Symmetry doi: 10.3390/sym15061237

Authors: Daud Ahmad Kiran Naz Mariyam Ehsan Buttar Pompei C. Darab Mohammed Sallah

A Coons patch is characterized by a finite set of boundary curves, which are dependent on the choice of blending functions. For a bicubically blended Coons patch (BBCP), the Hermite cubic polynomials (interpolants) are used as blending functions. A BBCP comprises information about its four corner points, including the curvature represented by eight tangent vectors, as well as the twisting behavior determined by the four twist vectors at these corner points. The interior shape of the BBCP depends not only on the tangent vectors at the corner points but on the twist vectors as well. The alteration in the twist vectors at the corner points can change the interior shape of the BBCP even for the same arrangement of tangent vectors at these corner points. In this study, we aim to determine the optimal twist vectors that would make the surface an extremal of the minimal energy functional. To achieve this, we obtain the constraints on the optimal twist vectors (MPDs) of the BBCP for the specified corner points by computing the extremal of the Dirichlet and quasi-harmonic functionals over the entire surface with respect to the twist vectors. These twist vectors can then be used to construct various quasi-minimal and quasi-harmonic BBCPs by varying corner points and tangent vectors. The optimization techniques involve minimizing a functional subject to certain constraints. The methods used to optimize twist vectors of BBCPs can have potential applications in various fields. They can be applied to fuzzy optimal control problems, allowing us to find the solution of complex and uncertain systems with fuzzy constraints. They provide us an opportunity to incorporate symmetry considerations for the partial differential equations associated with minimal surface equations, an outcome of zero-mean curvature for such surfaces. By exploring and utilizing the underlying symmetries, the optimization strategies can be further enhanced in terms of robustness and adaptability.

]]>Symmetry doi: 10.3390/sym15061234

Authors: Shouwang Sun Zhiwen Wang Zili Xia Letian Yi Zixiang Yue Youliang Ding

Changes in the deflection of cable-stayed bridges due to thermal effects may adversely affect the bridge structure and reflect the degradation of bridge performance. Therefore, complete deflection field data are important for bridge health monitoring. A strong linear correlation has been found between temperature-induced deflections in different positions of the same span of a cable-stayed bridge in many studies, which make the deflection data matrix/tensor have a low-rank structure. Therefore, it is appropriate to use a low-rank matrix/tensor learning to model the temperature&ndash;deflection field of a cable-stayed bridge. Moreover, to avoid disturbing the recovery results via abnormal data (e.g., baseline shift and outliers), a Bayesian robust tensor learning method is proposed to extract the spatio-temporal characteristics of the bridge temperature&ndash;deflection field. The missing data recovery and abnormal data cleaning are achieved simultaneously in the process of reconstructing the temperature-induced field via tensor learning. The performance of the method is verified with actual continuous monitoring data from a cable-stayed bridge. The experimental results show that low-order tensor (i.e., matrix) learning has a good recovery and cleaning performance. The extension to higher-order tensor learning is proposed to extract the spatial symmetry of the sensor locations, which is experimentally proven to have better missing recovery and abnormal data cleaning performance.

]]>Symmetry doi: 10.3390/sym15061235

Authors: Ye Ren Hao Yin Li Wang Honghai Ji

Fast-changing demand in real traffic systems always leads to asymmetrical traffic flow and queues, which aggravates congestion and energy waste. In this paper, the traffic signal control problem of multi-phase intersections was studied with fast-changing traffic flows. First, a novel model-free adaptive control-based symmetrical queuing balancing method was designed by using the full-format dynamic linearization (FFDL) technique. Second, in order to deal with the fast-changing traffic flow, a radial basis function neural network (RBFNN) was added to adjust parameters in a two-layer structure. Moreover, a variable cycle tuning algorithm was introduced to further reduce the time loss. Using the simulation, the proposed algorithm was compared with three other control strategies under low and high traffic demand, respectively, and the results showed the capability of the proposed algorithm.

]]>Symmetry doi: 10.3390/sym15061236

Authors: Lina Draudvilienė Renaldas Raišutis

The application of non-stationary Lamb wave signals is a promising tool in various industrial applications where information about changes inside a structure is required. Phase velocity is one of the Lamb wave parameters that can be used for inhomogeneities detection. The possibility of reconstructing the segment of the phase velocity in a strong dispersion range using only two signals is proposed. The theoretical study is performed using signals of the A0 mode propagating in an aluminium plate at a frequency of 150 kHz, 300 kHz, 500 kHz and 900 kHz. The experiment was carried out at a value of 300 kHz. The studies conducted indicated that the maximum distance between two signals, at which the time-of-flight can be measured between the same phase points, is the main parameter for the two signals technique application. Theoretical and experimental studies were performed, and the mean relative error was calculated by comparing the obtained results with those calculated via the SAFE method. In the theoretical study, the mean relative error of 0.33% was obtained at 150 kHz, 0.22% at 300 kHz, 0.23% at 500 kHz and 0.11% at 900 kHz. The calculated mean relative errors &delta;cph=0.91% and &delta;cph=1.36% were obtained at different distances in the experimental study. The results obtained show that the estimation of the phase velocity in dispersion ranges using only two received signals was a useful tool that saved time and effort.

]]>Symmetry doi: 10.3390/sym15061233

Authors: Ali Omar M. Alsharif Assaad Jmal Omar Naifar Abdellatif Ben Makhlouf Mohamed Rhaima Lassaad Mchiri

In this study, an unknown input observer is proposed for a class of nonlinear GPFOSs. For this class of systems, both full-order and reduced-order observers have been established. The investigated system satisfies the one-sided Lipschitz nonlinear condition, which is an improvement of the classic Lipschitz condition. Sufficient conditions have been proposed to ensure the error dynamics&rsquo; Mittag&ndash;Leffler stability. The value of this work lies in the fact that, to the best of the authors&rsquo; knowledge, this is the first research work that investigates the issue of Observer Design (OD) for GPFOSs. To exemplify the usefulness of the suggested observers, an illustrative numerical example is suggested.

]]>Symmetry doi: 10.3390/sym15061232

Authors: Luxiang Wang Zhende Zhu Shu Zhu Junyu Wu

Columnar jointed rock mass (CJRM) formed by intact rock divided by special symmetrical columnar joints is a special type of rock with poor mechanical properties, strong anisotropy, and weak self-supporting ability, severely affecting the excavation safety and stability of underground tunnels. In this study, taking the Baihetan hydropower station as the engineering background, CJRM geological numerical models with different dip angles that combined well with the natural CJRM were generated based on the geological statistical parameters of the engineering site and were verified to have high rationality and accuracy. Tunnel excavation and overloading tests were carried out on these numerical models, and the results showed that the stress and displacement distributions after excavation exhibited strong anisotropic characteristics under different dip angles, and the positions where engineering safety problems are most likely to occur are the side walls, which are prone to stress-structure-controlled failure mode. The self-supporting ability at different dip angles after excavation from weak to strong are 45&deg;, 60&deg;, 75&deg;, 90&deg;, 30&deg;, 0&deg;, and 15&deg;. The safety factors assessed by overloading for CJRM with dip angles of 0&ndash;90&deg; degrees were 2.5, 2.6, 2.6, 1.8, 2.1, and 2.2, respectively, providing a valuable reference for the construction safety and support measures of CJRM excavation.

]]>Symmetry doi: 10.3390/sym15061231

Authors: Virginia Uralde Fernando Veiga Alfredo Suarez Eider Aldalur Tomas Ballesteros

The field of additive manufacturing has experienced a surge in popularity over recent decades, particularly as a viable alternative to traditional metal part production. Directed energy deposition (DED) is one of the most promising additive technologies, characterized by its high deposition rate, with wire arc additive manufacturing (WAAM) being a prominent example. Despite its advantages, DED is known to produce parts with suboptimal surface quality and geometric accuracy, which has been a major obstacle to its widespread adoption. This is due, in part, to a lack of understanding of the complex geometries produced by the additive layer. To address this challenge, researchers have focused on characterizing the geometry of the additive layer, particularly the outer part of the bead. This paper specifically investigates the geometrical characteristics and symmetry of walls produced by comparing two different techniques: an oscillated strategy and overlapping beads.

]]>Symmetry doi: 10.3390/sym15061230

Authors: Chunxiao Li Honghui Jin Wen Wu Mei Yang Qingyue Wang Yuanpeng Pei

Vehicular ad hoc network (VANET) communications face severe fading problems due to the signal reflections and diffractions within tunnels. Unlike the open road, the space of a tunnel is very limited, so VANET communication performance in a tunnel is seriously affected. In the process of signal transmission, the reflected signal is symmetrical with the incident signal after it is reflected by the road and the wall. In this paper, we establish a mathematical model of path loss for V2V (Vehicle-to-Vehicle) communication based on the principle of signal reflection symmetry in tunnels and considering several factors, such as the tunnel surface and the color of the tunnel wall. In addition, we use cooperative communication to form a virtual multiple-input multiple-output (V-MIMO) system, to improve the communication quality in tunnels. In the proposed system, the OBU (On-Board-unit) and RSU (Road-Side-Unit) share each other&rsquo;s antennas, so that wireless cooperative communication can be employed, without increasing the number of antennas in a one-way tunnel. Therefore, this multipath fading internal electromagnetic wave propagation model can be used to improve performance. A deep reinforcement learning algorithm was used to solve the pairing problem to obtain a more accurate OBU and RSU pair, to form a V-MIMO system. Here, the RSU is regarded as an agent and interacts with the OBU in the tunnel. The optimal strategy was learned in a real-time changing simulation environment, and the experiment verified the convergence of the algorithm. The simulation results showed that, compared with the Q-learning based scheme, the optimal matching algorithm based on V-MIMO and a DQN (Deep Q-network) could effectively reduce the probability of transmission outages and improve the communication efficiency in tunnels.

]]>Symmetry doi: 10.3390/sym15061229

Authors: Yazhuo Li Qian Luo Quandong Feng

The Schr&ouml;dinger equation is one of the most basic equations in quantum mechanics. In this paper, we study the convergence of symmetric discretization models for the nonlinear Schr&ouml;dinger equation in dark solitons&rsquo; motion and verify the theoretical results through numerical experiments. Via the second-order symmetric difference, we can obtain two popular space-symmetric discretization models of the nonlinear Schr&ouml;dinger equation in dark solitons&rsquo; motion: the direct-discrete model and the Ablowitz&ndash;Ladik model. Furthermore, applying the midpoint scheme with symmetry to the space discretization models, we obtain two time&ndash;space discretization models: the Crank&ndash;Nicolson method and the new difference method. Secondly, we demonstrate that the solutions of the two space-symmetric discretization models converge to the solution of the nonlinear Schr&ouml;dinger equation. Additionally, we prove that the convergence order of the two time&ndash;space discretization models is O(h2+&tau;2) in discrete L2-norm error estimates. Finally, we present some numerical experiments to verify the theoretical results and show that our numerical experiments agree well with the proven theoretical results.

