Symmetry

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. Full article

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. Full article

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. Full article

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 λ₁ = λ₂ = 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. Full article

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. Full article

We study the (3+1)-dimensional stochastic Jimbo–Miwa (SJM) equation induced by multiplicative white noise in the Itô sense. We employ the Riccati equation mapping and He’s semi-inverse techniques to provide trigonometric, hyperbolic, and rational function solutions of SJME. Due to the applications of the Jimbo–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. Full article

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–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. Full article

In this article, we have investigated solutions to a symmetry chaotic system with fractional derivative order using two different methods—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. Full article

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. Full article

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—outer perianths (‘falls’), inner perianths (‘standards’), and style branches—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—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. Full article

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 $0<\xi <\infty$ , and the Prandtl parameter range $0.1\le \mathrm{Pr}\le 7.0$ 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. Full article

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. Full article

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. Full article

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’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. Full article

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–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. Full article

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’ 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. Full article

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–retest reliability for the power production asymmetry index (AI). An ANOVA revealed no significant intensity–visit interactions for the power production AI (f = 0.835, p = 0.485, η² = 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. Full article

We investigate the Chandrasekhar mass limit of white dwarfs in various models of $f\left(R\right)$ 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–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 $f\left(R\right)=R+\beta R^m$ ($m\ge 2$, $\beta >0$) 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 $f\left(R\right)$ gravity. Full article

Given a smooth-plane Jordan curve with bounded absolute curvature $\kappa >0$, 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 “half version” of the Pestov–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. Full article