limb.
Full article
(This article belongs to the Special Issue Symmetry in Medicine and Biomechanics)
Open AccessArticle
Existence Theory for Positive Iterative Solutions to a Type of Boundary Value Problem
by
Symmetry 2021, 13(9), 1585; https://doi.org/10.3390/sym13091585 (registering DOI) - 28 Aug 2021
Abstract
We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the
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We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the effectiveness of our results was presented.
Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering III)
Open AccessReview
Blue Phase Liquid Crystals with Tailored Crystal Orientation for Photonic Applications
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and
Symmetry 2021, 13(9), 1584; https://doi.org/10.3390/sym13091584 (registering DOI) - 27 Aug 2021
Abstract
Blue phase (BP) liquid crystals, which self-assemble into soft three-dimensional (3D) photonic crystals, have attracted enormous research interest due to their ability to control light and potential photonic applications. BPs have long been known as optically isotropic materials, but recent works have revealed
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Blue phase (BP) liquid crystals, which self-assemble into soft three-dimensional (3D) photonic crystals, have attracted enormous research interest due to their ability to control light and potential photonic applications. BPs have long been known as optically isotropic materials, but recent works have revealed that achieving on-demand 3D orientation of BP crystals is necessary to obtain improved electro-optical performance and tailored optical characteristics. Various approaches have been proposed to precisely manipulate the crystal orientation of BPs on a substrate, through the assistance of external stimuli and directing self-assembly processes. Here, we discuss the various orientation-controlling technologies of BP crystals, with their mechanisms, advantages, drawbacks, and promising applications. This review first focuses on technologies to achieve the uniform crystal plane orientation of BPs on a substrate. Further, we review a strategy to control the azimuthal orientation of BPs along predesigned directions with a uniform crystal plane, allowing the 3D orientation to be uniquely defined on a substrate. The potential applications such as volume holograms are also discussed with their operation principle. This review provides significant advances in 3D photonic crystals and gives a huge potential for intelligent photonic devices with tailored optical characteristics.
Full article
(This article belongs to the Special Issue Symmetry and Liquid Crystals)
Open AccessArticle
Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
Symmetry 2021, 13(9), 1583; https://doi.org/10.3390/sym13091583 (registering DOI) - 27 Aug 2021
Abstract
The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point
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The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case.
Full article
(This article belongs to the Section Physics and Symmetry/Asymmetry)
Open AccessArticle
A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts
Symmetry 2021, 13(9), 1582; https://doi.org/10.3390/sym13091582 (registering DOI) - 27 Aug 2021
Abstract
Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile
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Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the contact problem as a zero-order approximation. This allows to give an exact contact solution during each fretting cycle, depending on the current worn profile, and thus for the explicit statement of an ordinary integro-differential equation system for the time-evolution of the fretting profile, which can be easily solved numerically. The proposed method gives the same results as a known, contact mechanically more rigorous simulation procedure that also operates within the framework of the Hertz–Mindlin approximation, but works significantly faster than the latter one. Tangential and torsional fretting wear are considered in detail. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreement with experimental results from the literature.
Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
Open AccessArticle
Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II
Symmetry 2021, 13(9), 1581; https://doi.org/10.3390/sym13091581 (registering DOI) - 27 Aug 2021
Abstract
Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms
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Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms of ordinary spacetime fields. We note that the spectrum can be consistent with unitarity while still preserving Lorentz covariance, albeit not in the usual way, but by employing an infinite-dimensional unitary representation of the Lorentz group.
Full article
(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)
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Open AccessArticle
Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations
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and
Symmetry 2021, 13(9), 1580; https://doi.org/10.3390/sym13091580 (registering DOI) - 27 Aug 2021
Abstract
The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition
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The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.
Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)
Open AccessArticle
A Combined Model Based on EOBL-CSSA-LSSVM for Power Load Forecasting
Symmetry 2021, 13(9), 1579; https://doi.org/10.3390/sym13091579 (registering DOI) - 27 Aug 2021
Abstract
Inaccurate electricity load forecasting can lead to the power sector gaining asymmetric information in the supply and demand relationship. This asymmetric information can lead to incorrect production or generation plans for the power sector. In order to improve the accuracy of load forecasting,
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Inaccurate electricity load forecasting can lead to the power sector gaining asymmetric information in the supply and demand relationship. This asymmetric information can lead to incorrect production or generation plans for the power sector. In order to improve the accuracy of load forecasting, a combined power load forecasting model based on machine learning algorithms, swarm intelligence optimization algorithms, and data pre-processing is proposed. Firstly, the original signal is pre-processed by the VMD–singular spectrum analysis data pre-processing method. Secondly, the noise-reduced signals are predicted using the Elman prediction model optimized by the sparrow search algorithm, the ELM prediction model optimized by the chaotic adaptive whale algorithm (CAWOA-ELM), and the LSSVM prediction model optimized by the chaotic sparrow search algorithm based on elite opposition-based learning (EOBL-CSSA-LSSVM) for electricity load data, respectively. Finally, the weighting coefficients of the three prediction models are calculated using the simulated annealing algorithm and weighted to obtain the prediction results. Comparative simulation experiments show that the VMD–singular spectrum analysis method and two improved intelligent optimization algorithms proposed in this paper can effectively improve the prediction accuracy. Additionally, the combined forecasting model proposed in this paper has extremely high forecasting accuracy, which can help the power sector to develop a reasonable production plan and power generation plans.