]]>Symmetry doi: 10.3390/sym15061228

Authors: Juan Liu Min Hu Ying Wang Zhong Huang Julang Jiang

To extract facial features with different receptive fields and improve the decision fusion performance of network ensemble, a symmetric multi-scale residual network (SMResNet) ensemble with a weighted evidence fusion (WEF) strategy for facial expression recognition (FER) was proposed. Firstly, aiming at the defect of connecting different filter groups of Res2Net only from one direction in a hierarchical residual-like style, a symmetric multi-scale residual (SMR) block, which can symmetrically extract the features from two directions, was improved. Secondly, to highlight the role of different facial regions, a network ensemble was constructed based on three networks of SMResNet to extract the decision-level semantic of the whole face, eyes, and mouth regions, respectively. Meanwhile, the decision-level semantics of three regions were regarded as different pieces of evidence for decision-level fusion based on the Dempster-Shafer (D-S) evidence theory. Finally, to fuse the different regional expression evidence of the network ensemble, which has ambiguity and uncertainty, a WEF strategy was introduced to overcome conflicts within evidence based on the support degree adjustment. The experimental results showed that the facial expression recognition rates achieved 88.73%, 88.46%, and 88.52% on FERPlus, RAF-DB, and CAER-S datasets, respectively. Compared with other state-of-the-art methods on three datasets, the proposed network ensemble, which not only focuses the decision-level semantics of key regions, but also addresses to the whole face for the absence of regional semantics under occlusion and posture variations, improved the performance of facial expression recognition in the wild.

]]>Symmetry doi: 10.3390/sym15061227

Authors: Haroon Ahmad Mudasir Younis Afrah Ahmad Noman Abdou

In this article, we develop a new notion that combines fixed-point theory and graph theory: graphical bipolar b-metric spaces. We demonstrate fixed-point solutions in the framework of graphical bipolar b-metric spaces, employing covariant and contravariant mapping contractions, which is a new addition to this end. This article also features illustrative examples drawn from various contexts to further demonstrate our findings. This is a significant study since it melds ideas from graph theory with those from generalized bipolar metric spaces, and considers that the symmetry of the edges of the underlying graphs connected with the enunciated metric spaces is essential in the graphical metric spaces.

]]>Symmetry doi: 10.3390/sym15061226

Authors: Georgy I. Burde

The analysis of the present paper reveals that, besides the relativistic symmetry expressed by the Lorentz group of coordinate transformations which leave invariant the Minkowski metric of space-time of inertial frames, there exists one more relativistic symmetry expressed by a group of coordinate transformations leaving invariant the space-time metric of the frames with a constant proper-acceleration. It is remarkable that, in the flat space-time, only those two relativistic symmetries, corresponding to groups of continuous transformations leaving invariant the metric of space-time of extended rigid reference frames, exist. Therefore, the new relativistic symmetry should be considered on an equal footing with the Lorentz symmetry. The groups of transformations leaving invariant the metric of the space-time of constant proper-acceleration are determined using the Lie group analysis, supplemented by the requirement that the group include transformations to or from an inertial to an accelerated frame. Two-parameter groups of two-dimensional (1 + 1), three-dimensional (2 + 1), and four-dimensional (3 + 1) transformations, with the group parameters related to the ratio of accelerations of the frames and the relative velocity of the frame space origins at the initial moment, can be considered as counterparts of the Lorentz group of corresponding dimensions. Defining the form of the interval and the groups of coordinate transformations satisfying the relativity principle paves the way to defining the invariant forms of the laws of dynamics and electrodynamics in accelerated frames. Thus, the problem of extending the relativity principle from inertial to uniformly accelerated frames has been resolved without use of the equivalence principle and/or the general relativity equations. As an application of the transformations to purely kinematic phenomena, the problem of differential aging between accelerated twins is treated.

]]>Symmetry doi: 10.3390/sym15061225

Authors: P. Priyadharshini M. Vanitha Archana Nehad Ali Shah Mansoor H. Alshehri

Nanofluids holding three distinct sorts of nanosized particles suspended in base fluid possess excellent thermal performance. In light of this novel use in coolant applications, the current work dealt with the optimal design and performance estimation of a ternary hybrid nanofluid, based on a modern machine learning prediction technique. The synthesis of (Cu), (TiO2), and (SiO2) ternary hybrid nanoparticles suspended in water over a symmetrically stretching sheet was scrutinized. The flow over a stretching sheet is the most noteworthy symmetry analysis for momentum and thermal boundary layers, due to the implications of heat transfer, and is applied in various industries and technological fields. The governing equations were transformed to a dimension-free series of ODEs, by handling similarity transformable with symmetry variables, after which, the series of ODEs were treated scientifically, with the help of the Wolfram Language tool. The precision of the current estimates was assessed by comparison to existing research. Moreover, the natures of the physical phenomena were forecast by designing a support vector machine algorithm with an emphasis on machine learning, which delivers a robust and efficient structure for every fluid application that infers physical influences. To validate the proposed research, some of the statistical metrics were taken for error assessment between true and anticipated values. It was revealed that the presented approach is the best strategy for predicting physical quantities. This investigation established that ternary hybrid nanofluid possesses excellent thermal performance, greater than that of hybrid nanofluid. The current optimization process delivers a new beneficial viewpoint on the production of polymer sheets, glass fiber, petroleum, plastic films, heat exchangers, and electronic devices. Hence, the obtained results are recommended for the development of industrial devices setups.

]]>Symmetry doi: 10.3390/sym15061223

Authors: Nor Syahmina Kamarudin Syahida Che Dzul-Kifli

In this article, we present a measurable version of the spectral decomposition theorem for a Z2-action on a compact metric space. In the process, we obtain some relationships for a Z2-action with shadowing property and k-type weak extending property. Then, we introduce a definition of measure expanding for a Z2-action by using some properties of a Borel measure. We also prove one property that occurs whenever a Z2-action is invariantly measure expanding. All of the supporting results are necessary to prove the spectral decomposition theorem, which is the main result of this paper. More precisely, we prove that if a Z2-action is invariantly measure expanding, has shadowing property and has k-type weak extending property, then it has spectral decomposition.

]]>Symmetry doi: 10.3390/sym15061224

Authors: Aníbal Coronel Fernando Huancas Esperanza Lozada Marko Rojas-Medar

This article is focused on investigating the mathematical model calibration of a reaction&ndash;diffusion system arising in the mathematical model of the spread of an epidemic in a society. We consider that the total population is divided into two classes of individuals, called susceptible and infectious, where a susceptible individual can become infectious, and that upon recovery, an infected individual can become susceptible again. We consider that the population lives in a spatially heterogeneous environment, and that the spread of the dynamics is governed by a reaction&ndash;diffusion system consisting of two equations, where the variables of the model are the densities of susceptible and infected individuals. In the reaction term, the coefficients are the rates of disease transmission and the rate of infective recovery. The main contribution of this study is the identification of the reaction coefficients by assuming that the infective and susceptible densities at the end time of the process and on overall spatial domain are observed. We apply the optimal control methodology to prove the main findings: the existence of positive solutions for the state system, the existence of at least one solution for the identification problem, the introduction of first-order necessary conditions, and the local uniqueness of optimal solutions.

]]>Symmetry doi: 10.3390/sym15061222

Authors: Liansheng Sui Han Li Jie Liu Zhaolin Xiao Ailing Tian

As an interesting technique that allows data extraction and image recovery without any loss, reversible data hiding in encrypted images is an area of great concern in the field of information security. In this paper, a new reversible data hiding method with high embedding capacity is proposed based on hybrid prediction and Huffman coding. The combination of two embedding mechanisms is innovatively designed to improve the embedding capacity according to different parts of the original image, i.e., the most significant bit-plane and the remaining seven bit-planes. In the first part of this method, the prediction value of each pixel is obtained by calculating the average value of its two neighboring pixels, and all of the most significant bits can be vacated to accommodate additional data. In the second part, the prediction value of each pixel is calculated using the median edge detector predictor, on which the tag map is built. Then, Huffman coding is used to compress the tag map so that a large amount of vacant space is obtained. Finally, the secret data can be embedded into the vacated space by directly using bit substitution. Compared with some recently reported methods, experimental results and analysis have demonstrated that an original image with high visual symmetry/quality can be recovered. Also, larger embedding capacity can be achieved, such as 3.3894 bpp and 3.2824 bpp, for BOSSBase and BOWS2 databases, respectively.

]]>Symmetry doi: 10.3390/sym15061220

Authors: Reetu Malhotra Faten S. Alamri Hamiden Abd El-Wahed Khalifa

Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit&rsquo;s failure rate exceeding a predetermined threshold. The cold standby system&rsquo;s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ.

]]>Symmetry doi: 10.3390/sym15061221

Authors: Hao Liu Jianjun Wang Yu Liu Zhi Wang Yifu Long

Flange joints with spigots are widely used in aero-engines. The spigot will restrict the shear slipping between flanges, which, in turn, affects the stiffness characteristics of the joint. The current model and research on flange joints without spigots may not be suitable for the dynamic characteristics of aero-engines. Moreover, the complexity of contact pairs limits the application of the flange joint finite element (FE) model in aero-engine dynamics analysis. Therefore, a simplified analytical model of a flange joint with a spigot is proposed in this paper. First, the stiffness characteristic of the flange joint with a spigot is studied using the FE method. Second, a corresponding experiment is executed to verify the result of the FE analysis. Furthermore, based on the former FE and experimental analysis, one section of a flange joint is simulated by the Jenkins friction model and a spring. Then, a simplified analytical model of the entire flange joint is built according to the different statuses of each section. Finally, a simulation analysis of the stiffness characteristic is performed. The result shows that the simplified analytical model can be utilized to describe the bending stiffness characteristic of the flange joint with a spigot.

]]>Symmetry doi: 10.3390/sym15061219

Authors: Yuzhe Zhang Zhenbin Zhang Oluleke Babayomi Zhen Li

The rapid growth of energy demand requires progressive energy generation. This, together with the demand for higher efficiency and flexibility, has promoted the application of power electronics in energy systems. During the past decade, model predictive control (MPC) of power electronics has witnessed significant advancements in both dynamic performance and optimal control of the multi-objective terms. Several of these terms can have equal control priorities, resulting in a symmetrical cost function; however, most objectives have different priorities and require weighting factors to resolve the asymmetry in the cost function. Currently, researchers continue to encounter challenges in the optimal design of weighting factors. Moreover, the relative performance of different techniques that either utilize or avoid the weighting factor are uncertain. Therefore, this study focuses on weighting factor design techniques in the literature as applied to wind/solar energy conversion, microgrids, grid-connected converters, and other high-performance converter-based systems. These are grouped under the heuristic, offline tuning, sequential, and online optimization methods. This study demonstrates that optimal online tuning of weighting factors and sequential MPC methods can both offer improved robustness against parameter uncertainties. In addition, the advantages and limitations of different techniques are highlighted.

]]>Symmetry doi: 10.3390/sym15061218

Authors: Massimo Tessarotto Claudio Cremaschini

The theoretical prediction of the stochastic property of the quantum cosmological constant and the quantum stochastic nature of event horizons has crucial implications on the physics of space-time and black holes in particular. One of these consequences concerns a new mechanism, which is investigated here, for the stochastic regularization of singular black-hole solutions of classical general relativity. The problem is posed in the context of the theory of covariant quantum gravity (CQG-theory), namely the manifestly covariant, constraint-free and finite graviton-mass quantum Hamiltonian approach developed by Cremaschini and Tessarotto (2015&ndash;2022), which permits to cast the theory in a frame-independent setting. It is precisely the trajectory-dependence feature of the theory and the intrinsic stochastic property of quantum gravity which turn out to be crucial properties for reaching quantum regularization of classical singular solutions.

