Symmetry doi: 10.3390/sym16030372
Authors: Ayed. R. A. Alanzi Raouf Fakhfakh Fatimah Alshahrani
A notion of generalized (two-parameterized) t-transformation of free convolution, also called (t=(a,b))-deformed free convolution, is introduced for a∈R and b>0. In this article, some results of t-deformed free convolution are given within the theory of Cauchy-Stieltjes Kernel (CSK) families. The variance function is a fundamental concept in CSK families. An expression is provided for the variance function under t-deformed free convolution power. In addition, through the use of the variance function, an approximation is provided for members of the t-deformed free Gaussian CSK family and members of the t-deformed free Poisson CSK family respectively. Furthermore, by involving the free multiplicative convolution, a new limit theorem is provided with respect to t-deformed free convolution.
]]>Symmetry doi: 10.3390/sym16030371
Authors: Li Wang
The Hamilton–Waterloo problem is a problem of graph factorization. The Hamilton–Waterloo problem HWP(H;m,n;α,β) asks for a two-factorization of a graph H containing α Cm-factors and β Cn-factors. Let Kv* denote the complete graph Kv if v is odd and Kv minus a one-factor if v is even. In this paper, we completely solve the Hamilton–Waterloo problem HWP(Kv*;m,16;α,β) for odd m≥9 and α≥15.
]]>Symmetry doi: 10.3390/sym16030370
Authors: Juan Carlos Vielma-Quintero Edgar Giovanny Diaz-Segura Juan Carlos Vielma
Seismic-resistant design incorporates measures to ensure that structures perform adequately under specific limit states, focusing on seismic forces derived from both the equivalent static and spectral modal methods. This study examined buildings on slopes in densely built urban areas, a common scenario in Latin American cities with high seismic risks. The adjustment of high-rise buildings to sloping terrains induces structural asymmetry, leading to plan and elevation irregularities that significantly impact their seismic response. This paper explores the asymmetry in medium-height reinforced concrete frame buildings on variable inclines (0°, 15°, 30°, and 45°) and its effect on their nonlinear response, assessed via displacements, rotations, and damage. Synthetic accelerograms matched with Chile’s high seismic hazard design spectrum, scaled for different performance states and seismic records from the Chilean subduction zone, were applied. The findings highlight structural asymmetry’s role in influencing nonlinear response parameters such as ductility, transient interstory drifts, and roof rotations, and uncover element demand distributions surpassing conventional analysis and in earthquake-resistant design expectations.
]]>Symmetry doi: 10.3390/sym16030369
Authors: Zeyuan Liu Xingcheng Wu Wenfeng Zhang Yan Yang Chengzi Liu
In the traditional control scheme of a 12/8-pole bearingless switched reluctance motor (BSRM), radial force and torque are usually controlled as a compromise due to the conflict between their effective output areas. Additionally, each phase requires individual power circuits and is excited in turn to produce a continuous levitation force, resulting in high power device requirements and high controller costs. This paper discusses a 12/8-pole single-winding hybrid-rotor bearingless switched reluctance motor (HBSRM) with a hybrid rotor consisting of cylindrical and salient-pole lamination segments. The asymmetric rotor of the HBSRM slightly increases the complexity of its structure and magnetic circuit, but makes it possible to generate the desired radial force at any rotor angular position. A control scheme for the HBSRM is developed to utilize the independent excitation of the four windings in one phase to generate the desired levitation force at any rotor angular position, and it requires only half the number of power circuits used in the conventional control scheme of a 12/8-pole single-winding BSRM. Different from the average torque chosen to be controlled in traditional methods, this scheme directly regulates the instantaneous total torque produced by all excited phases together and presents a current algorithm to optimize the torque contribution of each phase so as to reduce torque pulsation, and the improved performance of this bearingless motor is finally validated by simulation analysis.
]]>Symmetry doi: 10.3390/sym16030368
Authors: Aasma Shaheen Afshan Batool Amjad Ali Hamed Al Sulami Aftab Hussain
This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper.
]]>Symmetry doi: 10.3390/sym16030367
Authors: Yicheng Chi Hao Pan Qinghui Meng Lidong Zhang Peng Zhang
Accurate thermochemical data are of great importance in developing quantitatively predictive reaction mechanisms for transportation fuels, such as diesel and jet fuels, which are primarily composed of large hydrocarbon molecules, especially large straight-chain alkanes containing more than 10 carbon atoms. This paper presents an ONIOM[QCISD(T)/CBS:DFT]-based theoretical thermochemistry study on the hydrogen abstraction reactions of straight-chain alkanes, n-CnH2n+2, (n = 1–16) by hydrogen (H), hydroxyl (OH), and hydroperoxyl (HO2) radicals. These reactions, with n ≥ 10, pose significant computational challenges for prevalent high-level ab initio methods. However, they are effectively addressed using the ONIOM-based method. One notable aspect of this study is the consideration of the high symmetry of straight-chain alkanes. This symmetry allows us to study half of the reactions, employing a generalized approach. Therefore, a total of 216 reactions are systematically studied for the three reaction systems. Our results align very well with those from the widely accepted high-level QCISD(T)/CBS method, with discrepancies between the two generally less than 0.10 kcal/mol. Furthermore, we compared large straight-chain alkanes (n-C16H34 and n-C18H38) with large methyl ester molecules (C15H31COOCH3 and C17H33COOCH3) to elucidate the impact of functional groups (ester group and C=C double bond) on the reactivity of the long-chain structure. These findings underscore the accuracy and efficiency of the ONIOM-based method in computational thermochemistry, particularly for large straight-chain hydrocarbons in transportation fuels.
]]>Symmetry doi: 10.3390/sym16030366
Authors: Syed Ibrar Hussain Elena Toscano
Skin cancer poses a serious risk to one’s health and can only be effectively treated with early detection. Early identification is critical since skin cancer has a higher fatality rate, and it expands gradually to different areas of the body. The rapid growth of automated diagnosis frameworks has led to the combination of diverse machine learning, deep learning, and computer vision algorithms for detecting clinical samples and atypical skin lesion specimens. Automated methods for recognizing skin cancer that use deep learning techniques are discussed in this article: convolutional neural networks, and, in general, artificial neural networks. The recognition of symmetries is a key point in dealing with the skin cancer image datasets; hence, in developing the appropriate architecture of neural networks, as it can improve the performance and release capacities of the network. The current study emphasizes the need for an automated method to identify skin lesions to reduce the amount of time and effort required for the diagnostic process, as well as the novel aspect of using algorithms based on deep learning for skin lesion detection. The analysis concludes with underlying research directions for the future, which will assist in better addressing the difficulties encountered in human skin cancer recognition. By highlighting the drawbacks and advantages of prior techniques, the authors hope to establish a standard for future analysis in the domain of human skin lesion diagnostics.
]]>Symmetry doi: 10.3390/sym16030365
Authors: Wenru Chen Xu Zhao Mi Zhou Haiqing Chen Qingqing Ji Weihu Cheng
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions.
]]>Symmetry doi: 10.3390/sym16030364
Authors: Osvaldo Civitarese
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)strong × SU(2)weak × U(1)elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics.
]]>Symmetry doi: 10.3390/sym16030363
Authors: Rose Maluleka Godwin Chidi Ugwunnadi Maggie Aphane Hammed A. Abass Abdul Rahim Khan
This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce a modified Halpern iterative technique combined with an inertial approach and Tseng methods for finding a common solution of the fixed-point problem of Bregman strongly nonexpansive mapping and the pseudomonotone variational inequality problem. Using our iterative approach, we develop a strong convergence result for approximating the solution of the aforementioned problems. We also discuss some consequences of our major finding. The results presented in this paper complement and build upon many relevant discoveries in the literature.
]]>Symmetry doi: 10.3390/sym16030362
Authors: Marianty Ionel Miguel Ángel Javaloyes
We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversibility. As a consequence, reversible pseudo-Finsler manifolds with constant flag curvature are radially symmetric.
]]>Symmetry doi: 10.3390/sym16030361
Authors: Yue Zhang Qing-Wen Wang Lv-Ming Xie
This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.
]]>Symmetry doi: 10.3390/sym16030360
Authors: Faizah M. Alharbi Nafeesa G. Alhendi
In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.
]]>Symmetry doi: 10.3390/sym16030359
Authors: Giulia Frau Christoph Langenbruch
We review the experimental status of searches for lepton-flavour violation in the charged sector. We give an overview of searches for lepton-flavour violation in purely leptonic decays, hadron decays, and decays of heavy bosons. We focus on the most stringent constraints on lepton-flavour violating processes in these areas and give prospects for ongoing and future experiments.
]]>Symmetry doi: 10.3390/sym16030358
Authors: Zhaohui Qin Faguo Huang Jiafang Pan Junlin Niu Haihua Qin
Fault data under real operating conditions are often difficult to collect, making the number of trained fault data small and out of proportion to normal data. Thus, fault diagnosis symmetry (balance) is compromised. This will result in less effective fault diagnosis methods for cases with a small number of data and data imbalances (S&I). We present an innovative solution to overcome this problem, which is composed of two components: data augmentation and fault diagnosis. In the data augmentation section, the S&I dataset is supplemented with a deep convolutional generative adversarial network based on a gradient penalty and Wasserstein distance (WDCGAN-GP), which solve the problems of the generative adversarial network (GAN) being prone to model collapse and the gradient vanishing during the training time. The addition of self-attention allows for a better identification and generation of sample features. Finally, the addition of spectral normalization can stabilize the training of the model. In the fault diagnosis section, fault diagnosis is performed through a convolutional neural network with coordinate attention (CNN-CA). Our experiments conducted on two bearing fault datasets for comparison demonstrate that the proposed method surpasses other comparative approaches in terms of the quality of data augmentation and the accuracy of fault diagnosis. It effectively addresses S&I fault diagnosis challenges.
]]>Symmetry doi: 10.3390/sym16030357
Authors: Nikolai S. Akintsov Artem P. Nevecheria Gennadii F. Kopytov Yongjie Yang Tun Cao
This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz spacetime coordinates are obtained. The descriptions of particle motion using the old and new Lorentz spacetime coordinates as applied to plane laser pulses are compared in terms of the particle kinetic energy. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and that of a plane laser pulse, rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions. The new and old Lorentz spacetime coordinates are compared with the Fermi spacetime coordinates. The proper Lorentz groups SO(1,3) with coupled parameters using the old and new Lorentz spacetime coordinates are also compared. As a special case, the application of Lorentz spacetime coordinates to a relativistic hydrodynamic system with coupled parameters in 1+1 dimensions is demonstrated.
]]>Symmetry doi: 10.3390/sym16030356
Authors: Qianwang Liang Tianyu Yan Nan Wang Zhiying Zhu Jiongyao Ye
A tone mapping operator (TMO) is a module in the image signal processing pipeline that is used to convert high dynamic range images to low dynamic range images for display. Currently, state-of-the-art TMOs typically take complex algorithms and are implemented on graphics processing units, making it difficult to run with low latency on edge devices, and TMOs implemented in hardware circuits often lack additional noise suppression because of latency and hardware resource constraints. To address these issues, we proposed a low-latency noise-aware TMO for hardware implementation. Firstly, a locally weighted guided filter is proposed to decompose the luminance image into a base layer and a detail layer, with the weight function symmetric concerning the central pixel value of a window. Secondly, the mean and standard deviation of the basic layer and the detail layer are used to estimate the noise visibility according to the human visual characteristics. Finally, the gain for the detail layer is calculated to achieve adaptive noise suppression. In this process, luminance is first processed by the log2 function before being filtered and then symmetrically converted back to the linear domain by the exp2 function after compression. Meanwhile, the algorithms within the proposed TMO were optimized for hardware implementation to minimize latency and cache, achieving a low latency of 60.32 μs under video specification of 1080 P at 60 frames per second and objective metric smoothness in dark flat regions could be improved by more than 10% compared to similar methods.