Full article
(This article belongs to the Special Issue Advanced Technologies in Electrical and Electronic Engineering)
Open AccessArticle
Integrability of the Multi-Species TASEP with Species-Dependent Rates
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Symmetry 2021, 13(9), 1578; https://doi.org/10.3390/sym13091578 (registering DOI) - 27 Aug 2021
Abstract
Assume that each species l has its own jump rate in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for
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Assume that each species l has its own jump rate in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.
Full article
(This article belongs to the Special Issue Mathematical Aspects in Non-equilibrium Thermodynamics)
Open AccessFeature PaperReview
The Jahn–Teller and Pseudo-Jahn–Teller Effects: A Unique and Only Source of Spontaneous Symmetry Breaking in Atomic Matter
Symmetry 2021, 13(9), 1577; https://doi.org/10.3390/sym13091577 (registering DOI) - 27 Aug 2021
Abstract
In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these
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In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.
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(This article belongs to the Special Issue New Frontiers in Stereochemistry)
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Open AccessArticle
On New Generalized Dunkel Type Integral Inequalities with Applications
Symmetry 2021, 13(9), 1576; https://doi.org/10.3390/sym13091576 (registering DOI) - 27 Aug 2021
Abstract
In this paper, by applying majorization theory, we study the Schur convexity of functions related to Dunkel integral inequality. We establish some new generalized Dunkel type integral inequalities and their applications to inequality theory.
Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications)
Open AccessFeature PaperArticle
Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
Symmetry 2021, 13(9), 1575; https://doi.org/10.3390/sym13091575 (registering DOI) - 26 Aug 2021
Abstract
Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions
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Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions that the second fundamental form is parallel with respect to the induced connection and the normal connection is compatible with a metric on the transversal bundle. Both connections are induced by a canonical transversal plane bundle, which is defined by certain symmetry conditions. The obtained surfaces are always products of an ellipse and a conical planar curve.
Full article
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
Open AccessFeature PaperArticle
A Novel Shuffled Frog-Leaping Algorithm for Unrelated Parallel Machine Scheduling with Deteriorating Maintenance and Setup Time
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Symmetry 2021, 13(9), 1574; https://doi.org/10.3390/sym13091574 (registering DOI) - 26 Aug 2021
Abstract
Unrelated parallel machine scheduling problems (UPMSP) with various processing constraints have been considered fully; however, a UPMSP with deteriorating preventive maintenance (PM) and sequence-dependent setup time (SDST) is seldom considered. In this study, a new differentiated shuffled frog-leaping algorithm (DSFLA) is presented to
[...] Read more.
Unrelated parallel machine scheduling problems (UPMSP) with various processing constraints have been considered fully; however, a UPMSP with deteriorating preventive maintenance (PM) and sequence-dependent setup time (SDST) is seldom considered. In this study, a new differentiated shuffled frog-leaping algorithm (DSFLA) is presented to solve the problem with makespan minimization. The whole search procedure consists of two phases. In the second phase, quality evaluation is done on each memeplex, then the differentiated search processes are implemented between good memeplexes and other ones, and a new population shuffling is proposed. We conducted a number of experiments. The computational results show that the main strategies of DSFLA were effective and reasonable and DSFLA was very competitive at solving UPMSP with deteriorating PM and SDST.
Full article
(This article belongs to the Special Issue Meta-heuristics for Manufacturing Systems Optimization)
Open AccessFeature PaperArticle
Categorical Nonstandard Analysis
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and
Symmetry 2021, 13(9), 1573; https://doi.org/10.3390/sym13091573 (registering DOI) - 26 Aug 2021
Abstract
In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while we make use
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In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while we make use of an endofunctor on a topos of sets S together with a natural transformation , instead of the terms as “standard”, “internal”, or “external”. Moreover, we propose a general notion of a space called -space, and the category whose objects are -spaces and morphisms are functions called -spatial morphisms. The category , which is shown to be Cartesian closed, gives a unified viewpoint toward topological and coarse geometric structure. It will also be useful to further study symmetries/asymmetries of the systems with infinite degrees of freedom, such as quantum fields.
Full article
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
Open AccessArticle
Bifuzzy-Bilevel Programming Model: Solution and Application
Symmetry 2021, 13(9), 1572; https://doi.org/10.3390/sym13091572 (registering DOI) - 26 Aug 2021
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Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems. In order to solve such problems better with intricate and vague information that can be efficiently handled by bifuzzy theory, a
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Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems. In order to solve such problems better with intricate and vague information that can be efficiently handled by bifuzzy theory, a bifuzzy–bilevel programming model that sets the parameters to bifuzzy variables is proposed in this paper, which can process complex realistic data more accurately and improve the feasibility and validity of bi-level programming models. To ensure the solvability of the model, the equivalent form of the bifuzzy–bilevel programming model is obtained by utilizing the expected value operator. According to the linear and nonlinear characteristics of the model, the Karush–Kuhn–Tucker condition and particle swarm optimization algorithm are employed to handle the problem, respectively. Finally, by taking the distribution center location problem of the supplier as an example, the bifuzzy–bilevel programming model is applied in practice to balance highly intricate customer demands and corporate cost minimization, obtaining the feasible solution of functions at the upper and lower levels, and the bifuzzy information in the problem can also be processed well, which proves the effectiveness of the proposed methodology.
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Nucleosynthesis in the Era of Multi-Messenger Astronomy
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