]]>Symmetry doi: 10.3390/sym15061217

Authors: Predrag S. Stanimirović Branislav D. Ivanov Dragiša Stanujkić Lev A. Kazakovtsev Vladimir N. Krutikov Darjan Karabašević

The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai&ndash;Liao conjugate gradient (CG) iterative method. In particular, we suggest and explore a new neutrosophic logic system intended to compute the essential parameter t required in Dai&ndash;Liao CG iterations. Theoretical examination and numerical experiments signify the effectiveness of the introduced method for controlling t. By incorporation of the neutrosophy in the Dai&ndash;Liao conjugate gradient principle, we established novel Dai&ndash;Liao CG iterations for solving large-scale unconstrained optimization problems. Global convergence is proved under standard assumptions and with the use of the inexact line search. Finally, computational evidence shows the computational effectiveness of the proposed fuzzy neutrosophic Dai&ndash;Liao CG method.

]]>Symmetry doi: 10.3390/sym15061216

Authors: Warisa Thangjai Sa-Aat Niwitpong

A delta-lognormal distribution consists of zero and positive values. The positive values follow a lognormal distribution, which is an asymmetric distribution. It is well known that the logarithm of these values follows a normal distribution, which is a symmetric distribution. The delta-lognormal distribution is used in medical and environmental sciences. This study considers the challenges of constructing confidence intervals for the mean and difference between means of delta-lognormal distributions containing left-censored data and applies them to compare two daily rainfall average areas in Thailand. Three different approaches for constructing confidence intervals for the mean of the delta-lognormal distribution containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, and the parametric bootstrap approach, are developed. Moreover, four different approaches for constructing confidence intervals for the difference between means of delta-lognormal distributions containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, the parametric bootstrap approach, and the method of variance estimates recovery approach, are considered. The performance of the proposed confidence intervals is evaluated by Monte Carlo simulation. The simulation studies indicate that the Bayesian approach can be considered as an alternative to construct a credible interval for the mean of the delta-lognormal distribution containing left-censored data. Additionally, the generalized confidence interval and Bayesian approaches can be recommended as alternatives to estimate the confidence interval for the difference between means of delta-lognormal distributions containing left-censored data. All approaches are illustrated using the daily rainfall data from Chiang Mai and Lampang provinces in Thailand.

]]>Symmetry doi: 10.3390/sym15061215

Authors: Vladimir Rovenski

A weak f-contact structure, introduced in our recent works, generalizes the classical f-contact structure on a smooth manifold, and its characteristic distribution defines a totally geodesic foliation with flat leaves. We find the splitting tensor of this foliation and use it to show positive definiteness of the Jacobi operators in the characteristic directions and to obtain a topological obstruction (including the Adams number) to the existence of weak f-K-contact manifolds, and prove integral formulas for a compact weak f-contact manifold. Based on applications of the weak f-contact structure in Riemannian contact geometry considered in the article, we expect that this structure will also be fruitful in theoretical physics, e.g., in QFT.

]]>Symmetry doi: 10.3390/sym15061214

Authors: Kamran Sharif Ullah Khan Salma Haque Nabil Mlaiki

Differential equations of fractional order arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. In this article, a numerical method based on Laplace transform and numerical inverse Laplace transform for the numerical modeling of differential equations of fractional order is developed. The analytic inversion can be very difficult for complex forms of the transform function. Therefore, numerical methods are used for the inversion of the Laplace transform. In general, the numerical inverse Laplace transform is an ill-posed problem. This difficulty has led to various numerical methods for the inversion of the Laplace transform. In this work, the Weeks method is utilized for the numerical inversion of the Laplace transform. In our proposed numerical method, first, the fractional-order differential equation is converted to an algebraic equation using Laplace transform. Then, the transformed equation is solved in Laplace space using algebraic techniques. Finally, the Weeks method is utilized for the inversion of the Laplace transform. Weeks method is one of the most efficient numerical methods for the computation of the inverse Laplace transform. We have considered five test problems for validation of the proposed numerical method. Based on the comparison between analytical results and the Weeks method results, the reliability and effectiveness of the Weeks method for fractional-order differential equations was confirmed.

]]>Symmetry doi: 10.3390/sym15061213

Authors: Si-Wen Li Xiao-Tong Zhang

As a top-down holographic approach, the D4/D8 model is expected to be a holographic version of QCD, since it almost includes all the elementary features of QCD based on string theory. In this manuscript, we review the fundamental properties of the D4/D8 model with respect to the D4-brane background and the embedding of the flavor branes, holographic quark, gluon, meson, baryon and glueball with various symmetries; then, we take a look at some interesting applications and developments based on this model.

]]>Symmetry doi: 10.3390/sym15061212

Authors: Borut Žalik Damjan Strnad David Podgorelec Ivana Kolingerová Andrej Nerat Niko Lukač Štefan Kohek Luka Lukač

The characterisation of geometric shapes produces their concise description and is, therefore, important for subsequent analyses, for example in Computer Vision, Machine Learning, or shape matching. A new method for extracting characterisation vectors of 2D geometric shapes is proposed in this paper. The shape of interest, embedded into a raster space, is swept several times by sweep-lines having different slopes. The interior shape&rsquo;s points, being in the middle of its boundary and laying on the actual sweep-line, are identified at each stage of the sweeping process. The midpoints are then connected iteratively into chains. The chains are filtered, vectorised, and normalised. The obtained polylines from the vectorisation step are used to design the shape&rsquo;s characterisation vector for further application-specific analyses. The proposed method was verified on numerous shapes, where single- and multi-threaded implementations were compared. Finally, characterisation vectors, among which some were rotated and scaled, were determined for these shapes. The proposed method demonstrated a good rotation- and scaling-invariant identification of equal shapes.

]]>Symmetry doi: 10.3390/sym15061211

Authors: Sheng Zhang Feng Zhu Bo Xu

The existence of solutions with localized solitary wave structures is one of the significant characteristics of nonlinear integrable systems. Darboux transformation (DT) is a well-known method for constructing multi-soliton solutions, using a type of localized solitary wave, of integrable systems, but there are still no reports on extending DT techniques to construct such solitary wave solutions of fractional integrable models. This article takes the coupled nonlinear Schr&ouml;dinger (CNLS) equations with conformable fractional derivatives as an example to illustrate the feasibility of extending the DT and generalized DT (GDT) methods to construct symmetric and asymmetric solitary wave solutions for fractional integrable systems. Specifically, the traditional n-fold DT and the first-, second-, and third-step GDTs are extended for the fractional CNLS equations. Based on the extended GDTs, explicit solutions with symmetric/asymmetric soliton and soliton&ndash;rogon (solitrogon) spatial structures of the fractional CNLS equations are obtained. This study found that the symmetric solitary wave solutions of the integer-order CNLS equations exhibit asymmetry in the fractional order case.

]]>Symmetry doi: 10.3390/sym15061210

Authors: Damien Bissessar Thibault Thierry Julien Egly Valerio Giuso Thierry Achard Pascal Steffanut Matteo Mauro Stéphane Bellemin-Laponnaz

We present here the synthesis, chemical, and photophysical study of a series of three new copper halide derivatives, namely 2a&ndash;c. They are all tetranuclear copper-iodide clusters of general formula [Cu(&mu;3-I)P]4 consisting of a cubane-like {Cu4I4} motif and P = phosphine. They differ in the type of the phosphines used as ligands: a monophosphine with a single pendant ester unit (complex 2a), two pendant ester units (2b), and a diphosphine containing two esters in the linker (2c). The molecular structure of the complexes was determined by single-crystal X-ray diffraction analysis. All the investigated derivatives were found to be photo- and thermally-stable luminescent species. In the solid state, the complexes display intense and long-lived photoluminescence in the orange region with PLQY values of 0.43&ndash;0.84 at room temperature associated mainly with a 3CC excited state with mixed 3XMCT character.

]]>Symmetry doi: 10.3390/sym15061209

Authors: Bakhtiyor Kh. Khuzhayorov Gafurjan Ibragimov Usmonali Saydullaev Bruno Antonio Pansera

In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy&rsquo;s law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied.

]]>Symmetry doi: 10.3390/sym15061208

Authors: Aeshah A. Raezah Rahat Zarin Zehba Raizah

This paper explored the impact of population symmetry on the spread and control of a norovirus epidemic. The study proposed a mathematical model for the norovirus epidemic that takes into account asymptomatic infected individuals and vaccination effects using a non-singular fractional operator of Atanganaa&ndash;Baleanu Caputo (ABC). Fixed point theory, specifically Schauder and Banach&rsquo;s fixed point theory, was used to investigate the existence and uniqueness of solutions for the proposed model. The study employed MATLAB software to generate simulation results and demonstrate the effectiveness of the fractional order q. A general numerical algorithm based on Adams&ndash;Bashforth and Newton&rsquo;s Polynomial method was developed to approximate the solution. Furthermore, the stability of the proposed model was analyzed using Ulam&ndash;Hyers stability techniques. The basic reproductive number was calculated with the help of next-generation matrix techniques. The sensitivity analysis of the model parameters was performed to test which parameter is the most sensitive for the epidemic. The values of the parameters were estimated with the help of least square curve fitting tools. The results of the study provide valuable insights into the behavior of the proposed model and demonstrate the potential applications of fractional calculus in solving complex problems related to disease transmission.

]]>Symmetry doi: 10.3390/sym15061207

Authors: Guoxin Wang Shengwei Yao Mingyang Pei Jieqiong Xu

In this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be chosen between a symmetric quadratic model and a conic model by specific criteria. Moreover, the idea of a WLY conjugate gradient method is applied to characterize the change of gradient direction between adjacent iteration points. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method.

]]>Symmetry doi: 10.3390/sym15061206

Authors: Yuriy Kozhubaev Elena Ovchinnikova Ivanov Viacheslav Svetlana Krotova

Soft robotics is a specialized field of robotics that focuses on the design, manufacture, and control of robots made of soft materials, as opposed to those made of rigid links. One of the primary challenges for the future use of continuous or hyper-redundant robotics systems in industrial and medical technology is the development of suitable modeling and control approaches. Due to the complex non-linear behavior of soft materials and the unpredictable motion of actuators, the task of modeling complex soft actuators is very time-consuming. As a result, earlier studies have undertaken research into model-free methods for controlling soft actuators. In recent years, machine learning (ML) methods have become widely popular in research. The adaptability of an ML model to a non-linear soft drive system alongside the varying actuation behavior of soft drives over time as a result of material characteristics and performance requirements is the key rationale for including an ML model. The system requires the online updating of the ML model in order to work with the non-linear system. Sequential data collected from the test bench and converted into a hypothesis are used to perform incremental learning. These methods are called lifelong learning and progressive learning. Real-time data flow training is combined with incremental learning (IL), and a neural network model is tuned sequentially for each data input. In this article, a method for the intelligent control of soft pneumatic actuators based on an incremental learning algorithm is proposed. A soft pneumatic actuator was subjected to three distinct test conditions in a controlled test environment for a specified duration of data gathering. Additionally, data were collected through finite element method simulations. The collected data were used to incrementally train a neural network, and the resulting model was analyzed for errors with both training and test data. The training and testing errors were compared for different incremental learning (IL) algorithms, including K-nearest neighbors, a decision tree, linear regression, and a neural network. The feasibility of the modulo-free intelligent control of soft pneumatic actuators based on an incremental learning algorithm was verified, solving the problem of the control of software actuators.