]]>Symmetry doi: 10.3390/sym16030355
Authors: Victor Vasilyevich Dyakin Nika Viktorovna Dyakina-Fagnano
The mechanism of brain information processing unfolds within spatial and temporal domains inherently linked to the concept of space–time symmetry. Biological evolution, beginning with the prevalent molecular chirality, results in the handedness of human cognitive and psychological functions (the phenomena known as biochirality). The key element in the chain of chirality transfer from the downstream to upstream processes is the pyramidal neuron (PyrN) morphology–function paradigm (archetype). The most apparent landmark of PyrNs is the geometry of the cell soma. However, “why/how PyrN’s soma gains the shape of quasi-tetrahedral symmetry” has never been explicitly articulated. Resolving the above inquiry is only possible based on the broad-view assumption that encoding 3D space requires specific 3D geometry of the neuronal detector and corresponding network. Accordingly, our hypothesis states that if the primary function of PyrNs, at the organism level, is sensory space symmetry perception, then the pyramidal shape of soma is the best evolutionary-selected geometry to support sensory-motor coupling. The biological system’s non-equilibrium (NE) state is fundamentally linked to an asymmetric, non-racemic, steady state of molecular constituents. The chiral theory of pyramidal soma shape conceptually agrees that living systems have evolved as non-equilibrium systems that exchange energy with the environment. The molecular mechanism involved in developing PyrN’s soma is studied in detail. However, the crucial missing element—the reference to the fundamental link between molecular chirality and the function of spatial navigation—is the main obstacle to resolving the question in demand: why did PyrNs’ soma gain the shape of quasi-tetrahedral symmetry?
]]>Symmetry doi: 10.3390/sym16030354
Authors: Gang Yang Jialun Ping Jorge Segovia
The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content, Pcs(4338) and Pcs(4459); its analysis points towards having both hadrons’ isospins equal to zero and spin-parity quantum numbers 12− and 32−, respectively. Herein, we perform a systematical investigation of the qqscc¯(q=u,d) system by means of a chiral quark model, along with a highly accurate computational method, the Gaussian expansion approach combined with the complex scaling technique. baryon-meson configurations in both singlet- and hidden-color channels are considered. The Pcs(4338) and Pcs(4459) signals can be well identified as molecular bound states with dominant components ΛJ/ψ(60%) and ΞcD(23%) for the lowest-energy case and ΞcD∗(72%) for the highest-energy one. In addition, it seems that some narrow resonances can also be found in each allowed I(JP) channel in the energy region of 4.6–5.5 GeV, except for the 1(12−) channel where a shallow bound state with dominant Ξc∗D∗ structure is obtained at 4673 MeV with binding energy EB=−3 MeV. These exotic states are expected to be confirmed in future high-energy experiments.
]]>Symmetry doi: 10.3390/sym16030353
Authors: Miloslav Znojil
A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable N−state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrödinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators Λj) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric Θ). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian H≡Λ1). Then, out of all of the eligible and Hamiltonian-dependent “Hermitizing” inner-product metrics Θ=Θ(H), we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution.
]]>Symmetry doi: 10.3390/sym16030352
Authors: Khalil Jouili Monia Charfeddine Mohammed Alqarni
The inherent negative impedance characteristics of a Constant Power Load (CPL) pose a potential threat to the stability of the bus voltage in a DC microgrid consisting of a symmetrical parallel boost converter. We suggest an adaptive feedback control technique using the input–output exact feedback linearization theory for a boost converter integrated into a DC microgrid to improve the stability of the DC bus voltage. This approach involves a transformation of the model into a Brunovsky canonical form, effectively addressing the nonlinear challenges arising from the CPL and the nonminimum phase characteristics of the boost converter. Subsequently, guided by the Lyapunov approach, an adaptation law is established to fine-tune the controller’s gain vector, facilitating the tracking of a predefined linearizing feedback control. We methodically create a method to choose the gains of the adaptive controller in order to guarantee an adequate output response. We validate our suggested controller’s performance using simulation.
]]>Symmetry doi: 10.3390/sym16030351
Authors: Andriy Bandura Tetyana Salo Oleh Skaskiv
The manuscript is an initiative to construct a full and exhaustive theory of analytical multivariate functions in any complete Reinhardt domain by introducing the concept of L-index in joint variables for these functions for a given continuous, non-negative, non-vanishing, vector-valued mapping L defined in an interior of the domain with some behavior restrictions. The complete Reinhardt domain is an example of a domain having a circular symmetry in each complex dimension. Our results are based on the results obtained for such classes of holomorphic functions: entire multivariate functions, as well as functions which are analytical in the unit ball, in the unit polydisc, and in the Cartesian product of the complex plane and the unit disc. For a full exhaustion of the domain, polydiscs with some radii and centers are used. Estimates of the maximum modulus for partial derivatives of the functions belonging to the class are presented. The maximum is evaluated at the skeleton of some polydiscs with any center and with some radii depending on the center and the function L and, at most, it equals a some constant multiplied by the partial derivative modulus at the center of the polydisc. Other obtained statements are similar to the described one.
]]>Symmetry doi: 10.3390/sym16030350
Authors: Ze Chen Mulun Zhu Chuanzhi Sun Yongmeng Liu Jiubin Tan
The aero-engine serves as the “heart” of an aircraft and is a primary factor determining the aircraft’s performance. Among the crucial components in the core of aero-engines, aero-engine compressor blades stand out as extremely important. They are not only numerous but also characterized by a multitude of parameters, making them the most complex parts in an aero-engine. This paper aims to address the trade-off between accuracy and efficiency in the existing measurement methods for asymmetric blades. Non-contact measurements were conducted using a structured light system composed of a stereo camera and a DLC projector. The point cloud data of the blades are processed using methods such as the PCA (Principal Component Analysis) algorithm, binary search, and least squares fitting. This paper established a fringe-projection profilometry light sensor system for the multi-view measurement of the blades. High-precision rotary tables are utilized to rotate and extract complete spatial point cloud data of aviation blades. Finally, measurements and comparative experiments on the blade body are conducted. The obtained blade point cloud data undergo sorting and denoising processes, resulting in improved measurement accuracy. The measurement error of the blade chord length is 0.001%, the measurement error of blade maximum thickness is 0.895%, compared to CMM (Coordinate Measuring Machine), where the measurement error of chord is 0.06%.
]]>Symmetry doi: 10.3390/sym16030349
Authors: Sajad A. Sheikh Mohammad Ibrahim Mir Osama Abdulaziz Alamri Javid Gani Dar
This paper investigates various aspects of the distribution of roots and critical points of a complex polynomial, including their variance and the relationships between their moduli using an inequality due to de Bruijn. Making use of two other inequalities-again due to de Bruijn-we derive two probabilistic results concerning upper bounds for the average moduli of the imaginary parts of zeros and those of critical points, assuming uniform distribution of the zeros over a unit disc and employing the Markov inequality. The paper also provides an explicit formula for the variance of the roots of a complex polynomial for the case when all the zeros are real. In addition, for polynomials with uniform distribution of roots over the unit disc, the expected variance of the zeros is computed. Furthermore, a bound on the variance of the critical points in terms of the variance of the zeros of a general polynomial is derived, whereby it is established that the variance of the critical points of a polynomial cannot exceed the variance of its roots. Finally, we conjecture a relation between the real parts of the zeros and the critical points of a polynomial.
]]>Symmetry doi: 10.3390/sym16030348
Authors: Hassen Mestiri Imen Barraj Mouna Bedoui Mohsen Machhout
Cryptographic devices’ complexity necessitates fast security simulation environments against fault attacks. SystemC, a promising candidate in Electronic System Levels (ESLs), can achieve higher simulation speeds while maintaining accuracy and reliability, and its modular and hierarchical design allows for efficient modeling of complex cryptographic algorithms and protocols. However, code modification is required for fault injection and detection. Aspect-Oriented Programming (AOP) can test cryptographic models’ robustness without modifications, potentially replacing real cryptanalysis schemes and reducing the time and effort required for fault injection and detection. Through the utilization of a fault injection/detection environment, this paper presents a novel approach to simulating the security fault attacks of ASCON cryptographic systems at the ESL. The purpose of this methodology is to evaluate the resistance of ASCON SystemC models against fault attacks. The proposed methodology leverages the advantages of AOP to enhance the fault injection and detection process. By applying AOP techniques, we inject faults into the SystemC models without making any changes to the main codebase. This approach not only improves the efficiency of testing cryptographic systems but also ensures that the main functionality remains intact during the fault injection process. The methodology was validated using three scenarios and SystemC ASCON as a case study. The first simulation involved evaluating fault detection capabilities, the second focused on the impact of AOP on executable file size and simulation time, and the third focused on the ESL impact on the ASCON design process. Simulation results show that this methodology can perfectly evaluate the robustness of the ASCON design against fault injection attacks with no significant impact on simulation time and file executable size. Additionally, the simulation results prove that the ASCON development life cycle at the ESL reduces the amount of time devoted to the design procedure by 83.34%, and the ASCON security attack simulations at the ESL decrease the simulation time by 40% compared to the register transfer level (RTL).
]]>Symmetry doi: 10.3390/sym16030347
Authors: Tania Álvarez-Yates Mario Iglesias-Caamaño Alba Cuba-Dorado Virginia Serrano-Gómez Victor Ferreira-Lima Fábio Yuzo Nakamura Oscar García-García
Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for canoeists’ neuromuscular properties, ROM and lower-limb strength; and (3) to determine the relationship of canoeists’ neuromuscular properties, ROM and lower-limb strength asymmetries with a specific canoe–dynamometer performance test. Twenty-one international canoeists were assessed through tensiomyography (TMG), ROM, lower-limb explosive strength, and a specific canoe incremental dynamometric test. The magnitude of asymmetry assessed through TMG and ROM was not modulated either by sex or performance level (international medal vs. non-medal). Females showed greater asymmetry than males on muscle tone of the erector spinae towards non-stroke side (22.75% vs. 9.72%) and the tibialis anterior (30.97% vs. 16.29%), and Fmax in explosive leg press (2.41% vs. 0.63%) towards the stroke side. International medalists showed greater asymmetry in semitendinosus contraction time towards non-stroke side (20.51% vs. 9.43%) and reached Vmax earlier in explosive leg press towards stroke side leg (19.20% vs. 9.40%). A greater asymmetry in Fmax and in Vm, and a smaller asymmetry in Tvmax and in leg press showed a small predictive capacity for canoeists’ performance on a specific canoe incremental dynamometry test. Reporting reference data from world-class canoeists’ asymmetries can be of great importance for coaches to periodically control lateral asymmetry.
]]>Symmetry doi: 10.3390/sym16030346
Authors: Sergii Panchenko Juraj Gerlici Alyona Lovska Vasyl Ravlyuk Ján Dižo Miroslav Blatnický
This article presents the results of a study focused on identifying the main causes of the asymmetric (clinodual) wear of composite brake pads on freight wagons. A new scientific approach to determining the clinodual wear of composite brake pads on freight wagons is proposed. It is established that the harmful abrasion of the pad occurs during the movement of the freight train due to an imperfection in the bogie-brake lever transmission. The causes of the non-normative frictional wear of composite brake pads were investigated. This kind of wear leads to the tilting and abutting of the upper end of the brake pads against the rotating wheel during train running. The results of geometric and kinetostatic studies of the “pad–wheel” tribotechnical pair are provided to establish the causes and consequences of the accelerated clinodual frictional wear of composite brake pads on pendulum suspension in the bogies of freight wagons. The conditions of rotation of the wheels during braking “for” and “against” the clockwise direction depending on the direction of the train are considered. A new approach to brake-pad-wear prediction depending on the mileage of wagons under operational conditions is proposed. The research conducted in this study contributes to the development of the mechanical parts of freight-wagon brakes, increasing the efficiency of brake operation and improving the safety of train traffic.
]]>Symmetry doi: 10.3390/sym16030345
Authors: Yan Wang Lizhong Zhang Lixin Meng Hongjie Lu Yongheng Ma
A flexure hinge composed of elliptical and hyperbolic hybrid configurations is developed and analyzed in this paper. The analytical models of compliance, rotation accuracy, and maximum stress of the flexure hinge are established, and the correctness of the models is validated by finite element analysis and experiments. The influence of structural parameters on compliance and rotation accuracy is discussed. The concept of compliance stress ratio is proposed to assess the deformation capacity of flexure hinges when subjected to the same stress, which provides a basis for quantitatively comparing the comprehensive performance of flexure hinges. The performance of the hybrid flexure hinge is compared with that of elliptical, hyperbolic, and circular flexure hinges by taking the compliance accuracy ratio and the compliance stress ratio as the performance evaluation indexes. The results show that the hybrid flexure hinge combines the advantages of hyperbolic and elliptical hinges and has a balanced performance in compliance, rotation accuracy, and low stress. The designed hybrid flexure hinge is suitable for the support structure of fast steering mirrors, which provides a valuable reference for the engineering optimization design of flexure hinges.
]]>Symmetry doi: 10.3390/sym16030344
Authors: Jiexuan Hou Yangwei Liu Yumeng Tang
A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent structures (LCSs). The computational method of the FTLE field in three-dimensional unsteady flow fields is discussed and then applied to the instantaneous flow fields at both the design and near-stall conditions. Results show that the accuracy of the particle trajectory and the density of the initial grid of the particle trajectory greatly affect the results of the FTLE field and, thus, the LCSs. Compared to the Eulerian Q method, which is calculated based on the symmetric and anti-symmetric components of the local velocity gradient tensor, the Lagrangian method has great potential in unraveling the mechanism of complex vortex structures. The LCSs show a transport barrier between the TLV and the secondary TLV, indicating two separate vortices. The aLCSs show the bubble-like and bar-like structure in the isosurfaces corresponding to the bubble and spiral breakdown patterns.
]]>Symmetry doi: 10.3390/sym16030343
Authors: Yufeng Luo Antonios Tsokaros Roland Haas Kōji Uryū
Triaxial neutron stars can be sources of continuous gravitational radiation detectable by ground-based interferometers. The amplitude of the emitted gravitational wave can be greatly affected by the state of the hydrodynamical fluid flow inside the neutron star. In this work, we examine the most triaxial models along two sequences of constant rest mass, confirming their dynamical stability. We also study the response of a triaxial figure of quasiequilibrium under a variety of perturbations that lead to different fluid flows. Starting from the general relativistic compressible analog of the Newtonian Jacobi ellipsoid, we perform simulations of Dedekind-type flows. We find that in some cases the triaxial neutron star resembles a Riemann-S-type ellipsoid with minor rotation and gravitational wave emission as it evolves towards axisymmetry. The present results highlight the importance of understanding the fluid flow in the interior of a neutron star in terms of its gravitational wave content.
]]>Symmetry doi: 10.3390/sym16030342
Authors: Oleg I. Kolodiazhnyi Anastasy O. Kolodiazhna
The review is devoted to the theoretical and synthetic aspects of the stereochemistry of organophosphorus compounds. Organophosphorus compounds are not only widely exist in biologically active pharmaceuticals and agrochemicals, but also have widespread applications in material science and organic synthesis as ligands for transition metal complexes. One of the mainstreams for the development in this field is the creation of biologically active organophosphorus compounds that are searched and used as drugs or plant-protecting agents, which leads to the elaboration of advanced methods and monitoring, yielding up-to-date approaches to perform synthesis in an environmentally friendly manner. The review consists of two parts. The first part presents methods for the asymmetric synthesis of organophosphorus compounds using asymmetric organocatalysis and metal complex catalysis. In the review is described the nature of the chirality generation in the prebiotic period, the mechanisms of asymmetric induction, and double stereodifferentiation are discussed. The use of these methods for the preparation of chiral phosphorus analogs of natural compounds (phosphono-isonorstatin, phosphono-GABOB, phosphacarnitine, bis-phosphonates, and others) is described. Some data concerning of λ5-phosphanediones as metaphosphate anion analogues are also reported. The second part of the presented review shows examples of the use of these methods for the synthesis of phosphorus analogues of natural compounds—chiral phosphonoamino acids and hydroxyphosphonates: phosphonoaspartic acid, phosphonoglutamic acid, phosphonohomoproline, chiral bis-phosphonates. The reaction of dehydration aromatization with the formation of pho sphono isoindolinones, including isoindolinone bis-phosphonates, has been studied. Some of the synthesized compounds showed biological activity as protein tyrosine phosphatase inhibitors. A phosphonic analogue of iso-norstatine was synthesized. A stereoselective method for the synthesis of tetradecapentaenoic acid derivatives was developed.
]]>Symmetry doi: 10.3390/sym16030341
Authors: Luis Herrera Alicia Di Prisco Justo Ospino
A seminumerical approach proposed many years ago for describing gravitational collapse in the post-quasi-static approximation is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi-homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post-quasi-static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids, and therefore, we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g., luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well-known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.
]]>Symmetry doi: 10.3390/sym16030340
Authors: Roberto Montemanni Derek H. Smith
In the Set Orienteering Problem, a single vehicle, leaving from and returning to a depot, has to serve some customers, each one associated with a given spacial location. Customers are grouped in clusters and a given prize is collected once a customer in a cluster is visited. The prize associated with a cluster can be collected at most once. Travel times among locations are provided, together with a maximum available mission time, which normally makes it impossible to visit all the clusters. The target is to design a route for the vehicle that maximizes the total prize collected within the given time limit. In this study, building on the recent literature, we present new preprocessing rules and a new constraint programming model for the problem. Thanks to the symmetry exploitation carried out by the constraint programming solver, new state-of-the-art results are established.
]]>Symmetry doi: 10.3390/sym16030339
Authors: Fangfang Dong Yanbin Luo Jianxun Chen Chuanwu Wang Yahui Liu Wenjie Xun
Temperature stress has a significant impact on the structural stress of (super) large-span tunnel lining, which can easily lead to structural fatigue damage and premature cracking. With the increasing scale and quantity of super large-span tunnels, the issue of temperature stress in secondary lining has attracted widespread attention. Previous studies have paid little attention to the influence of temperature stress on the structural internal forces of ordinary small–medium-span tunnels, but this influence cannot be ignored for super large-span tunnels. We take the Letuan Tunnel (a double-hole eight-lane tunnel) of the Binzhou-Laiwu expressway renovation and expansion project in Shandong Province as a case study and analyze the mechanical response of the secondary lining through on-site measurement. Moreover, a numerical simulation was conducted to evaluate the effects of self-weight and temperature stress on the secondary lining of the case tunnel. The results indicate that: the stress of the secondary lining concrete and steel bars is greatly affected by seasonal temperature changes. The compressive stress of the concrete and steel bars is significantly greater in summer than in winter, and the tensile stress is greater in winter than in summer. Furthermore, multiple measurement points have shown a phenomenon of transition between tensile and compressive stress states. The stress of concrete and steel bars fluctuates periodically with a sine function over time, with a fluctuation period of one year. The structural stress increases with the increase of summer temperature and decreases with the decrease of winter temperature. The fluctuation amplitude of stress in the inner side of the lining concrete and steel bars is greater than that on the outer side. Among them, the stress amplitudes of the inner and outer sides of the concrete are between 0.77–1.75 MPa and 0.44–1.07 MPa, respectively, and the stress amplitudes of the inner and outer steel bars are between 5–31 MPa and 7–13 MPa, respectively. The safety factors in summer are lower than those in winter. The minimum safety factors for secondary lining in summer and winter are 3.4 and 4.6, respectively, which can meet the safety requirements for service. The average axial forces of the secondary lining under the coupling effects of self-weight and temperature in winter and summer are 528 MPa and 563 MPa, respectively, which are significantly greater than the combined axial forces under their individual effects. The bending moment distribution of the secondary lining at the tunnel vault, inverted arch, wall spring and other positions under the coupling effect of self-weight and temperature is different from or even opposite to the bending moment superposition result under the two individual actions. The achieved results reveal that the influence of temperature stress on the service performance of the lining structure cannot be ignored, and the research results can provide useful reference for similar tunnels and related studies.
]]>Symmetry doi: 10.3390/sym16030338
Authors: Rubén Capeáns Miguel A. F. Sanjuan
Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent symmetry and geometric structure of chaotic saddles, the topological object responsible of transient chaos, to enable surprising control with only small perturbations. Here, we review the latest findings in partial control techniques with the aim to sustain chaos or accelerate escapes by exploiting these intricate invariant sets. We introduce the fundamental concept of safe sets regions where orbits persist despite noise. This paper presents recent generalizations through safety functions and escape functions that automatically find the minimum control needed. Efficient numerical algorithms are presented and several examples of application are illustrated. Rather than eliminating chaos entirely, partial control techniques provide a framework to reliably control transient chaotic dynamics with minimal interventions. This approach has promising applications across diverse fields including physics, engineering, biology, and more.
]]>Symmetry doi: 10.3390/sym16030337
Authors: Pshtiwan Othman Mohammed Ravi P. Agarwal Majeed A. Yousif Eman Al-Sarairah Sarkhel Akbar Mahmood Nejmeddine Chorfi
Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green’s function kernel. In the deterministic case, Green’s function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type.
]]>Symmetry doi: 10.3390/sym16030336
Authors: Qianhao Miao Tianyu Ren Jiahan Dong Yanjiao Chen Wenyuan Xu
As an important component of the smart grid, vehicle-to-grid (V2G) networks can deliver diverse auxiliary services and enhance the overall resilience of electrical power systems. However, V2G networks face two main challenges due to a large number of devices that connect to it. First, V2G networks suffer from serious security threats, such as doubtful authenticity and privacy leakage. Second, the efficiency will decrease significantly due to the massive requirements of authentication. To tackle these problems, this paper proposes a cross-domain authentication scheme for V2G networks based on consortium blockchain and certificateless signature technology. Featuring decentralized, open, and transparent transactions that cannot be tampered with, this scheme achieves good performance on both security and efficiency, which proves to be suitable for V2G scenarios in the smart grid.
]]>Symmetry doi: 10.3390/sym16030335
Authors: Carmen Ionescu Radu Constantinescu
This paper addresses an important method for finding traveling wave solutions of nonlinear partial differential equations, solutions that correspond to a specific symmetry reduction of the equations. The method is known as the simplest equation method and it is usually applied with two a priori choices: a power series in which solutions are sought and a predefined auxiliary equation. Uninspired choices can block the solving process. We propose a procedure that allows for the establishment of their optimal forms, compatible with the nonlinear equation to be solved. The procedure will be illustrated on the rather large class of reaction–diffusion equations, with examples of two of its subclasses: those containing the Chafee–Infante and Dodd–Bullough–Mikhailov models, respectively. We will see that Riccati is the optimal auxiliary equation for solving the first model, while it cannot directly solve the second. The elliptic Jacobi equation represents the most natural and suitable choice in this second case.