]]>Symmetry doi: 10.3390/sym15061205

Authors: Haitao Liu Haifeng Wang

Network traffic anomaly detection mainly detects and analyzes abnormal traffic by extracting the statistical features of network traffic. It is necessary to fully understand the concept of symmetry in anomaly detection and anomaly mitigation. However, the original information on network traffic is easily lost, and the adjustment of dynamic network configuration becomes gradually complicated. To solve this problem, we designed and realized a new online anomaly detection system based on software defined networks. The system uses the convolutional neural network to directly extract the original features of the network flow for analysis, which can realize online real- time packet extraction and detection. It utilizes SDN to flexibly adapt to changes in the network, allowing for a zero-configuration anomaly detection system. The packet filter of the anomaly detection system is used to automatically implement mitigation strategies to achieve online real-time mitigation of abnormal traffic. The experimental results show that the proposed method is more accurate and can warn the network manager in time that security measures can be taken, which fully demonstrates that the method can effectively detect abnormal traffic problems and improve the security performance of edge clustering networks.

]]>Symmetry doi: 10.3390/sym15061204

Authors: R. S. Varun Kumar Ioannis E. Sarris G. Sowmya Amal Abdulrahman

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized in the present investigation. The nonlinear variation of thermal conductivity and heat transfer coefficient governed by the power law is considered. The analytical approximation for the non-dimensional temperature profile is obtained using the differential transform method (DTM)-Pade approximant. The nondimensionalization of the governing energy equation using dimensionless terms yields a nonlinear ordinary differential equation (ODE) with corresponding boundary conditions. The resulting ODE is analytically solved with the assistance of the DTM-Pade approximant procedure. Furthermore, the impact of thermal parameters on the temperature field and thermal stress is elaborated with graphs. The important results of the report divulge that temperature distribution greatly enhances with an augmentation of the heat generation parameter, but it gradually reduces with an increment in the magnitude of the thermogeometric and radiative-conductive parameter.

]]>Symmetry doi: 10.3390/sym15061203

Authors: Eltiyeb Ali Salem Mahdi

The most important advantage of conjugate gradient methods (CGs) is that these methods have low memory requirements and convergence speed. This paper contains two main parts that deal with two application problems, as follows. In the first part, three new parameters of the CG methods are designed and then combined by employing a convex combination. The search direction is a four-term hybrid form for modified classical CG methods with some newly proposed parameters. The result of this hybridization is the acquisition of a newly developed hybrid CGCG method containing four terms. The proposed CGCG has sufficient descent properties. The convergence analysis of the proposed method is considered under some reasonable conditions. A numerical investigation is carried out for an unconstrained optimization problem. The comparison between the newly suggested algorithm (CGCG) and five other classical CG algorithms shows that the new method is competitive with and in all statuses superior to the five methods in terms of efficiency reliability and effectiveness in solving large-scale, unconstrained optimization problems. The second main part of this paper discusses the image restoration problem. By using the adaptive median filter method, the noise in an image is detected, and then the corrupted pixels of the image are restored by using a new family of modified hybrid CG methods. This new family has four terms: the first is the negative gradient; the second one consists of either the HS-CG method or the HZ-CG method; and the third and fourth terms are taken from our proposed CGCG method. Additionally, a change in the size of the filter window plays a key role in improving the performance of this family of CG methods, according to the noise level. Four famous images (test problems) are used to examine the performance of the new family of modified hybrid CG methods. The outstanding clearness of the restored images indicates that the new family of modified hybrid CG methods has reliable efficiency and effectiveness in dealing with image restoration problems.

]]>Symmetry doi: 10.3390/sym15061202

Authors: Suha Wazzan Hanan Ahmed

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure&ndash;property relationships (QSPRs), and topological indices are a valuable source of information about molecular properties, such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. A molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs and windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results show that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

]]>Symmetry doi: 10.3390/sym15061201

Authors: Lidya Amon Susam Ayberk Yilmaz Ghada ALMisned Hatice Yilmaz Alan Gizem Ozturk Gokhan Kilic Bahar Tuysuz Selin Ece Topuzlar Baki Akkus Antoaneta Ene Huseyin Ozan Tekin

We present the behavioral changes and symmetrical enhancement on KERMA, mass stopping power and projected range parameters against heavy-charged particles through Indium (In) and Tantalum (Ta) incorporations for various zinc-tellurite glass groups such as TZI and ZTT for nuclear applications. SRIM and PAGEX codes are utilized for the determination of investigated attenuation parameters for alpha and proton particles. In KERMA calculations, the ZTT7 sample is reported to have the greatest release of charged particles because of an increase in kinetic energy. The mass stopping power values of all absorbent glass materials are steadily increased from 0 MeV to 0.1 MeV. TZI and ZTT attained their maximum mass stopping power at a kinetic energy value of 0.1 MeV. While comparable behavior patterns are seen for various energy values on the examined energy scale, the ZTT7 sample is observed with lower mass stopping power and projected range values against proton particles than the other samples. It can be concluded that zinc-telluride glasses through maximum Ta-reinforcement may be considered as promising materials for stopping the proton and alpha particles. Moreover, Ta-reinforcement may be considered as a monotonic tool in terms of providing a symmetry for attenuation enhancement against heavy-charged particles.

]]>Symmetry doi: 10.3390/sym15061200

Authors: Victor Orlov Alexander Chichurin

In this paper, we substantiate the analytical approximate method for Cauchy problem of the Van der Pol equation in the complex domain. These approximate solutions allow analytical continuation for both real and complex cases. We follow the influence of variation in the initial data of the problem in order to control the computational process and improve the accuracy of the final results. Several simple applications of the method are given. A numerical study confirms the consistency of the developed method.

]]>Symmetry doi: 10.3390/sym15061199

Authors: Sergey V. Bolokhov Vladimir D. Ivashchuk

This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and n scalar fields coupled to n Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank n. The set of n moduli functions Hs(z) comply with n non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in z (so-called &ldquo;fluxbrane&rdquo; polynomials) depending upon certain parameters ps&gt;0, s=1,&hellip;,n. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks n=1,2,3,4,5 and exceptional algebra E6. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored.

]]>Symmetry doi: 10.3390/sym15061198

Authors: John H. Graham Rachel Christopher

The simple leaves of deciduous forest trees in temperate zones have more irregular and asymmetric shapes than comparable non-deciduous leaves of trees in the tropics and subtropics. These shapes manifest as the irregular lobes and sinuses of temperate species of Quercus and Acer, as well as the greater bilateral asymmetry of Ulmaceae and Betulaceae, the serrated margins of many species, and the greater frequency of compound leaves generally (Fraxinus and Carya). These modifications may contribute to an early transition from laminar to turbulent flow, thus reducing the lateral movement of leaves when they drop during the onset of either winter or the dry season, or when they are simply shed for replacement. Such leaves are more likely to drop over the critical root zone than large, thin, broadly elliptic, and symmetric leaves. Here, we evaluate evidence for and against self-mulching as an explanation for differences in leaf shape between temperate and tropical forests. We suggest that the main evolutionary trade-offs are between competition for (1) light among tropical trees and temperate subcanopy trees, and (2) competition for water and soil nutrients among temperate canopy trees.

]]>Symmetry doi: 10.3390/sym15061196

Authors: Yongze Kang Qingyuan Yu Lingyue Qin Guoyan Zhang

Differential fault analysis (DFA) was introduced by Biham and Shamir. It is a powerful analysis technique to retrieve the secret key by injecting fault into an internal state and utilizing the differences between the correct ciphertexts and the faulty ciphertexts. Based on the idea of meet-in-the-middle, some differential characters can help to recover the key of some symmetric ciphers. At CHES 2011, this technique was utilized to give analyses on AES. In this article, we propose several DFA schemes on ITUbee, a software-oriented block symmetric cipher for resource-constrained devices based on the meet-in-the-middle idea. Our attacks are efficient enough and more powerful than previous works. Furthermore, the attacks in this article break the protection countermeasure, meaning we have to review the protection method on devices for ITUbee.

]]>Symmetry doi: 10.3390/sym15061197

Authors: Peter O. Hess

A review of several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage of symmetries. This enables us to describe very involved systems in a greatly simplified manner. Some problems are also discussed, when ignoring basic principles of nature, such as the Pauli exclusion principle. We also show that occasionally one can rescue these omissions. In a couple of representative models, applications of symmetries are explicitly applied in order to illustrate how extremely complicated systems can be treated. This contribution is meant as a review of the use of algebraic models in nuclear physics, leading to a better understanding of the articles in the same special volume.

]]>Symmetry doi: 10.3390/sym15061194

Authors: Ramachandran Alagarsamy Dhamodaran Muneeswaran

Multiple-Object Tracking (MOT) has become more popular because of its commercial and academic potential. Though various techniques were devised for managing this issue, it becomes a challenge because of factors such as severe object occlusions and abrupt appearance changes. Tracking presents the optimal outcomes whenever the object moves uniformly without occlusion and in the same direction. However, this is generally not a real scenario, particularly in complicated scenes such as dance events or sporting where a greater number of players are tracked, moving quickly, varying their speed and direction, along with distance and position from the camera and activity they are executing. In dynamic scenes, MOT remains the main difficulty due to the symmetrical shape, structure, and size of the objects. Therefore, this study develops a new reptile search optimization algorithm with deep learning-based multiple object detection and tracking (RSOADL&ndash;MODT) techniques. The presented RSOADL&ndash;MODT model intends to recognize and track the objects that exist with position estimation, tracking, and action recognition. It follows a series of processes, namely object detection, object classification, and object tracking. At the initial stage, the presented RSOADL&ndash;MODT technique applies a path-augmented RetinaNet-based (PA&ndash;RetinaNet) object detection module, which improves the feature extraction process. To improvise the network potentiality of the PA&ndash;RetinaNet method, the RSOA is utilized as a hyperparameter optimizer. Finally, the quasi-recurrent neural network (QRNN) classifier is exploited for classification procedures. A wide-ranging experimental validation process takes place on DanceTrack and MOT17 datasets for examining the effectual object detection outcomes of the RSOADL&ndash;MODT algorithm. The simulation values confirmed the enhancements of the RSOADL&ndash;MODT method over other DL approaches.

]]>Symmetry doi: 10.3390/sym15061195

Authors: Sergio Elaskar Ezequiel del Río

Chaotic intermittency is characterized by a signal that alternates aleatory between long regular (pseudo-laminar) phases and irregular bursts (pseudo-turbulent or chaotic phases). This phenomenon has been found in physics, chemistry, engineering, medicine, neuroscience, economy, etc. As a control parameter increases, the number of chaotic phases also increases. Therefore, intermittency presents a continuous route from regular behavior to chaotic motion. In this paper, a review of different types of intermittency is carried out. In addition, the description of two recent formulations to evaluate the reinjection processes is developed. The new theoretical formulations have allowed us to explain several tests previously called pathological. The theoretical background also includes the noise effects in the reinjection mechanism.

]]>Symmetry doi: 10.3390/sym15061193

Authors: Mahmoud M. Abdelwahab Anis Ben Ghorbal Amal S. Hassan Mohammed Elgarhy Ehab M. Almetwally Atef F. Hashem

This manuscript focuses on the statistical inference of the Kavya&ndash;Manoharan generalized exponential distribution under the generalized type-I progressive hybrid censoring sample (GTI-PHCS). Different classical approaches of estimation, such as maximum likelihood, the maximum product of spacing, least squares (LS), weighted LS, and percentiles under GTI-PHCS, are investigated. Based on the squared error and linear exponential loss functions, the Bayes estimates for the unknown parameters utilizing separate gamma priors under GTI-PHCS have been derived. Point and interval estimates of unknown parameters are developed. We carry out a simulation using the Monte Carlo algorithm to show the performance of the inferential procedures. Finally, real-world data collection is examined for illustration purposes.