]]>Symmetry doi: 10.3390/sym16030334
Authors: Peter Grabusts Oleg Uzhga-Rebrov
One of the geometric figures that has symmetry properties is the Cassini oval. The Cassini oval is a curve defined as the locus of points in the plane such that the product of the distances to two fixed points is constant. Cassini ovals are named after the astronomer Giovanni Domenico Cassini, who studied them in 1680. Today, the geometric properties of Cassini ovals are used in many fields: analytical geometry, nuclear physics, radiolocation, and industrial applications. The bistatic radar uses Cassini ovals to detect various targets in radiolocation. Until now, there have been no studies on the clustering capabilities of Cassini ovals. As a novelty, it is hypothesized that clustering possibilities could be used for Cassini ovals. In this article, a study of the capabilities of Cassini ovals in radiolocation was carried out, and their suitability for clustering purposes was shown.
]]>Symmetry doi: 10.3390/sym16030333
Authors: Claudia Salera Camilla Vallebella Marco Iosa Anna Pecchinenda
The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for the golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking them to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimatum Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio.
]]>Symmetry doi: 10.3390/sym16030332
Authors: Longxing Su
A facile and low-cost strategy to fabricate CsPbBr3 single crystals is essential for developing perovskite optoelectronic devices. Herein, we have presented a room temperature anti-solvent precipitate method for growing sub-centimeter-sized CsPbBr3 single crystals. The as-prepared CsPbBr3 single crystal has an orthorhombic structure, and phase transition occurs as the measured temperature increases. The as-grown CsPbBr3 single crystal also shows abundant surface morphologies including footsteps, precipitated crystals, cracks, and pits. Subsequently, a metal–semiconductor–metal (MSM)-structured photodetector was fabricated based on the CsPbBr3 single crystal. Under 525 nm green light illumination, the photodetector exhibits an obvious response and the photocurrent linearly increases with the increase in the light intensity. The rise time of the photodetector increases from 0.82 s to 2.19 s as the light intensity is enhanced from 15 mW/cm2 to 160 mW/cm2, indicating that more time is required to reach to a stable photocurrent. However, the decay time is as fast as ~0.82 ms, irrelevant of the light intensity. The photocurrent, under continuous light illumination, was further studied and this indicates that a stronger light intensity can accelerate the attenuation of the device.
]]>Symmetry doi: 10.3390/sym16030331
Authors: Wasana Chankham Sa-Aat Niwitpong Suparat Niwitpong
Due to slash/burn agricultural activity and frequent forest fires, PM2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating PM2.5 concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys’ rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily PM2.5 datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys’ rule prior for the highest posterior density yielded favorable results.
]]>Symmetry doi: 10.3390/sym16030330
Authors: Ioannis K. Argyros Stepan Shakhno Samundra Regmi Halyna Yarmola Michael I. Argyros
Symmetric-type methods (STM) without derivatives have been used extensively to solve nonlinear equations in various spaces. In particular, multi-step STMs of a higher order of convergence are very useful. By freezing the divided differences in the methods and using a weight operator a method is generated using m steps (m a natural number) of convergence order 2 m. This method avoids a large increase in the number of operator evaluations. However, there are several problems with the conditions used to show the convergence: the existence of high order derivatives is assumed, which are not in the method; there are no a priori results for the error distances or information on the uniqueness of the solutions. Therefore, the earlier studies cannot guarantee the convergence of the method to solve nondifferentiable equations. However, the method may converge to the solution. Thus, the convergence conditions can be weakened. These problems arise since the convergence order is determined using the Taylor series which requires the existence of high-order derivatives which are not present in the method, and they may not even exist. These concerns are our motivation for authoring this article. Moreover, the novelty of this article is that all the aforementioned problems are addressed positively, and by using conditions only related to the divided differences in the method. Furthermore, a more challenging and important semi-local analysis of convergence is presented utilizing majorizing sequences in combination with the concept of the generalized continuity of the divided difference involved. The convergence is also extended from the Euclidean to the Banach space. We have chosen to demonstrate our technique in the present method. But it can be used in other studies using the Taylor series to show the convergence of the method. The applicability of other single- or multi-step methods using the inverses of linear operators with or without derivatives can also be extended with the same methodology along the same lines. Several examples are provided to test the theoretical results and validate the performance of the method.
]]>Symmetry doi: 10.3390/sym16030329
Authors: Borhen Halouani Khalid Nowar
The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow.
]]>Symmetry doi: 10.3390/sym16030328
Authors: Cheng Guo Xinyuan Zhang Mi He Linling Wang Xuanming Yang
Voltage sags resulting from symmetrical or asymmetrical faults pose a significant threat to power quality. In response to this challenge, a voltage sag loss assessment method based on a two-stage Taguchi quality perspective approach is proposed to address the quantitative analysis of voltage sag economic losses. Initially, using the Taguchi quality perspective method, single-index quality loss functions are separately established for voltage sag magnitude and fault duration. Subsequently, by introducing a comprehensive load tolerance curve, sensitivity parameters within the quality loss function are accurately calculated. This yields a deterministic model for voltage sag assessment. Building upon this, the relative impact of the two indices on voltage sag loss is evaluated using the quality loss function. Consequently, a comprehensive loss model under the influence of multiple indices is formed by integrating two single-index evaluation models. The simulation results indicate that this method can effectively assess the economic losses of voltage sags under the combined influence of multiple factors. Compared to the original economic loss assessment method, it improves quantitative accuracy by approximately 3.72%. Moreover, the method reduces the computational complexity of loss assessment through the consolidation of intervals with similar sensitivity parameters.
]]>Symmetry doi: 10.3390/sym16030327
Authors: Panagiota Papadopoulou Kyriakos Ovaliadis Eleni Philippousi Michael P. Hanias Lykourgos Magafas Stavros G. Stavrinides
In this paper, the effect of temperature on Single-Electron Transistor (SET) electrical behavior is investigated. In particular, a study of the current-voltage (I-V) curves according to parameter (temperature and gate voltage) variation is presented. Among others, the interesting phenomenon of the N-type negative differential resistance is reported as the temperature increases from absolute zero (0 K) to room temperature. Finally, theoretical analysis and simulation shows that the choice of the appropriate temperature and gate-voltage combination the SET I-V curves demonstrates either a negative differential resistance region, a switching effect, or a simple resistance behavior.
]]>Symmetry doi: 10.3390/sym16030326
Authors: Sergey Sekatskii
Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeros of the Hurwitz zeta function ζ(s,z), including the sum over the inverse first power of its appropriately defined non-trivial zeros. We also study some related properties of the Hurwitz zeta function zeros. In particular, we show that, for any natural N and small real ε, when z tends to n = 0, −1, −2… we can find at least N zeros of ζ(s,z) in the ε neighborhood of 0 for sufficiently small |z+n|, as well as one simple zero tending to 1, etc.
]]>Symmetry doi: 10.3390/sym16030325
Authors: Włodzimierz Fechner Maria Słomian
In this paper, we explore a model of an N-player, non-cooperative stochastic game, drawing inspiration from the discrete formulation of the red-and-black gambling problem, as initially introduced by Dubins and Savage in 1965. We extend upon the work of Pontiggia from 2007, presenting a main theorem that broadens the conditions under which bold strategies by all players can achieve a Nash equilibrium. This is obtained through the introduction of a novel functional inequality, which serves as a key analytical tool in our study. This inequality enables us to circumvent the restrictive conditions of super-multiplicativity and super-additivity prevalent in the works of Pontiggia and others. We conclude this paper with a series of illustrative examples that demonstrate the efficacy of our approach, notably highlighting its ability to accommodate a broader spectrum of probability functions than previously recognized in the existing literature.
]]>Symmetry doi: 10.3390/sym16030324
Authors: Xuedi Mao Bing Wang Wenjian Ye Yuxin Chai
The pathfinder algorithm (PFA) starts with a random search for the initial population, which is then partitioned into only a pathfinder phase and a follower phase. This approach often results in issues like poor solution accuracy, slow convergence, and susceptibility to local optima in the PFA. To address these challenges, a multi-strategy fusion approach is proposed in the symmetry-enhanced, improved pathfinder algorithm-based multi-strategy fusion for engineering optimization problems (IPFA) for function optimization problems. First, the elite opposition-based learning mechanism is incorporated to improve the population diversity and population quality, to enhance the solution accuracy of the algorithm; second, to enhance the convergence speed of the algorithm, the escape energy factor is embedded into the prey-hunting phase of the GWO and replaces the follower phase in the PFA, which increases the diversity of the algorithm and improves the search efficiency of the algorithm; lastly, to solve the problem of easily falling into the local optimum, the optimal individual position is perturbed using the dimension-by-dimension mutation method of t-distribution, which helps the individual to jump out of the local optimum rapidly and advance toward other regions. The IPFA is used for testing on 16 classical benchmark test functions and 29 complex CEC2017 function sets. The final optimization results of PFA and IPFA in pressure vessels are 5984.8222 and 5948.3597, respectively. The final optimization results in tension springs are 0.012719 and 0.012699, respectively, which are comparable with the original algorithm and other algorithms. A comparison between the original algorithm and other algorithms shows that the IPFA algorithm is significantly enhanced in terms of solution accuracy, and the lower engineering cost further verifies the robustness of the IPFA algorithm.
]]>Symmetry doi: 10.3390/sym16030323
Authors: Filiz Ertem Kaya Süleyman Şenyurt
Willmore defined embedded surfaces on f:S→E3, which is the embedding of S into Euclidean 3-space. He investigated the Euclidean metric of E3, inducing a Riemannian structure on f(S). The expression analogous to the left-hand member of the curvature K is replaced by the mean curvature H2 on f(S). Our aim is to observe the Gaussian and mean curvatures of curve–surface pairs using embedded surfaces in different curve–surface pairs and to define some developable operations on their curve–surface pairs. We also investigate the embedded surfaces using the Willmore method. We first recall the Darboux curve–surface and derive the new characterizations. This curve–surface pair is called the osculating Darboux curve–surface if its position vector always lies in the osculating Darboux plane spanned by a Darboux frame. Thus, we observed an osculating Darboux curve–surface pair. We also obtained the D∼-scroll of the curve–surface pair and involute D∼-scroll of the curve–surface pair with some differential geometric elements and found D∼(α,M)(s) and D∗∼(α,M)(s)-scrolls of the curve–surface pair (α,M).
]]>Symmetry doi: 10.3390/sym16030322
Authors: Min Wu Dakui Ma Kaiqing Xiong Linkun Yuan
To address the issues of instability and inefficiency that the fluctuating and uncertain characteristics of renewable energy sources impose on low-carbon microgrids, this research introduces a novel Knowledge-Data-Driven Load Frequency Control (KDD-LFC) approach. This advanced strategy seamlessly combines pre-existing knowledge frameworks with the capabilities of deep learning neural networks, enabling the adaptive management and multi-faceted optimization of microgrid functionalities, with a keen emphasis on the symmetry and equilibrium of active power. Initially, the process involves the cultivation of foundational knowledge through established methodologies to augment the reservoir of experience. Following this, a Knowledge-Aggregation-based Proximal Policy Optimization (KA-PPO) technique is employed, which proficiently acquires an understanding of the microgrid’s state representations and operational tactics. This strategy meticulously navigates the delicate balance between the exploration of new strategies and the exploitation of known efficacies, ensuring the harmonization of frequency stability, precision in tracking, and the optimization of control expenditures through the strategic formulation of the reward function. The empirical validation of the KDD-LFC method’s effectiveness and its superiority are demonstrated via simulation tests conducted on the load frequency control (LFC) framework of the Sansha isolated island microgrid, which is under the administration of the China Southern Grid.
]]>Symmetry doi: 10.3390/sym16030321
Authors: Xuliang Liu Xinwei Yue Zhiping Lu Tianwei Hou
Active reconfigurable intelligent surface (ARIS) has sparked more attention due to its capability to overcome the impact of double fading. This paper introduces using an ARIS to aid non-orthogonal multiple access (NOMA) communications over cascade Rician fading channels, where the direct links between the base station and users are seriously blocked. By applying ARIS, it can amplify the superposed signals to overcome the double pass loss effect caused by passive RIS. Both ARIS and NOMA can have synergistic impacts on sixth-generation communication systems. New approximated and asymptotic expressions in terms of outage probability and ergodic data rate of the k-th user are deduced for ARIS-NOMA systems. Based on asymptotic analytical results, we further calculate the diversity order and high signal-to-noise ratio slope of the k-th user. Finally, the system throughput of ARIS-NOMA is discussed in the delay-constrained transmission mode. Monte Carlo numerical results are performed to verify that: (1) the outage behaviors of ARIS-NOMA are better than that of ARIS-assisted orthogonal multiple access (OMA); (2) as the impact of thermal noise caused by ARIS becomes larger, the communication performance from the base station to ARIS, then to users, becomes worse; (3) the ARIS-NOMA systems have the ability to provide the improved ergodic data rate relative to ARIS-OMA.
]]>Symmetry doi: 10.3390/sym16030320
Authors: Galina L. Klimchitskaya Constantine C. Korikov Vladimir M. Mostepanenko
The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, μ, and mass gap, Δ, of the graphene coating depends on the relationship between Δ and 2μ. If 2μ>Δ, the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with μ=0. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed.
]]>Symmetry doi: 10.3390/sym16030319
Authors: Takashiro Akitsu Yuya Higashi Rin Tsuchiya Taiga Imae Keishiro Komatsu Daisuke Nakane Dohyun Moon
As a recent cutting-edge research target, the prediction of crystal systems or space groups using machine learning based on databases has been actively reported [...]
]]>Symmetry doi: 10.3390/sym16030318
Authors: Tuba Gulsen Ayşe Çiğdem Yar Emrah Yilmaz
In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the proposal of improved approximation expressions for computational application. One such expression is the diamond alpha (⋄α) derivative, which is defined as a linear combination of delta and nabla derivatives. Several dynamic equations and inequalities, as well as hybrid dynamic behavior—which does not occur in the real line or on discrete time scales—are analyzed using this combined concept. In this study, we consider a ⋄α Dirac system under boundary conditions on a uniform time scale. We examined some basic spectral properties of the problem we are considering, such as the simplicity, the reality of eigenvalues, orthogonality of eigenfunctions, and self adjointness of the operator. Finally, we construct an expression for the eigenfunction of the ⋄α Dirac boundary value problem (BVP) on a uniform time scale.
]]>Symmetry doi: 10.3390/sym16030317
Authors: Maria N. Rapti Avrilia Konguetsof Basil K. Papadopoulos
In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form.
]]>Symmetry doi: 10.3390/sym16030316
Authors: David Chester Xerxes D. Arsiwalla Louis H. Kauffman Michel Planat Klee Irwin
We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras.
]]>Symmetry doi: 10.3390/sym16030314
Authors: Yizhou Wang Shigeyuki Yamada Motohiro Yasui Tsutomu Konno
Solution-state photoluminescence (PL) is affected by the electronic state; however, solid-state PL varies widely depending on the aggregated state. Although the synthesis and photophysical properties of unsymmetrical and C3-symmetrical hexaarylbenzenes (HABs) have been reported, the influence of their terminal alkoxy chains on their physical properties remains unclear. Therefore, we synthesized a series of unsymmetrical and C3-symmetrical partially fluorinated HABs with different alkoxy chains and investigated the effects of alkoxy chain length on the thermophysical and photophysical properties. While investigating phase transition behavior, the ethoxy-substituted unsymmetrical derivative revealed a columnar liquid-crystalline phase, whereas the other derivatives only exhibited a phase transition between crystalline and isotropic phases. While evaluating PL behavior, both the unsymmetrical and C3-symmetrical analogs exhibited relatively strong blue PL, independent of the alkoxy chain length. Through-space π-conjugation caused the PL spectra of C3-symmetrical derivatives to redshift compared to those of unsymmetrical derivatives. Partially fluorinated HABs exhibited relatively strong fluorescence, even in the crystalline state, depending on the alkoxy chain length, owing to the formation of various aggregated structures. Crystalline fluorinated HABs exhibited photochromism, resulting in the appearance of long-wavelength PL bands when exposed to ultraviolet (UV) irradiation, making them promising candidates for PL sensing materials for UV detection.
]]>Symmetry doi: 10.3390/sym16030315
Authors: Xiaojun Bai Sizhe Wang Xin Zhang Haohua Wang
Gene expression comprises many asymmetric and complex processes. Transcriptional details revealed by the whole genome indicate that genes resort to transcriptional bursting and accumulate molecular memory. However, it is still unclear how the interplay of transcriptional bursting and memory regulates robustness and expression noise. Here, we consider a model of multiple coupled processes of protein polymerization to focus on decoding the effect of molecular memory. Using non-Markovian transformation technology, we first define the memory index to measure the correlation window of expression to decipher the mechanism of regulation. The results indicate that memory from synthesis can amplify expression noise, while memory originating from polymerization can reduce the lower bound of the noise of gene products; that is, the memory from different sources plays distinct regulatory roles to induce non-symmetry. Moreover, it is counterintuitive that the dual regulation from memory and bursting expression can directly suppress system noise, violating the principle that transcriptional bursting enhances noise. Our results not only provide a theoretical framework for investigating the function of memory but also imply that expression noise is not part of a half-power relationship with, nor mediated by, memory.
]]>Symmetry doi: 10.3390/sym16030312
Authors: Shunli Li Chunli Song Linzhang Lu Zhen Chen
Nowadays, deep representations have gained significant attention due to their outstanding performance in a wide range of tasks. However, the interpretability of deep representations in specific applications poses a significant challenge. For instances where the generated quantity matrices exhibit symmetry, this paper introduces a variant of deep matrix factorization (deep MF) called deep Lp smooth symmetric non-negative matrix factorization (DSSNMF), which aims to improve the extraction of clustering structures inherent in complex hierarchical and graphical representations in high-dimensional datasets by improving the sparsity of the factor matrices. We successfully applied DSSNMF to synthetic datasets as well as datasets related to post-traumatic stress disorder (PTSD) to extract several hierarchical communities. Specifically, we identified non-disjoint communities within the partial correlation networks of PTSD psychiatric symptoms, resulting in highly meaningful clinical interpretations. Numerical experiments demonstrate the promising applications of DSSNMF in fields like network analysis and medicine.
]]>Symmetry doi: 10.3390/sym16030313
Authors: Pier Luigi Novi Inverardi Aldo Tagliani
The aim of this paper is to consider the indeterminate Stieltjes moment problem together with all its probability density functions that have the positive real or the entire real axis as support. As a consequence of the concavity of the entropy function in both cases, there is one such density that has the largest entropy: we call it fhmax, the largest entropy density. We will prove that the Jaynes maximum entropy density (MaxEnt), constrained by an increasing number of integer moments, converges in entropy to the largest entropy density fhmax. Note that this kind of convergence implies convergence almost everywhere, with remarkable consequences in real applications in terms of the reliability of the results obtained by the MaxEnt approximation of the underlying unknown distribution, both for the determinate and the indeterminate case.
]]>Symmetry doi: 10.3390/sym16030311
Authors: Vitaly A. Beylin Maxim Yu. Khlopov Danila O. Sopin
New heavy particles with electroweak charges arise in extensions of the standard model. They should take part in sphaleron transitions in the early Universe, which balance baryon asymmetry with the excess of new charged particles. If electrically charged with charge −2n, they bind with n nuclei of primordial helium in dark atoms of dark matter. This makes it possible to find the ratio of densities of asymmetric dark matter and baryonic matter. Examples of the model with new, successive, and stable generation of quarks and leptons and the minimal walking technicolor model are considered.
]]>Symmetry doi: 10.3390/sym16030310
Authors: Fajiang Yu Yanting Huang
Efficient safeguarding of the security of interconnected devices, which are often resource-constrained, can be achieved through collective remote attestation schemes. However, in existing schemes, the attestation keys are independent of the device configuration, leading to increased requirements for the trusted computing base. This paper introduces a symmetrical aggregate trust attestation that is compatible with devices adhering to the device identifier composition engine framework. The proposed scheme simplifies the trusted computing base requirements by generating an attestation key that is derived from the device configuration. Moreover, the scheme employs distributed aggregate message authentication codes to reduce both the communication volume within the device network and the size of the attestation report, thereby enhancing the aggregation efficiency. In addition, the scheme incorporates interactive authentication to accurately identify compromised devices.
]]>Symmetry doi: 10.3390/sym16030309
Authors: Eman H. Khalifa Dina A. Ramadan Hana N. Alqifari Beih S. El-Desouky
Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.
]]>Symmetry doi: 10.3390/sym16030308
Authors: Chenyang Cao Yinxin Bao Quan Shi Qinqin Shen
Accurate and real-time traffic speed prediction remains challenging due to the irregularity and asymmetry of real-traffic road networks. Existing models based on graph convolutional networks commonly use multi-layer graph convolution to extract an undirected static adjacency matrix to map the correlation of nodes, which ignores the dynamic symmetry change of correlation over time and faces the challenge of oversmoothing during training iterations, making it difficult to learn the spatial structure and temporal trend of the traffic network. To overcome the above challenges, we propose a novel multi-head self-attention gated spatiotemporal graph convolutional network (MSGSGCN) for traffic speed prediction. The MSGSGCN model mainly consists of the Node Correlation Estimator (NCE) module, the Time Residual Learner (TRL) module, and the Gated Graph Convolutional Fusion (GGCF) module. Specifically, the NCE module aims to capture the dynamic spatiotemporal correlations between nodes. The TRL module utilizes a residual structure to learn the long-term temporal features of traffic data. The GGCF module relies on adaptive diffusion graph convolution and gated recurrent units to learn the key spatial features of traffic data. Experimental analysis on a pair of real-world datasets indicates that the proposed MSGSGCN model enhances prediction accuracy by more than 4% when contrasted with state-of-the-art models.
]]>Symmetry doi: 10.3390/sym16030307
Authors: Komalpreet Kaur Gurjinder Singh Daniele Ritelli
In this article, we present a five-step block method coupled with an existing fourth-order symmetric compact finite difference scheme for solving time-dependent initial-boundary value partial differential equations (PDEs) numerically. Firstly, a five-step block method has been designed to solve a first-order system of ordinary differential equations that arise in the semi-discretisation of a given initial boundary value PDE. The five-step block method is derived by utilising the theory of interpolation and collocation approaches, resulting in a method with eighth-order accuracy. Further, characteristics of the method have been analysed, and it is found that the block method possesses A-stability properties. The block method is coupled with an existing fourth-order symmetric compact finite difference scheme to solve a given PDE, resulting in an efficient combined numerical scheme. The discretisation of spatial derivatives appearing in the given equation using symmetric compact finite difference scheme results in a tridiagonal system of equations that can be solved by using any computer algebra system to get the approximate values of the spatial derivatives at different grid points. Two well-known test problems, namely the nonlinear Burgers equation and the FitzHugh-Nagumo equation, have been considered to analyse the proposed scheme. Numerical experiments reveal the good performance of the scheme considered in the article.