]]>Symmetry doi: 10.3390/sym15061192

Authors: Sercan Kazımoğlu Erhan Deniz Luminiţa-Ioana Cotîrlă

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator Dq0&lt;q&lt;1 and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc &Lambda;=&weierp;:&weierp;&isin;Cand&weierp;&lt;1. For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete&ndash;Szeg&ouml; inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper.

]]>Symmetry doi: 10.3390/sym15061191

Authors: Serkan Çelik Hacı Bayram Karadağ Hatice Kuşak Samancı

A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or M&ouml;bius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.

]]>Symmetry doi: 10.3390/sym15061190

Authors: Darius McAdam Lior Shamir

Despite over a century of research, the physics of galaxy rotation is not yet fully understood, and there is a clear discrepancy between the observed mass of galaxies and their rotational velocity. Here, we report on another observation of tension between the physical properties of galaxies and their rotational velocity. We compare the apparent magnitude of galaxies and find a statistically significant asymmetry between galaxies that rotate in the same direction relative to the Milky Way and galaxies that rotate in the opposite direction relative to the Milky Way. While asymmetry in the brightness is expected due to the Doppler shift effect, such asymmetry is expected to be subtle. The observations shown here suggest that the magnitude difference is sufficiently large to be detected by Earth-based telescopes. The asymmetry is consistent in both the northern and southern galactic poles. The difference is also consistent across several different instruments such as DECam, SDSS, Pan-STARRS, and HST as well as different annotation methods, which include automatic, manual, or crowdsourcing annotations through &ldquo;Galaxy Zoo&rdquo;. The observation can also explain other anomalies such as the Ho tension. Analysis of Ia supernovae where the host galaxies rotate in the same direction relative to the Milky Way shows a much smaller tension with the Ho value as estimated by the CMB.

]]>Symmetry doi: 10.3390/sym15061189

Authors: Aftab Hussain

In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions.

]]>Symmetry doi: 10.3390/sym15061188

Authors: Amir Baklouti

In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the probabilistic dominance relationship between alternatives, which can lead to inconsistent and inaccurate rankings. In this paper, we propose a new ranking method for IFNs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method is able to handle incomplete and uncertain information and can generate consistent and accurate rankings.

]]>Symmetry doi: 10.3390/sym15061187

Authors: Ning Zhao Haixing Zhao Yinkui Li

Vulnerability refers to the ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. In this paper, the rupture degree of graphs is employed to measure the vulnerability of uniform linear hypergraphs. First, we discuss the bounds of the rupture degrees of k-uniform linear hypergraphs. Then, we give a recursive algorithm for computing the rupture degree of k-uniform hypertrees.

]]>Symmetry doi: 10.3390/sym15061186

Authors: Semih Bal Zoltán Ádám Tamus

The increasing penetration of distributed generation sources in low-voltage distribution grids, electric vehicles, and new appliances from the consumer side can generate short repetitive overloads on the low-voltage cable network. This work investigates the change in the dielectric properties of low-voltage cable insulation caused by short-term overloads, examining how the cable structure affects the dielectric characteristics of the cable specimens in the case of cyclic short-term thermal aging. PVC-insulated low-voltage cable samples were exposed to an accelerated aging test in a temperature-controlled oven after changing their structures by removing different layers. Three aging cycles, each of six hours, were applied to the samples. After each cycle, the tan &delta; and capacitance were measured by an Omicron DIRANA Dielectric Response Analyzer in the laboratory at room temperature 24 &plusmn;&nbsp;0.5 &deg;C. Furthermore, the polarization and depolarization currents were also studied. The results show that changing the cable structure impacts the dielectric parameters; in particular, the effect of the belting layer is significant. From the point of view of aging, the PVC belting layer protects the diffusion of the plasticizers of the inner structure. The findings of the study show that an asymmetric aging phenomenon can be observed in different polymeric components of the cables, even though the cables were aged in an air-circulated oven ensuring a homogeneous temperature distribution in the samples.

]]>Symmetry doi: 10.3390/sym15061185

Authors: Suha B. Al-Shaikh

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing the ideas of subordination and the S&#259;l&#259;gean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of q-starlike and q-convex functions in the open unit disc U. For this novel family, bounds of the first two Taylor-Maclaurin coefficients, the Fekete-Szeg&ouml;-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of q-starlike and q-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions.

]]>Symmetry doi: 10.3390/sym15061184

Authors: S. V. Mousavi S. Miret-Artés

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner&ndash;Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities, including probability density plots, scaled trajectories, and arrival times, was analyzed.

]]>Symmetry doi: 10.3390/sym15061183

Authors: Manal M. Yousef Aisha Fayomi Ehab M. Almetwally

Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of &delta;=P(Y&lt;X) were proposed when the strength variable was subjected to the step&ndash;stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of &delta;. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out.

]]>Symmetry doi: 10.3390/sym15061182

Authors: Songyuan Tian Sheng Zhang Hongmei Mao Rui Liu Xiaowu Xiong

Link prediction accuracy in temporal networks is easily affected by the time granularity of network snapshots. This is due to the insufficient information conveyed by snapshots and the lack of temporal continuity between snapshots. We propose a temporal network link prediction method based on the optimized exponential smoothing model and node interaction entropy (OESMNIE). This method utilizes fine-grained interaction information between nodes within snapshot periods and incorporates the information entropy theory to improve the construction of node similarity in the gravity model as well as the prediction process of node similarity. Experiment results on several real-world datasets demonstrate the superiority and reliability of this proposed method in adapting to link prediction requirements over other methods across different time granularities of snapshots, which is essential for studying the evolution of temporal networks.

]]>Symmetry doi: 10.3390/sym15061181

Authors: Meixia Wang Susu Wang Xiaoqin Ju Yanhong Wang

Salt-and-pepper noise (SPN) is a common type of image noise that appears as randomly distributed white and black pixels in an image. It is also known as impulse noise or random noise. This paper aims to introduce a new weighted average based on the Atangana&ndash;Baleanu fractional integral operator, which is a well-known idea in fractional calculus. Our proposed method also incorporates the concept of symmetry in the window mask structures, resulting in efficient and easily implementable filters for real-time applications. The distinguishing point of these techniques compared to similar methods is that we employ a novel idea for calculating the mean of regular pixels rather than the existing used mean formula along with the median. An iterative procedure has also been provided to integrate the power of removing high-density noise. Moreover, we will explore the different approaches to image denoising and their effectiveness in removing noise from images. The symmetrical structure of this tool will help in the ease and efficiency of these techniques. The outputs are compared in terms of peak signal-to-noise ratio, the mean-square error and structural similarity values. It was found that our proposed methodologies outperform some well-known compared methods. Moreover, they boast several advantages over alternative denoising techniques, including computational efficiency, the ability to eliminate noise while preserving image features, and real-time applicability.

]]>Symmetry doi: 10.3390/sym15061180

Authors: Sergei V. Ryzhkov

Symmetrically designed fusion and heat concepts, space propulsion, and energy conversion issues with a particular interest in kinetic analysis, plasma power balance, advanced fuels, and alternative systems as new trends in experiments and theory, in physics, power engineering, and in very specific related areas such as space processes, cosmology, and turbulence are very important in fundamental and applied science from an engineering physics perspective [...]

]]>Symmetry doi: 10.3390/sym15061179

Authors: Ghobad Behzadi Pour Hassan Ashourifar Leila Fekri Aval Shahram Solaymani

Carbon nanotubes (CNTs), due to mechanical, electrical, and surface area properties and their ability to adapt to different nanocomposite structures, are very substantial in supercapacitor electrodes. In this review, we have summarized high-performance, flexible, and symmetry CNT supercapacitors based on the CNTs/graphene, CNTs/metal, and CNTs/polymer electrodes. To present recent developments in CNT supercapacitors, we discuss the performance of supercapacitors based on electrical properties such as specific capacitance (SC), power and energy densities, and capacitance retention (CR). The comparison of supercapacitor nanocomposite electrodes and their results are reported for future researchers.

]]>Symmetry doi: 10.3390/sym15061178

Authors: Congcong Xu Jing Feng Xiaomin Hu Xiaobin Xu Yi Li Pingzhi Hou

Many real-world scenarios can be naturally modeled as heterogeneous graphs, which contain both symmetry and asymmetry information. How to learn useful knowledge from the graph has become one of the hot spots of research in artificial intelligence. Based on Metapath2vec algorithm, an improved Metapath2vec algorithm is presented, which combines Metapath random walk, used to capture semantics and structure information between different nodes of a heterogeneous network, and GloVe model to consider the advantage of global text representation. In order to verify the feasibility and effectiveness of the model, node clustering and link prediction experiments were conducted on the self-generated ideal dataset and the MOOC course data. The analysis of experimental data on these tasks shows that the Metapath&ndash;GloVe algorithm learns consistently better embedding of heterogeneous nodes, and the algorithm improves the node embedding performance to better characterize the heterogeneous network structure and learn the characteristics of nodes, which proves the effectiveness and scalability of the proposed method in heterogeneous network mining tasks. It is also shown through extensive experiments that the Metapath&ndash;GloVe algorithm is more efficient than the non-negative matrix decomposition algorithm (NMF), and it can obtain better clustering results and more accurate prediction results in the video recommendation task.

]]>Symmetry doi: 10.3390/sym15061177

Authors: Diego Roldán Francisco Roldán-Aráuz

While superluminal phenomena are not empirically substantiated, they present an intriguing hypothetical case. For this speculative framework, the Lorentz transformations would necessitate a revision: instead of the standard&nbsp;&gamma;(x&minus;vt), the absolute value of&nbsp;x&prime;&nbsp;ought to be expressed as&nbsp;&gamma;(vt&minus;x), because if v were to exceed c, then the interval&nbsp;vt&nbsp;traversed by the superluminal frame&nbsp;S&prime;&nbsp;would surpass the distance covered by light. Under the postulates of relativity, the subluminal scenario leads to the conventional Lorentz factor. Meanwhile, the superluminal scenario introduces an alternative transformation factor that accounts for the presence of the speed of light (c) barrier. This factor is also invariant within Minkowski spacetime, meaning it symmetrically preserves spacetime intervals. The details of this derivation become more evident when using a reverse coordinate system. This result is not, per se, evidence for the existence of superluminal phenomena, but it does allow us to speculate with a new argument about the possibility of their existence.

]]>Symmetry doi: 10.3390/sym15061176

Authors: Dong Guo Huo Tang Jun Zhang Zongtao Li Qingbing Xu En Ao

LetN be the class of functions that convex in one direction and M denote the class of functions zf&prime;(z), where f&isin;N. In the paper, the third-order Hankel determinants for these classes are estimated. The estimates of H3,1(f) obtained in the paper are improved.

]]>Symmetry doi: 10.3390/sym15061175

Authors: Yanlin Li Huchchappa A. Kumara Mallannara Siddalingappa Siddesha Devaraja Mallesha Naik

Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric u-connection (SSM-connection). First, we show that any quasi-Einstein Lorentzian manifold having a SSM-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with SSM-connection admitting RS whose soliton vector Z is parallel to the vector u. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting SSM-connection.