]]>Symmetry doi: 10.3390/sym16030306
Authors: Giovanni Montani Nakia Carlevaro
We present a new perspective on the symmetries that govern the formation of large-scale structures across the Universe, particularly focusing on the transition from the seeds of galaxy clusters to the seeds of galaxies themselves. We address two main features of cosmological fluid dynamics pertaining to both the linear and non-linear regimes. The linear dynamics of cosmological perturbations within the Hubble horizon is characterized by the Jeans length, which separates stable configurations from unstable fluctuations due to the gravitational effect on sufficiently large (and therefore, massive enough) overdensities. On the other hand, the non-linear dynamics of the cosmological fluid is associated with a turbulent behavior once the Reynolds numbers reach a sufficiently high level. This turbulent regime leads to energy dissipation across smaller and smaller scales, resulting in a fractal distribution of eddies throughout physical space. The proposed scenario suggests that the spatial scale of eddy formation is associated with the Jeans length of various levels of fragmentation from an original large-scale structure. By focusing on the fragmentation of galaxy cluster seeds versus galaxy seeds, we arrived at a phenomenological law that links the ratio of the two structure densities to the number of galaxies in each cluster and to the Hausdorff number of the Universe matter distribution. Finally, we introduced a primordial magnetic field and studied its influence on the Jeans length dynamics. The resulting anisotropic behavior of the density contrast led us to infer that the main features of the turbulence could be reduced to a 2D Euler equation. Numerical simulations showed that the two lowest wavenumbers contained the major energy contribution of the spectrum.
]]>Symmetry doi: 10.3390/sym16030305
Authors: Guo Liang Xiangwei Chen Zhanmei Ren Qi Guo
Two systems of mathematical physics are defined by us, which are the first-order differential system (FODS) and the second-order differential system (SODS). Basing on the conventional Legendre transformation, we obtain a new kind of canonical equations of Hamilton (CEH) with some kind of symmetry. We show that the FODS can only be expressed by the new CEH, but do not by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs, on basis of the same conventional Legendre transformation. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way. Based on the new CEH, the approximate soliton solution of the nonlocal nonlinear Schrödinger equation is obtained, and the soliton stability is analysed analytically as well. Furthermore, because the symmetry of a system is closely connected with certain conservation theorem of the system, the new CEH may be useful in some complicated systems when the symmetry considerations are used.
]]>Symmetry doi: 10.3390/sym16030304
Authors: Erdenesukh Altanzaya Jiwon Heo Songyuan Xu Chan-Soo Lee Bierng-Chearl Ahn Sung-Soo Kim Seong-Gon Choi
This paper presents a computer-simulation-based design of an in-line, coaxial-to-circular waveguide adapter for converting the coaxial transverse electromagnetic (TEM) mode to the circular waveguide TE11 mode over more than a one-octave bandwidth. The proposed adapter consists of a coaxial-to-rectangular waveguide transformer employing a stepped-ridge converter and a rectangular-to-circular waveguide transformer employing a curved transition. The proposed adapter has been optimized using a commercial simulation tool. The dimensions of the designed adapter are given so that it can be verified by anyone who is interested. The designed adapter operates from 8.00 GHz to 22.95 GHz (2.87:1 bandwidth) with a reflection coefficient of less than −20 dB and a higher-order mode level of less than −25.0 dB.
]]>Symmetry doi: 10.3390/sym16030303
Authors: Weiwei Ding Youlin Shang Zhengfen Jin Yibao Fan
The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the l1-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms.
]]>Symmetry doi: 10.3390/sym16030302
Authors: Shengzhi Wang Shuzhen Niu Xintian Li Guosheng He
Aquatic organisms have evolved exceptional propulsion and even transoceanic migrating capabilities, surpassing artificial vessels significantly in maneuverability and efficiency. Understanding the hydrodynamic mechanisms of aquatic organisms is crucial for developing advanced biomimetic underwater propulsion vehicles. Underwater tetrapods such as sea turtles use fins or flippers for propulsion, which exhibit three rotational degrees of freedom, including flapping, sweeping, and pitching motions. Unlike previous studies that often simplify motion kinematics, this study employs a specially designed experimental device to mimic sea turtle fins’ motion and explore the impact of pitching amplitude, asymmetric pitching kinematics, and pausing time on lift and thrust generation. Force transducers and particle image velocimetry techniques are used to examine the hydrodynamic forces and flow field, respectively. It is found that boosting the fin’s pitching amplitude enhances both its lift and thrust efficiency to a certain extent, with a more pronounced effect on thrust performance. Surprisingly, the asymmetrical nature of the pitching angle’s pausing time within one flapping cycle significantly influences the lift and thrust characteristics during sea turtle swimming; extending the pausing time during the forward and upward flapping process improves lift efficiency; and prolonging the pausing time during the downward flapping process enhances thrust efficiency. Furthermore, the mechanism for high lift and thrust efficiency is revealed by examining the vortices shed from the fin during different motion kinematics. This research contributes to a more comprehensive understanding of the fin’s hydrodynamic characteristic, providing insights that can guide the design of more efficient biomimetic underwater propulsion systems.
]]>Symmetry doi: 10.3390/sym16030301
Authors: Kevyn Gallegos-Moncayo Justine Jean Nicolas Folastre Arash Jamali Arnaud Demortière
This study focuses on NMC 811 (LiNi0.8Mn0.1Co0.1O2), a promising material for high-capacity batteries, and investigates the challenges associated with its use, specifically the formation of the cathode electrolyte interphase (CEI) layer due to chemical reactions. This layer is a consequence of the position of the Lowest Unoccupied Molecular Orbital (LUMO) energy level of NMC 811 that is close to the Highest Occupied Molecular Orbital (HOMO) level of liquid electrolytes, resulting in electrolyte oxidation and cathode surface alterations during charging. A stable CEI layer can mitigate further degradation by reducing the interaction between the reactive cathode material and the electrolyte. Our research analyzed the CEI layer on NMC 811 using advanced techniques, such as 4D-STEM ACOM (automated crystal orientation mapping) and STEM-EDX, focusing on the effects of different charging voltages (4.3 V and 4.5 V). The findings revealed varying degrees of degradation and the formation of a fluorine-rich layer on the secondary particles. Detailed analysis showed that the composition of this layer differed based on the voltage: only LiF at 4.5 V and a combination of lithium fluoride (LiF) and lithium hydroxide (LiOH) at 4.3 V. Despite LiF’s known stability as a CEI protective layer, our observations indicate that it does not effectively prevent degradation in NMC 811. The study concluded that impurities and unwanted chemical reactions leading to suboptimal CEI formation are inevitable. Therefore, future efforts should focus on developing protective strategies for NMC 811, such as the use of specific additives or coatings.
]]>Symmetry doi: 10.3390/sym16030300
Authors: Shang Wu Yaxin Zhu Pengchen Liang
With the rapid development of intelligent manufacturing and electronic information technology, integrated circuits play a vital role in high-end chips. The semiconductor chip manufacturing process requires precise operation and strict control to ensure chip quality. The traditional manual visual inspection method has a high workforce cost and intense subjectivity and is accompanied by a high level of misdetection and leakage. Computer vision-based wafer defect detection technology is gaining popularity in the industry. However, previous methods still find it challenging to meet the production requirements regarding accuracy. To solve the problem, we propose a defect detection network based on a coding and decoding structure, Dense Skip-Connection U-Net (DSCU-Net), which optimizes the skip connection between the encoder and decoder and enhances the profound fusion of high-level semantics and low-level semantics to improve accuracy. To verify the effectiveness of DSCU-Net, we validate it in actual microelectromechanical systems (MEMS) data, and the results show that DSCU-Net reaches an optimal level. Therefore, the DSCU-Net proposed in this paper effectively solves the defect detection problem in semiconductor chip manufacturing. This method reduces workforce cost and subjectivity interference and improves inspection efficiency and accuracy. It will help to promote further development in the field of intelligent manufacturing and electronic information technology.
]]>Symmetry doi: 10.3390/sym16030299
Authors: Mouke Mo Chuntao Wang Shan Bian
Given the substantial value and considerable training costs associated with deep neural network models, the field of deep neural network model watermarking has come to the forefront. While black-box model watermarking has made commendable strides, the current methodology for constructing poisoned images in the existing literature is simplistic and susceptible to forgery. Notably, there is a scarcity of black-box model watermarking techniques capable of discerning a unique user in a multi-user model distribution setting. For this reason, this paper proposes a novel black-box model watermarking method for unique identity identification, which is denoted as the ID watermarking of neural networks (IDwNet). Specifically, to enhance the distinguishability of deep neural network models in multi-user scenarios and mitigate the likelihood of poisoned image counterfeiting, this study develops a discrete cosine transform (DCT) and singular value decomposition (SVD)-based symmetrical embedding method to form the poisoned image. As this ID embedding method leads to indistinguishable deep features, the study constructs a poisoned adversary training strategy by simultaneously inputting clean images, poisoned images with the correct ID, and poisoned adversary images with incorrect IDs to train a deep neural network. Extensive simulation experiments show that the proposed scheme achieves excellent invisibility for the concealed ID, surpassing remarkably the state-of-the-art. In addition, the proposed scheme obtains a validation success rate exceeding 99% for the poisoned images at the cost of a marginal classification accuracy reduction of less than 0.5%. Moreover, even though there is only a 1-bit discrepancy between IDs, the proposed scheme still results in an accurate validation of user copyright. These results indicate that the proposed scheme is promising.
]]>Symmetry doi: 10.3390/sym16030298
Authors: Oem Trivedi
The discovery of the Universe’s late-time acceleration and dark energy has led to a great deal of research into cosmological singularities, and in this brief review, we discuss all the prominent developments in this field for the best part of the last two decades. We discuss the fundamentals of spacetime singularities, after which we discuss in detail all the different forms of cosmological singularities that have been discovered in recent times. We then address methods and techniques to avoid or moderate these singularities in various theories and discuss how these singularities can also occur in non-conventional cosmologies. We then discuss a useful dynamical systems approach to deal with these singularities and finish up with some outlooks for the field. We hope that this work serves as a good resource to anyone who wants to update themselves with the developments in this very exciting area.
]]>Symmetry doi: 10.3390/sym16030295
Authors: Yoichi Miyata Takayuki Shiohama Toshihiro Abe
A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models.
]]>Symmetry doi: 10.3390/sym16030297
Authors: Anna Mazhar Jeremy Canfield Wesley N. Mathews James K. Freericks
Using a flexible form for ladder operators that incorporates confluent hypergeometric functions, we show how one can determine all of the discrete energy eigenvalues and eigenvectors of the time-independent Schrödinger equation via a single factorization step and the satisfaction of boundary (or normalizability) conditions. This approach determines the bound states of all exactly solvable problems whose wavefunctions can be expressed in terms of confluent hypergeometric functions. It is an alternative that shares aspects of the conventional differential equation approach and Schrödinger’s factorization method, but is different from both. We also explain how this approach relates to Natanzon’s treatment of the same problem and illustrate how to numerically determine nontrivial potentials that can be solved this way.
]]>Symmetry doi: 10.3390/sym16030296
Authors: Paweł Bednarz Mateusz Pirga
This paper introduces the concept of proper 2-dominating sets in graphs, providing a comprehensive characterisation of graphs that possess such sets. We give the necessary and sufficient conditions for a graph to have a proper 2-dominating set. Graphs with proper dominating sets can have a symmetric structure. Moreover, we estimate the bounds of the proper 2-domination number in the graphs with respect to the 2-domination and 3-domination numbers. We show that the cardinality of γ2¯-set is greater by one at most than the cardinality of γ2-set.
]]>Symmetry doi: 10.3390/sym16030294
Authors: Xueyan Liu Qiong Liu Jia Wang Hao Sun
In recent years, with the rapid development of intelligent technology, information security and privacy issues have become increasingly prominent. Epidemiological survey data (ESD) research plays a vital role in understanding the laws and trends of disease transmission. However, epidemiological investigations (EI) involve a large amount of privacy-sensitive data which, once leaked, will cause serious harm to individuals and society. Collecting EI data is also a huge task. To solve these problems and meet personalized privacy protection requirements in EIs, we improve the uOUE protocol based on utility-optimized local differential privacy to improve the efficiency and accuracy of data coding. At the same time, aiming at the collection and processing of ESD, a multidimensional epidemiological survey data aggregation scheme based on uOUE is designed. By using Paillier homomorphic encryption and an identity-based signature scheme to further prevent differential attacks and achieve multidimensional data aggregation, the safe, efficient, and accurate aggregation processing of ESD is executed. Through security proof and performance comparison, it is verified that our algorithm meets the requirements of local differential privacy and unbiased estimation. The experimental evaluation results on two data sets show that the algorithm has good practicability and accuracy in ESD collection and provides reliable and effective privacy protection.
]]>Symmetry doi: 10.3390/sym16030292
Authors: Tao Yang Yuan Ma Peng Zhang
This study computationally investigates small-scale flickering buoyant diffusion flames in externally swirling flows and focuses on identifying and characterizing various distinct dynamical behaviors of the flames. To explore the impact of finite rate chemistry on flame flicker, especially in sufficiently strong swirling flows, a one-step reaction mechanism is utilized for investigation. By adjusting the external swirling flow conditions (the intensity R and the inlet angle α), six flame modes in distinct dynamical behaviors were computationally identified in both physical and phase spaces. These modes, including the flickering flame, oscillating flame, steady flame, lifted flame, spiral flame, and flame with a vortex bubble, were analyzed from the perspective of vortex dynamics. The numerical investigation provides relatively comprehensive information on these flames. Under the weakly swirling condition, the flames retain flickering (the periodic pinch-off of the flame) and are axisymmetric, while the frequency nonlinearly increases with the swirling intensity. A relatively high swirling intensity can cause the disappearance of the flame pinch-off, as the toroidal vortex sheds around either the tip or the downstream of the flame. The flicker vanishes, but the flame retains axisymmetric in a small amplitude oscillation or a steady stay. A sufficiently high swirling intensity causes a small Damköhler number, leading to the lift-off of the flame (the local extinction occurs at the flame base). Under the same swirling intensity but large swirling angles, the asymmetric modes of the spiral and vortex bubble flames were likely to occur. With R and α increasing, these flames exhibit axisymmetric and asymmetric patterns, and their dynamical behaviors become more complex. To feature the vortical flows in flames, the phase portraits are established based on the velocity information of six positions along the axis of the flame, and the dynamical behaviors of various flames are presented and compared in the phase space. Observing the phase portraits and their differences in distinct modes could help identify the dynamical behaviors of flames and understand complex phenomena.
]]>Symmetry doi: 10.3390/sym16030293
Authors: Tidjani Négadi
In this study, we once again use a set of Fibonacci-like sequences to examine the symmetries within the genetic code. This time, our focus is on the physiological state of the amino acids, considering them as charged, in contrast to our previous work where they were seen as neutral. In a pH environment around 7.4, there are four charged amino acids. We utilize the properties of our sequences to accurately describe the symmetries in the genetic code table. These include Rumer’s symmetry, the third-base symmetry and the “ideal” symmetry, along with the “supersymmetry” classification schemes. We also explore the special chemical structure of the amino acid proline, presenting two perspectives—shCherbak’s view and the Downes–Richardson view—which are included in the description of the above-mentioned symmetries. Our investigation also employs elementary modular arithmetic to precisely describe the chemical structure of proline, connecting the two views seamlessly. Finally, our Fibonacci-like sequences prove instrumental in quickly establishing the multiplet structure of non-standard versions of the genetic code. We illustrate this with an example, showcasing the efficiency of our method in unraveling the complex relationships within the genetic code.
]]>Symmetry doi: 10.3390/sym16030291
Authors: Mohamed Ben Ayed Khalil El Mehdi Fatimetou Mohamed Salem
In this paper, we consider the nonlinear Neumann problem (Pε): −Δu+V(x)u=K(x)u(n+2)/(n−2)−ε, u>0 in Ω, ∂u/∂ν=0 on ∂Ω, where Ω is a smooth bounded domain in Rn, n≥4, ε is a small positive real, and V and K are non-constant smooth positive functions on Ω¯. First, we study the asymptotic behavior of solutions for (Pε) which blow up at interior points as ε moves towards zero. In particular, we give the precise location of blow-up points and blow-up rates. This description of the interior blow-up picture of solutions shows that, in contrast to a case where K≡1, problem (Pε) has no interior bubbling solutions with clustered bubbles. Second, we construct simple interior multi-peak solutions for (Pε) which allow us to provide multiplicity results for (Pε). The strategy of our proofs consists of testing the equation with vector fields which make it possible to obtain balancing conditions which are satisfied by the concentration parameters. Thanks to a careful analysis of these balancing conditions, we were able to obtain our results. Our results are proved without any assumptions of the symmetry or periodicity of the function K. Furthermore, no assumption of the symmetry of the domain is needed.
]]>Symmetry doi: 10.3390/sym16030290
Authors: Yu-Hsin Chen I-Huan Wu Sheng D. Chao
Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, we gradually increase the complexity in the number of particles and the interaction patterns. Our goal in the mini-review is to advocate for the utility of the KEP method in front-line research, in particular for research beginners in quantum many-body problems.
]]>Symmetry doi: 10.3390/sym16030289
Authors: Eun-Hyeok Kang Kunal Sandip Garud Su Cheong Park Moo-Yeon Lee
The continuously increasing energy density of electric motors to match the performance of electric vehicles with internal-combustion-engine vehicles demands an advanced cooling strategy. Direct dripping/spray cooling is one of such potential cooling strategies to replace the conventional cooling method for achieving the desired thermal management of next-generation electric motors. In the present work, the heat transfer characteristics of an electric motor with oil-dripping cooling were experimentally investigated considering overload operating conditions. An experimental set-up comprising a 15 kW electric motor and an oil-dripping cooling system was developed. The experimental data were used to evaluate the maximum temperature, heat transfer coefficient and power consumption under the influence of a dripping hole diameter (2 mm, 3 mm, 4 mm), oil flow rate (8 LPM, 12 LPM, 16 LPM) and overload operating power (8.28 kW, 12.05 kW, 14.21 kW). The symmetrical oil distribution over the electric motor and the superior heat transfer from the electric motor to the oil was achieved when the oil-dripping cooling system was designed with the combination of a 4 mm dripping hole diameter and a 12 LPM oil flow rate. The combination of the 4 mm dripping hole diameter and 12 LPM oil flow rate showed the lowest maximum temperatures of 31.9 °C and 46.3 °C for electric motor under overload operating powers of 8.28 kW and 14.21 kW, respectively. In addition, the highest heat transfer coefficient of 7528.61 W/m2-K and lowest power consumption of 18.07 W were achieved for the oil-dripping cooling system with the combination of a 4 mm dripping hole diameter and 12 LPM oil flow rate. The best combination of the operating parameters is proposed for developing the oil-dripping cooling system that enables superior heat transfer characteristics and, thus, an enhanced thermal management of electric motors under overload conditions.
]]>Symmetry doi: 10.3390/sym16030288
Authors: Ahmed M. Ahmed Ahmed I. Saied Maha Ali Mohammed Zakarya Haytham M. Rezk
This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder’s inequality, Minkowski’s inequality, the chain rule on time scales, and the properties of power rules on time scales. As special cases of our results, particularly when the time scale T equals the real line (T=R), we derive some classical continuous analogs of previous inequalities. Furthermore, when T corresponds to the set of natural numbers including zero (T=N0), the obtained results, to the best of the authors’ knowledge, represent innovative contributions to the field.
]]>Symmetry doi: 10.3390/sym16030287
Authors: Yan Chen Qing-Wen Wang Lv-Ming Xie
Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.
]]>Symmetry doi: 10.3390/sym16030286
Authors: Yun Ou Feng Qin Kai-Qing Zhou Peng-Fei Yin Li-Ping Mo Azlan Mohd Zain
For wireless sensor network (WSN) coverage problems, since the sensing range of sensor nodes is a circular area with symmetry, taking symmetry into account when deploying nodes will help simplify problem solving. In addition, in view of two specific problems of high node deployment costs and insufficient effective coverage in WSNs, this paper proposes a WSN coverage optimization method based on the improved grey wolf optimizer with multi-strategies (IGWO-MS). As far as IGWO-MS is concerned, first of all, it uses Sobol sequences to initialize the population so that the initial values of the population are evenly distributed in the search space, ensuring high ergodicity and diversity. Secondly, it introduces a search space strategy to increase the search range of the population, avoid premature convergence, and improve search accuracy. And then, it combines reverse learning and mirror mapping to expand the population richness. Finally, it adds Levy flight to increase the disturbance and improve the probability of the algorithm jumping out of the local optimum. To verify the performance of IGWO-MS in WSN coverage optimization, this paper rasterizes the coverage area of the WSN into multiple grids of the same size and symmetry with each other, thereby transforming the node coverage problem into a single-objective optimization problem. In the simulation experiment, not only was IGWO-MS selected, but four other algorithms were also selected for comparison, namely particle swarm optimization (PSO), grey wolf optimizer (GWO), grey wolf optimization based on drunk walk (DGWO), and grey wolf optimization led by two-headed wolves (GWO-THW). The experimental results demonstrate that when the number of nodes for WSN coverage optimization is 20 and 30, the optimal coverage rate and average coverage rate using IGWO-MS are both improved compared to the other four comparison algorithms. To make this clear, in the case of 20 nodes, the optimal coverage rate of IGWO-MS is increased by 13.19%, 1.68%, 4.92%, and 3.62%, respectively, compared with PSO, GWO, DGWO, and GWO-THW; while IGWO-MS performs even better in terms of average coverage rate, which is 16.45%, 3.13%, 11.25%, and 6.19% higher than that of PSO, GWO, DGWO, and GWO-THW, respectively. Similarly, in the case of 30 nodes, compared with PSO, GWO, DGWO, and GWO-THW, the optimal coverage rate of the IGWO-MS is increased by 15.23%, 1.36%, 5.55%, and 3.66%; the average coverage rate is increased by 16.78%, 1.56%, 10.91%, and 8.55%. Therefore, it can be concluded that IGWO-MS has certain advantages in solving WSN coverage problems, which is reflected in that not only can it effectively improve the coverage quality of network nodes, but it also has good stability.