]]>Symmetry doi: 10.3390/sym15061174

Authors: Menghan Lv Peng Wang Yaoquan Wei Chunxue Wen Jianlin Li Pengyu Jia Qingxuan Wei

Direct current transformer (DCT) is a key piece of equipment in direct current (DC) microgrids, and the mainstream topologies mainly include LLC resonant converter (LLC) and dual active bridge (DAB). In this paper, a novel bi-directional buck/boost + CLLLC cascade topology is proposed for the input-series-output-parallel cascade converter system of a DC microgrid. To solve the problem that frequency variation causes the converter to deviate from the optimal operating point, resulting in low efficiency, and the inability to achieve a soft switching function. The CLLLC converter operates near the resonant frequency point as a DCT, only providing electrical isolation and voltage matching, while the buck/boost converter controls the output voltage and the voltage and current sharing of each module. Compared to other cascaded converter systems, the cascaded converter proposed in this paper has high efficiency, simplifies the parameter design, and is suitable for wide input and wide output operating conditions. The system adopts a three-loop control strategy, establishes the small-signal modeling of the system, and its stability is verified by theoretical analysis and simulation. The simulation and experimental results verify the correctness of the proposed cascaded converter based on buck/boost + CLLLC and the effectiveness of the control strategy.

]]>Symmetry doi: 10.3390/sym15061173

Authors: Song Zhou Tianhan Gao Jun Xu

There is an important application value in assessing an operator&rsquo;s mental pressure (MP) level in human&ndash;computer cooperative tasks through continuous asymmetric electroencephalogram (EEG) signals, which can help predict hidden risks. Due to the different distributions of EEG features in different periods, it is particularly challenging to accurately identify brain states by training and testing asymmetric EEG signals with static pattern classifiers. Due to the limitations of non-stationary neurophysiological data capture technology, cross-session MP recognition schemes can only be used as an auxiliary means in practical applications. Deep learning methods can achieve stable feature extraction at a high level. Based on this advantage, this paper proposes a triplet loss (TL)-based CNN model that can automatically update the weights of shallow hidden neurons in cross-session MP classification tasks. Firstly, the generalization ability of the CNN model under both intra-session and cross-session conditions is evaluated. Moreover, the proposed model is compared with the existing MP classifier under different feature selection and noise destruction modes. According to the results, our TL-based CNN model has high performance in processing cross-session EEG features.

]]>Symmetry doi: 10.3390/sym15061172

Authors: K. Michał Pietrusiewicz Anna E. Kozioł Hanna Małuszyńska Sylwia Sowa

1,4- and 1,2-additons of secondary phosphine oxides to (1R)-myrtenal and (1S)-myrtanal were evaluated as potential routes to P,C-stereogenic phosphine oxides bearing additional hydroxyl or aldehyde functions. 1,4-Additions of racemic secondary phosphine oxides to (1R)-myrtenal were found to offer moderate to good stereoselectivity which shows some promise for utility in kinetic resolution processes, especially at lower conversions. In case of 1,2-additions making the process doubly asymmetric by using an enantiomerically pure secondary phosphine oxide as substrate turned out to be practical. The stereochemical course of the addition reactions under study is presented. The P-resolved 1,2-addition products were demonstrated to undergo facile reduction by BH3 at room temperature leading to the formation of the corresponding &alpha;-hydroxyphosphine-boranes with clean inversion of configuration at the P-centre. All P,C-stereogenic phosphine oxides and boranes that were isolated in the form of a single diastereoisomer were assigned their absolute configurations by means of X-ray crystallography and/or 2D NMR spectral techniques.

]]>Symmetry doi: 10.3390/sym15061171

Authors: Hang Fan Fei Gao Wenhao Li Kun Zhang

Traditional Lamb wave inspection and imaging methods heavily rely on prior knowledge of dispersion curves and baseline recordings, which may not be feasible in the majority of real cases due to production uncertainties and environmental variations. In order to solve this problem, a two-step Lamb wave strategy utilizing adaptive multiple signal classification (MUSIC) and sparse reconstruction of dispersion reconstruction is proposed. The multimodal Lamb waves are initially reconstructed in the f-k domain using random measurements, allowing for the identification and characterization of multimodal Lamb waves. Then, using local polynomial expansion and derivation, the phase and group velocities for each Lamb wave mode could be computed. Thus, the steering vectors of all potential scattering Lamb waves for each grid in the scanning area can be established, thereby allowing for the formulation of the MUSIC algorithm. To increase the precision and adaptability of the MUSIC method, the local wave components resulting from potential scatters are extracted with an adaptive window, which is governed by the group velocities and distances of Lamb wave propagation. As a result, the reconstructed dispersion relations and windowed wave components can be used to highlight the scattering features. For the method investigation, both a simulation and experiment are carried out, and both the dispersion curves and damage locations can be detected. The results demonstrate that damage localization is possible without theoretical dispersion data and baseline recordings while exhibiting a considerable accuracy and resolution.

]]>Symmetry doi: 10.3390/sym15061170

Authors: Yuan Liu Yue Li Lin Li Mengli He

To address the need for massive connections in Internet-of-Vehicle communications, local wireless networks utilize non-orthogonal multiple access (NOMA). Scholars have introduced deep reinforcement learning networks for user grouping and power allocation to reduce computational complexity. However, the traditional algorithm based on DQN (Deep Q-Network) still exhibits slow convergence speed and low training stability, while the uniform sampling method in the sample playback process suffers from low sampling efficiency. In order to address these issues, this paper proposes a user grouping and power allocation method for NOMA systems based on Prioritized Dueling DQN-DDPG joint optimization. Firstly, the paper introduces the user grouping network based on Dueling DQN, which considers both the state value and action value in the entire connection layer. The two values compete with each other, are summed up, and re-evaluated. The network significantly improves training stability and increases the convergence speed. Secondly, in this paper, a depth deterministic strategy gradient (DDPG) algorithm with symmetric properties is used. This algorithm works well for continuous action spaces and avoids the power quantization error because of the continuity of power value in the power allocation stage. Finally, the priority sampling based on TD-error (Temporal-difference error) is combined with the Dueling DQN network and DDPG network to ensure random sampling and improve the replay probability of important samples. Simulation results show that the proposed priority-based Dueling DQN-DDPG algorithm significantly improves the convergence speed of sample training. The research results of this paper provide a solid foundation for the following research content, which focuses on NOMA system resource allocation under the mobile user state.

]]>Symmetry doi: 10.3390/sym15061169

Authors: Ammara Nosheen Sana Ijaz Khuram Ali Khan Khalid Mahmood Awan Marwan Ali Albahar Mohammed Thanoon

The q-symmetric analogues of H&ouml;lder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite&ndash;Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

]]>Symmetry doi: 10.3390/sym15061168

Authors: Ali Omar M. Alsharif Assaad Jmal Omar Naifar Abdellatif Ben Makhlouf Mohamed Rhaima Lassaad Mchiri

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors&rsquo; knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system&rsquo;s generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions.

]]>Symmetry doi: 10.3390/sym15061167

Authors: Giovanni Cantatore Serkant A. Çetin Horst Fischer Wolfgang Funk Marin Karuza Abaz Kryemadhi Marios Maroudas Kaan Özbozduman Yannis K. Semertzidis Konstantin Zioutas

We investigate the prospects for the direct detection of dark matter (DM) particles, incident on the upper atmosphere. A recent work relating the burst-like temperature excursions in the stratosphere at heights of &asymp;38&ndash;47 km with low speed incident invisible streaming matter is the motivation behind this proposal. As an example, dark photons could match the reasoning presented in that work provided they constitute part of the local DM density. Dark photons emerge as a U(1) symmetry within extensions of the standard model. Dark photons mix with real photons with the same total energy without the need for an external field, as would be required, for instance, for axions. Furthermore, the ionospheric plasma column above the stratosphere can resonantly enhance the dark photon-to-photon conversion. Noticeably, the stratosphere is easily accessible with balloon flights. Balloon missions with up to a few tons of payload can be readily assembled to operate for months at such atmospheric heights. This proposal is not limited to streaming dark photons, as other DM constituents could be involved in the observed seasonal heating of the upper stratosphere. Therefore, we advocate a combination of different types of measurements within a multi-purpose parallel detector system, in order to increase the direct detection potential for invisible streaming constituents that affect, annually and around January, the upper stratosphere.

]]>Symmetry doi: 10.3390/sym15061166

Authors: Busyra Latif Md Yushalify Misro Samsul Ariffin Abdul Karim Ishak Hashim

This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new approximations for second-order derivatives. The flexibility and high order precision of B-spline functions allow them to approximate the answers. These functions have a symmetrical property. The new second-order approximation plays an important role in producing more accurate results up to a fifth-order accuracy. To verify the proposed method&rsquo;s accuracy, it is tested on three linear systems of ordinary differential equations with multiple step sizes. The numerical findings by the present method are quite similar to the exact solutions available in the literature. We discovered that when the step size decreased, the computational errors decreased, resulting in better precision. In addition, details of maximum errors are investigated. Moreover, simple implementation and straightforward computations are the main advantages of the offered method. This method yields improved results, even if it does not require using free parameters. Thus, it can be concluded that the offered scheme is reliable and efficient.

]]>Symmetry doi: 10.3390/sym15061165

Authors: Munirah Aldiaiji Belgees Qaraad Loredana Florentina Iambor Elmetwally M. Elabbasy

In this paper, we aimed to study some asymptotic properties of a class of third-order neutral differential equations with advanced argument in canonical form. We provide new and simplified oscillation criteria that improve and complement a number of existing results. We also show some examples to illustrate the importance of our results.

]]>Symmetry doi: 10.3390/sym15061164

Authors: Kazuhiko Sawada Shigeyoshi Saito

Cerebral sulcal infolding exhibits unique species-related lateralization patterns. The present investigation aimed to characterize the asymmetric patterns of sulcal infolding in cynomolgus monkeys and their sexual dimorphism. Three-dimensional magnetic resonance (MR) images were acquired at 7-Tesla from the fixed brains of adult male (n = 5) and female (n = 5) monkeys. The gyrification index (GI) was estimated on MR images throughout the cerebral cortex (global-GI) or in the representative primary sulci (sulcal-GI). The global-GI did not differ between the sexes when the ipsilateral sides were compared. Although there was no sex difference in the sulcal-GI of the ipsilateral sides of any primary sulci, a significant right bias of the sulcal-GI was noted in the inferior rams of the arcuate sulcus and circular sulcus in males but not in females. Secondary sulcal emergence was examined to assess sulcal infolding asymmetry at the individual and population levels. Nonbiased asymmetric emergence was noted in the posterior supraprincipal dimple in both sexes and the rostral sulcus in females. Notably, the emergence of the superior postcentral dimple was significantly right-lateralized in females. The findings revealed right-biased sulcal infolding in male and female cynomolgus monkeys, although the lateralized cortical regions differed between the sexes.

]]>Symmetry doi: 10.3390/sym15061163

Authors: Siraj Khan Muhammad Asim Samia Allaoua Chelloug Basma Abdelrahiem Salabat Khan Ahmad Musyafa

Unsupervised domain adaptation (UDA) is a popular approach to reducing distributional discrepancies between labeled source and the unlabeled target domain (TD) in machine learning. However, current UDA approaches often align feature distributions between two domains explicitly without considering the target distribution and intra-domain category information, potentially leading to reduced classifier efficiency when the distribution between training and test sets differs. To address this limitation, we propose a novel approach called Cluster Matching-based Improved Kernel Fisher criterion (CM-IKFC) for object classification in image analysis using machine learning techniques. CM-IKFC generates accurate pseudo-labels for each target sample by considering both domain distributions. Our approach employs K-means clustering to cluster samples in the latent subspace in both domains and then conducts cluster matching in the TD. During the model component training stage, the Improved Kernel Fisher Criterion (IKFC) is presented to extend cluster matching and preserve the semantic structure and class transitions. To further enhance the performance of the Kernel Fisher criterion, we use a normalized parameter, due to the difficulty in solving the characteristic equation that draws inspiration from symmetry theory. The proposed CM-IKFC method minimizes intra-class variability while boosting inter-class variants in all domains. We evaluated our approach on benchmark datasets for UDA tasks and our experimental findings show that CM-IKFC is superior to current state-of-the-art methods.