]]>Symmetry doi: 10.3390/sym16030285
Authors: Wenlong Fu Ke Yang Bin Wen Yahui Shan Shuai Li Bo Zheng
As vital equipment in modern industry, the health state of rotating machinery influences the production process and equipment safety. However, rotating machinery generally operates in a normal state most of the time, which results in limited fault data, thus greatly constraining the performance of intelligent fault diagnosis methods. To solve this problem, this paper proposes a novel fault diagnosis method for rotating machinery with limited multisensor fusion samples based on the fused attention-guided Wasserstein generative adversarial network (WGAN). Firstly, the dimensionality of collected multisensor data is reduced to three channels by principal component analysis, and then the one-dimensional data of each channel are converted into a two-dimensional pixel matrix, of which the RGB images are obtained by fusing the three-channel two-dimensional images. Subsequently, the limited RGB samples are augmented to obtain sufficient samples utilizing the fused attention-guided WGAN combined with the gradient penalty (FAWGAN-GP) method. Lastly, the augmented samples are applied to train a residual convolutional neural network for fault diagnosis. The effectiveness of the proposed method is demonstrated by two case studies. When training samples per class are 50, 35, 25, and 15 on the KAT-bearing dataset, the average classification accuracy is 99.9%, 99.65%, 99.6%, and 98.7%, respectively. Meanwhile, the methods of multisensor fusion and the fused attention mechanism have an average improvement of 1.51% and 1.09%, respectively, by ablation experiments on the WT gearbox dataset.
]]>Symmetry doi: 10.3390/sym16030284
Authors: Guoqiang Wang Jiyuan Tao
Optimization is an important branch of operations research in applied mathematics and computer science, where functions are optimized over a range of feasible solutions [...]
]]>Symmetry doi: 10.3390/sym16030283
Authors: Bayartsetseg Kalina Ju-Hong Lee Kwang-Tek Na
The objective of portfolio diversification is to reduce risk and potentially enhance returns by spreading investments across different asset classes. Existing portfolio diversification models have traditionally been trained on historical financial time series data. However, several issues arise with historical financial time series data, making it challenging to train models effectively to achieve the portfolio diversification objective: an insufficient amount of training data and the uncertainty deficiency problem, wherein the uncertainty that existed in the past is not visible in the present. Insufficient datasets, characterized by small data size, result in information asymmetry and compromise portfolio performance. This limitation underscores the importance of adopting a pattern-centric data augmentation approach, capable of unveiling hidden patterns and structures within the financial time series data. To address these challenges, this paper introduces the financial time series decomposition-based variational encoder-decoder (FED) method to augment financial time series data, overcoming the limitations of insufficient training data and providing a more realistic and dynamic simulation of the financial market environment. By decomposing the data into distinct components, such as trend, dispersion, and residual, FED leverages pattern-centric data augmentation within the financial time series data. In the environment generated using the FED method, this paper proposes a two-class portfolio diversification, called FED2Port. It integrates stochastic elements into the reward function, enabling a reinforcement learning algorithm to learn from a comprehensive spectrum of financial market uncertainties. The experimental results demonstrate that the proposed model significantly enhances portfolio performance.
]]>Symmetry doi: 10.3390/sym16030282
Authors: Gregory Natanson
This paper exploits two remarkable features of the translationally form-invariant (TFI) canonical Sturm–Liouville equation (CSLE) transfigured by Liouville transformation into the Schrödinger equation with the shape-invariant Gendenshtein (Scarf II) potential. First, the Darboux–Crum net of rationally extended Gendenshtein potentials can be specified by a single series of Maya diagrams. Second, the exponent differences for the poles of the CSLE in the finite plane are energy-independent. The cornerstone of the presented analysis is the reformulation of the conventional supersymmetric (SUSY) quantum mechanics of exactly solvable rational potentials in terms of ‘generalized Darboux transformations’ of canonical Sturm–Liouville equations introduced by Rudyak and Zakhariev at the end of the last century. It has been proven by the author that the first feature assures that all the eigenfunctions of the TFI CSLE are expressible in terms of Wronskians of seed solutions of the same type, while the second feature makes it possible to represent each of the mentioned Wronskians as a weighted Wronskian of Routh polynomials. It is shown that the numerators of the polynomial fractions in question form the exceptional orthogonal polynomial (EOP) sequences composed of Wronskian transforms of the given finite set of Romanovski–Routh polynomials excluding their juxtaposed pairs, which have already been used as seed polynomials.
]]>Symmetry doi: 10.3390/sym16030281
Authors: Fatimah Alghamdi
In this paper, we investigate the pointwise hemi-slant submanifolds of a locally conformal Kähler manifold and their warped products. Moreover, we derive the necessary and sufficient conditions for integrability and totally geodesic foliation. We establish characterization theorems for pointwise hemi-slant submanifolds. Several fundamental results that extend the CR submanifold warped product in Kähler manifolds are proven in this study. We also provide some non-trivial examples and applications.
]]>Symmetry doi: 10.3390/sym16030280
Authors: Ying Yang Rekha Srivastava Jin-Lin Liu
A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized.
]]>Symmetry doi: 10.3390/sym16030279
Authors: Daniel Hodgson Sara Kanzi Almut Beige
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.
]]>Symmetry doi: 10.3390/sym16030278
Authors: Cheng Guo Lingrui Yang Jianbo Dai Bo Chen Ke Yin Jing Dai
The accurate identification of the broadband oscillation mode is the premise of solving the resonance risk of new energy stations. Reviewing the traditional Prony algorithm, the problems of the high model order and poor noise immunity in broadband oscillation mode are identified. The accuracy and running time of the Variational mode decomposition (VMD) is a symmetric trade-off problem. An improved strategy based on VMD is proposed. Firstly, the optimal value of the number of modes and penalty factors obtained by a particle swarm optimization algorithm is input into VMD to decompose the signal into multiple modes. Then, combined with the energy threshold method, the denoising and signal reconstruction of each mode component after decomposition are carried out. Finally, the Prony algorithm is used to identify the oscillation mode of the original signal and the reconstructed signal, respectively. The Signal-to-noise ratio (SNR) and model order are compared and analyzed. Through the analysis of the example and simulation data, it is shown that the proposed method effectively solves the problem of poor engineering adaptability of the traditional Prony algorithm. It also can accurately obtain the time-domain characteristics of broadband oscillation, which has a promising future in the engineering application.
]]>Symmetry doi: 10.3390/sym16030277
Authors: Hongpeng Wang Caikuan Tuo Zhiqin Wang Guoye Feng Chenglong Li
Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. The limited existing measures on FFSs sometimes yield counter-intuitive outcomes, which can obfuscate the accurate quantification of similarity and difference among FFSs. This paper introduces a suite of similarity and distance measures tailored for FFSs, drawing inspiration from the Tanimoto measure. We delve into the characteristics of these novel measures and offer some comparative studies with existing FFSs measures, highlighting their superior efficacy in the processing of fuzzy data from FFSs. Our proposed measures effectively rectify the counter-intuitive situations encountered with many existing measures and demonstrate a significant enhancement in differentiating between diverse FFSs. Moreover, we showcase the real-world applicability of our proposed measures through case studies in pattern recognition, medical diagnostics, and multi-attribute decision-making.
]]>Symmetry doi: 10.3390/sym16030276
Authors: Jing Bai Xiaofeng Qin Lu Huang Qianqian Chen
Dynamic decision-making is the process of seeking optimal choice with multiple related attributes under the multi-time-point situation. Considering that the time-varying nature of decision information can have a specific impact on the psychology of decision makers, in this paper, a dynamic decision-making method based on the cumulative prospect theory is proposed. Combining this with infinite parameterization of fuzzy soft sets, a time series interval triangular fuzzy soft set is presented, which has characteristics of boundedness, monotonicity, and symmetry. Then, based on the new information priority principle, the exponential decay model is used to determine the time weight coefficient, and a static fuzzy soft matrix is obtained. Furthermore, a method of calculating psychological utility values is proposed, in which the threshold-reference point set is introduced to analyze the psychological “profit and loss” values. Simultaneously, the time probability of the decision-making scenario is transformed into the corresponding weight function. On the basis of prospect maximization theory and maximum entropy theory, an optimization model for determining the weight of decision parameters is established. The cumulative prospect values of the alternatives are given to achieve the best choice for the alternatives. Finally, an example showed the feasibility and effectiveness of this method.
]]>Symmetry doi: 10.3390/sym16030275
Authors: Hailong Wang Yaolu Chen Hongshan Wang
In order to improve the mechanical properties and durability of lightweight aggregate concrete in extreme environments, this study utilized Inner Mongolia pumice as the coarse aggregate to formulate pumice lightweight aggregate concrete (P-LWAC) with a silica powder content of 0%, 2%, 4%, 6%, 8%, and 10%. Under sulfate dry–wet cycling conditions, this study mainly conducted a mass loss rate test, compressive strength test, NMR test, and SEM test to investigate the improvement effect of silica powder content on the corrosion resistance performance of P-LWAC. In addition, using grey prediction theory, the relationship between pore characteristic parameters and compressive strength was elucidated, and a grey prediction model GM (1,3) was established to predict the compressive strength of P-LWAC after cycling. Research indicates that under sulfate corrosion conditions, as the cycle times and silica powder content increased, the corrosion resistance of P-LWAC showed a trend of first increasing and then decreasing. At 60 cycles, P-LWAC with a content of 6% exhibited the lowest mass loss rate and the highest relative dynamic elastic modulus, compressive strength, and corrosion resistance coefficient. From the perspective of data distribution, various durability indicators showed a clear mirror symmetry towards both sides with a silica powder content of 6% as the symmetrical center. The addition of silica fume reduced the porosity and permeability of P-LWAC, enhanced the saturation degree of bound fluid, and facilitated internal structural development from harmful pores towards less harmful and harmless pores, a feature most prominent at the 6% silica fume mixing ratio. In addition, a bound fluid saturation and pore size of 0.02~0.05 μm/% exerted the most significant influence on the compressive strength of P-LWAC subjected to 90 dry–wet cycles. Based on these two factors, grey prediction model GM (1,3) was established. This model can accurately evaluate the durability of P-LWAC, improving the efficiency of curing decision-making and construction of concrete materials.
]]>Symmetry doi: 10.3390/sym16030274
Authors: Galina L. Klimchitskaya Constantine C. Korikov Vladimir M. Mostepanenko Oleg Yu. Tsybin
The authors wish to make the following corrections in their paper [...]
]]>Symmetry doi: 10.3390/sym16030273
Authors: Yiheng Chen Jinbai Zou Lihai Liu Chuanbo Hu
The problems of imbalanced datasets are generally considered asymmetric issues. In asymmetric problems, artificial intelligence models may exhibit different biases or preferences when dealing with different classes. In the process of addressing class imbalance learning problems, the classification model will pay too much attention to the majority class samples and cannot guarantee the classification performance of the minority class samples, which might be more valuable. By synthesizing the minority class samples and changing the data distribution, unbalanced datasets can be optimized. Traditional oversampling algorithms have problems of blindness and boundary ambiguity when synthesizing new samples. A modified reclassification algorithm based on Gaussian distribution is put forward. First, the minority class samples are reclassified by the KNN algorithm. Then, different synthesis strategies are selected according to the combination of the minority class samples, and the Gaussian distribution is used to replace the uniform random distribution for interpolation operation under certain classification conditions to reduce the possibility of generating noise samples. The experimental results indicate that the proposed oversampling algorithm can achieve a performance improvement of 2∼8% in evaluation metrics, including G-mean, F-measure, and AUC, compared to traditional oversampling algorithms.
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