]]>Symmetry doi: 10.3390/sym15061162

Authors: Naeem Saleem Bilal Iqbal Fady Hasan Wasfi Shatanawi

The purpose of this paper is to define the notion of extended convex &#8497; contraction by imposing less conditions on the function &#8497; satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

]]>Symmetry doi: 10.3390/sym15061161

Authors: Jean Nestor M. Dahj Kingsley A. Ogudo

Machine learning (ML) in wireless mobile communication is becoming more and more customary, with application trends leaning toward performance improvement and network automation. The radio access network (RAN), critical for service access, frequently generates performance data that mobile network operators (MNOs) and researchers leverage for planning, self-optimization, and intelligent network operations. However, missing values in the RAN performance data, as in any valuable data, impact analysis. Poor handling of such missing data in the RAN can distort the relationships between different metrics, leading to inaccurate and unreliable conclusions and predictions. Therefore, there is a need for imputation methods that preserve the overall structure of the RAN data to an optimal level. In this study, we present an imputation approach for handling RAN performance missing data based on machine learning algorithms. The method customizes the feature-extraction mechanism by using dynamic correlation analysis. We apply the method to actual RAN performance indicator data to evaluate its performance. We finally compare and evaluate the proposed approach with statistical imputation techniques such as the mean, median, and mode. The results show that machine learning-based imputation, as approached in this experimental study, preserves some relationships between KPIs compared to non-ML techniques. Random Forest regressor gave the best performance in imputing the data.

]]>Symmetry doi: 10.3390/sym15061160

Authors: Suha Wazzan Nurten Urlu Urlu Ozalan

Quantitative structure-property relationship (QSPR) modeling is crucial in cheminformatics and computational drug discovery for predicting the activity of compounds. Topological indices are a popular molecular descriptor in QSPR modeling due to their ability to concisely capture the structural and electronic properties of molecules. Here, we investigate the use of curvilinear regression models to analyze fibrates drug activity through topological indices, which modulate lipid metabolism and improve the lipid profile. Our QSPR approach predicts the physicochemical properties of fibrates based on degrees and distances from topological indices. Our results demonstrate that topological indices can enhance the accuracy of predicting physicochemical properties and biological activities of molecules, including drugs. We also conducted density functional theory (DFT) calculations on the investigated derivatives to gain insights into their optimized geometries and electronic properties, including symmetry. The use of topological indices in QSPR modeling, which considers the symmetry of molecules, shows significant potential in improving our understanding of the structural and electronic properties of compounds.

]]>Symmetry doi: 10.3390/sym15061158

Authors: Xingli Zhou Guoliang Li Hongbin Zhang Xin Cao

The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise.

]]>Symmetry doi: 10.3390/sym15061157

Authors: Hareem Abbasi Muhammad Hanif Usman Shahzad Walid Emam Yusra Tashkandy Soofia Iftikhar Shabnam Shahzadi

Outliers are observations that are significantly different from the other observations in a dataset. These types of observations are asymmetric in nature due to a lack of symmetry. The estimation of the cumulative distribution function (CDF) is an important statistical measure commonly discussed for symmetric datasets. However, the estimation of the CDF in the case of the asymmetric nature of the dataset is not a much-explored topic. In this article, we use calibration methodology with auxiliary information for modifying the traditional stratification weight, and hence, we obtain efficient estimates of the CDF using robust measures, i.e., mid-range and tri-mean, under the different distance functions. A simulation study is carried out to see the performance of proposed and existing estimators using asymmetric real-life datasets.

]]>Symmetry doi: 10.3390/sym15061159

Authors: Svetlin G. Georgiev A. Boukarou Keltoum Bouhali Khaled Zennir Hatim M. Elkhair Eltegani I. Hassan Alnadhief H. A. Alfedeel Almonther Alarfaj

In this article, we investigate the generalized Kawahara&ndash;KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are based upon recent theoretical results.

]]>Symmetry doi: 10.3390/sym15061156

Authors: Ibrahim Al-Dayel

In this paper, we estimate Ricci curvature inequalities for a hemi-slant warped product submanifold immersed isometrically in a generalized complex space form with a nearly Kaehler structure, and the equality cases are also discussed. Moreover, we also gave the equivalent version of these inequalities. In a later study, we will exhibit the application of differential equations to the acquired results. In fact, we prove that the base manifold is isometric to Euclidean space under a specific condition.

]]>Symmetry doi: 10.3390/sym15061155

Authors: Wenhao Wu Aipeng Jiang Kai Mao Haodong Wang Yamei Lin

To improve the speed and dynamic adaptability of robotic arm trajectory planning, a collision-free optimal trajectory planning method combining non-uniform adaptive time meshing and bounding box collision detection was proposed. First, the dynamics and objective function of the asymmetric industrial robotic arm with three degrees of freedom (DOF) was formulated in the form of the dynamic optimization problem. Second, the control vector parameterization (CVP) was improved to enhance the computational performance of the problem. The discrete grid was adaptively adjusted according the trend of control variables. Then, a quick and effective collision detection strategy was used to avoid obstacles and to speed up calculation efficiency. The non-collision constraint is built by transforming the collision detection into the distance between two points, and then is combined into the dynamic optimization problem. The solution of the new optimization problem with the improved CVP leads to the higher calculation performance and the avoidance of obstacles. Lastly, the Siemens Manutec R3 robotic arm is taken as an example to verify the effectiveness of the planning method. The approach not only reduces computation time but also maintains accurate calculations, so that optimal trajectory can be selected from symmetric paths near the obstacles. When weights were set as &lambda;1 = &lambda;2 = 0.5, the solution efficiency was improved by 33%, and the minimum distance between the robotic arm and obstacle could be 0.08 m, which ensured that there was no collision.

]]>Symmetry doi: 10.3390/sym15061154

Authors: Imre Pázsit

As is known in stochastic particle theory, the same random process can be described by two different master equations for the evolution of the probability density, namely, by a forward or a backward master equation. These are the generalised analogues of the direct and adjoint equations of traditional transport theory. At the level of the first moment, these two equations show considerable resemblance to each other, but they become increasingly different with increasing moment order. The purpose of this paper is to demonstrate this increasing asymmetry and to discuss the underlying reasons. It is argued that since the reason of the different forms of the forward and the backward equations lies in the lack of invariance of the process to time reversal, the reason for the increasing asymmetry between the two forms for higher-order moments or processes with several variables (particle types) can be related to the increasing level of the violation of the invariance to time reversal, as is illustrated with some examples.

]]>Symmetry doi: 10.3390/sym15061153

Authors: Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed

We study the (3+1)-dimensional stochastic Jimbo&ndash;Miwa (SJM) equation induced by multiplicative white noise in the It&ocirc; sense. We employ the Riccati equation mapping and He&rsquo;s semi-inverse techniques to provide trigonometric, hyperbolic, and rational function solutions of SJME. Due to the applications of the Jimbo&ndash;Miwa equation in ocean studies and other disciplines, the acquired solutions may explain numerous fascinating physical phenomena. Using a variety of 2D and 3D diagrams, we illustrate how white noise influences the analytical solutions of SJM equation. We deduce that the noise destroys the symmetry of the solutions of SJM equation and stabilizes them at zero.

]]>Symmetry doi: 10.3390/sym15061152

Authors: Ahmed M. Alhassan Eithar Issam Syed Alwee Aljunid Mohd Rashidi Che Beson Syed Mohammad Ammar Norshamsuri Ali Rosdisham Endut

In this paper, we investigate the performance of spectral amplitude coding optical code division multiple access (SAC OCDMA) systems under the effect of beat noise and turbulence. Three different multi-laser source configurations are considered in this analysis: shared multi-laser, separate multi-laser, and carefully controlled center frequency separate multi-laser. We demonstrate through Monte Carlo simulation that the gamma&ndash;gamma probability density function (pdf) cannot adequately approximate the measured intensity of overlapping lasers and that an empirical pdf is required. Results also show it is possible to achieve error-free transmission at a symmetrical data rate of 10 Gbps for all active users when only beat noise is taken into account by precisely controlling the center frequencies. However, only 30% of the active users can be supported when both beat noise and turbulence are considered.

]]>Symmetry doi: 10.3390/sym15061151

Authors: Mohamed Elbadri Mohamed A. Abdoon Mohammed Berir Dalal Khalid Almutairi

In this article, we have investigated solutions to a symmetry chaotic system with fractional derivative order using two different methods&mdash;the numerical scheme for the ABC fractional derivative, and the Laplace decomposition method, with help from the MATLAB and Mathematica platforms. We have explored progressive and efficient solutions to the chaotic model through the successful implementation of two mathematical methods. For the phase portrait of the model, the profiles of chaos are plotted by assigning values to the attached parameters. Hence, the offered techniques are relevant for advanced studies on other models. We believe that the unique techniques that have been proposed in this study will be applied in the future to build and simulate a wide range of fractional models, which can be used to address more challenging physics and engineering problems.

]]>Symmetry doi: 10.3390/sym15061150

Authors: Larry McLerran

This paper discusses high-baryon-density quarkyonic matter in the context of recent observations concerning neutron stars and the qualitative reasons why quarkyonic matter explains certain features of the equation of state that arises from these observations. The paper then provides a qualitative discussion of the quarkyonic hypotheses, and the essential features of quarkyonic matter that explain the outstanding features of the equation of state.

]]>Symmetry doi: 10.3390/sym15061149

Authors: Sanja Budečević Katarina Hočevar Sanja Manitašević Jovanović Ana Vuleta

To gain insight into the evolution of flower traits in the generalized food-deceptive plant Iris pumila, we assessed the color, size, shape, and fluctuating asymmetry (FA) of three functionally distinct floral organs&mdash;outer perianths (&lsquo;falls&rsquo;), inner perianths (&lsquo;standards&rsquo;), and style branches&mdash;and estimated pollinator-mediated selection on these traits. We evaluated the perianth color as the achromatic brightness of the fall, measured the flower stem height, and analyzed the floral organ size, shape, and FA using geometric morphometrics. Pollinated flowers had significantly higher brightness, longer flower stems, and larger floral organs compared to non-pollinated flowers. The shape and FA of the floral organs did not differ, except for the fall FA, where higher values were found for falls of pollinated flowers. Pollinator-mediated selection was confirmed for flower stem height and for subtle changes in the shape of the fall and style branch&mdash;organs that form the pollination tunnel. This study provides evidence that, although all analyzed flower traits play significant roles in pollinator attraction, flower stem height and pollination tunnel shape evolved under the pollinator-mediated selection, whereas achromatic brightness, size, and symmetry of floral organs did not directly affect pollination success.

]]>Symmetry doi: 10.3390/sym15061148

Authors: Khalid Abdulkhaliq M. Alharbi Zia Ullah Nawishta Jabeen Muhammad Ashraf

Numerical and physical simulations of the magnetohydrodynamic mixed convective flow of electrically conducting fluid along avertical magnetized and symmetrically heated plate with slip velocity and thermal slip effects have been performed. The novelty of the present work is to evaluate heat transfer and magnetic flux along the symmetrically magnetized plate with thermal and velocity slip effects. For a smooth algorithm and integration, the linked partial differential equations of the existing fluid flow system are converted into coupled nonlinear ordinary differential equations with specified streaming features and similarity components. By employing the Keller Box strategy, the modified ordinary differential equations (ODEs) are again translated in a suitable format for numerical results. The MATLAB software is used to compute the numerical results, which are then displayed in graphical and tabular form. The influence of several governing parameters on velocity, temperature distribution and magnetic fields in addition to the friction quantity, magnetic flux and heat transfer quantity has been explored. Computational evaluation is performed along the symmetrically heated plate to evaluate the velocity, magnetic field, and temperature together with their gradients. The selection of the magnetic force element, the buoyancy factor 0&lt;&xi;&lt;&infin; , and the Prandtl parameter range 0.1&le;Pr&le;7.0 were used to set the impacts of magnetic energy and diffusion, respectively. In the domains of magnetic resonance imaging (MRI), artificial heart wolves, interior heart cavities, and nanoburning systems, the present thermodynamic and magnetohydrodynamic issuesare significant.

]]>Symmetry doi: 10.3390/sym15061147

Authors: Syed Hussain Ali Kazmi Rosilah Hassan Faizan Qamar Kashif Nisar Ag Asri Ag Ibrahim

Challenges faced in network security have significantly steered the deployment timeline of Fifth Generation (5G) communication at a global level; therefore, research in Sixth Generation (6G) security analysis is profoundly necessitated. The prerogative of this paper is to present a survey on the emerging 6G cellular communication paradigm to highlight symmetry with legacy security concepts along with asymmetric innovative aspects such Artificial Intelligence (AI), Quantum Computing, Federated Learning, etc. We present a taxonomy of the threat model in 6G communication in five security legacy concepts, including Confidentiality, Integrity, Availability, Authentication and Access control (CIA3). We also suggest categorization of threat-countering techniques specific to 6G communication into three types: cryptographic methods, entity attributes and Intrusion Detection System (IDS). Thus, with this premise, we distributed the authentication techniques in eight types, including handover authentication, mutual authentication, physical layer authentication, deniable authentication, token-based authentication, certificate-based authentication, key agreement-based authentication and multi-factor authentication. We specifically suggested a series of future research directions at the conclusive edge of this survey.

]]>Symmetry doi: 10.3390/sym15061146

Authors: Yulan Lu Junbin Yuan Haoyang Tian Zhengwei Qin Siyuan Chen Hongji Zhou

We propose explicit K-symplectic and explicit symplectic-like methods for the charged particle system in a general strong magnetic field. The K-symplectic methods are also symmetric. The charged particle system can be expressed both in a canonical and a non-canonical Hamiltonian system. If the three components of the magnetic field can be integrated in closed forms, we construct explicit K-symplectic methods for the non-canonical charged particle system; otherwise, explicit symplectic-like methods can be constructed for the canonical charged particle system. The symplectic-like methods are constructed by extending the original phase space and obtaining the augmented separable Hamiltonian, and then by using the splitting method and the midpoint permutation. The numerical experiments have shown that compared with the higher order implicit Runge-Kutta method, the explicit K-symplectic and explicit symplectic-like methods have obvious advantages in long-term energy conservation and higher computational efficiency. It is also shown that the influence of the parameter &epsilon; in the general strong magnetic field on the Runge-Kutta method is bigger than the two kinds of symplectic methods.

]]>Symmetry doi: 10.3390/sym15061145

Authors: Nor Ain Azeany Mohd Nasir Tanveer Sajid Wasim Jamshed Gilder Cieza Altamirano Mohamed R. Eid Fayza Abdel Aziz ElSeabee

Exploration related to chemical processes in nanomaterial flows contains astonishing features. Nanoparticles have unique physical and chemical properties, so they are continuously used in almost every field of nanotechnology and nanoscience. The motive behind this article is to investigate the Cross nanofluid model along with its chemical processes via auto catalysts, inclined magnetic field phenomena, heat generation, Brownian movement, and thermophoresis phenomena over a symmetric shrinking (stretching) wedge. The transport of heat via nonuniform heat sources/sinks, the impact of thermophoretic diffusion, and Brownian motion are considered. The Buongiorno nanofluid model is used to investigate the impact of nanofluids on fluid flow. Modeled PDEs are transformed into ODEs by utilizing similarity variables and handling dimensionless ODEs numerically with the adoption of MATLAB&rsquo;s developed bvp4c technique. This software performs a finite difference method that uses the collocation method with a three-stage LobattoIIIA strategy. Obtained outcomes are strictly for the case of a symmetric wedge. The velocity field lessens due to amplification in the magneto field variable. Fluid temperature is amplified through the enhancement of Brownian diffusion and the concentration field improves under magnification in a homogeneous reaction effect.

]]>Symmetry doi: 10.3390/sym15061143

Authors: Nana Zhao Jinghan Wang Yufeng Shi Qingfeng Zhu

In this paper, a general class of time-symmetric mean-field stochastic systems, namely the so-called mean-field forward-backward doubly stochastic differential equations (mean-field FBDSDEs, in short) are studied, where coefficients depend not only on the solution processes but also on their law. We first verify the existence and uniqueness of solutions for the forward equation of general mean-field FBDSDEs under Lipschitz conditions, and we obtain the associated comparison theorem; similarly, we also verify those results about the backward equation. As the above two comparison theorems&rsquo; application, we prove the existence of the maximal solution for general mean-field FBDSDEs under some much weaker monotone continuity conditions. Furthermore, under appropriate assumptions we prove the uniqueness of the solution for the equations. Finally, we also obtain a comparison theorem for coupled general mean-field FBDSDEs.

]]>Symmetry doi: 10.3390/sym15061144

Authors: Hawsar HamaRashid Hari Mohan Srivastava Mudhafar Hama Pshtiwan Othman Mohammed Eman Al-Sarairah Musawa Yahya Almusawa

Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra&ndash;Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach.

]]>Symmetry doi: 10.3390/sym15061139

Authors: Suresh Sagadevan Ramesh Poonchi Sivasankaran J. Anita Lett Is Fatimah Getu Kassegn Weldegebrieal Estelle Léonard Minh-Vien Le Tetsuo Soga

The symmetric nano morphologies, asymmetric electronic structures, and as well as the heterojunctions of the developed photocatalytic systems perform a vital role in promoting light absorption, separation of electron and hole pairs and charge carrier transport to the surface when exposed to near-infrared (NIR) light. In this present work, we synthesized hematite (&alpha;-Fe2O3) nanoparticles (NPs) by a facile hydrothermal method and studied their structural, optical, and photocatalytic properties. Powder X-ray diffraction (XRD) confirmed the rhombohedral phase of the &alpha;-Fe2O3 NPs, and Fourier transform infrared spectroscopy (FT-IR) was used to investigate symmetric and asymmetric stretching vibrations of the functional groups on the surface of the catalysts. The optical bandgap energy was estimated to be 2.25 eV using UV-Vis diffuse reflectance spectroscopy (UV-Vis DRS) and scanning electron microscopy (SEM) images indicated sphere like morphology. The oxidation and reduction properties of &alpha;-Fe2O3 NPs were analyzed by cyclic voltammetry (CV). The &alpha;-Fe2O3 NPs were utilized for the degradation of methylene blue (MB) dye under natural sunlight. The experimental results demonstrate that the degradation efficiency was achieved at 33% in 2 h, and the pseudo-first-order rate constant was calculated to be 0.0033 min&minus;1.

]]>Symmetry doi: 10.3390/sym15061142

Authors: John W. Farrell Valerie E. Neira

The purpose of the current investigation was to examine the effects of exercise intensity on asymmetry in pedal forces when the accumulation of fatigue is controlled for, and to assess the reliability of asymmetry outcomes during cycling. Participants completed an incremental cycling test to determine maximal oxygen consumption and the power that elicited maximal oxygen consumption (pVO2max). Participants were allotted 30 min of recovery before then cycling at 60%, 70%, 80%, and 90% of pVO2max for 3 min each, with 5 min of active recovery between each intensity. Participants returned to the laboratory on separate days to repeat all measures. A two-way repeated measures analysis of variance (ANOVA) was utilized to detect differences in power production AI at each of the submaximal exercise intensities and between Trials 1 and 2. Intraclass correlations were utilized to assess the test&ndash;retest reliability for the power production asymmetry index (AI). An ANOVA revealed no significant intensity&ndash;visit interactions for the power production AI (f = 0.835, p = 0.485, &eta;2 = 0.077), with no significant main effects present. ICC indicated excellent reliability in the power production AI at all intensities. Exercise intensity did not appear to affect asymmetry in pedal forces, while excellent reliability was observed in asymmetry outcomes.

]]>Symmetry doi: 10.3390/sym15061141

Authors: Artyom V. Astashenok Sergey D. Odintsov Vasilis K. Oikonomou

We investigate the Chandrasekhar mass limit of white dwarfs in various models of f(R) gravity. Two equations of state for stellar matter are used: the simple relativistic polytropic equation with polytropic index n=3 and the realistic Chandrasekhar equation of state. For calculations, it is convenient to use the equivalent scalar&ndash;tensor theory in the Einstein frame and then to return to the Jordan frame picture. For white dwarfs, we can neglect terms containing relativistic effects from General Relativity and we consider the reduced system of equations. Its solution for any model of f(R)=R+&beta;Rm (m&ge;2, &beta;&gt;0) gravity leads to the conclusion that the stellar mass decreases in comparison with standard General Relativity. For realistic equations of state, we find that there is a value of the central density for which the mass of a white dwarf peaks. Therefore, in frames of modified gravity, there is a lower limit on the radius of stable white dwarfs, and this minimal radius is greater than in General Relativity. We also investigate the behavior of the Chandrasekhar mass limit in f(R) gravity.

]]>Symmetry doi: 10.3390/sym15061140

Authors: José Ayala Hoffmann Victor Ayala

Given a smooth-plane Jordan curve with bounded absolute curvature &kappa;&gt;0, we determine equivalence classes of distinctive disks of radius 1/&kappa; included in both plane regions separated by the curve. The bound on absolute curvature leads to a completely symmetric trajectory behaviour with respect to the curve turning. These lead to a decomposition of the plane into a finite number of maximal regions with respect to set inclusion leading to natural lower bounds for the length an area enclosed by the curve. We present a &ldquo;half version&rdquo; of the Pestov&ndash;Ionin theorem, and subsequently a generalisation of the classical Blaschke rolling disk theorem. An interesting consequence is that we describe geometric conditions relying exclusively on curvature and independent of any kind of convexity that allows us to give necessary and sufficient conditions for the existence of families of rolling disks for planar domains that are not necessarily convex. We expect this approach would lead to further generalisations as, for example, characterising volumetric objects in closed surfaces as first studied by Lagunov. Although this is a classical problem in differential geometry, recent developments in industrial manufacturing when cutting along some prescribed shapes on prescribed materials have revived the necessity of a deeper understanding on disks enclosed by sufficiently smooth Jordan curves.

]]>Symmetry doi: 10.3390/sym15061138

Authors: Aymen Laadhari Ahmad Deeb

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes.

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